ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΙΑΤΡΙΚΗΣ ΙΑΤΜΗΜΑΤΙΚΟ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥ ΩΝ ΣΤΗΝ ΙΑΤΡΙΚΗ ΦΥΣΙΚΗ

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1 ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΙΑΤΡΙΚΗΣ ΙΑΤΜΗΜΑΤΙΚΟ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥ ΩΝ ΣΤΗΝ ΙΑΤΡΙΚΗ ΦΥΣΙΚΗ ΥΠΟΛΟΓΙΣΤΙΚΗ ΤΟΜΟΓΡΑΦΙΑ ΙΠΛΗΣ ΕΝΕΡΓΕΙΑΣ : ΦΥΣΙΚΕΣ ΑΡΧΕΣ ΚΑΙ ΜΕΘΟ ΟΙ Κοντογιάννη Λουκία Μεταπτυχιακή ιπλωµατική Εργασία Φεβρουάριος 2013 Πάτρα

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3 UNIVERSITY OF PATRAS SCHOOL OF MEDICINE INTERDEPARTMENTAL PROGRAM OF POSTGRADUATE STUDIES IN MEDICAL PHYSICS DUAL ENERGY COMPUTED TOMOGRAPHY: PHYSICAL PRINCIPLES AND METHODS Kontogianni Loukia Master Degree Thesis February 2013 Patras 3

4 Τριµελής Εξεταστική επιτροπή Αναπληρώτρια Καθηγήτρια Ιατρικής Φυσικής Ελένη Κωσταρίδου (Eπιβλέπουσα) Καθηγητής Ιατρικής Φυσικής Γεώργιος Παναγιωτάκης Επίκουρος Καθηγήτρια Ακτινολογίας Χριστίνα Καλογεροπούλου Three-member Examination Committee Associate Professor of Medical Physics Lena Costaridou (Supervisor) Professor of Medical Physics George Panayiotakis Assistant Professor of Radiology Christina Kalogeropoulou 4

5 ΕΥΧΑΡΙΣΤΙΕΣ Ευχαριστώ θερµά την επιβλέπουσα µου, κυρία Ελένη Κωσταρίδου, Αναπληρώτρια Καθηγήτρια Ιατρικής Φυσικής, για την ευκαιρία που µου έδωσε να ασχοληθώ µε το εξελισσόµενο πεδίο της Υπολογιστικής Τοµογραφίας ιπλής Ενέργειας, αλλά κυρίως για την επιστηµονική της καθοδήγηση και γενικότερη στήριξη κατά την εκπόνηση αυτής της διπλωµατικής εργασίας. Επιπλέον, θα ήθελα να ευχαριστήσω τον κύριο Σπύρο Σκιαδόπουλο, ιδάκτορα Ιατρικής Φυσικής - Ακτινοφυσικό για τη στήριξη και την καθοδήγησή του κατά τη διάρκεια εκπόνησης των πειραµάτων, αλλά και για την γενικότερη επιστηµονική συµβολή του στην εργασία, καθώς επίσης και την κυρία Άννα Καραχάλιου, ιδάκτορα Ιατρικής Φυσικής - Ακτινοφυσικό για τη συµβολή της στo πειραµατικό µέρος και την γενικότερη βοήθεια της. Θα ήθελα επίσης να ευχαριστήσω την κυρία Χριστίνα Καλογεροπούλου, Επίκουρο Καθηγήτρια Ακτινολογίας και τον κύριο Γεώργιο Παναγιωτάκη, Καθηγητή Ιατρικής Φυσικής, για τη συµµετοχή τους στην εξεταστική επιτροπή της διπλωµατικής µου εργασίας. Επίσης, θα ήθελα να ευχαριστήσω τον συνάδελφο µου Ανδρέα Πετρόπουλο για τη συνεργασία του κατά τη διάρκεια των πειραµάτων και τη γενικότερη στήριξή του. Τέλος, θα ήθελα να ευχαριστήσω το ΟΛΥΜΠΙΟΝ Θεραπευτήριο Πάτρας (Γενική Κλινική Πατρών, Τµήµα Ακτινολογίας ) για την ευγενική παραχώρηση του εξοπλισµού κατά τη διάρκεια των πειραµάτων. 5

6 ABSTRACT The current thesis concerns Dual Energy Computed Tomography and specifically the physical principles and methods it is based on. Dual Energy CT offers the potential of not only anatomical, but also functional information from Computed Tomography (CT) exams. This is achieved by utilizing the energy dependence of X-rays attenuation within matter. In this way, materials are divided into those that are characterized by energy-dependent attenuation (strong spectral behavior), due to strong photoelectric effect contribution to total attenuation, and those that do not exhibit important photoelectric attenuation at radiological energies and therefore they attenuate X-rays in a much less energy dependent way. This information is useful for the identification of materials that, despite the fact that they are completely different as far as their chemical composition is concerned, they have the same or similar CT number values at a particular kvp level. The energy dependence of attenuation leads to the determination of a polychromatic linear attenuation coefficient. This coefficient may be approximated either by considering an equivalent monoenergetic attenuation coefficient that is characterized by the same half value layer as the the polyenergetic beam, or by a local linear attenuation coefficient that is determined by knowledge of the local x-ray spectrum. The energy dependence of attenuation is the cause of beam hardening effects. The basic fields where dual energy CT has become feasible and its current clinical applications are described in the thesis. The utility of DECT ranges from artifact elimination (beam hardening, metal artifacts) to tissue discrimination, material selective images and conventional CT acquisition equivalent images. The implementations of dual energy CT are also presented in the thesis and include consecutive scans at two different kvp values, fast kv-switching, dual source CT and dual layer CT. The algorithms for dual energy processing, may be implemented in the projection domain or after reconstruction, in the image domain and are further divided into ρ-ζ methods and material decomposition methods. The ρ-ζ methods are named after the output of the algorithms, which are electron density and Z effective maps (or Compton and photoelectric components of attenuation). Material decomposition algorithms decompose the irradiated material into basis materials based on their different spectral behavior. The basic requirements 6

7 for successful implementation of dual energy CT methods are adequate energy separation and distinct dual energy behavior of basic materials when we refer to material decomposition analysis (thus, different energy dependence of attenuation). Effective atomic number is an important concept (mentioned in the previous). It is a continuous variable that replaces the dicrete atomic number of elements, and is used to characterize mixtures or compounds. The contribution of each element in the mixture or compound to the effective atomic number is determined by its electronic or mass fraction in the mixture. Electron density (electrons per unit volume) is proportional to mass density (mass per unit volume) and electron mass density (electrons per unit mass). Photoelectric effect includes the information about the spectral behavior of materials, due to the strong energy dependence of its cross section. By using NIST (National Institute of Standards and Technology) data (mass attenuation coefficients) of 35 materials with Z effective in the range 1-87, at 4 energy levels (18, 65, 75 and 130 kev), the exponent n of the n photoelectric dependence on the effective atomic number ( ρ Z ) was estimated to be 4, for low Z effective, tissue-like materials. For increased Z effective materials, the presence of discontinuties due to absorption edges makes dual energy ρ-ζ methods inaccurate and a three energy approach is required. However, the exponent n was determined to be 3 for the regions in between of the discontinuties. Compton effect linear attenuation coefficient was confirmed to be almost entirely dependent on mass density, since mass electron density (e/g) does not differ significantly between various materials in most cases (although it has a slightly lower value for high atomic number elements and mixtures or compounds that contain such elements). Since photoelectric effect is responsible for the dual energy behavior of materials, it is interesting to investigate its contribution to total attenuation for various interesting materials like iodine (contrast agent), calcium (present in plaques), iron (present in malfunctional liver), bone and tissue-like materials. The linear attenuation coefficient energy dependence of these materials was approximated by utilizing NIST attenuation data and x-mudat (appendix of thesis) data of material density values. It was concluded that iodine is characterized by dominant photoelectric attenuation in the whole radiological range investigated (1-140 kev) and therefore its dual energy behavior is very strong (also due to the presence of the k-edge at 33.2 kev). Calcium and iron have also strong dual energy behavior, but the approximation of µ(ε) at high radiological energies was fitted by exponential decay. Additionaly, neither el eff 7

8 calcium nor iron have absorption edges in the CT radiological range of interest. Therefore, they are expected to have weaker dual energy behavior than iodine. For bone, the photoelectric effect dominance energy region is even more restricted, although more extended than that of low effective atomic number, tissue-like materials. As far as the energy dependence of CT number values is concerned, it was observed (again by plotting NIST data in the energy range kev), that for materials of Z effective below 7.5 (approx. Z eff of water), a general trend of slightly increasing CT number values with increasing photon energy is observed and for materials of Z effective above 7.5 the general trend is decreasing CT number values with increasing photon energy. The higher the Z effective value, the stronger is this decreasing tendency. This division may offer the opportunity for tissue discrimination or image contrast increase, especially if photon counting detectors and multiple energy windows are used. For instance, at low energy windows, contrast between soft tissue (Z effective = 7.37) and adipose tissue (Z effective = 6.47) may be increased. Moreover, absorption edges are evident in the relationship HU (E) of materials. Again energy windows below and above the k-edge energy level may be useful for discrimination, even for materials that have k-edges at very close energies. An experimental evaluation of the dual energy behavior of iodine solutions (12 different concentrations from 1.25 to 50 mg/ml), calcium solutions (6 different concentrations from 43.3 to 300 mg/ml) in saline and tissue-like materials (polycarbonate, polyethylene, polystyrene, nylon, PMMA, bone equivalent, plastic water) is also included in current thesis.the experiment was performed with Siemens SOMATOM Definition (first generation dual source CT). Scanning included single energy protocol at 80, 100, 120 and 140 kvp and dual energy protocol (80 kvp, 140 kvp and blending after reconstruction: 0.3*80 kvp+0.7*140 kvp, known as virtual 120 kvp image because it attempts to imitate the conventional 120 kvp scan in diagnostic value and CT number values). As expected, all tissue-like materials are characterized by a small increase of CT number value with increasing kvp value. Iodine solutions, calcium solutions and bone have decreasing CT number values with increasing photon energy, as expected. The CT number values of real and virtual 120 kvp images are quite close for most tissue-like materials and iodine and calcium solutions (although differences are more prominent for solutions of increased concentration). Calculating the difference of CT number values between images of different kvps does not always give us a clue about the chemical composition of the solution (iodine or calcium), 8

9 since this difference is dependent on the concentration of the solution. The slope of the material specific vector, however, (iodine vector, calcium vector, bone vector) in the dual kvp space (x axis: HU 140 kvp - y axis: HU 80 kvp) is characteristic of the solute and the solvent and is independent of the concentration of the solution. This slope is called dual energy ratio and the difference of the slopes of two different material vectors is called dual energy contrast. Increased dual energy contrast is important for successful dual energy discrimination and low noise levels in material specific images and is the basis of material decomposition and material labeling methods. The results of the experiment revealed a dual energy ratio of 1.93 for iodine and 1.62 for calcium and 1.5 for bone and are in good agreement with recent bibliography. Moreover, applications available by the commercial syngo Siemens software were successfully applied in phantom study. 9

10 ΕΚΤΕΤΑΜΕΝΗ ΠΕΡΙΛΗΨΗ Η παρούσα διπλωµατική εργασία αφορά στην τοµογραφία διπλής ενέργειας και ειδικότερα τις φυσικές αρχές και µεθόδους στις οποίες βασίζεται. H τοµογραφία διπλής ενέργειας δίνει την προοπτική της απόκτησης όχι µόνο ανατοµικής, αλλά και λειτουργικής πληροφορίας από τις εξετάσεις αξονικής τοµογραφίας. Αυτό το επιτυγχάνει χρησιµοποιώντας την εξάρτηση της εξασθένησης των ακτίνων X µέσα στην ύλη από την ενέργεια των φωτονίων. Με αυτό τον τρόπο, τα υλικά διαχωρίζονται σε αυτά που εξασθενούν τα φωτόνια µε πολύ διαφορετικό τρόπο σε διαφορετικές ενέργειες λόγω έντονου φωτοηλεκτρικού φαινοµένου και σε αυτά που η ενεργειακή εξάρτηση του συντελεστή εξασθένησης τους είναι λιγότερο έντονη (λιγότερη συµµετοχή του φωτοηλεκτρικού φαινοµένου στη συνολική εξασθένηση). Η πληροφορία αυτή είναι χρήσιµη για την ταυτοποίηση της σύστασης υλικών, που ενώ είναι εντελώς διαφορετικά σε χηµική σύσταση, έχουν τον ίδιο αριθµό CT (CT number) σε συγκεκριµένη τάση λειτουργίας της πηγής ακτίνων X. Στην εκτεταµένη περίληψη αυτής της εργασίας, αρχικά γίνεται σύντοµη αναφορά στην εξάρτηση του συντελεστή εξασθένησης από την ενέργεια και πώς αυτή επηρεάζει τον ορισµό του συντελεστή γραµµικής εξασθένησης για πολυχρωµατικές ακτινοβολίες. Στη συνέχεια ακολουθεί µια συνοπτική περιγραφή υλοποιήσεων της τοµογραφίας διπλής ενέργειας καθώς επίσης και των αλγορίθµων και των κλινικών εφαρµογών που είναι διαθέσιµες σήµερα. Τέλος, περνώντας στην περιγραφή του κυρίως µέρους της διπλωµατικής, ακολουθεί συνοπτική περιγραφή της θεωρητικής και πειραµατικής µελέτης της συµπεριφοράς διπλής ενέργειας του ιωδίου, του ασβεστίου, του οστού και υλικών που προσοµοιάζουν το µαλακό και λιπώδη ιστό. Στη θεωρητική περιγραφή, η διπλωµατική εστιάζει στις εξαρτήσεις του συντελεστή γραµµικής εξασθένησης, πρώτα από τα χαρακτηριστικά του ίδιου του υλικού (πυκνότητα, χηµική σύσταση) και έπειτα από την ενέργεια των φωτονίων. Ο προβληµατισµός σχετικά µε την εξάρτηση του συντελεστή εξασθένησης µε την ενέργεια έχει οδηγήσει συχνά σε τρόπους προσέγγισης και ορισµού ενός συντελεστή γραµµικής εξασθένησης που να ανταποκρίνεται σε πολυενεργειακές δέσµες, όπως αυτές που χρησιµοποιεί ο αξονικός τοµογράφος. Ο συντελεστής γραµµικής εξασθένησης µιας πολυενεργειακής δέσµης από ένα συγκεκριµένο υλικό, προσδιορίζεται είτε µέσω ενός ισοδύναµου µονοενεργειακού συντελεστή εξασθένησης που να χαρακτηρίζεται από το ίδιο half value layer (HVL) µε την πολυενεργειακή δέσµη είτε µέσω ενός «τοπικού» συντελεστή εξασθένησης. που για να προσδιοριστεί απαιτείται γνώση του φάσµατος στην συγκεκριµένη θέση και στο συγκεκριµένο υλικό. Η εξάρτηση του συντελεστή εξασθένησης από την 10

11 ενέργεια των φωτονίων ευθύνεται για τεχνήµατα σκλήρυνσης δέσµης (beam hardening artifacts). Συνοπτικά, οι βασικoί στόχοι που αφορούν στην απεικόνιση διπλής ενέργειας και την τοµογραφία ειδικότερα είναι οι εξής : Εξακρίβωση της χηµικής σύστασης των ιστών και παραγωγή εικόνων απεικόνισης συγκεκριµένων υλικών (material selective images). Εξαγωγή ποσοτικοποιηµένων και ακριβών αποτελεσµάτων µέσω της απεικόνισης (π.χ ανάλυση των αλάτων του οστού ή αξιολόγηση της περιεκτικότητας σε λίπος του ήπατος). Αυτοµατοποιηµένη αφαίρεση ενός υλικού, π.χ. αφαίρεση οστού ή σκιαγραφικού από την εικόνα Παραγωγή εικόνων από µίξη δεδοµένων λήψεων υψηλής και χαµηλής τάσης της λυχνίας (blended images) και ψευδοµονοχρωµατικών εικόνων που προσοµοιάζουν τις εικόνες συµβατικής λήψης σε ποιότητα εικόνας και διαγνωστική αξία. Οι εικόνες αυτές αποτελούν έναν τρόπο να παραχθούν εικόνες απαλλαγµένες από φαινόµενα σκλήρυνσης δέσµης (beam hardening effects) σε διάφορες τιµές ενέργειας. Η αντίθεση µεταξύ συγκεκριµένων ιστών στην εικόνα µπορεί να αυξηθεί. Υπολογισµός ηλεκτρονιακών πυκνοτήτων και ενεργών ατοµικών αριθµών για το σχεδιασµό ακτινοθεραπείας. Σήµερα οι διαθέσιµοι τοµογραφίας διπλής ενέργειας είναι: και ευρέως χρησιµοποιούµενοι τρόποι υλοποίησης αξονικής 1. Γρήγορης εναλλαγής της τάσης στην λυχνία (fast kv-switching). Τέτοιας τεχνολογίας αξονικός ήταν ο πρώτος αξονικός διπλής ενέργειας (SOMATOM DR). Στον αξονικό της GE (General Electric) που είναι τέτοιας τεχνολογίας, είναι διαθέσιµες ψευδοµονοχρωµατικές εικόνες, εικόνες µε αφαίρεση σκιαγραφικού και εικόνες πυκνότητας υλικού ή ατοµικού αριθµού. 2. Αξονικοί µε 2 λυχνίες που µπορούν να λειτουργούν στην ίδια ή σε διαφορετικές τάσεις ή ακόµα και ανεξάρτητα η µία από την άλλη (Dual Source CT DSCT). H Siemens κατασκευάζει τέτοιους τοµογράφους 2 γενεών, στους οποίους οi ανιχνευτές αντιστοιχούν σε διαφορετικό πεδίο (FOV). Ο αξονικός δεύτερης γενιάς (SOMATOM Definition Flash) ωστόσο παρέχει µεγαλύτερο πεδίο στον ανιχνευτή χαµηλής τάσης (80kVp) απ ό,τι ο 11

12 αξονικός πρώτης γενιάς (SOMATOM Definition). Έτσι είναι δυνατή η απεικόνιση µεγαλύτερων ανατοµικών περιοχών και παχύσαρκων ασθενών. Επίσης στον SOMATOM Flash η λυχνία υψηλής τάσης (140kVp) έχει επιπλέον φίλτρο 0.5mm Sn, και έτσι ο φασµατικός διαχωρισµός είναι καλύτερος απ ότι στον SOMATOM. Το αποτέλεσµα είναι καλύτερη απόδοση των αλγορίθµων διάκρισης υλικών και η µείωση της δόσης. Στους αξονικούς µε 2 λυχνίες οι κλινικές εφαρµογές πραγµατοποιούνται είτε µε την ανάλυση στον διανυσµατικό χώρο που δηµιουργούν 3 βασικά υλικά, είτε µε την µέθοδο της διχοτόµου της γωνίας που δηµιουργούν τα διανύσµατα µειγµάτων ενός βασικού υλικού µε κάθε ένα από δύο άλλα υλικά που πρέπει να διαφοροποιηθούν µεταξύ τους. 3. Τεχνολογία δύο στρωµατοποιηµένων ανιχνευτών και µίας λυχνίας (dual-layer detector scanner). Ο ανιχνευτής στο πάνω στρώµα απορροφά τα χαµηλότερης ενέργειας φωτόνια και ο ανιχνευτής στο κάτω στρώµα τα υψηλότερης ενέργειας φωτόνια. Για να είναι επιτυχής ο διαχωρισµός των υλικών µε τοµογραφία διπλής ενέργειας πρέπει να ικανοποιούνται κάποιες προϋποθέσεις. Οι πιο βασικές είναι τα φάσµατα να είναι επαρκώς διαχωρισµένα και η εξασθένηση των ακτίνων X από τα βασικά υλικά που θέλουµε να διακρίνουµε να έχει διαφορετική ενεργειακή εξάρτηση. Για να ισχύει η δεύτερη προϋπόθεση πρέπει η διαφορά των (ενεργών) ατοµικών αριθµών να είναι επαρκής. Για πιο εύκολη περιγραφή της τεχνικής διπλής ενέργειας, τα υλικά διακρίνονται σε αυτά που έχουν ισχυρή «συµπεριφορά διπλής ενέργειας» (dual energy behavior) που δηλαδή εξασθενούν µε πολύ διαφορετικό τρόπο τα φάσµατα υψηλών από τα φάσµατα χαµηλών τάσεων και σε αυτά µε ασθενή συµπεριφορά διπλής ενέργειας, όπως είναι τα υλικά ισοδύναµου µαλακού ή λιπώδους ιστού. Οι αλγόριθµοι µε τους οποίους γίνεται η διάκριση των διαφορετικών εξαρτήσεων της εξασθένησης ακτίνων Χ από την ύλη διαχωρίζονται σε 2 κατηγορίες αναλόγως των συναρτήσεων που χρησιµοποιούνται ως βάση ανάλυσης του συντελεστή εξασθένησης. Οι αλγόριθµοι που χρησιµοποιούν ως βάσεις την ενεργειακή εξάρτηση του φωτοηλεκτρικού φαινοµένου και του φαινοµένου Compton καλούνται «ρ-ζ µέθοδοι» επειδή οδηγούν στον υπολογισµό της ηλεκτρονιακής πυκνότητας και του ενεργόυ ατοµικού αριθµού του υλικού. Οι µέθοδοι διπλής ενέργειας που αναλύουν ένα υλικό σε 2 ή 3 βασικά υλικά ονοµάζονται µέθοδοι «αποδόµησης υλικού» (material decomposition methods). Οι αλγόριθµοι περαιτέρω αναλύονται σε αυτούς που επεξεργάζονται το πρόβληµα πριν και µετά την ανακατασκευή της εικόνας στον αξονικό. Για παράδειγµα οι σύγχρονοι αξονικοί τοµογράφοι της GE µε την γρήγορη εναλλαγή τάσης χρησιµοποιούν επεξεργασία πριν την ανακατασκευή εικόνας 12

13 (projection based analysis), ενώ οι τοµογράφοι διπλής λυχνίας (dual source) χρησιµοποιούν επεξεργασία µετά την ανακατασκευή (image-based analysis). Στους αλγόριθµους αποδόµησης υλικού, η ανάλυση του συντελεστή γραµµικής εξασθένησης σε 3 βασικά υλικά και µόνο 2 φάσµατα διαθέσιµα µπορεί να γίνει θεωρώντας ότι το υλικό που αναλύεται είναι ένα µείγµα 3 υλικών που το άθροισµα των όγκων τους δίνει τον ολικό όγκο. Αν δεν γίνει αυτή η παραδοχή (που δεν ισχύει πάντα), οι αλγόριθµοι πρέπει να αξιοποιήσουν το γεγονός ότι το άθροισµα των µαζών των βασικών υλικών αποτελεί την συνολική µάζα του µείγµατος. (κάτι που ισχύει σε όλες τις περιπτώσεις). Με τους αλγορίθµους διαθέσιµους στο λογισµικό των τοµογράφων διπλής ενέργειας, κατασκευάζονται εικόνες πυκνότητας (material density), εικόνες ατοµικού αριθµού, ψευδοµονοχρωµατικές εικόνες (virtual monochromatic), µίξη εικόνων από δύο τάσεις (blended images), εικόνες συγκεκριµένου υλικού ή µε αφαίρεση υλικών (material specific images, virtual non enhanced, bone removal) καθώς και εικόνες µε χρωµατική κωδικοποίηση (color coding) των βασικών υλικών ανάλυσης (πχ. οστό, ιώδιο, ασβέστιο, ουρικά οξέα). Στη θεωρητική περιγραφή της συµπεριφοράς διπλής ενέργειας υλικών έγινε χρήση των εννοιών «ενεργός ατοµικός αριθµός» και ηλεκτρονιακή πυκνότητα. Ο ενεργός ατοµικός αριθµός (που αναφέρθηκε στα προηγούµενα-z effective ) είναι µια συνεχής µεταβλητή, που εννοιολογικά αντικαθιστά τη διακριτή µεταβλητή του ατοµικού αριθµού των χηµικών στοιχείων και αναφέρεται σε χηµικές ενώσεις ή µείγµατα. Η συµµετοχή του ατοµικού αριθµού κάθε στοιχείου της ένωσης στον ενεργό ατοµικό αριθµό της ένωσης, εξαρτάται από το ποσοστό µάζας ή αριθµού ηλεκτρονίων του στοιχείου στο µείγµα ή τη χηµική ένωση. Για κάθε αλληλεπίδραση ακτινοβολίας-ύλης έχει διαφορετική τιµή, ενώ έχει προταθεί και ενοποιηµένος ορισµός του. Ωστόσο, η σύγκλιση των διαφορετικών ορισµών ατοµικών αριθµών της ένωσης δείχνει να επιτυγχάνεται µόνο για υλικά που περιέχουν χηµικά στοιχεία των οποίων οι ατοµικοί αριθµοί δε διαφέρουν πολύ µεταξύ τους. Η ηλεκτρονιακή πυκνότητα (αριθµός ηλεκτρονίων ανά µονάδα όγκου) για καθαρά χηµικά στοιχεία αλλά και για χηµικές ενώσεις ή µείγµατα, είναι ανάλογη της µαζικής πυκνότητας (µάζα ανά µονάδα όγκου) του υλικού. Η µαζική ηλεκτρονιακή πυκνότητα (αριθµός ηλεκτρονίων ανά µονάδα µάζας) για στοιχεία µικρού ατοµικού αριθµού είναι ελαφρώς µεγαλύτερη απ ότι για στοιχεία µεγάλου ατοµικού αριθµού. Για µείγµατα ή χηµικές ενώσεις στοιχείων παρόµοιας τιµής ατοµικού αριθµού δεν εξαρτάται από την ακριβή χηµική σύσταση του υλικού, ενώ επηρεάζεται ελάχιστα από αυτή σε περιπτώσεις που τα συστατικά του 13

14 µείγµατος διαφέρουν κατά πολύ στην τιµή του ατοµικού τους αριθµού (π.χ. διαλύµατα ιωδίου µε νερό). Είναι γνωστό πως η πιθανότητα φωτοηλεκτρικής εξασθένησης της ακτινοβολίας X στην ύλη εµφανίζει µεγάλη εξάρτηση από τον (ενεργό) ατοµικό αριθµό του υλικού, σε αντίθεση µε την πιθανότητα σκέδασης Compton. Η πιθανότητα φωτοηλεκτρικού φαινοµένου επίσης παρουσιάζει µεγαλύτερη εξάρτηση από την ενέργεια των φωτονίων. Εποµένως η πληροφορία της τεχνικής απεικόνισης διπλής ενέργειας περιέχεται στην πιθανότητα φωτοηλεκτρικής αλληλεπίδρασης. Κατά το πρώτο µέρος της θεωρητικής µελέτης της εργασίας διερευνήθηκε η εξάρτηση του συντελεστή µαζικής εξασθένησης από τη χηµική σύσταση των υλικών.η µελέτη έγινε για 4 διαφορετικές ενέργειες (18, 65, 75 και 130 kev) χρησιµοποιώντας δεδοµένα συντελεστή εξασθένησης 35 υλικών, µε τιµές (ενεργών) ατοµικών αριθµών στο εύρος Χρησιµοποήθηκε η βάση δεδοµένων του NIST (National Institute of Standards and Technology) και η βάση δεδοµένων x-mudat.(παράρτηµα διπλωµατικής εργασίας) Τα αποτελέσµατά επιβεβαίωσαν την πολύ µικρή εξάρτηση του (µ/ρ) comp από την ακριβή χηµική σύσταση του υλικού. Ο συντελεστής Compton γραµµικής εξασθένησης των υλικών εξαρτάται κυρίως από την πυκνότητα του υλικού. Γενικότερα ωστόσο, τα υλικά µε χηµική σύσταση από ελαφρά στοιχεία (όπως τα υλικά ισοδύναµα ιστού), παρουσιάζουν τάση για ελαφρώς µεγαλύτερο συντελεστή µαζικής εξασθένησης Compton από τα υλικά µε σύσταση στοιχείων µεγάλου ατοµικού αριθµού. Στη συνέχεια έγινε προσέγγιση της εξάρτησης (µ/ρ) ph (Ζ eff ). Λόγω αιχµών απορρόφησης, η εξάρτηση αυτή παρουσιάζει ασυνέχειες για υλικά µέσου και µεγάλου ενεργού ατοµικού αριθµού σε ακτινολογικές ενέργειες. Το αποτέλεσµα είναι να υπάρχουν υλικά µεγάλου ατοµικού αριθµού που σε συγκεκριµένο ενεργειακό επίπεδο έχουν µικρότερο µαζικό συντελεστή εξασθένησης (φωτοηλεκτρικό και ολικό) από υλικά µικρότερου ατοµικού αριθµού. Ωστόσο, ο νόµος που περιγράφει την συµπεριφορά (µ/ρ) ph (Ζ eff ) µεταξύ των ασυνεχειών για µέσους και µεγάλους ατοµικούς αριθµούς (πάνω από 11-12) είναι νόµος δύναµης µε εκθέτη περίπου 3, ενώ για µικρότερου ατοµικού αριθµού υλικά (κάτω από 8-10) και υλικά ισοδύναµα ιστού, είναι νόµος δύναµης µε εκθέτη περίπου 4 σε όλες τις ενέργειες που εξετάστηκαν. H ανάλυση αυτή οδήγησε στο συµπέρασµα ότι οι ρ-ζ µέθοδοι µπορούν να είναι αποτελεσµατικές σε υλικά χαµηλού ενεργού ατοµικού αριθµού και σύστασης που να 14

15 προσεγγίζει τους ιστούς (tissue-like materials). Ανάλυση µε ενέργειες αρκετά µεγαλύτερες των ενεργειών οπου συναντώνται αιχµές απορρόφησης (π.χ ενέργειες από πηγές ραδιενεργών υλικών) µπορεί να οδηγήσει σε εξακρίβωση υλικών µεγαλύτερων ενεργών ατοµικών αριθµών. Για καλύτερη κατανόηση της διαφορετικότητας στην ενεργειακή εξάρτηση της εξασθένησης των ακτίνων X που προκαλείται από υλικά διαφορετικών ατοµικών αριθµών στο δεύτερο µέρος της θεωρητικής ανάλυσης της διπλωµατικής, έγινε διερεύνηση της ενεργειακής εξάρτησης του συντελεστή εξασθένησης στο ενεργειακό εύρος kev για υλικά διαφορετικών (ενεργών) ατοµικών αριθµών (ιώδιο, σίδηρος, ασβέστιο, οστό, µαλακός ιστός και παραπλήσια υλικά). Τα υλικά αυτά είναι βασικής σηµασίας, καθώς η αναγνώριση της ύπαρξης τους στο ακτινοβολούµενο σώµα είναι ο σκοπός των αλγορίθµων αποδόµησης υλικού που χρησιµοποιούνται κλινικά σήµερα. Τα δεδοµένα προήλθαν από τη βάση δεδοµένων NIST. Η σχέση µ ph (Ε) για όλα τα υλικά, ανεξαρτήτως χηµικής σύστασης και ατοµικού αριθµού, στο p2 ακτινολογικό ενεργειακό εύρος είναι νόµος δύναµης µ = p E που διακόπτεται από τυχόν αιχµές απορρόφησης. Ο εκθέτης p 2 που δίνει η προσαρµογή της εξίσωσης στα δεδοµένα κυµαίνεται από περίπου αναλόγως το υλικό και την ενεργειακή περιοχή. Για υλικά που δεν παρουσιάζουν αιχµές απορρόφησης στο ακτινολογικό εύρος ενεργειών, το φωτοηλεκτρικό φαινόµενο περιγράφεται, όπως αναµένεται από τη θεωρία, µε νόµο δύναµης εκθέτη p 2 περίπου 3 σε όλο το εύρος ενεργειών kev. Για υλικά µε αιχµές ωστόσο, η προσαρµογή του νόµου δύναµης στα δεδοµένα γίνεται στα διαστήµατα που ορίζουν οι αιχµές και ο εκθέτης µπορεί να παρουσιάσει µικρές µεταβολές σε αυτά τα διαστήµατα. Η σχέση µ tot (E) για τα διάφορα υλικά, αποκαλύπτει το ενεργειακό εύρος της κυριαρχίας του φωτοηλεκτρικού φαινοµένου, αναλόγως µε το µέχρι ποια ενέργεια ισχύει ο νόµος δύναµης. Με αυτό τον τρόπο µπορεί να αξιολογηθεί η συµπεριφορά διπλής ενέργειας βασικών υλικών, εφόσον το φωτοηλεκτρικό φαινόµενο, µε την µεγάλη ενεργειακή εξάρτηση του και την ύπαρξη αιχµών απορρόφησης, ευθύνεται για αυτή τη συµπεριφορά. Οι γραφικές του φωτοηλεκτρικού και του ολικού συντελεστή εξασθένησης για το ιώδιο, υποδεικνύουν ότι το ιώδιο σε όλο το ακτινολογικό εύρος ενεργειών, ακόµα και στις υψηλές ενέργειες πάνω από 100 kev εξασθενεί την ακτινοβολία σχεδόν αποκλειστικά µέσω του φωτοηλεκτρικού φαινοµένου. Τα σκιαγραφικά υλικά όπως το ιώδιο, εξασθενούν τα χαµηλής τάσης φάσµατα περισσότερο από τα υψηλής τάσης φάσµατα, λόγω των αιχµών απορρόφησης 1 15

16 και γενικότερα της κυριαρχίας του φωτοηλεκτρικού φαινοµένου. Εξαίρεση ίσως να αποτελούν υλικά τα οποία έχουν αιχµές απορρόφησης σε ενεργειακά επίπεδα που υπάρχουν µόνο σε δέσµες υψηλής τάσης. Αντιστοίχως, για το σίδηρο και το ασβέστιο, η µ tot (E) είναι νόµος δύναµης για αρκετά µεγάλο εύρος ενεργειών (προσεγγιστικά 70 kev για τον σίδηρο και 50 kev για το ασβέστιο), ενώ σε µεγαλύτερες ενέργειες εκθετικός νόµος εξασθένησης προσεγγίζει καλύτερα τα δεδοµένα. Επιπλέον αυτά τα υλικά εµφανίζουν αιχµές απορρόφησης σε πολύ µικρές ενέργειες. Αυτή τους η συµπεριφορά τα καθιστά υλικά µε σηµαντική συµπεριφορά διπλής ενέργειας, δείχνει όµως να είναι λιγότερο σηµαντική όµως από αυτή του ιωδίου. Για το οστό η ενεργειακή εξάρτηση του συντελεστή συνολικής γραµµικής εξασθένησης ακολουθεί νόµο δύναµης ενδεικτικό της κυριαρχίας του φωτοηλεκτρικού φαινοµένου έως τα 35 kev περίπου, ενώ για υλικά ισοδύναµα µαλακού και λιπώδους ιστού περίπου ως τα 25 kev. Εποµένως η συµπεριφορά διπλής ενέργειας του οστού αναµένεται να είναι πιο έντονη από αυτήν του µαλακού και λιπώδους ιστού, αλλά λιγότερο σηµαντική από αυτήν του ασβεστίου, του σιδήρου και φυσικά του ιωδίου. To γενικό συµπέρασµα της πιο πάνω ανάλυσης είναι ότι ο διαχωρισµός υλικών µε πολύ κοντινό ατοµικό αριθµό είναι δύσκολος µε συµβατικές dual energy τεχνικές καθώς η οµοιότητα της ενεργειακής εξάρτησης της εξασθένησης των ακτίνων X που παρουσιάζουν τους προσδίδει παρόµοια συµπεριφορά διπλής ενέργειας. Οι συµβατικές τεχνικές διπλής ενέργειας δεν είναι ευαίσθητες σε µικρές διαφορές στην ενεργειακή εξάρτηση της εξασθένησης. Υπάρχει όµως η προοπτική του φασµατοσκοπικού CT µε ανιχνευτές µέτρησης φωτονίων που µπορεί να διακρίνει υλικά µε πολύ κοντινές αιχµές απορρόφησης. Ωστόσο, ακόµα και µε συµβατικές τεχνικές διπλής ενέργειας, η διάκριση ιωδίου από οστό, ασβέστιο και σίδηρο είναι δυνατή. Σηµειώνεται επίσης πως, εφόσον οι αιχµές απορρόφησης είναι σηµαντικές στη διαµόρφωση της ενεργειακής εξάρτησης της εξασθένησης, η ακριβής χηµική σύσταση του υλικού είναι επίσης σηµαντική και όχι απλά η τιµή του ενεργού ατοµικού αριθµού. Σε ότι αφορά την σχέση CT αριθµού και ενέργειας φωτονίων, υλικά µε πολύ χαµηλό ενεργό ατοµικό αριθµό (Ζ eff <7.5(περίπου ο ενεργός ατοµκός αριθµός του νερού)) όπως ο λιπώδης ιστός και τα ισοδύναµα του, χαρακτηρίζονται από καµπύλη HU(E) που ξεκινάει από αρνητικές τιµές αριθµού CT και έχει µια ανοδική πορεία, στην αρχή γρήγορη περίπου ως τα 65 kev και στην συνέχεια σχεδόν σταθεροποιείται. Υλικά µε 7.5< Ζ eff <8 που µελετήθηκαν 16

17 (ισοδύναµα µαλακού ιστού και αίµατος) χαρακτηρίζονται από άνοδο του αριθµού CT πιο γρήγορη από την προηγούµενη οµάδα µέχρι τα 25keV περίπου και µετά από ελαφριά πτώση και σταθεροποίηση. Αυτές οι διαφορές µπορούν να αποτελέσουν υλικό για κατασκευή εικόνων σε συγκεκριµένα ενεργειακά παράθυρα, µε την βοήθεια ανιχνευτών µέτρησης φωτονίων έτσι ώστε να βελτιστοποιείται η αντίθεση µεταξύ συγκεκριµένων ιστών, όπως λίπος και µαλακός ιστός ή να επιτυγχάνεται ακόµα και η διάκριση τους. Για υλικά µεγάλου ενεργού ατοµικού αριθµού οι αιχµές απορρόφησης είναι εµφανείς και στα διαγράµµατα HU(E), ενώ όσο αυξάνεται ο ενεργός ατοµικός αριθµός,αυξάνεται και η µειωτική τάση των αριθµών CT µε την αυξανόµενη ενέργεια. Απο την συµπεριφορά HU(E) για µονοενεργειακά δεδοµένα, οµοια µε αυτά που χρησιµοποιήθηκαν στην µελέτη µ(ε), αναµένεται ο λιπώδης ιστός και τα ισοδύναµα του να παρουσιάζουν µικρή αύξηση του CT αριθµού µε αυξανόµενη ενέργεια ενώ το αντίθετο αναµένεται για ισοδύναµα µαλακού ιστού και αίµατος (αλλά σε µικρότερο βαθµό). Αυτές οι θεωρητικές παρατηρήσεις επιβεβαιώνονται και από κλινικά δεδοµένα, όπως και η µείωση του αριθµού CT µε την αυξανόµενη ενέργεια φωτονίων,για το ιώδιο,το ασβέστιο και τα διαλύµατα τους αλλά και για το οστό. Στην παρούσα εργασία µελετήθηκε πειραµατικά (σε αξονικό τοµογράφο Siemens SOMATOM Definition-αξονικός πρώτης γενιάς µε 2 λυχνίες), η συµπεριφορά διπλής ενέργειας διαλυµάτων ιωδίου 12 διαφορετικών συγκεντρώσεων (από 1.25 έως 50 mg/ml) και 6 συγκεντρώσεων ασβεστίου (από 43.3 έως 300 mg/ml) σε φυσιολογικό ορό, καθώς και υλικών όπως το nylon, το πολυκαρβονύλιο, το πολυστυρένιο, το πολυαιθυλένιο, PMMA, ισοδύναµο οστού πειραµατικά. Η µελέτη περιελάµβανε εικόνες συµβατικού µονοενεργειακού πρωτοκόλλου σε τάσεις 80, 100, 120 και 140 kvp, ενώ κατασκευάστηκαν και εικόνες διπλής ενέργειας µε µίξη των CT αριθµών σε ποσοστό 30% από την 80 kvp και 70% από την 140 kvp εικόνα, µε χαρακτηριστικά λήψης πρωτοκόλλου διπλής ενέργειας, δηλαδή διαφορετικές τιµές mas από το πρωτόκολλο µιας ενέργειας. Οι εικόνες µίξης καλούνται «εικονικές 120 kvp εικόνες» επειδή στοχεύουν στο να µιµηθούν διαγνωστικά τις συµβατικές 120 kvp εικόνες. Τα διαλύµατα ιωδίου και ασβεστίου, καθώς και το υλικό ισοδύναµο οστού παρουσιάζουν, όπως είναι και θεωρητικά αναµενόµενο, µείωση της εξασθένησης σε µεγαλύτερες τιµές kvp, ενώ αντιθέτως, τα υλικά πολυαιθυλένιο, πολυστυρένιο, πολυκαρβονύλιο, PMMA, nylon παρουσιάζουν µικρή αύξηση τoυ CT αριθµού. Για τα διαλύµατα ιωδίου και ασβεστίου η 17

18 απόλυτη τιµή της διαφοράς CT αριθµού µεταξύ υψηλής και χαµηλής τάσης είναι µεγαλύτερη όσο µεγαλύτερη είναι η συγκέντρωση του διαλύµατος. Οι µετρήσεις µέσων τιµών CT αριθµού στην εικόνα µίξης και στη συµβατική 120 kvp εικόνα δίνουν κοντινές τιµές στις περισσότερες περιπτώσεις διαλυµάτων ιωδίου και ασβεστίου µικρής και µέσης συγκέντρωσης και σχεδόν για όλα τα υλικά. Οι διαφορές ωστόσο είναι µεγαλύτερες σε µεγαλύτερες συγκεντρώσεις των διαλυµάτων ιωδίου και ασβεστίου.επιπλέον, εφαρµογές του λογισµικού επεξεργασίας για αφαίρεση οστού στο phantom έδωσαν ικανοποιητικά αποτελέσµατα στο πείραµα µε τις σύριγγες ιωδίου καθώς και στο πείραµα µε διαλύµατα ασβεστίου. Όπως προαναφέρθηκε, η διαφορά αριθµών CT µεταξύ υψηλής (π.χ 140 kvp) και χαµηλής τάσης, εξαρτάται από τη συγκέντρωση του διαλύµατος. Εποµένως, δεν είναι ασφαλής δείκτης αναγνώρισης της παρουσίας σκιαγραφικού στο διάλυµα. Με σκοπό την ποσοτικοποίηση της συµπεριφοράς διπλής ενέργειας των διαλυµάτων ιωδίου και ασβεστίου υπολογίστηκαν οι ποσότητες «λόγος διπλής ενέργειας» και «αντίθεση διπλής ενέργειας». Ο λόγος διπλής ενέργειας για τα διαλύµατα ενός υλικού σε ένα διαλύτη (π.χ. ιώδιο ή ασβέστιο) προσδιορίζεται πειραµατικά µετρώντας την κλίση που σχηµατίζει η ευθεία των διαλυµάτων της συγκεκριµένης διαλυµένης ουσίας στο χώρο (HU highkvp -HU lowkvp ). Η αντίθεση διπλής ενέργειας δίνεται από τη διαφορά των λόγων διπλής ενέργειας για 2 υλικά. Το πείραµά κατέλήξε σε τιµές λόγων διπλής ενέργειας 1.93 για το ιώδιο και 1.62 για το ασβέστιο και άρα αντίθεση διπλής ενέργειας 0.31, αν θεωρήσουµε υψηλή τάση τα 140 kvp και χαµηλή τάση τα 80 kvp, ενώ η αντίθεση διπλής ενέργειας µειώνεται αν η χαµηλή και υψηλή τάση έχουν πιο κοντινές τιµές (φασµατική επικάλυψη). Αυτοί οι υπολογισµοί είναι πολύ κοντά σε τιµές που δίνονται στην πρόσφατη βιβλιογραφία. Είναι σηµαντική η επίτευξη µεγάλης αντίθεσης διπλής ενέργειας επειδή ο θόρυβος στις εικόνες συγκεκριµένων υλικών (material specific images) εξαρτάται και από την αντίθεση διπλής ενέργειας. 18

19 CONTENTS CHAPTER 1 AIM AND LAYOUT OF THESIS...22 CHAPTER 2 INTERACTIONS OF PHOTONS WITH MATTER AND CONCEPTS OF EFFECTIVE ATOMIC NUMBER & ELECTRON DENSITY Compton scattering Photoelectric effect Effective atomic number and electron density CHAPTER 3 COMPUTED TOMOGRAPHY (CT): GENERAL CHARACTERISTICS The advent of modern computed tomography scanner CT generations and developments CT scanner components and set-up What do we measure in CT? Attenuation coefficients, Hounsfield units and their significance Reconstruction in CT CT image contrast Image display Dose and safety in CT Image noise in CT Artifacts in CT...58 CHAPTER 4 PRODUCTION AND ESTIMATION OF X-RAY POLYCHROMATIC SPECTRA Bremstrahlung and fluorescence radiation X-ray spectrum in CT Effective energy of spectrum Methods for photon energy spectrum estimation Polychromatic attenuation coefficient

20 CHAPTER 5 DUAL ENERGY CT: ALGORITHMS, TECHNOLOGY AND APPLICATIONS General purposes of DECT Physical background of DECT Algorithms of DECT Evolution and technical characteristics of DECT Comparison of methods for DECT implementation Workstations of DECT configurations Clinical applications of DECT Multi-energy imaging Tissue classification using single-energy CT scans Basic requirements for DECT CHAPTER 6 THEORETICAL STUDY: THE DEPENDENCES OF X-RAY ATTENUATION PROBABILITY WITHIN MATTER IN RADIOLOGICAL ENERGIES Dependence of Compton effect attenuation from the absorber Dependence of photoelectric effect attenuation from the absorber Energy dependence of attenuation Absorption edges and their effect on attenuation Energy dependence of CT number values Dual-energy ratio Conclusions of chapter CHAPTER 7 EXPERIMENTAL EVALUATION OF IODINE CALCIUM AND TISSUE LIKE MATERIALS DUAL ENERGY BEHAVIOUR Aim of the experiment Iodine and tissue-like materials experiment Calcium experiment Comparison of dual energy ratios with results from current bibliography Conclusions of chapter CHAPTER 8 DISCUSSION AND OPEN ISSUES

21 APPENDICES REFERENCES

22 CHAPTER 1: AIM AND LAYOUT OF THESIS A polychromatic energy beam that is emitted by a computed tomography (CT) system can be perceived as a sum of photons of different energies, travelling through matter. As far as the possibility for attenuation of an X-ray photon within matter is concerned, there are two important dependencies: a. The dependence on material specific attenuator characteristics (atomic number, density) and b. The dependence on the energy of the photon. As a result of the first dependence, it is well known for X-ray imaging systems, including CT, that some materials attenuate more than others in typical examinations. Therefore, an X-ray beam after passing through an absorber carries information about the nature of the attenuator. Thus, tissue characterisation becomes feasible. Dual-energy CT extends the gained information by focusing on the second aforementioned dependence, the energy dependence of attenuation. Dual energy CT is based on the use of two well separated X-ray CT spectra. In this way, material differentiation is enabled by analysing the material and energy dependent contribution of photo-electric and Compton effects to total attenuation. This is possible since the energy dependence of the photoelectric effect possibility is much stronger than that of Compton scattering. In that way, materials of high density (Compton scattering dominant) can be differentiated from materials of high atomic number (photoelectric effect dominant). The utilization of the energy dependence of X-ray attenuation constitutes a possibility that was not available with conventional CT imaging, where high attenuation could be either due to high density or due to high atomic number (or both), without any other indication of the elemental composition. Emerging from this basic idea of different material attenuation at different energies, a variety of applications has revealed new potentials for CT imaging. The purpose of the thesis is to describe dual energy CT by emphasizing on the physical principles that it is based on. In this frame, the thesis attempts an analysis on concepts and physical quantities that pertain to X-ray radiation and its attenuation within matter. Specifically, the aims and basic points of the current thesis on dual energy CT may be summarized as following: 22

23 1. To provide a description of current dual energy CT technology, applications and algorithm background, as well as a theoretical analysis of the dual energy behaviour of matter. In this frame, description of the energy dependence of attenuation for several materials(iodine,iron,calcium,bone,soft tissue e.t.c) was attempted, by using NIST data. The emerging information is related to the possibility for dual energy discrimination for these or similar materials. Moreover, the dependence of X-rays attenuation probability from the chemical composition of the attenuator is investigated. 2. To experimentally investigate the dual energy behaviour of iodine and calcium solutions in water as well as the dual energy behavior of tissue-like materials by means of a phantom study that attempts to mimic mainly head CT examinations. Iodine (Z=53) is a very common contrast agent in CT and calcium (Z=20) is a basic element of human anatomy but also a finding in many common pathological situations that concern neurological or myocardial malfunction as well as kidney stones. Evaluation of the results confirms the behaviour adopted by the software package used in this study. The thesis begins with basic theoretical background concerning photon interactions with matter, effective atomic number and electron density (Chapter 2) as well as CT general principles and characteristics (Chapter 3). Chapter 4 concerns information on X-ray spectra production and estimation as well as the concept of polychromatic attenuation coefficient and effective energy of polychromatic beam which are quantities of importance in spectral CT. A chapter focused on dual energy CT physical principles, mathematical background, technology and applications follows (Chapter 5). In Chapter 6 a closer view of material suitability for dual energy applications is presented, by means of evaluation of their attenuation energy dependence. The inspection of graphs depicting the change of linear attenuation coefficient and CT number with photon energy for materials like iodine, calcium, iron, soft tissue, brain, bone e.t.c.), leads to better comprehension of the ability (or inability) of dual energy techniques to discriminate between these materials. Also, the dependence of Compton and photoelectric effect probability on the chemical composition of the attenuator is discussed. Chapter 7 includes the experimental phantom study, focusing on the concept of dual energy ratio for iodine and calcium, as this measure is used for evaluation of their dual energy behaviour. Finally, in chapter 8 the general conclusions as well as the open issues for future study in spectral CT are included. 23

24 CHAPTER 2 INTERACTIONS OF PHOTONS WITH MATTER AND CONCEPTS OF EFFECTIVE ATOMIC NUMBER AND ELECTRON DENSITY Photons are indirectly ionizing radiation and they deposit energy in the absorbing medium through a two-step process: in the first step energy is transferred to an energetic light charged particle and in the second step energy is deposited in the absorbing medium by the charged particle. The energy transferred to charged particles from the interacting photon generally exceeds the energy subsequently deposited in the absorbing medium by the charged particles, because some of the transferred energy may be radiated from the charged particles in the form of photons. Therefore, mean energy transferred from photon to secondary charged particles in the absorber E tr can be expressed as a sum of two components: E absorbed in the medium and E radiated, the mean energy lost by secondary charged particles and radiated from the secondary charged particles in the form of photons through bremsstrahlung and in-flight annihilation or emitted as fluorescence photons during atomic relaxation after impulse ionization or impulse excitation of absorber atoms. In penetrating an absorbing medium, photons may experience various interactions with the atoms of the medium. These interactions involve either the nuclei of the absorbing medium or the orbital electrons of the absorbing medium: 1. The interactions with nuclei may be direct photon nucleus interactions (photodisintegration) or interactions between the photon and the electrostatic field of the nucleus (pair production). 2. The photon orbital electron interactions are characterized as interactions between the photon and either a loosely bound electron (Thomson scattering, Compton effect, triplet production) or a tightly bound electron (photoelectric effect, Rayleigh scattering). A loosely bound electron is an electron whose binding energy E B is small in comparison with photon energy hν, i.e. E B hv. An interaction between a photon and a loosely bound electron is considered to be an interaction between a photon and a free (i.e. unbound) electron. A tightly bound electron is an electron whose binding energy E B is comparable to, larger than, 24

25 or slightly smaller than the photon energy hν. For a photon interaction to occur with a tightly bound electron, the binding energy E B of the electron must be of the order of, but slightly smaller, than the photon energy. An interaction between a photon and a tightly bound electron is considered an interaction between a photon and the atom as a whole [1]. As far as the photon fate after the interaction with an atom is concerned, there are two possible outcomes: 1. Photon disappears (i.e., is absorbed completely) and a portion of its energy is transferred to light charged particles (electrons and positrons). 2. Photon is scattered and two outcomes are possible: a. The resulting photon has the same energy as the incident photon and no light charged particles are released in the interaction. b. The resulting scattered photon has a lower energy than the incident photon and the energy excess is transferred to a light charged particle (electron). The light charged particles (electrons and positrons) released or produced in the absorbing medium through photon interactions will either deposit their energy to the medium through Coulomb interactions with orbital electrons of the absorbing medium (collision loss also referred to as ionization loss) or radiate their kinetic energy away in the form of photons through Coulomb interactions with the nuclei of the absorbing medium (radiation loss). The most important parameter used for characterization of X-ray or gamma ray penetration into absorbing media is the linear attenuation coefficient µ. This coefficient depends on energy hν of the photon and atomic number Z of the absorber and may be described as the probability per unit path length that a photon will have an interaction with the absorber. In addition to the linear attenuation coefficient µ, three other related attenuation coefficients (often referred to as cross sections) are in use for describing photon beam attenuation characteristics. They are: the mass attenuation coefficient µ m, atomic attenuation coefficient aµ, and electronic attenuation coefficient e µ [1]. 1. Mass attenuation coefficient µ m is defined as the linear attenuation coefficient µ divided by the mass per unit volume of the absorber (absorber mass density) ρ. The mass attenuation coefficient µ m = µ/ρ is independent of absorber density and its SI unit is m 2 /kg. The older unit cm 2 /g is still often used 1 m 2 /kg = 10 cm 2 /g. 25

26 2. Atomic attenuation coefficient or atomic cross section α µ is defined as linear attenuation coefficient µ divided by the number of atoms N a per volume V of the absorber. It can also be defined as the mass attenuation coefficient µ/ρ divided by the number of atoms N a per mass of the absorber. The SI unit of the atomic attenuation coefficient is m 2 /atom; however, a smaller unit cm 2 /atom is still in common use (1 m 2 /atom = 10 4 cm 2 /atom). Barns is the mostly used unit (1 Barn=10-24 cm 2 ). 3. Electronic attenuation coefficient or electronic cross section e µ is defined as the linear attenuation coefficient µ divided by the number of electrons N e per volume V of the absorber. It can also be defined as the mass attenuation coefficient µ/ρ divided by the number of electrons N e per mass of the absorber. The SI unit of the electronic attenuation coefficient is m 2 /electron; however, a smaller unit cm 2 /electron is still in common use (barns are also used here). It can be shown that: µ = ρµ = n µ = Zn µ (2.1) m α e where ρ the mass density of the absorber, Z the atomic number of the absorber, Zn the number of electrons per volume V of absorber (i.e. Zn = ρzn A /A), n the number of atoms Ν a per volume V of the absorber, i.e. n = N a /V and N a /V = ρn a /m = ρn A /A with m the mass of the absorber, N A the Avogadro number and A the molar mass of the absorber. The total linear (or total mass) attenuation coefficient is the sum of the partial linear mass attenuation coefficients respectively for all interactions taking place. Interactions of major importance in radiological medical physics are the photoelectric and the Compton effect. 2.1 COMPTON SCATTERING An interaction of a photon of energy hν with a loosely bound orbital electron of an absorber is called Compton effect (Compton scattering) in honour of Arthur Compton who made the first measurements of photon free electron scattering in Compton was awarded the Nobel Prize in 1927 for the "discovery of the effect named after him". The effect is also known as incoherent scattering. In theoretical studies of the Compton effect an assumption is made that the incident photon interacts with a free and stationary electron. A photon, referred to as a scattered photon with energy hν that is smaller than the incident photon energy hν, is produced in Compton effect and an electron, referred to as a Compton (recoil) electron, is ejected from the atom with kinetic energy E K. 26

27 Figure 2.1: Diagram of Compton effect. An incident photon with energy hν interacts with a stationary and free electron. A photon with energy hν is produced and scattered with a scattering angle θ. The difference between the incident photon energy hν and the scattered photon energy hν is given as kinetic energy to the recoil electron. (a) Schematic diagram; (b) vector representation of the effect. Compton explained and modelled the data by assuming a particle (photon) nature for light and applying conservation of energy and conservation of momentum to the collision between the photon and the electron. The scattered photon has lower energy and therefore a longer wavelength. The total electronic Klein-Nishina cross section for the Compton scattering on a free electron e σ [in cm 2 /electron] is given by the following relationship KN c 1+ γ 2 γ (1 + γ ) γ 8π σ = 2π r ln( 1 2γ) ln( 1 2γ) r f γ + 1 2γ + + = + 2γ ( 1+ 2γ) 3 KN 2 2 e c e 3 2 e KN (2.2) with γ = E/mc 2, m the mass of the electron and c the velocity of light in vacuum (mc 2 = kev), r e = 2.82 x cm the electron radius and f KN the Klein-Nishina factor. In the energy region not affected by electron binding energy effects, the Compton atomic cross section a σ is determined from the electronic cross section of relationship (2.2) using the standard KN c relationship σ σ KN ( KN a c = Z e c ) (2.3) where Z is the atomic number of the absorber. The Klein Nishina Compton electronic cross section is given for free electrons and is thus independent of Z. This makes the atomic cross 27

28 section linearly dependent on Z. The Compton mass attenuation coefficient according to relationship (2.2) is then calculated as following: σ KN c ρ N A KN ZN A KN 1 KN = aσ c = eσ c N A( eσ c ) (2.4) A A 2 Since Z/A = 0.5 for all elements with the exception of hydrogen for which Z/A = 1, σ C /ρ is essentially independent of Z. In fact, Z/A = and gradually decreases with increasing Z. It is actually expected that Compton will not be dependent on atomic composition, since the Compton interaction occurs with relatively unbound (free) electrons. It can mathematically be proven that if Z/A has the same value for all constituents of a mixture, the electron density does not depend on the exact chemical composition. The Compton process is most important for energy absorption for soft tissues in the range from around 100 kev to 10MeV. At low energies the probabilities for forward scattering (θ=0) and backscattering (θ=π) are equal. As energy increases, the scattering becomes increasingly more forward peaked and backscattering rapidly diminishes. 2.2 PHOTOELECTRIC EFFECT An interaction between a photon and a tightly bound orbital electron of an absorber atom is called photoelectric effect (colloquially often referred to as photoeffect). In the interaction the photon is absorbed completely and the orbital electron is ejected with kinetic energy E K. The ejected orbital electron is called a photoelectron. The photoelectric interaction between a photon of energy hν and a K-shell atomic electron is shown schematically in Fig 2.2. Figure 2.2: Schematic diagram of the photoelectric effect. A photon with energy hν interacts with a K-shell electron. The photon is absorbed completely and the K-shell electron is ejected from the atom as photoelectron with kinetic energy E K =hν E B (K), where E B (K) is the binding energy of the K-shell electron. The vacancy in the K shell is subsequently filled with a higher orbit electron and the energy of the electronic transition will be emitted either in the form of a characteristic (fluorescence) photon or in the form of an Auger electron. 28

29 The main characteristics of the photoelectric effect are the following: 1. The extra energy and momentum carried by the photon are transferred to the absorbing atom; however, because of the relatively large nuclear mass, the atomic recoil energy is exceedingly small and may be neglected. The kinetic energy E K of the ejected photoelectron is assumed to be equal to the incident photon energy hν less the binding energy E B of the orbital electron, i.e. E K = hν E B (2.5) 2. When the photon energy hν exceeds the K-shell binding energy E B (K) of the absorber, about 80% of all photoelectric absorptions occur with the K-shell electrons of the absorber and the remaining 20% occur with less tightly bound higher shell electrons. 3. The energy uptake by the photoelectron may be insufficient to bring about its ejection from the atom in a process referred to as atomic ionization but may be sufficient to raise the photoelectron to a higher orbit in a process referred to as atomic excitation. 4. The vacancy that results from the emission of the photoelectron from a given shell will be filled by a higher shell electron and the transition energy will be emitted either as a characteristic (fluorescence) photon or as an Auger electron. Photoelectric effect is an important phenomenon which proves the particle nature of light or any radiation beyond doubt. It could not be explained using classical physics and it lead to the foundation of quantum physics. The maximum kinetic energy of the ejected electron is independent of the intensity of light. Even when the intensity of light is low, photoelectrons are emitted. There is a critical frequency below which no electrons are emitted regardless of the intensity of light. The angular distribution of photoelectrons depends on the incident photon energy hν. The photoelectron emission angle φ is defined as the angle between the incident photon direction and the direction of the emitted photoelectron, similarly to the definition of the recoil electron angle φ in Compton scattering. At low hν of the order of 10 kev photoelectrons tend to be emitted at angles close to 90 o to the incident photon direction. As hν increases, however, the photoelectron emission peak moves progressively to more forward photoelectron emission angles. The atomic cross section (attenuation coefficient) for the photoelectric effect as a function of the incident photon energy hν exhibits a characteristic structure in which the sharp discontinuities, referred to as absorption edges, arise whenever the photon energy coincides with the binding energy of a particular electron shell. 29

30 Three distinct energy regions characterize the photoelectric atomic cross section a τ 1. Region in the immediate vicinity of absorption edges. 2. Region at some distance from the absorption edge. 3. Region in the relativistic region far from the K absorption edge. Theoretical predictions for a τ in region (1) are difficult and uncertain. For region (2) the atomic attenuation coefficient for K-shell electrons a τ is given as follows: where 4 a τ K α e σ Th Z ε the usual normalized photon energy, i.e., ε = hν/(m e c 2 ) α the fine structure constant (1/137) Z the atomic number of the absorber K n 32 = ( ) (2.6) 7 ε 8 2 σ Th= r the Thomson electronic cross section where r e e is the classical electron radius and 3 e n the power for the Z dependence of α τ Κ ranging from n = 4 at relatively low photon energies to n = 4.6 at high photon energies. In the relativistic region (ε>>1), a τ K is given as follows: 1.5 = Z ( ) (2.7) ε 4 5 aτ K α eσth In the energy range of CT scanning, even though the Compton effect dominates, photoelectric or coherent scattering may correspond to a significant fraction of the total mass attenuation coefficient. Although the following figure from [3] is taken from an early study it is indicative of the relative percentages of the three photon interactions contributing to attenuation in CT scanning for a representative low Z material (ICRU muscle). 30

31 Figure 2.3: Relative percentages of the three photon interactions contributing to attenuation in CT scanning is presented,for a representative low Z material (ICRU muscle). 2.3 EFFECTIVE ATOMIC NUMBER AND ELECTRON DENSITY When referring to mixtures or compounds, the continuous variable of effective atomic number replaces the discrete variable Z (element atomic number). The compound is regarded as a single element characterized by its effective atomic number and electron density. Common definitions of these two important quantities are mentioned in following. Let us consider a mixture of different types of molecules, each one of which is designated by j. Each type of atom is designated by i, so that n(j,i) stands for the concentration of atoms i in molecule j (number of atoms of type i in the molecule of type j / total number of atoms in molecule j). Let us also name c(j) the concentration of the component j in the mixture (number of molecules of j / the total number of molecules). Then,commond definitions are: and ρ = N ρ Z e p eff = A j j i i j i j c( j) n( j, i) Z c( j) n( j, i) M c( j) n( j, i) Z i i i p+ 1 i c( j) n( j, i) Z i (2.8) (2.9) 31

32 where p 1, M i the molar mass of element i and N A the Avogadro number. It is clear from the above definition that for a compound or for mixtures of compounds, the value of Z eff changes for different choices of p. Various authors have used different values for p and hence different values appear in the literature for the Z eff of a given compound. This is so even for water, which is accepted as a standard. For example, p = 4 is usually used [2]. In [4] it has been pointed out that there is a different effective atomic number for each absorption process but an expression could be derived only for photoelectric effect and pair production. That is because the equations of Hine and Spiers may be expressed as [5] Zeff = (2.10) n 1 n 1 wi Zi where w i is the fractional part by weight of the whole mixture occupied by the element (or, almost equally, the fractional electronic content) the atomic number of which is Z i and n has values of 4 to 5,1 and 2 respectively for the photoelectric, Compton and pair production processes. In a similar way, Z effective is approached in [5]. Therefore, we can see that the value of p in equation [2.9] or n in equation [2.10] depend on the interaction process involved. Those different effective numbers seem to be approximated to a single effective atomic number. Z i eff = i wi Z Ai wi A i i (2.11) where w i is again the weight fraction of the element in the heterogeneous material, A i the atomic weight (or molar mass) of the element i and Z i the atomic number of the element i [5]. It has been observed that materials containing elements the atomic number of which do not differ greatly, all the expressions for effective atomic number (that is, the ones for photoelectric effective atomic number, pair production effective atomic number, general effective atomic number) give similar values for the effective atomic number. For materials containing very light elements such as hydrogen (e.g. Perspex) and for materials containing elements of very widely differing atomic numbers (e.g. NaI) different values for effective atomic number are obtained [5]. Electron density, taking into account that w i is the fractional part by weight of the whole mixture occupied by the element, can be expressed as: ρ Z i e = N Aρ wi (2.12) i A i 32

33 CHAPTER 3 COMPUTED TOMOGRAPHY: GENERAL CHARACTERISTICS 3.1 THE ADVENT OF MODERN COMPUTED TOMOGRAPHY SCANNER Before CT (Computed Tomography) came into use, planar radiography and fluoroscopy were all non-nuclear applications of ionising radiation in imaging. Planar X-ray radiography is used for a number of different purposes: intravenous pyelography (IVP) to detect diseases of the genitourinary tract including kidney stones; abdominal radiography to study the liver, bladder, abdomen, and pelvis; chest radiography for diseases of the lung and broken ribs; and X-ray fluoroscopy (in which images are acquired continuously over a period of several minutes) for a number of different genitourinary and gastrointestinal diseases. The radiograph is restricted by the fact that the image is a 2D projection of a 3D object and that small differences in X-ray linear absorption coefficient cannot be seen in projection radiology without the aid of contrast enhancement. Imaging of brain by radiographs yields insufficient results in most cases. Roentgenologists tried to copy with the difficulties by using contrast media such as air in pneumoencephalography, but still the yielded information did not increase dramatically [6]. Conventional radiography offers a superposition image: all structures along the rays from X-ray focus to detector contribute to the attenuation of the radiation intensity. So, what we see on the radiographic image is actually the print of the integral of the attenuation components along a projection line. X-ray computerized tomography or CT goes a long way to solving these problems and so the diagnosis of many diseases affecting soft tissue can be made a great deal easier. Before Hounsfield s introduction of computerised tomography in 1972, there were in fact several socalled classical tomographic X-ray methods that involved moving X-ray generators and films to selectively highlight particular planes within the body. These methods were generally filmbased and cumbersome and so have become obsolete after the advent of CT. Image contrast is defined by the difference in intensity of two neighboring picture elements or regions. This definition holds true in the same way for conventional radiographs and for CT images. Contrast in radiographs is dominated by structures with high attenuation, such as bone and contrast media or by differences in object thicknesses. Contributions from structures with low attenuation, typically soft tissue structures are thereby completely hidden in most 33

34 practical cases. This fundamental problem is eliminated in CT tomography, because for slice images contrast is given directly by the attenuation values of neighboring voxels and not by line integrals representing a path through the complete object. This local determination of contrast eliminated the influence of neighboring or superimposed structures. This statement is true for all slice imaging modalities. Contrast resolution or tissue resolution, that is, the ability of the CT imaging system to differentiate small attenuation differences (tissues that vary only slightly in density and atomic number) is better than in conventional radiography. Dual energy CT is a way to improve contrast because even if attenuation characteristics of two tissues are similar for a particular X-ray spectrum, there may be different behaviour for a different X-ray spectrum, therefore additional information will lead to better image quality. Dual-energy (DE) imaging was introduced more than 30 years ago and was applied both to dual-energy CT (DECT) and dual-energy radiography (DER). The theoretical basis for DE material decomposition was described in early works by Alvarez and Macovski and Kalender et al for DECT,and Lehmann et al. for DER,as it will be analysed in following chapter. While clinical interest in DER has been maintained over the years, especially for chest imaging and bone densitometry, DECT was not widely adopted due to the technical limitations of earlier CT systems. There was a long time delay between Roentgen s discovery in 1896 of X-rays (Roentgen received the first Nobel Prize in Physics in 1901) and the appearance of the first CT scanner (the EMI scanner) in 1972 (Godfrey N.Hounsfield, 1972). The earliest description of a tomographic method, applied incidentally to astronomical observations, is due to Radon (Radon, 1917). Perhaps the most obvious reason for the long delay was the need for cheap digital computing facilities. These did not appear until the late 1960 s. Without the computer, all modern medical imaging would not be achievable. Hounsfield s work was based on mathematical and experimental methods developed by A.M. Cormack a decade earlier. Hounsfield and Cormack shared the Nobel Prize in Medicine in CT GENERATIONS AND DEVELOPMENTS The basic demand for every development in CT imaging is the reduction of scan time and in that way, the achievement of lower absorbed dose and less motion artefacts. Since the seventies, 4 generations of CT scanners were developed. The first generation CT scanner 34

35 (1970) used an X-ray tube providing a pencile-like beam. Opposite to the X-ray tube, there was a single detector. This system provided a translate-rotate acquisition (Fig. 3.1).. The duration of a complete scan was 5 minutes. The second generation CT scanner (1972) also provided a translate-rotate data acquisition and was the first commercial scanner [6]. The number of detectors was increased (usually 30) and therefore a small fan beam was used. Scanning time was reduced in some cases to even less than a minute. In third generation scanners (1976) the translatory motion becomes obsolete and the system only executes a rotatory motion (the X-ray tube synchronized with the detectors). The fan beam is larger than 40 degrees and therefore the whole cross-section is covered. The number of detectors increased too (300,500,700). In some modern systems the scan time is les than 1 second. Only a little later scanners with a full ring-like stationary detector fully encircling the patient followed (fourth generation-1978). In those systems only the X-ray tube rotated. The third generation scanners are the rotation system scanners that seem to have prevailed so far in clinical use [6]. The most powerful scanners offered commercially today are all 3rd generation scanners. The goal of providing shorter scan times was pursued in the eighties in the form of many creative approaches. Conventional systems with the possibility for continuous rotation and data acquisition will be mentioned here. Continuously rotating CT systems, which were first introduced in 1987 by Siemens Medical Systems (SOMATOM PLUS) and Toshiba Medical Systems (TCT 900S) were based on slip ring technology [6]. The necessary electrical energy for the X-ray tube is transferred by slip rings instead of cables. Consequently it was possible to abandon the start and stop operation and to replace it with continuous data acquisition. In that way, not only were scan times reduced to typically one second but also provides the basis for dynamic examinations and for spiral CT. The majority of today s CT scanners of both the 3 rd and 4 th generation, make use of the principle of continuous rotation. Since the introduction of helical and multi-slice CT (respectively in 1989 and 1998), CT has opened the way to 3D images and dynamic studies. Multiple-row detector CT (MDCT) is the latest scanner development. The introduction of multi-row detector systems seems to mark the end of the 4th CT generation. Rather than one detector row, multiple detector rows are placed opposite the X-ray tube. This shortens the examination time and improves the temporal resolution, allowing for instance, the determination of the rate of vascular enhancement. The detector rows along the z-axis opposite the X-ray tube are not equal in width.the outer rows are wider than the inner rows to provide better conditions for 35

36 image reconstruction after data acquisition [7]. This type of multi-detector arrays are called adaptive detector arrays. If there were no unequal dimensions in the detector elements, that would be called an isotropic detector array. Adaptive detector arrays allow various combinations of thicknesses and numbers of acquired sections. In such an anisotropic system only the central detectors are used for acquiring thinnest slices; to acquire thicker slices multiple detector are combined. The SOMATOM Definition Dual Source CT, uses adaptive detector arrays of 40 detectors. There are 32 central rows having a 0.6-mm collimated slice width and four outer rows on each side having a 1.2-mm collimated slice width (Fig. 3.3). As already mentioned, only the central most detectors are engaged for acquisition of the thinnest slices (32 x 0.6 mm). The detectors are combined to produce thicker slices. For example, for a slice thickness of 1.2 mm the central 32 detectors are paired to form 16 slices of 1.2 mm in additional to the 8 outer 1.2 mm detectors resulting in 24 slices of 1.2 mm per rotation. Figure 3.1: The mode of operation of a first generation CT scanner Figure 3.2: Second, third and fourth generation CT scanner configuration 36

37 Figure 3.3: Detector configuration of the dual source system [8] In current study, Dual Source SOMATOM Definition CT functions in spiral mode. Spiral CT means the fast and continuous scanning of complete volumes [6]. It is a volume scanning mode in non planar geometry with the patient being scanned continuously in space and in time. The focus of the x ray tube continues to travel on a circular path; however relative to the patient it follows a spiral or helical trajectory. Spiral CT is based on discrete sampling along the z-axis and the technical prerequisites for its implementation have been provided by slip ring technology in continuously rotating scanners. In conventional sequential CT, on the other hand, a series of equally spaced images is acquired sequentially through a specific region, e.g. the abdomen or the head.there is a short pause after each section in order to advance the patient table to the next preset position. The section thickness and overlap/intersection gap are selected. The raw data for each image level is stored separately. The short pause between sections allows the conscious patient to breathe without causing major respiratory artefacts [7]. Sequential CT is based on two basic requirements: the object to be scanned may not move during data acquisition and the scan geometry must be perfectly planar. Spiral CT however builds upon violating those two principles. This explains the first reservations with the advent of helical CT. Those reservations with respect to image quality in spiral CT have in the meantime been eliminated. The movement of the table occurs mostly continuously and towards both directions. The table movement may be several mm during a tube rotation (e.g 20mm/360 degrees). For multi slice systems and subsecond rotation times the table speed can be increased significantly [6]. The choice of parameters in spiral CT corresponds largely to that of sequential CT. Parameter values may vary though. For spiral scans one additional parameter has to be chosen:the table feed d in mm per 360 degrees rotation.for MDCT the ratio of the table feed to total slice collimation is termed the pitch or pitch factor. d p= (3.1) MS 37

38 where d the table feed (table movement per rotation), M the number of simultaneously scanned slices and S the nominal slice width. Pitch is a dimensionless quantity of great importance for image quality and dose considerations. Usually pitch values between 1 and 2 are chosen. It should be larger than 1 to cover a given scan volume as fast as possible and to reduce the dose compared to sequential CT. Generally it should not exceed the value 2 in order to exclude gaps in sampling the object along the z-axis. In spiral CT, the table increment per rotation can be selected independently of the selected slice thickness. A larger table increment gives faster acquisition, but leads to lower resolution [9]. As already mentioned, data collection in spiral CT is very fast, therefore the produced images do not suffer from discontinuities due to patient breathing. With conventional CT, the exposure of the patient to radiation for data collection occurs first and the interpretation of these data follows. With Spiral CT though, patient exposure and data interpretation may occur at the same time. During one X-ray tube rotation sequential CT produces data that correspond to vertical slices of the body. Spiral CT however, produces data that belong to a plane that is oblique to the patient s body (z-axis). The vertical slices are reconstructed by parts of the data of those planes. The common data of an oblique and a vertical plane is a straight line (Fig. 3.5). The mathematical evaluation of the data needed to fill the regions between the lines is produced by interpolation algorithms (z-interpolation) [10]. (a) (b) Figure 3.4: (a) sequential CT scanner and (b) spiral CT scanner 38

39 Figure 3.5: Spiral CT interpolation 3.3 CT SCANNER COMPONENTS AND SETUP A modern CT scanner comprises of the following constituents: The scanning unit, i.e. the gantry, with tube and detector system The patient table The image processor for image reconstruction The console A CT scanning system consists of an X-ray unit, which functions as a transmitter, and a data acquisition unit, which functions as a receiver. In commercial CT systems these two components are housed in a ringshaped unit called the gantry, which contains the X-ray tube, collimator, filters and detector X-RAY SOURCE CT has always demanded relatively high X-ray power. This demand has risen. Tubes used in modern CT scanners usually have a power rating of kw at voltages of 80 to 140 kv. The systems can, however, be operated at maximum power for a limited time only. These limits are defined by the properties of the anode and the generator. To prevent overloading of the X-ray tube, the power must be reduced for long scans. The development of multi-row detector systems has practically excluded this limitation, since these detector systems make much more efficient use of the available tube power. 39

40 Figure 3.6: A schematic of an X-ray source used for clinical imaging (media.wiley.com: x-ray imaging and computed tomography, 2002). The typical X-ray tube used for clinical diagnoses has two electrodes, a negatively charged cathode, which acts as the electron source, and a positively charged anode, which contains the metal target (Fig. 3.6). A potential difference is applied between the cathode and the anode; the exact value depends upon the particular application. This potential difference is characterized by its maximum value, the kilovolts peak (kvp). The maximum value of the voltage is also referred to as the accelerating voltage. The cathode consists of a filament of tungsten wire ( 200µm in diameter) coiled to form a spiral 2 mm in diameter and less than 1 cm in height. An electric current from a power source passes through the cathode, causing it to heat up. When the cathode temperature reaches 2200 C the thermal energy absorbed by the tungsten atoms allows a small number of electrons to move away from the metallic surface, a process termed thermionic emission. A dynamic equilibrium is set up, with electrons having sufficient energy to escape from the surface of the cathode, but also being attracted back to the metal surface. The large positive voltage applied to the anode causes these free electrons created at the cathode surface to accelerate toward the anode. The spatial distribution of these electrons striking the anode correlates directly with the geometry of the X-ray beam that enters the patient. In order to achieve a tight, uniform beam of electrons a negatively charged focusing cup is placed around the cathode to reduce divergence of the electron beam. The larger the negative potential applied to the cup, the narrower is the electron beam. If an extremely large potential ( 2 kv) is applied, then the flux of electrons can be switched off completely. This switching process forms the basis for pulsing the X- ray source on and off in CT. 40

41 At the anode, X-rays are produced as the accelerated electrons penetrate a few tens of micrometers into the metal target and lose their kinetic energy. The higher the atomic number of the metal in the target, the higher is the efficiency of X-ray production or radiation yield. The most commonly used anode metal is tungsten, which has a high atomic number of 74, a high melting point of 3370 C. X-ray tubes are generally characterized in terms of either the tube output or tube power rating. The tube output, measured in Watts, is defined as the product of the tube current and the applied potential difference between the anode and cathode. The tube power rating is defined as the maximum power dissipated in an exposure time of 0.1 s COLLIMATION The radiation beam emitted by the X-ray tube is shaped using special diaphragms also referred to as collimators. A distinction can be made between two types of collimators. The source collimator is located directly in front of the radiation source i.e. the X-ray tube. Itreduces the radiation beam to form the maximum required fan beam, thus also determining the emitted dose. The detector collimator, which is positioned directly in front of the detectors, is primarily used to shield the detector against scattered radiation, thus preventing image artifacts. The collimation and focal size determine the quality of the slice profile. From the data volume from a multislice scanner images can be reconstructed with slice thickness equal to or larger than the detector collimation. For example, a 5 mm collimation allows images to be reconstructed with a slice thickness of 5 mm or more FILTRATION The filtration in X-ray tube and housing absorbs the low energy photons, which contribute to patient dose but not to image quality (beam hardening). This filtration is equivalent to at least 2,5 mm of Aluminium. In addition to this inherent filtration of the X-ray tube, flat or shaped filters are also used [6]. Flat filters, for example copper sheets of 0.1 to 0.4 mm thickness, shift the spectrum to higher energies. A CT-unit also includes a bow-tie filter (Fig. 3.7). This type of filter is shaped as an arch with less filter material in the centre. This filtration material is typically of a low Z (e.g. teflon). It compensates for the shorter path length in the outer parts of the scanned body. The image of 41

42 the body will then have a more uniform appearance, because the X-ray beam that reaches the detector is more uniform. Figure 3.7: Beam shaping filter: Nick Keat ImPACT, St.George s hospital, BSc. Biomedical Science (impactscan.org) DETECTOR SYSTEMS The detector, the system for quantitative recording of the incident ionizing radiation, constitutes one of the most important and technologically most critical components of the entire CT system. It has to transform the incident X-ray intensity into a corresponding electrical signal, to amplify this signal and to convert it from analog to digital form. In CT the dominant detector types are [6]: Ionization chambers, mostly filled with the noble gas xenon under high pressure. Scintillation detectors in the form of crystals, such as caesium iodide or cadmium tungstate and ceramic materials such as gadolinium oxysulfide in combination with a photodiode. For example, Siemens uses UFC (Ultra Fast Ceramic) detectors. Scintillation detectors are energy integrating detectors. The scintillator material converts X-rays into visible light (scintillations) which then hits the photodiode, causing it to produce an electric current. The multichannel readout electronics or data acquisition system (DAS) connects to the photodiode. The DAS integrates the photocurrent from the diode and converts the electric charge signal to voltage. The DAS also performs the analog to digital conversion. One limitation of these detectors is the susceptibility to electronic noise. 42

43 Photon counting detectors: material such as cadmium telluride (CdTe) or cadmiumzinc-telluride (CZT) converts an X-ray photon into a certain electronic charge proportional to its energy. The charge produced in direct conversion is about ten times that produced by the scintillator/photodiode combination and the electronic noise no longer dominates the signal from individual X-rays. This difference allows an electronic circuit to detect these charge packages and count the number of photons. The fact that these detectors count the number of photons instead of integrating their energy improves the CNR by 10 to 20% [11] OTHER PARAMETERS OF CT SCANNER INCREMENT The increment determines the distance between images reconstructed from a data volume. If an appropriate increment is used, overlapping images can be reconstructed. In sequential CT, overlapping images are obtained only if the table feed between two sequences is smaller than the collimated slice thickness. This, however, increases the patient dose. In spiral CT the increment is freely selectable as a reconstruction parameter, i.e. by selecting the increment the user can retrospectively and freely determine the degree of overlap without increasing the dose. Overlapping reconstructions offer the advantage of better image quality due to lower noise and easier and more accurate diagnosis of small structures. mas The mas value (e.g. 100 mas) is the product of the tube current (number of electrons per second travelling from the cathode to the anode e.g. 200 ma) and the rotation time (e.g. 0.5s). In multi-row CT systems we use what is commonly called effective mas. This is the product of the tube current and the exposure time for one slice. The selected mas and tube voltage determine the dose. The mas value selected depends on the type of examination. Higher mas values reduce the image noise, thus improving the detectability of lower contrasts. For visualizations of soft tissue, i.e. regions of low contrast, a higher dose and larger slice thickness are required. The abdomen and brain are typical regions of soft-tissue contrast. Visualizations of bones or the lungs, i.e. regions of high contrast, as well as contrast studies of vessels require lower doses and thinner slices. Also, obese patients examinations require higher values of mas. 43

44 kvp By changing the peak kilovoltage of the tube, that is, the voltage that accelerates the electrons from the cathode to the anode, the quality of the beam(its ability to penetrate the patient) as well as the quantity of the emitted photons from the X-ray tube are affected. In fact, the amount of the emitted bremstrahlung radiation is proportional to (kvp) 2. The quality of the beam is characterized by the mean energy of the X-ray spectrum which increases as kvp increases. In the current thesis, one of the goals is to demonstrate the change in the attenuation of materials at different energies (kvp values). The utility of this change in dual energy CT methods will be discussed. 3.4 WHAT DO WE MEASURE IN CT? ATTENUATION COEFFICIENTS, HOUNSFIELD UNITS AND THEIR SIGNIFICANCE The principle of computed tomography lies upon computing the spatial distribution of a physical quantity in the body by using projection measurements. The physical quantity is the linear attenuation coefficient of voxels (volume elements of the anatomical subject) or more specifically the quantity CT K µ µ µ w = (3.2) where µ the linear attenuation coefficient of the voxel, µ w the linear attenuation coefficient of water and Κ a numerical constant quantity called magnifying or contrast factor, usually having the value of The ideal tomographic imaging system would provide a complete description of µ for every position in the entire field of view and for a wide range of energies E. In practice, the goal is to reconstruct an estimate of µ from a finite collection of lineintegral measurements by using mathematical procedures known as reconstruction algorithms. Lung tissue and fat exhibit negative CT values due to their lower density and the resulting lower attenuation (µ lung < µ water ). Most of other body areas exhibit positive CT values due to the physical density of muscle, connective tissues and most soft tissue organs. Generally, the major body tissues exhibit CT numbers that range between -100 to 100 HU. Fat has CT number of around For bone and calcifications the higher atomic number of calcium in addition to increased density, is responsible for increased attenuation and therefore for higher CT values of typically up to 2000 HU. The Hounsfield scale has no upper limit. In most w 44

45 clinical systems, the range of CT number is limited by the number of bits used to represent the data. For example, in a 12 bit system the CT numbers range from to 3071 (2 12 values). Therefore, for medical scanners a range from HU to HU is typically provided. One cannot still expect all CT scanners to give the same CT number for the same material. This is because measured CT numbers are also subject to a number of inherent physical and design variations and limitations. The selection of beam quality and beam hardening algorithms is among the more important ones. Another is the day-to-day stability of the measured CT numbers for water and air. Measured CT numbers can also be different in different regions of a scan for identically the same material due to beam hardening and partial volume effects. Figure 3.8: The Hounsfield scale [6] It can be observed that CT is an imaging modality where the depicted information depends both on the chemical composition and the density of the tissues, since the CT number depends on the linear attenuation coefficients. So, if we consider µ = µ ρ (3.3) linear att. coeff. mass att. coeff. where ρ the mass density of the tissue (mass density is unity for water), then µ mass att. coeff. tissue CT(HU) = 1000 ρ ( ρ 1) µ = mass att. coeff. water (3.4) if µ µ mass att. coeff. tissue mass att. coeff. water 45

46 Most body tissues except bone and lung tissue have attenuation similar to water attenuation and so the CT value mostly represents material density. Of course that is only an approach we can make in order to comprehend the significance of the CT image information and it only indicates that for tissues with similar mass attenuation to that of water, the CT number mainly depends on the mass density. It is also obvious that, no matter what material we refer to, the CT number always increases with increasing density at particular kvp. Therefore, conventional CT images offer only a qualitative idea on the distribution of materials in the investigated object, since density and chemical composition effects are not separated in the CT values acquired. This is exactly the challenge for dual energy CT. CT value differences due to effective atomic numbers decrease for higher energies. Contrast at higher energies is dominated by density differences. This holds true for tissues of high atomic number, such as bone, in the same way as for tissues with low atomic numbers, such as fat [6]. In a CT image, the CT value of each voxel is the result of averaging the contribution of different materials to the attenuation coefficient. However, when it is important to clarify, for instance a case of an increased attenuation region in soft tissue, then it is important to find a way to discriminate between fresh bleeding or a different kind of lesion. That is where dual energy CT becomes clinically useful, because the energy dependence of µ due to materials atomic numbers will finally solve the question. The linear attenuation coefficient in CT is calculated by reconstruction of projection data in many different angles. Projections are attenuation profiles created during the scan. Typically images are produced for each 360 degrees rotation. Modern CT systems acquire 1400 projections over 360 degrees or approximately 4 projections per degree.[7] Consider the 2D parallel-beam geometry in Fig. 3.9 [11] in which µ(x,y) represents the distribution of the linear attenuation coefficient in the xy-plane. It is assumed that the patient lies along the z-axis and that µ(x,y) is zero outside a circular field of view with diameter FOV. The X-ray beam make an angle θ with the y-axis. The unattenuated intensity of the X-ray beam is I 0. A new coordinate system (r,s) is defined by rotating (x,y) over the angle θ, according to the following transformation formulas: r cos θ sinθ x s = sin θ cosθ y (3.5) 46

47 x cos θ sinθ r y = sin θ cosθ s (3.6) For a fixed angle θ, the measured intensity profile as a function of r is shown in Fig. 3.9 and is given by µ ( x, y) ds µ ( rcos ϑ ssin θ, rsin θ + scos θ ) ds, θ, θ L L I ( r) = I e = I e (3.7) θ 0 0 where L(r,θ) is the line that makes an angle θ with the y-axis at distance r from the origin. Actually, the spectrum σ(ε) of the X-ray tube and the attenuation depend on the energy, yielding I θ ( r) E, rcosθ s sin θ, rsinθ s cosθ ds de 0 L, θµ = σ ( E)exp ( + ) (3.8) P θ (r) is the projection of the function µ(x,y) along the angle θ ( ) p ( r) ln I r θ θ = (3.9) I 0 Note that p θ (r) is zero for r FOV/2. P θ (r) can be measured for θ ranging from 0 to 2π. Because concurrent beams coming from opposite sides theoretically yield identical measurements, attenuation profiles acquired at opposite sides contain redundant information. Therefore, as far as parallel beam geometry is concerned, it is sufficient to measure p θ (r) for θ ranging from 0 to π. Hence, an angular range of at least 180 degrees is required for measurements in CT. CT scanners nowadays measure typically in fan beam geometry over an angular range of 360 degrees. The extension to 360 degrees resulted from several considerations, initially focussing on image quality and better data sampling. For spiral CT, in particular, 360 degree scanning is a prerequisite [6]. Stacking all these projections results in a 2D dataset p(r,θ) called a sinogram. Τhe sinogram is the input in all reconstruction algorithms. 47

48 Figure 3.9: (a) Parallel-beam geometry with coordinate systems. The X-ray beams make an angle θ with the y- axis and are at distance r from the origin. (b) An intensity profile I θ (r) is measured for every view (defined by an angle θ). I 0 is the unattenuated intensity. (c) The attenuation profiles p θ (r), are the projections of the function µ(x, y) along the angle θ [11]. 3.5 RECONSTRUCTION IN CT A typical CT machine reconstructs one slice image of a matrix size from over one million projection data. Image reconstruction in CT is a mathematical process that generates images from X-ray projection data acquired at many different angles around the patient. Image reconstruction has a fundamental impact on image quality and therefore on radiation dose. For a given radiation dose it is desirable to reconstruct images with the lowest possible noise without sacrificing image accuracy and spatial resolution. Reconstructions that improve image quality can be translated into a reduction of radiation dose because images of acceptable quality can be reconstructed at lower dose. The mathematical procedures mostly used are Back Projection and Iterative Methods. The most common is filtered backprojection because of its computational efficiency. Iterative reconstruction has recently received much attention in CT because it has many advantages compared with conventional FBP techniques. Important physical factors including focal spot and detector geometry, photon statistics, X-ray beam spectrum and scattering can be more accurately incorporated into iterative reconstruction, yielding lower image noise and higher spatial resolution compared with FBP. In addition, iterative reconstruction can reduce image artifacts such as beam hardening and metal artifacts. To avoid the blurring problems of simple backprojection, each attenuation profile is subjected to a mathematical high-pass filter (also referred to as kernel ) prior to the backprojection. 48

49 The reconstruction kernel, also referred to as filter or algorithm by some CT vendors, is one of the most important parameters that affect the image quality. Generally speaking, there is a tradeoff between spatial resolution and noise for each kernel. A smooth kernel generates images with lower noise but with reduced spatial resolution. A sharp kernel generates images with higher spatial resolution, but increases the image noise. The selection of reconstruction kernel should be based on specific clinical applications. For example, smooth kernels are usually used in brain exams or liver tumor assessment to reduce image noise and enhance low contrast detectability. Radiation dose associated with these exams is usually higher than that for other exams due to the intrinsic lower contrast between tissues. On the other hand, sharper kernels are usually used in exams to assess bony structures due to the clinical requirement of better spatial resolution. Lower radiation dose can be used in these exams due to the inherent high contrast of the structures. 3.6 CT IMAGE CONTRAST As already mentioned, CT image contrast and CT contast resolution (or low contrast resolution or tissue resolution) are better than those of the conventional radiograph. Despite that, the density differences of body tissues are too small to differentiate them clearly from each other if it is within 10 HU differences due to the system limitation such detector efficiency, noise, and X-ray radiation safety issue etc. So, contrast agents are used in routine CT imaging to enhance the contrast difference between abnormal tissues and surrounding tissues. Various organic iodine solutions such Omnipaque, Ultravist, Optiray and Visipaque are widely used for the contrast agents. Iodine is five times denser (4.93g/cm3) than water and shows over times higher attenuation in the typical CT X-ray energy range, and so iodine-enhanced and unenhanced tissues become better differentiable through their relative contrast difference [12]. The more radiation detected, the better the signal-to-noise (S/R) ratio will be, improving the visibility of details of a given size and contrast. Contrast resolution indicates the details visible at a given X-ray dose and is limited by noise. In most protocols for spiral CT the contrast resolution is less than that obtained with conventional protocols. Even with comparable scan parameters, the contrast resolution in spiral CT will be slightly less than that in conventional CT. This is due on one hand to the interpolation algorithm, which has an adverse effect on the S/R ratio, and on the other hand to an increase in the partial volume effect, so that the outlines of the structures are less clearly defined. 49

50 3.7 IMAGE DISPLAY WINDOWING Medical images are meant to be used for diagnostic purpose. Theferore, not only the calculation, but also the display of anatomical and/or functional information is quite crucial. Medical images can be colorful or in gray scale, whereas windowing is an important parameter that affects the image display. Chromatic light has 3 descriptors. 1. Hue: the dominant wavelength in the spectrum representing the different colours. 2. Saturation: the amount of white light present in the spectrum. If no white light is present, the saturation is 100%. Saturation distinguishes colourful tones from pastel tones at the same hue. 3. Brightness: Intensity levels must be spaced logarithmically, rather than linearly, to achieve equal steps in perceived brightness. Achromatic light has only one descriptor, its brightness or gray value. Achromatic light is light with a saturation of 0%. It contains only white light. Given a set of possible gray levels or colors and a (rectangular) grid, a digital image attributes a grayvalue (i.e. brightness) or a color (i.e. hue, saturation and brightness) to each of the grid points or pixels. In a digital image, the gray levels are integers. Although brightness values are continuous in real life, in a digital image we have only a limited number of gray levels at our disposal. The conversion from analog samples to discrete-valued samples is called quantization [11]. Most digital medical images today use 4096 = 2 12 grey values (12 bits per pixel are required as we already mentioned when referred to CT number range). Too many gray levels, however, are useless because human observers can typically discern up to a maximum of 60 to 80 gray levels [6]. Therefore, the complete gray scale is assigned to the CT value interval of interest only, the so called window. Values above the chosen window will be displayed as white and values below the window as black. The center of the desired CT value interval (window level) is chosen approximately to the mean CT value of the interesting structures, while the window width determines the contrast of the image. For the display of very small attenuation differences, for example, a narrow window is chosen. 50

51 Figure 3.10: Lung window and Soft tissue window ( TWO-DIMENSIONAL DISPLAYS CT mainly uses the transverse plane as the imaging plane. Therefore, views of other orientations usually have to be reconstructed from the original images. This is done by Multi Planar Reformation (MPR). With MPR, a series of axial images are combined to form a stack. By aligning the same columns and rows of all images of a series, the computer reconstructs contiguous images for any arbitrary plane. MPR has become a valuable tool in the diagnosis of fractures and other orthopaedic indications THREE-DIMENSIONAL DISPLAYS Because the helical or spiral technique acquires a continuous, single volume dataset for an entire body region, imaging of fractures and blood vessels has improved markedly since several different methods of 3D reconstruction have become established [7]. For 3D visualizations the position and viewing direction with respect to the volume of interest must be indicated. Along this viewing direction through the data volume a spatial image is reconstructed from the CT numbers pixel by pixel. Such virtual views are especially suitable for structures which clearly stand out against their surrounding area, such as the skeletal system or contrast-filled vessels. Maximal Intensity Projection MIP is a mathematical method that extracts hyperintense voxels from 2D or 3D datasets, These voxels are selected from several different angles through the dataset and then projected as a 2Dimage.A 3D impression is acquired by altering the projection angle in small steps and 51

52 then viewing the reconstructed images in quick succession (i.e. in cine mode). This procedure is also used for examining contrast-enhanced blood vessels. Volume Rendering Technique (VRT) Volume Rendering Technique (VRT) refers to the process of reconstructing a 3D model from a 2D image stack. VR techniques go beyond MIP techniques in their basic approach and performance.they are not limited to a certain threshold or maximum density value. Instead, all density values along a virtual beam which have a suitable weighting can contribute to the result image. In contrast to MIP, the entire Hounsfield scale can be included in VRT. Each CT number is assigned an opacity and color via freely selectable and interactively modifiable transfer functions. This makes it possible to simultaneously display an extremely wide variety of tissue structures of various density or HU value in a single volume data set. 3.8 DOSE AND SAFETY IN CT Radiation doses are relatively high in CT. For example, the effective dose of a CT of the head is 1 2 msv and of the chest, abdomen or pelvis on the order of 5 8 msv each. A low-dose lung CT is responsible for an effective dose of msv and a whole-body screening for 7.0 msv or more. This is on the order of 10 to 100 times higher than a radiographic image of the same region [11]. A single CT scan will produce a dose exceeding four years of natural background radiation and thus CT is not used for mass population screening nor as a real-time 3D visual aid to surgery. The issue of dose effectively blocks further development of CT to very much higher spatial resolution. Some scanners apply a modulated tube current to reduce the dose. They use a larger tube current in views with higher attenuation. Optimal condition of the equipment requires a daily calibration of the CT scanner by performing a number of blankscans (i.e., scans with only air inside the gantry). Image quality and constancy must be checked by phantom measurements. Maintenance and safety inspections must occur several times a year [11]. Useful information about dose in CT can be found in references [13],[14]. In the following table, the mathematical expressions and descriptions for MSAD and CTDI variants are presented. 52

53 Table 3.1: mathematical expressions and descriptions for MSAD and CTDI variants CTDI in any form is an estimate of average radiation dose only in the irradiated volume. Risk from ionizing radiation, however, is more closely related to the total amount of the radiation dose (i.e. energy) deposited in the patient. One indicator that is proportional to total deposited energy is the dose length product, defined as follows: Dose-length product = L * CTDIvolume (3.13) where L is the total z-direction length of the examination. Some CT scanners display dose length product along with CTDI for each scan. Although proportional to total deposited energy, dose length product is not in itself an appropriate risk indicator, because dose length product takes no account of the radiosensitivity of the irradiated tissues. For that purpose, the concept of effective dose equivalent (HE) has been introduced. Therefore, Volume CT dose index (CTDI vol) is a measure of exposure per slice and doselength product (DLP) is a measure of total radiation exposure for the whole series of images. We will give two more useful dose unit definitions: Air Kerma and Effective dose. Air kerma in air is also used in CT dosimetry and is defined as the sum of kinetic energy of all charged particles liberated per unit mass. The unit is the joule per kilogram (J/kg) and is given the special name gray (Gy). H E is defined as the radiation dose that, if received by the entire body, provides the same radiation risk (i.e. of cancer) as does the higher dose received by the limited part of the 53

54 body actually exposed (i.e. the scanned volume). Formally, the calculation of H E is complicated: we must estimate the doses deposited in each type of organ and tissue, which then are weighted according to radiosensitivity and summed. The amount of anatomy irradiated and the weighting factors for the tissues involved dramatically affect the resulting H E. H E = w H (3.14) where i the number of organs considered and H i is the dose equivalent for each of the i organs. The value of H is given by the absorbed dose D multiplied by the quality factor (QF) of the radiation. The QF has a value of 1 for X-rays. The unit of H and H E is the Sievert (Sv). i i i Table 3.1 Effective Dose Equivalent HE for Clinical X-ray CT Exams (media.wiley.com: x-ray imaging and computed tomography,2002) It should be mentioned that because the CTDI represents an averaged dose to a homogeneous cylindrical phantom, the measurements are only an approximation of the patient dose. Further, CTDI is expressed as dose to air, not dose to tissue, thus leaving CTDI a step away from tissue dosimetry [14]. Both scanner design factors and clinical protocol factors affect radiation dose to the patient. Factors affecting the dose in CT that relate to the construction characteristics of a CT scanner include the scanner type(single-slice conventional scanners or spiral/helical volume scanners and beam geometry, detector type) and the beam quality. As far as clinical factors are concerned radiation dose depends on tube current (amperage), slice scan time and tube peak kilovoltage [13]. As in radiography, tube current and slice scan time are taken together as mas in relation to radiation dose and image quality. Increasing the mas (by increasing tube current or slice scan time) increases the dose proportionally: 300 mas deliver twice the dose of 150 mas. Thus, CT radiation dose is often expressed as dose per mas (or per 100 mas). 54

55 Increasing peak kilovoltage (with all else held constant) also increases radiation dose (roughly with the square of the tube voltage), because the beam carries more energy. However, increasing peak kilovoltage significantly increases the intensity of the X-rays penetrating the patient to reach the detectors. Therefore, significantly lower mas are needed to achieve similar image quality. Consequently, a higher peak kilovoltage does not necessarily mean an increased patient dose and, in fact, may allow the dose to be reduced. Spiral CT requires a sequence of several rotations one after the other. This means that the X- ray tube is under load for a longer time. Consequently, the maximum permissible tube current in spiral CT is less than that in conventional CT. Thus, the dose is lower [9]. The dose that a patient receives is strongly dependent on the patient s size. If the same protocols are used for all patients, the centre dose will be lower in obese patients due to the attenuation of the surrounding tissue. Siemens CT scanners feature the CARE Dose technical measures package (CARE = Combined Applications to Reduce Exposure), which was developed to reduce patient exposure to radiation. This package guarantees shorter examination times, the lowest possible exposure to radiation, and images of excellent quality. 3.9 IMAGE NOISE IN CT The two main problems of the CT imaging system can be summarized by the terms noise and artifacts. These two factors degrade image quality and several techniques for mininizing their effects are currently used. Noise is the most important limiting factor of CT image quality and it represents the portion of the signal that is not useful. It is characterized by a grainy appearance of the image. Noise of a radiological image, depending on its nature and origin, can be divided into two categories: statistical and systematic. Systematic is the kind of noise that is reproduced identically on every image of the modality and can be fully determined and eliminated. Statistical is the kind of noise that obeys to statistical laws and it can be reduced through digital processing techniques. The most important type of statistical noise is the so-called quantum noise. Photons (quanta of light) are the carriers of diagnostic information in X- ray modalities. The insufficiency and uneven distribution of those information carriers is the origin of quantum noise. 55

56 Let us assume that N is the mean value of photons incident on a unit area of detector.then the standard deviation N expressed the local deviations from the mean value N of the photons. Quantum noise contrast is defined as : N N 1 = (3.15) N and is the measure of quantum noise. The larger the standard deviation,the less accurate information is provided by the average CT number of the ROI (region of interest on the image) selected. It is obvious that when the number of photons increases, quantum noise decreases. In CT, quantum noise is also caused by scatter occurring through the interactions of photons with the scanned materials [8]. Other types of statistical noise are electronic noise and computational noise. Electronic noise is noise contained within the image due to mainly power fluctuations of the electronical part of CT. Computational noise is mainly due to all the statistical fluctuations that occur from the mathematical reconstruction. The level of noise in an image is recorded as the standard deviation in an ROI measurement. The larger the standard deviation, the less accurate the average CT number of the ROI. Specificaly, the definition of noise as the standard deviation of Hounsfield numbers (σ) within a region of interest (ROI) is adopted. However, in order to make a direct comparison between CT scanners with different contrast scales, a normalized standard deviation, S is required [15]. S σ = 100% (3.16) CT scale where σ the standard deviation of the pixel values within an ROI and CT scale = CT material CTair (CTwater and CTair are the CT values obtained for water and air, respectively). CT scanning utilizes a large photon flux in acquisition in order to achieve low noise images. However, this results in higher patient doses. These images allow the identification of low contrast structures, reflecting very small differences in photon attenuation in the tissue due to composition or density differences. While the image noise in a uniform material is usually a good indicator of the ability to visualize small contrasts in diagnostic images, a more versatile measure is that of CNR. To measure CNR, the contrast of two objects is determined by the difference of the mean CT numbers within selected ROIs and is divided by the average noise 56

57 for these two ROIs (or the noise difference of the mean CT numbers between a ROI and its background to the average noise of the background) [15]: CNR CT CT 1 2 = (3.17) ( σ1+ σ 2) / 2 This parameter is useful when optimizing a CT examination protocol for a particular contrast situation, e.g. tissue density contrast, iodine contrast and air tissue contrast. Image noise in generally influenced by a variety of factors such as kvp of X-ray tube ma exposure time collimation/reconstructed slice thickness reconstruction algorithm or filter helical pitch/table speed helical interpolation algorithm detector efficiency Image noise is also described by the following relationship [8]: I σ = f (3.18) A I ε Q S 0 1 ε : system efficiency Q : tube current x time product S : slice thickness I 0 /I : ratio of original to detected signal (measure of attenuation) f A : reconstruction Kernel (sharper Kernels increase image noise while smooth Kernels reduce image noise at expense of spatial resolution). Image noise is more important when looking at low contrast images, because it may mask the details (Fig. 3.11). 57

58 Figure 3.11 : Nick Keat ImPACT,St.George s hospital, BSc Biomedical Science (impactscan.org) In general, as beam width decreases, the dose to the patient increases because more photons are required to maintain the same signal-to-noise ratio at the detectors. Thus, noise is reduced because more photons produce a greater detector signal ARTIFACTS IN CT An artifact is considered to be any distortion in the image that is not related to the subject being studied.artifacts can appear as geometrical inconsistencies, blurring, streaks or inaccurate CT numbers. Streak artifacts are the most common distortions depicted on CT images. Motion, metallic objects, high-low frequency interfaces, equipment malfunctions etc. are all causes of streak artifacts. Some of the main types of artifacts in CT are described in the following. The beam hardening artifact is very important in CT and may have streak,dark band or cupping appearance on the image,since the high absorption of x-rays at the edge of the irradiated body gives the false impression that the skin of the irradiated body is made of more absorbing material,causing this edge to colour whiter than the core of the body in reconstructed CT models. It is the result of the polychromatic nature of the beam that leads to changes to the beam quality as it passes through the patient. More conventional ways for its elimination is special beam filtering or suitable postprocessing, as low energy photons are removed from the beam spectrum, the average energy of the spectrum becomes higher, that is, the beam hardens. The harder the beam, the less it is further attenuated. All beams passing through a particular voxel have suffered different amount of hardening, depending on the X- ray tube position they started from. Hence, different beams arrive at the particular pixel and attenuate inside it in a different way. The final reconstructed HU value of the voxel 58

59 corresponds to the mean value of µ calculated for all X-ray tube positions. Therefore, attenuation is dependent on the ray path inside the matter. Beam hardening artifacts can be perceived as reduced attenuation towards the center of an object (cupping) and streaks that connect objects with strong attenuation. In Fig a phantom of plexiglass (polymethyl methacrylate) plate with three amalgam fillings for a polychromatic spectrum is presented. Beam hardening streaks are obvious. Figure 3.12: Beam hardening artifacts in phantom Figure 3.13: Beam hardening: Beam1 and Beam2 emerge from the same scanner and before they attenuate in material,they are described by the same spectrum.at point 1 though,the spectrum of beam 1 has changed and at point 2 has changed even further. The same has happened between the spectra at points 3 and 2 for beam 2 The spectra of beams a and b that arrive at point 2. The number of photons of a polychromatic beam, hitting an X-ray detector is not strictly linearly related to the penetrated material thickness.most reconstruction algorithms nevertheless presume linear attenuation and a monochromatic reconstruction technique is applied directly onto the projection data. Image quality improvement by means of beam hardening correction refers to better surface appearance and a more homogeneous grey value throughout the same material. Basic 59

60 information about beam hardening correction can be found in the beginning of chapter 5, since dual energy imaging is one of the major ways of beam hardening correction. The partial volume averaging/blooming effect is the artifact occurring when two or more different tissue types are averaged together. Because of the finite beam width, every measurement represents an intensity averaged over this beam width. When a highly attenuating object partially covers a voxel, the intensity of the voxel appears higher than its true value. This increases the overall appearance of the object s size. This artifact is prominent with dense materials like calcium, iodine or metal implants. Reduction of slice thickness may lessen this artefact because of the resulting higher z-resolution and smaller voxel size. Also, acquiring images at higher X-ray energy decreases the extent of the artifact due to improved X-ray penetration and reduced intensity of dense objects [8]. Because spiral CT increases the width of the SSP, the partial volume effect will also increase. Partial volume effects are present in all tomographic imaging modalities. Scattering Not all photons that arrive at the detector follow a straight path from the X-ray tube. Typically, up to 30% of the detected radiation is due to scatter. The contribution of scattering to the measured intensity profile is very smooth. Because of the scattered photons, the attenuation of a particular beam is underestimated. The larger the integrated attenuation along a particular projection line, the smaller is the theoretical intensity and thus the larger the relative error resulting from scatter. Thus, scattering yields streak artefacts. The limitation of conventional CT imaging that this thesis mainly deals with, is the fact that different tissues may have similar attenuation characteristics at particular kvp and therefore they cannot be distinguished. This is where dual energy CT comes to offer a new potential, based on the quite obvious observation that information occurring from attenuation of two distinguishable spectra can reveal the differences between materials that happen to attenuate similarly when irradiated at particular kvp. 60

61 CHAPTER 4 PRODUCTION AND ESTIMATION OF X-RAY POLYCHROMATIC SPECTRA 4.1 BREMSTRAHLUNG AND FLUORESCENCE RADIATION There are two basic mechanisms for radiation production in an X-ray tube: 1. Interaction of electrons with the electric fields of atoms of the target. The inelastic scattering from the strong Coulomb field surrounding the nucleus gives rise to Bremstrahlung radiation [bremsen(=braking)+strahlung(=radiation)]. Maxwell s electromagnetic theory predicts: When an E/M field of a charged particle passes in the vicinity of a nucleus, suffers a sudden deflection and an acceleration. A part of its energy propagates in space as E/M radiation at a rate proportional to the square of the acceleration. Of all types of charged particles, only the accelerated light ones (electrons and positrons) are capable of producing an important amount of bremstrahlung photons. To describe it simply: An electron carries an electric charge. A stationary electron creates no magnetic field (like a wire with no current). An electron moving at constant velocity generates a steady magnetic field, but a constant magnetic field won't result in another electric field. An electron moving with a changing velocity (i.e. accelerating), however, generates a changing magnetic field, which will produce a changing electric field, which produces a changing magnetic field, etc. In other words, it generates an electromagnetic wave. The electric field E and the magnetic field B of an accelerated charged particle have two components [1]: a) Local (or near) velocity field component which falls off as 1/r 2. b) Far (or radiation) acceleration field component which falls off as 1/r. At large distances r of interest in medical physics and dosimetry the 1/r radiation component dominates and the 1/r 2 near field component may be ignored, since it approaches zero much faster than the 1/r component. The energy loss by radiation is thus determined by the far field components of the electric field E and the magnetic field B. According to the classical approach, the far field components of E and B are 61

62 q r ( r a) qasinθ E = E= (4.1a) 4πε c r 4πε c r qα r E B = or B= (4.1b) πε c r c where r : the radial vector connecting the charged particle with the point of observation. α : the acceleration vector of the charged particle. α : the magnitude of the acceleration vector. q : the charge of the charged particle, θ : the angle between r and υ. c : the speed of light in vacuum 0 The E and B fields propagate outward with velocity c and form the electromagnetic (EM) radiation (bremsstrahlung) emitted by the accelerated charged particle. The energy density ρ of the emitted radiation is given by 1 ρ= ε Ε + Β = Ε (4.2) ε0 µ 0 The intensity of the emitted radiation is defined as the energy flow per unit area A and is given by the vector product E Χ B/µ 0, known as the Poynting vector S (Ε and B are perpendicular to one another) Ε Β EB 1 q a sin θ S = = (4.3) µ µ π ε S = ε 0cΕ = r c The following characteristics of the emitted radiation intensity are notable: 1. Emitted radiation intensity S(r, θ) is linearly proportional to: q 2, square of particle s charge; a 2, square of particle s acceleration; and sin 2 θ. 2. Emitted radiation intensity S(r, θ) is inversely proportional to r 2, reflecting an inverse square law behaviour. 3. Emitted radiation intensity S(r, θ) exhibits a maximum at right angles to the direction of motion where θ = 1/2π. No radiation is emitted in the forward direction (θ = 0) or in the backward direction (θ = π). It is also worth mentioning that in a relativistic approach as β (u charged particle /c) increases, the radiation intensity becomes more and more forward-peaked and its peak intensity also 62

63 increases. However, the intensities for the forward direction (θ = 0) and the backward direction (θ = π) are still equal to zero, similarly to the classical approximation. The power P (energy per unit time) emitted by the accelerated charged particle in the form of bremsstrahlung radiation is obtained by integrating the intensity S(r, θ) over the area A. de 1 q a P= = S( r, θ ) da 3 dt = 6πε c (4.4) The previous equation is the classical Larmor relationship predicting that the power P emitted in the form of bremsstrahlung radiation by an accelerated charged particle is proportional to the square of particle s charge and the square of particle s acceleration. The Larmor expression represents one of the basic laws of nature and is of great importance to radiation physics. It can be expressed as follows: Any time a charged particle is accelerated or decelerated it emits part of its kinetic energy in the form of bremsstrahlung photons. Bremsstrahlung is only produced through inelastic Coulomb interactions between a charged particle and the nucleus of the absorber. The acceleration a produced in this type of Coulomb interaction can be evaluated through equating the Newton force with the Coulomb force. 2 zeze zze mα = α (4.5) 2 4πε r m 0 Thus, acceleration a experienced by a charged particle interacting with absorber nuclei is linearly proportional with the charge of the charged particle ze and the charge of the absorber nucleus Ze and inversely proportional to the mass of the charged particle and the square of the distance between the two interacting particles. As a result of the inverse m 2 dependence of the power of bremsstrahlung production, a heavy charged particle traversing a medium loses energy only through ionization (collision) losses and its radiation losses are negligible. The collision losses occur in interactions of the heavy charged particle with orbital electrons of the medium. The total stopping power for heavy charged particle is then given by the collision stopping power and the radiation stopping power is ignored, i.e. S tot = S col and S rad 0. Light charged particles, on the other hand, undergo collision as well as radiation loss, since they interact with both the orbital electrons and the nuclei of the absorber. The total stopping 63

64 power for light charged particles is then a sum of the collision stopping power and the radiation stopping power, i.e. S tot = S col + S rad. An electron may have more than one Bremsstrahlung interactions, every one may result in partial or complete loss of energy. All these result in photons having any energy up to the initial energy of the electron and different directions. As a result, bremsstrahlung radiation will have continuous spectrum where the maximum energy relates to the entire K E of the electron. The energy spectrum without filtration is a straight line according to the formula: I = kz( E E) (4.6) E m where I E the intensity of photons with energy E, k constant, Z the atomic number of the target and E m the maximum photon energy (numerically equal to applied kvp). The second way of X-ray production in an X-ray tube is the interaction of the electrons coming from the cathode with the orbital electrons of the atoms in the target. The bombarding electrons can eject electrons from the inner shells of the atoms of the metal target. Those vacancies will be quickly filled by electrons dropping down from higher levels, emitting X- rays with sharply defined frequencies associated with the difference between the atomic energy levels of the target atoms (characteristic radiation-fluorescent X-rays). Fluorescent radiation is emitted isotropically. The selection rules for allowed characteristic transitions leading to most intense characteristic lines are called the electric dipole selection rules and are stipulated as follows: l = ±1 and j = 0 or ± 1 Transitions between outer shells of an atom generally result in optical photons and are referred to as optical transitions (photon energy hν is of the order of a few ev), while transitions between inner shells of high atomic number elements may result in x rays and are referred to as X-ray transitions (photon energy hν is of the order of 10 kev to 100 kev). The X-rays produced by transitions from the n = 2 to n = 1 levels are called K-alpha X-rays, while those for the n = 3 1 transition are called K-beta X-rays. Transitions to the n = 2 or L- shell are designated as L X-rays (n = 3 2 is L-alpha, n = 4 2 is L-beta, etc.). Generally, the following rules are followed: 64

65 1) Transitions of electrons to the K shell are referred to as the K lines, to the L shell as L lines, to the M shell as M lines, etc. 2) Transitions from the nearest neighbour shell are designated as α transition; transitions from the second nearest neighbour shell or a higher-level shell are generally designated as β transition. However, other designations may also be used for some of these. Transitions from one shell to another do not all have the same energy because of the existence of sub-shells. The highest energy transition between two shells is usually designated with number 1, the second highest with number 2, etc. According to Moseley law Z ~ ν. The frequencies of the characteristic X-rays can be predicted from the Bohr model. Moseley measured the frequencies of the characteristic X-rays from a large fraction of the elements of the periodic table and produces a plot of them which is now called a "Moseley plot" (Fig. 4.1). Figure 4.1: Moseley plot of characteristic X-rays 65

66 4.2 X-RAY SPECTRUM IN CT In CT, the spectrum depends on the kvp, the voltage waveform (waveform describes the manner in which the kv changes with time during the X-ray production process) and the tube filtration. All of these factors affect the dose to the patient. Figure 4.2: In the following figure (Fig. 4.3) a typical X-ray spectrum from a tube with a kvp value of 150keV using a tungsten anode is shown. As already mentioned, Bremsstrahlung radiation is characterized by a linear decrease in X-ray intensity with increasing X-ray energy. However, many X-rayswith low energies are absorbed within the X-ray tube and its housing, resulting in the internally filtered spectrum as shown in figure. Additional filters external to the tube are used in order to reduce further the number of X-rays with low energies that are emitted from the tube because such X-rays do not have sufficient energy to pass through the patient and reach the detector, and therefore add to the patient dose, but are not useful for imaging. Figure 4.3: A typical X-ray energy spectrum produced from a tube with a kvp value of 150 kev, using a tungsten anode. Low-energy X-rays (dashed line) are absorbed by the components of the X-ray tube itself. Characteristic radiation lines from the anode occur at approximately 60 and 70 kev. 66

67 4.3 EFFECTIVE ENERGY OF SPECTRUM Although the X-ray energy spectrum is inherently polychromatic, it can be characterized in terms of an effective, or average, X-ray energy, the value of which usually lies between one-third and one-half of E max.. The effective energy is the equivalent energy of a theoretical monoenergetic photon beam that would be attenuated at the same rate as the beam in question. For megavoltage beams, the effective energy (related to bremsstrahlung radiation from an X-ray machine) is the monoenergetic photon energy which produces the same first half value layer in a given material as the X-ray beam. The effective energy can be perceived a method of describing a polyenergetic photon beam, by assigning it the energy of a monoenergetic photon beam that is attenuated by the same thickness of material. By using the Mini CT QC Phantom, if we consider (as described in the corresponding manual) µ ρ material 1 HUmaterial F= = + 1 (4.7) µ ρmaterial 1000 ρ water by knowing the physical density of the material (in the phantom insert) and the measured CT number (properly corrected for variations in the CT numbers for water and air), one can determine the F value for the material experimentally using the equation above and then use that number to estimate the effective beam energy at the location of the insert using an appropriate calibration graph shown in the following figure (Fig. 4.4). Figure 4.4 : Plots of F value against kev for selected insert materials (Nuclear Associates , Mini CT QC Phantom, Users Manual). 67

68 Therefore, a practical way of describing the attenuation of a polychromatic beam is by determining an effective energy level that best imitates this behaviour. Effective energy can be a useful parameter when comparison of the attenuation of different spectra is necessary as it is in the case of dual energy imaging. The larger the difference between the effective energies of two polychromatic spectra, the better the energy separation is expected to be. 4.4 METHODS FOR PHOTON ENERGY SPECTRUM ESTIMATION The estimation of the photon energy spectrum can be useful for many further calculations (Monte Carlo dose calculations, artefact corrections in CT, dual energy material decomposition analysis). However, because of the high photon flux produced by CT X-ray tubes, directly measuring spectra from a CT scanner is difficult. It is therefore interesting to briefly refer to the methods adopted for the estimation of X-ray spectra. Various methods have been developed to estimate CT spectra. These methods can be categorized into two groups: model-based and measurement-based methods. Analytical bibliography on articles regarding those two methods can be found in the references of article [16] MODEL BASED METHODS Model based methods usually generate spectra from empirical or semi-empirical physical models. The estimated spectrum (also referred to as equivalent spectrum) represents that measured by the scanner s detectors. That is, it includes the energy dependent efficiency of the detector, and is unique to the scanner. Boone defines an equivalent spectrum as one that accurately predicts the measured attenuation properties of the actual spectrum for a given X-ray tube. To generate an equivalent spectrum, one begins with a plausible model of the spectrum containing a few parameters which are adjusted until the best fit to the measured transmission data is obtained. In Boone s three parameter equivalent spectrum, the scanner kv, filtration thickness, and anode angle are used as parameters in the semiempirical spectral model of Birch and Marshall [17]. Considerable effort has been given to developing semi-empirical models which generate realistic diagnostic X-ray spectra. The cross section for the emission of bremsstrahlung between the energy E and E+dE can be written as Τ+ m de dσ Β( E, T) (4.8) T E 68

69 where T is the kinetic energy and m (511 kev) the rest mass energy of the electron. The function B is proportional to the photon intensity per energy interval. The analytic form of B is not well-known. Birch and Mashall propose a model for B and include characteristic radiation. The Birch and Marshall spectra are in good agreement with measured tungsten X- ray spectra from 30 to 150 kv and have been published for a wide range of kv, filtration, and target angles. More recently, Tucker, Barnes, and Chakraborty (TBC) have extended the work of Birch and Marshall by refining the treatment of characteristic radiation and fitting the adjustable parameters to more extensive data set available. Let I(X) be the detected intensity of the photon beam after traversing an absorber with surface density X (i.e., product of density and thickness in g/cm 2 ). The relation between the photon energy spectrum S(E), and the measured transmission, f (x)=i(x)/i(0), is f ( x) = α + ε ( Ε) S( E) exp[ m( E) X ] de 0 E kvp 0 (4.9) where m(e) the mass attenuation coefficient of the absorber and ε(e) is the detector response function. The term α 0 is added to account for background in the experimental measurement (e.g. scatter). The energy spectrum S(E) is equal to EdN/dE, where dn/de is the number of photons per energy bin de.the detected spectrum S d (E) is defined as the product of the detector response function and the incident spectrum (i.e. S d (E) = S(E)ε(E)). The detected spectrum is normalized so that f (0) = 1. We may refer to S d (E) as the estimated spectra. It is better to obtain S d (E) rather than S(E) since the detector response function is usually unknown and difficult to measure. As an example of X-ray spectra calculation we will shortly refer to the study [18]. In [18] the estimated spectrum for an electron beam computed tomography scanner (Siemens Medical Systems, Iselin, NJ) has been calculated by using two different spectral models. The first model is based on the TBC model, analyzes the electron s penetration into the anode and utilizes a bremstrahlung model to estimate S d. The second model contains limited physical constraints and considers the spectrum to be a sum of delta functions. Transmission measurements using aluminum, copper, and sodium iodide NaI attenuators were used to determine free parameters. The relevance of the derived spectrum was assessed by using it as input to a CT simulation program which generates images that are compared with phantom measurements. Both models fit the transmission data to an accuracy of 0.30%, which is consistent with the experimental error. The agreement between simulation and experiment ranged from 1.5% at 220 HU to 4.4% at 1700 HU. 69

70 4.4.2 MEASUREMENT BASED METHODS The measurement-based methods reconstruct spectra from measured data, essentially making an indirect measurement of the spectra. One potential method for indirect measurement involves estimating the spectrum from transmission measurements. Transmission methods usually consist of two steps: 1.Measuring the transmission data for different thicknesses of materials and 2.reconstructing the spectra by solving the linear equations that represent the attenuation. The expectation maximization (EM) method, which is based on statistical models [19], is an accurate and robust method to solve this problem. In [16] two step-wedges polycarbonate and aluminum were used to produce different attenuation levels. Transmission measurements were performed on the scanner and the measured data from the scanner were exported to an external computer to calculate the spectra. The EM method was applied to solve the equations that represent the attenuation processes of polychromatic X-ray photons. Estimated spectra were compared to the spectra simulated using a software provided by the manufacturer of the scanner. To test the accuracy of the spectra, a verification experiment was performed using a phantom containing different depths of water. The measured transmission data were compared to the transmission values calculated using the estimated spectra..this method could benefit studies relying on accurate knowledge of the X-ray spectra from CT scanner. 4.5 POLYCHROMATIC ATTENUATION COEFFICIENT So far, we have referred to what the X-ray spectrum is actually composed of and how important its accurate estimation is, for a variety of applications, including dual energy algorithms. A reasonable question that has been a subject of interest ever since computed tomography became available is what exactly is represented by the quantity called linear attenuation coefficient in CT. Monochromatic beams attenuation is quite simply described by a well known exponential law of attenuation (under conditions of narrow beam geometry). If the beam is considered independent of time, then Φ is the photon fluence rate (in units photons per unit area) and Ψ = ΕΦ (in units of energy per unit area) then, attenuation of a monoenergetic beam by transversing an absorber of length x. Those two quantities are described as: Φ=Φ exp( µ x), Ψ=Ψ exp( µ x) (4.10)

71 The linear attenuation coefficient µ of the monoenergetic beam remains unchanged with depth and can be calculated as (either with using energy fluence or photon fluence): Ψ Ψ = 1 exp( µ x) = 1 (1 µ x) = µ x µ = Ψ Ψ x 0 0 (4.11) For attenuation of polychromatic radiation however, the situation is a bit more complex [3]. Polychromatic beams are described by a spectrum, that is, photons of different energies distributed unequally (generally) in a specific energy range. Therefore, the special characteristics of the X-ray spectrum define the polychromatic linear attenuation coefficient of a material. In other words, if the desirable task is to theoretically estimate the CT attenuation or the attenuation coefficient of a material for a specific X-ray spectrum, then the accurate estimation of this spectrum is required. This knowledge is very important for dual energy calculation methods, because the attenuation of basis materials is an input to the algorithms. Moreover, since dual energy methods are based on utilizing two different spectra, it is also important to know how well those spectra are separated and if they are appropriate enough for dual energy applications. Under narrow beam geometry conditions, photons of all energies are attenuated as: Φ =Φ ( E) exp[ µ ( E) x], Ψ =Ψ ( E) exp[ µ ( E) x] (4.12) E E0 E E0 where Φ Ε and Ψ Ε are the spectrally distributed photon fluence(photons/area-energy interval) and energy fluence(energy/area-energy interval) respectively with initial values (before attenuation) Φ Ε0 and Ψ Ε0. The photon fluence and the energy fluence over the whole energy range at any distance into the absorber are given as ΦE0 ( E) exp [ µ ( E) x] de, ΨE0 ( E) exp [ µ ( E) x] de (4.13) Φ= Ψ= In order to describe the linear attenuation coefficient of a material for a polychromatic beam we need to obtain an equivalent quantity, that will describe how the specific material attenuates a specific incident photon spectrum. This may occur by measuring the half value layer (HVL), the amount(x) of a given material needed to reduce Φ or Ψ of the beam to one half. One can use an HVL determination to assign an equivalent attenuation coefficient from the relation: µ e= (4.14) HVL 71

72 Furthermore, an equivalent photon energy can be obtained by looking up in a table of attenuation values for the material used for the HVL determination the energy of the monochromatic photons that have the same equivalent linear attenuation coefficient as the original polychromatic beam. It would only be a coincidence if this equivalent energy would be exactly equal to the mean energy of the spectrum given by eq [4.15], since the latter is without regard to any attenuation of any material : E Φmean EΦ de EΨ de E =, E = Φ E de Ψmean Ψ E E de (4.15) where E Φmean the photon averaged mean value and Ε Ψmean the energy fluence averaged mean value. Moreover, for a polychromatic radiation a local attenuation coefficient can be calculated in an analogous to eq [4.11] manner as: 1 Φ 1 Ψ µ Φ =, µ Ψ = (4.16) Φ x Ψ x The values of µ Φ and µ ψ depend on depth (i.e the local spectral distribution Φ Ε and Ψ Ε. ). A measurement of local attenuation coefficient also permits the specification of an equivalent photon energy (i.e. the energy of a monoenergetic photon beam having an attenuation coefficient equal to the local attenuation coefficient of the polychromatic beam). From equations 4.12 and 4.16 we yield (4.17) µ ( E) ΦE( E) de µ ( E) ΨE( E) de µ Φ=, µ Ψ = Φ Ψ In other words, the local attenuation coefficient is identical to the attenuation coefficient averaged over the local differential spectra. Let us note that there may be some differences between µ, µ Φ Ψ and the corresponding equivalent energies as there are differences between the values obtained from the HVL and the local attenuation coefficient approximation. In the following, there is a table of the linear attenuation coefficient of water averaged over Φ,Ψ and X (exposure) and their equivalent energies (Table 4.1). The data come from the program XSPEC and refer to photon beams of the EMI scanner [3]. Although nowadays the EMI scanner has become obsolete, this table is mentioned in order to point out differences of local linear attenuation coefficient values, as well as the differences of the attenuation between different kvp spectra (although for water those last differences are marginal). 72

73 Table 4.1 : Attenuation coefficient of water 73

74 CHAPTER 5 DUAL ENERGY CT(DECT): ALGORITHMS, TECHNOLOGY AND APPLICATIONS 5.1 GENERAL PURPOSES OF DECT CT is an invaluable imaging modality nowadays, but yet there are some issues to be considered in clinical practice. For instance, materials of high X-ray attenuation are susceptible to beam hardening or spectral artifact in CT. Low energy photons are preferentially absorbed by matter (beam hardening effect). In order to cope with beam hardening effects, one could employ a radioisotope source with a monoenergetic spectrum, but the practical intensity is usually much lower leading to lower SNR. Higher intensities are obtained from monoenergetic synchrotron sources, which are quite expensive. Beam hardening artifact is a challenge for new CT developments. Dual spectral information of X-ray has been used to correct the spectral artifacts [20]. Dual energy processing before reconstruction takes place, means beam hardening elimination, therefore better image quality and more precise HU number calculations. If the polychromatic nature of the beam is not taken into account, in a non-corrected algorithm, then the anatomic information is limited because,as seen in chapter 4,attenuation coefficient is also dependent on the incident spectrum and therefore does not represent the material in a unique way. The use of a monoenergetic source for CT scanning is not generally recommended, since those sources have insufficient strength to provide a complete scan in a reasonable time interval. The spectral-shift distortions could be minimized if each projection had a similar energy spectrum. To accomplish this, many instruments, such as the early EMI head scanner, used a pathlength compensator which provides a water vessel on both sides of the object to produce a constant path length. These compensators, however, seriously increase the radiation dose to the patient since increased intensity must be applied to the patient to maintain a detector level. Even with these compensators however, different materials within the object, primarily bone, result in continued spectral shifts. These are minimized, in many instruments, by using relatively high energies where the bone attenuation is primarily due to Compton scattering as is that of soft tissue. This, however, removes much of the photoelectric absorption component of the attenuation coefficient, which is sensitive to atomic number. 74

75 Thus, the use of relatively high energies diminishes the diagnostic value of the resultant images. Nowadays generally, for beam hardening corrections there are roughly of four ways of solving the problem: hardware filtering, dual energy, statistical polychromatic reconstruction (by incorporating the polychromatic nature of the beam in an iterative maximum likelihood (ML) algorithm), and linearization(which aims to transform the measured polychromatic attenuation data into monochromatic attenuation data). Figure 5.1: The image above comes from a presentation of Rendon C.Nelson MD: Dual energy CT:Use of the virtual unenhanced image for quantifying enhancements, Stanford Radiology 10 th Symposium, May It is obvious that the monochromatic image is less noisy and without beam hardening artifacts. Apart from beam hardening effect treatment, dual energy CT offers the ability of direct tissue characterization and its early workers used to refer to it with the term tomochemistry. In that way, not only anatomical, but also functional information can be produced by dual energy CT. Special reference on this potential will be done in the chapter of Applications of Dual Energy CT. Therefore, in cases when two materials have the same attenuation behaviour for one spectrum, they may have different attenuation characteristics at a different spectrum and this information can lead to discrimination. Despite the new perspectives that keep increasing especially during the last decade, clinical importance of dual-energy imaging is still a matter under investigation. The killer application for dual-energy, that is, a clinical useful application that can t be done by other X- ray means has yet to be clearly identified. In order to summarize the major fields of importance for dual energy scanning, we would say that important applications of dual energy imaging, especially in CT, seem to be the following: 75

76 A means to produce images free of beam hardening at a range of monochromatic energies. Contrast between some tissue types could be increased. A means to identify the chemical composition of tissues, material selective images. More quantitative and accurate results, for instance, bone mineral analysis and the assessment of the fat content in liver for suitability for organ transplant. Automatic subtraction of a tissue type. For example, bone subtraction (predominately a photoelectric absorber) from soft tissue (predominately a scatterer) or subtraction of iodine contrast from image (virtual non enhanced images) or bone minerals for assessment of bone marrow. Attenuation correction in nuclear medicine. The dual-energy X-ray data are used to synthesize an object and energy-specific attenuation map which is incorporated into an algorithm to reconstruct an attenuation corrected SPECT image [21]. Blended images from high and low energy datasets and virtual monochromatic images for replacement of the conventional 120kVp image. Electron density and effective atomic number calculations for radiotherapy treatment planning. It is also worth mentioning that, beyond its medical applications, there are numerous potential applications of dual-energy imaging, including rock characterization for petrochemical industrial applications, soil sample analysis in agriculture, explosives detection. 5.2 PHYSICAL BACKGROUND OF DECT The display of human anatomy in CT (photon energies from about 20 to 150 kev) can be attributed to two main mechanisms: Compton scatter and photoelectric effect. High Z materials are dominated by photoelectric effect while low Z materials are dominated by Compton effect, as already discussed (Fig. 5.2). 76

77 Figure 5.2: Atomic number and energy dependence of attenuation processes In conventional CT imaging different materials, with considerably different atomic numbers may appear identical (for example calcified plaque and iodinated blood). The dual energy imaging technique is useful for tissue characterisation in computerised tomography and selective cancellation of unwanted tissues in digital radiography. The basic idea is to acquire two attenuation data sets at different energies and use the additional information emerging from processing those specta dependent data. Dual-energy CT imaging makes it possible to differentiate between certain materials, since X-ray absorption is material specific and dependent on the energy of the X-rays. Dual energy CT takes advantage only of the photoelectric attenuation differences of materials at two different energies, because the Compton effect energy dependence is not equally strong and because only photoelectric absorption depends on atomic number. It is true that CT numbers do not vary noticeably with beam energy for soft tissues, but the opposite is true for high Z materials. That is due to the photoelectric attenuation energy dependence. In addition, K-edges of several elements constitute their photoelectric attenuation identity and are strongly indicative of the material composition of the anatomical subject. The K-shell binding energy varies for each element, and it increases as the atomic number increases. The term K edge as already mentioned refers to the spike in attenuation that occurs at energy levels just greater than that of the K-shell binding because of the increased photoelectric absorption at these energy levels. K-edge values vary for each element, and they increase as the atomic number increases. The closer the energy level is to the K edge of a substance 77

78 such as iodine, the more the substance attenuates. With current dual-energy CT technology, the two peak kilovoltages most frequently employed are 80 kvp and 140 kvp. Because the K edge of iodine (33.2 kev) is closer to 80 kvp than it is to 140 kvp, the attenuation of iodine-containing substances is substantially higher at 80 kvp. There is a bell curve of energies for a set of photons at a certain kilovolt peak. Therefore, at 80 kvp, some photons have energy that is close to 33.2 kev, the K edge of iodine. For example, the main portal vein, aorta, and kidneys have higher attenuation at 80 kvp than at 140 kvp(due to their iodine content in contrast enhanced images) and in this case, the attenuation values of these structures are approximately 95%, 93%, and 101% greater at 80 kvp than at 140 kvp, respectively [22]. That is, in fact, very valuable information for dual energy imaging, because what we are interested in this case, is not only the attenuation of a tissue but the difference in the attenuation of the tissue at different energies and more specifically how different the energy dependent attenuation of different tissues is. In that way, considering a base of elementary substances with known attenuation properties that constitute the tissue, it is possible to understand the amount of each of the basis materials in the tissue and therefore discriminate the tissue from others that present similar attenuation in conventional CT imaging. That idea exactly is what mathematically is expressed by material decomposition algorithms. Table 5.1 : K-edges of physiologic substances and contrast agents [20] 5.3 ALGORITHMS OF DUAL ENERGY CT Dual energy techniques can be very useful in resolving problems that deal with material chemical composition identification. The procedure involving the mathematical analysis which provides this information could be divided into prereconstruction and postreconstruction techniques and then they can be further divided into material 78

79 decomposition and ρ-ζ techniques. Those two are similar;the difference lies on the basis functions that we use for further analysis of the attenuation coefficient function. Material decomposition expresses the algorithmic procedures that consider the anatomical subject as a mixture of basis materials and ρ-z methods provide electron density and atomic number maps by utilizing the energy dependence of photoelectric effect and Compton scattering as basis functions.the concept of determination of Z and ρ e from dual-energy CT scans was introduced by Rutherford et al [23], Millner et al [24] (postreconstruction) and Alvarez- Macovski [20] (prereconstruction) studies (1976) and Avrin,Macovski,Zatz [25] (1978) and further developed the next decades. We will start the description of dual energy algorithms from ρ-ζ methods DUAL ENERGY CT PRE-RECONSTRUCTION ρ-ζ TECHNIQUES The attenuation coefficient of the anatomical subject, as discussed in previous chapters is energy dependent and of course material dependent. The basic idea is to separate those two dependences by utilizing the different attenuation behavior of matter at different energies [20]. By assuming that the energy dependence of the two basic phenomena taking place in radiology (photoelectric and Compton effect) follow a known standard behavior (K-edge dependences are excluded), we are led to an estimation of electron density and atomic number. The analysis of the attenuation coefficient is expressed by the following equation [2]. 1 µ ( E, x) = aph( x) 3 + acomp ( x) fkn ( E) (5.1) E where α 256π 2 3 n n ph α0 I 0 ρelz ρelzeff = (5.2) I 0 = 13.5 kev, denoting the ionization energy of the hydrogen from the first Bohr orbit, α 0 = 5.29 x 10-9 cm) is the first Bohr radius of hydrogen and r e (2.82 x cm) is the classical electron radius and 8π 3 2 αcomp = re ρel ρel The electron density and the effective atomic number respectively are symbolized as ρ el and Z and f KN is the Klein-Nishina function (as already mentioned in chapter 1): (5.3) f KN 3 1+ γ 2 γ (1 + γ ) γ = ln(1 2 γ ) ln(1 2 γ ) γ 1+ 2γ 2 γ (1+ 2 γ ) (5.4) 79

80 with γ = Ε/mc 2, m being the mass of the electron and c the velocity of light in vacuum, with mc 2 = kev. The dimensions of a ph and a Compton are kev 3 /cm and cm -1 respectively. They are space dependent quantities, since each position in space is characterized by the local material composition and density of the anatomical subject. Experimental results indicate that photoelectric mass attenuation coefficient is proportional to Z n where n=3(approximately) for high Z materials and n is closer to 3.8 for low Z materials (like the bulk of the biological material like carbon, nitrogen and oxygen) ( This dependence will be further analyzed and confirmed in the current thesis in chapter 6. There it was concluded that, unless the material is of very small effective atomic number,n=3 is a good approximation.however, if the material is of effective atomic number larger than 11, k-edges appear. Thus, unless we refer to a specific energy region where k-edges do not exist, absorption edges must be taken into account. The justification of such a decomposition has been verified experimentally within the regime of diagnostic x-ray energies for elements with low atomic numbers Z, i.e., those elements whose K-edge discontinuities in the attenuation coefficient for x-rays lie well below the energy regime relevant for medical x-ray applications. In the presence of elements with a high atomic number Z, the above description of the attenuation properties of matter has to be modified. In order to correctly describe the attenuation of a sample containing a single element with K-edge discontinuity inside the relevant energy range, the decomposition has to be extended by the energy dependent attenuation function of this particular element as a third component [26]: 1 ( Ε, x) = a ( x) + a ( x) f ( E) + a ( x ) f ( E) (5.5) E µ ph 3 Comp KN k edge material k edge material In the above formula, α k-edge material (x) and f k-dge material (E) denote the local density and the energy dependence of the attenuation of the k-dge material. The latter includes the photoeffect, Compton-effect and k-edge contributions of the k-edge material. While in dual-energy systems (at least) two spectrally different measurements per x-ray path have to be performed in order to determine the line-integrals of the coefficients a ph (x) and a Co (x), the extended model mentionded here, relies on a minimum of three measurements.for this reason,photon counting detectors are utilized because they can provide information for attenuation characteristics in more than 2 energy bins. 80

81 In order to comprehend the utility of such a decomposition, someone has to consider the main dependences of photoelectric and Compton attenuation coefficients. Compton scattering depends on the electron density, which is proportional to the mass density for most materials. On the other hand, the photoelectric effect depends on the atomic number and thus the amount of photoelectric interactions is indicative of the molecular composition of the object. We have already clarified the fact that in conventional CT, a lesion of increased attenuation could be either due to increased density or increased atomic number. By distinguishing between the two phenomena, the cause of increased attenuation becomes evident. Projection data corresponding to each one of the two utilized spectra(low and high kvp) are measured: where p p L H Aph I0L( E) D( E)exp( A ( )) 3 comp fkn E de = ln[ E ] I D( E) de 0L Aph I0H ( E) D( E)exp( A ( )) 3 comp fkn E de = ln[ E ] I D( E) de 0H (5.6) A = a ( x) ds, A = a ( x ) ds (5.7) ph ph comp comp In these equations I 0L, and I 0H, may be photon number spectra with I L, I H total counts, or I 0L, and I 0H, may be energy spectra with I L,I H total energies. D(E) is the detector response function.the case of photon number spectra will be considered with similar results obtainable for energy spectra.the dimensions of α ph and α comp are kev 3 cm -1 and cm -1 respectively. As long as the Jacobian p1 / Aph p1 / Acomp J = det p2 / Aph p2 / A (5.8) comp is nonzero, one can solve for Aph and Acomp. If the beam was monoenergetic, the equations could be solved directly to obtain the line integrals A comp and A phot.. In 5.3.6, several methods are examined for solving the equations for a polyenergetic spectrum. After having calculated those line integrals at many angles and positions, it is possible to perform energy selective reconstructions, that is, to obtain photoelectric only and Compton-only images. Another important benefit of pre-reconstruction dual energy processing (either photo-compton or material decomposition) is that reconstruction of 81

82 projection data dependent only on material and not on x-ray beam characteristics automatically, corrects the beam hardening effect. Knowing a comp an a phot from equations [5.2] and [5.3], ρ e and Z (or Z eff ) may be calculated and electron density and effective atomic number images may be obtained DUAL ENERGY CT POSTRECONSTRUCTION ρ-ζ TECHNIQUES The information about the electron density in human body is of great importance in treatment planning for radiotherapy. Especially in treatment planning for proton and heavy ion radiotherapy, the electron density is indispensable in order to predict the range of the particle beams in the body. Heavy-ion and proton radiotherapy has a great advantage; it gives excellent localization of radiation dose on a target volume. In order to make the most use of the dose localization, precise and accurate treatment planning is required to predict the end of range of particle beams in less than a few millimetres in a body. More precise range estimation can reduce the uncertainty and then the irradiation of the particle beams on a target located closely to a critical organ such as the spinal cord will be feasible.the range of heavy ion is approximately proportional to electron density of an object. Monte Carlo (MC) dose calculations are performed on patient geometries derived from computed tomography (CT) images. For most available MC codes, the Hounsfield units (HU) in each voxel of a CT image have to be converted into mass density (ρ) and material type. However, the conversion is not a trivial procedure and it has been shown that inaccurate tissue segmentation can lead to large dose calculation errors. Conveniently for MC dose calculations the ρ el -maps can be directly converted into ρ-maps using a linear relationship, therefore dual energy methods for ρ el calculation may be implemented as a promising alternative to other conventional methods for HU conversion into mass density. Moreover, Z-maps from dual energy CT postprocessing can be used to improve material segmentation by taking advantage of Z differences of tissues or materials having similar densities. Various authors published studies on conversion of CT images into mass densities. Schneider et al (1996) described a method to determine improved CT calibrations for biological tissue, stoichiometric calibration, based on measurements using tissue-equivalent materials. Schneider et al (2000) simplified the stoichiometric calibration by introducing interpolation functions in the calibration procedure. The studies made use of single-energy CT scans of patients or phantoms. 82

83 The conventional approach to the conversion of CT numbers (or Hounsfield units (HU)) involves scanning a set of tissue-equivalent materials and creating a (HU; ρ) calibration curve. An example of a calibration curve created using a set of RMI electron density calibration materials is shown in figure 5.3 Material segmentation, done by assigning HU ranges to tissue types, is indicated by the dashed vertical lines. Figure 5.3: A typical (HU; ρ) calibration curve used for conversion of HU into mass densities and material types [27]. This conventional approach though suffers from inaccuracies regarding the types of tissueequivalent materials that are suitable for calibration, the boundaries between tissue types etc. In a proposed method of dual-energy X-ray CT using high intensity monochromatic synchrotron radiation (SR) by Torikoshi et al [28] Z eff and ρ el can be calculated by analyzing the linear attenuation coefficients at the particular(monochromatic) energies on the basis of photoelectric and scatter components. Measuring the linear attenuation coefficients with two x-rays and using Jackson and Hawkes (1981) approximation of the linear attenuation coefficient, the following two equations describing the photoelectric and scattering contribution to total linear attenuation coefficient are obtained. µ ( Ε ) = ρ ( Z F( Z, E ) + G( Z, E ) 4 1 e 1 1 µ ( Ε ) = ρ ( Z F( Z, E ) + G( Z, E ) 4 2 e 2 2 where ρ e is the electron density, Z is the (effective) atomic number and ρ e Z 4 F(E 1,Z),ρ e G(E 2,Z) denote a photoelectric term and a scattering term of the linear attenuation coefficient, respectively. It is clear from the formulation by Jackson and Hawkes [29] that this method is available for low Z elements, but not for high Z elements that have absorption edges at an (5.9) 83

84 energy of a few tens of kev or more.therefore the method is valid for light to medium elements at less tha a few hundred kev. Solving the simultaneous equations, Z and ρ e can be obtained as follows (assuming that neither the term F(k, Z) nor the term G(k, Z) strongly depends on Z) Z µ ( E ) G( Z, E ) µ ( E ) G( Z, E ) = µ ( E ) F( Z, E ) µ ( E ) F( Z, E ) (5.10) µ ( E1 ) F( Z, E2) µ ( E2) F( Z, E1 ) ρe = F( Z, E ) G( Z, E ) F( Z, E ) G( Z, E ) (5.11) F(Z,E) and G(Z,E) are obtained by fits of the NIST attenuation data. In [28] liquid samples of solutions of K 2 HPO 4 and solid samples of tissue equivalent materials were used to simulate human tissue. The experiments were carried out using monochromatic x-rays with energies of 40, 70 and 80 kev produced by monochromatizing synchrotron radiation. Using the CT image of 40 kev and the corresponding CT image of higher energy, the effective atomic number and electron density were derived. The solid samples were also measured in a complementary method using high-energy carbon beams to evaluate the electron densities. The measured electron densities were compared with the theoretical values or the values measured in the complementary method. It was found that these values were in agreement in 0.9% on average. Figures 5.4: CT image of the head phantom based on the linear attenuation coefficient for (a) 40 kev x-rays and (b) 70 kev x-rays. The schematic drawing of (c) shows the structure of the head phantom. Squares shown in (c) designate the ROIs [28]. 84

85 Figures 5.5: CT image of the head phantom based on (a) the electron density and (b) the effective atomic number [28]. Comparison between the CT images based on the linear attenuation coefficients shown in figures 5.4 (a) and (b) provides interesting points. The difference of the concentration in the liquid samples appears more clearly at 40 kev than at 70 kev. It is because the 40 kev image is more sensitive to the effective atomic number of the subject than that of 70 kev. The acrylic vessels appear more clearly in the image of 70 kev than that of the 40 kev image, because the 70 kev image has stronger sensitivity to the electron density than the 40 kev image. Both the images are, however, on the whole rather fuzzy. On the other hand, as shown in figures 5.5.(a) and (b), both the images based on the electron density and the effective atomic number give drastic improvement in the contrast between the acrylic wall and the other materials. In the electron density image, the acrylic wall indicates higher values than the other samples. However, in the effective atomic number image, the acrylic wall has the lowest values among the other materials. It indicates that the acrylic wall consists of relatively light elements and has a relatively high mass density. It is also interesting that the difference in the concentration of the K 2 HPO 4 solutions is more enhanced in the effective atomic number image than in the electron density image. These features shown in figures 5.5.(a) and (b) enable us to clearly discriminate one material from another material with different criteria from the conventional CT image based on the CT-numbers. In [27] (2008 study by Bazalova et al), a modified version of the previous method has been used, appropriate for polychromatic attenuation. By using this method, an interesting phantom study was performed. A 32 cm diameter solid water RMI electron density calibration phantom with 20 cylindrical inserts made of 17 tissue-equivalent materials was scanned at 100 and 140 kvp in a single-slice CT scanner. The mean HU of each insert of both 100 kvp and 140 kvp images were calculated and the ratios µ 1 /µ 1water and µ 2 /µ 2water, for the two energy spectra were 85

86 used to extract Z eff and ρ el. Then the values calculated were compared to the known values of the materials. The mean errors on Z and ρ e extraction were 2.8% and 1.8%, respectively. Phantom dose calculations were performed for 250 kvp and 18 MV photon beams and an 18 MeV electron beam in the EGSnrc/DOSXYZnrc code. Two methods for for conversion from HU to mass densities and materials were used: the conventional (HU; ρ) and the novel (HU; ρ, Z) dualenergy CT tissue segmentation (which does not require a calibration curve). The dose calculation errors using the conventional tissue segmentation were as high as 17% in a mis-assigned material for the 250 kvp photon beam. Similarly, the errors for the 18 MeV electron beam and the 18MVphoton beam were up to 6% and 3% in some mis-assigned media. The assignment of all tissue-equivalent inserts was accurate using the novel dualenergy CT material assignment. As a result, the dose calculation errors were below 1% in all beam arrangements. Comparable improvement in dose calculation accuracy is expected for human tissues. The dual-energy tissue segmentation offers a significantly higher accuracy compared to the conventional single-energy segmentation. Fig. 5.6: The geometry of the solid water RMI phantom with 17 different tissue-equivalent inserts for material extraction (phantom A). Phantom geometry for MC dose calculations using an orthovoltage 250 kvp photon beam and an 18 MeV electron beam (phantom B) and using 6 and 18 MV photon beams (phantom C). Medium 6 is the phantom material, solid water. The directions of the beams are indicated by the arrows [27]. Fig. 5.7: Material segmentation for electron and orthovoltage photon beam dose calculations: (a) exact geometry, (b) single-energy CT material segmentation and (c) the dual-energy CT material segmentation [27]. 86

87 Rizescu et al (2001) [30] developed their own method for dual-energy material extraction and built a CT scanner with an Ir-192 source emitting reported principle gamma radiation of and kev. They were able to extract Z with an error less than 3% and 10% for Z > 25 and Z < 15, respectively. The error on ρ determination was less than 3%. In 2003, Heismann et al [31] introduced a semiempirical ρz projection algorithm which allowed Z and ρ extraction of a set of chemical solutions with Z varying from 7.21 to 9.84 and ρ in the range from to Therefore,the model developed by Heismann et al. gives accurate effective density estimation for materials with effective density and effective atomic number close to water.the errors on Z extraction using this method were up to 5%. In this approach, the effective linear attenuation is modeled using the x-ray spectra S(E) and detector response function D(E). However, it fails when dealing with materials with relatively high effective atomic number and effective density because the effect of beam hardening was not fully considered in that model. Different from the initial work of Heismann et al., in [32] (Liu et al.), an empirical correction to the model is used, resulting in: µ ( ρ, Z ) = Cρ w( E) µ ( E, Z ) de (5.12) eff eff eff m eff where w( E) = S( E) D( E) / S( E) D( E) de and C is an empirically determined correction factor with a value dependent on Z eff,even for Z eff values above 10.The effective density ρ eff represents the ratio of the total mass to the total volume of the material with.µ linear attenuation coefficient and µ m mass attenuation coefficient. The ratio of the effective linear attenuation coefficients at the low energy spectrum µ eff,l and high energy spectrum µ eff,h can be expressed by: where f ( Z ) = w ( E) µ ( E, Z ) de (5.14) L,H eff L, H m eff ρ eff µ µ = = Cf ( Z ) Cf [ F ( / )] eff, L eff, L 1 L eff L µ eff, L µ eff, H (5.15) A numerical lookup table was constructed based on eq. [5.13] to [5.15] to allow determination of the effective atomic number Z eff and effective density ρ eff based on the ratio of the effective linear attenuation coefficients obtained from the dual-energy CT image data using the relationship µ µ f ( Z ) = = F( Zeff ) (5.13) f ( Z ) eff, L L eff eff, H H eff µ eff,l or H =[(CT# L or H /1000)+1]µ water,l or H (5.16) 87

88 It should be noted though, that the method may fail when dealing with materials with very high atomic numbers MATERIAL DECOMPOSITION: BASIC PRINCIPLES ANALYSIS TO BASIS MATERIALS: VOLUME AND MASS CONSERVATION The basis functions of the linear attenuation coefficient in [20] are f phot (E) and f KN (E). In the same way, any linear combination of those functions may be used as basis function. Therefore, if we consider two basis materials, we will have: µ µ = a ( x) f ( E) + a ( x) f ( E) mat.1 ph1 ph comp1 = a f ( E) + a f ( x) ( x) ( E) mat.2 ph2 ph comp2 KN KN (5.17) By using µ mat.1 and µ mat.2 as basis functions (that is, the linear attenuation coefficients of the two materials mentioned), the linear attenuation coefficient of the anatomical subject (that is,any material depicted) will be expressed as: µ ( Ε, x ) = aµ mat ( E) + a µ mat ( E) (5.18) where α 1 and α 2 are dimensionless quantities-weighting factors. This is true as long as the energy dependence, that is the extent to which photoelectric and Compton effect contribute to the attenuation, are not identical between the two basis materials (in other words µ 1 ( E ) and µ 2 ( E ) must be different enough to form a new system of basis mat mat functions). This is necessary for their dual energy discrimination as it will later be described. Therefore, if we consider the equation 5.18 for 2 energies (or two spectra), we may solve the system to obtain α 1 and α 2. This may happen in the projection or in the image domain. In prereconstruction material decomposition analysis is possible by appropriately modifying the projections: p p L H I0L ( E) D( E) exp[ A1µ 1L ( E) A2µ 2L ( E)] de = ln I0LD( E) de I0H ( E) D( E)exp[ A1µ 1H ( E) A2µ 2H ( E)] de = ln I0H D( E) de where A1 = α1( x) ds, A2 = α2( x ) ds, D( E) the detector response function. (5.19) 88

89 In that way, material specific or virtual monochromatic images are obtained. Details about solving for A 1 and A 2, which are called equivalent lengths or equivalent thicknesses of the basis materials along the X-ray path are discussed later in Same here as before, k-edges should not be in the energy range of the spectrum investigated, although is has been reported [33] that even for a material whose K-edge is within this range such as iodine, the error may be small enough to be ignored. The weighting factors α 1 and α 2 not energy dependent. It is important to investigate, what physical quantities they represent. To find this out, we may express α 1 and α 2 as a function of α comp and α phot of the material depicted(let us refer to it as mixture ) and those of the basis materials (α ph1, α comp1, α ph2, α comp2 ). The relationship is given in the study of Lehman et al. [34] and can be further analyzed as following: a a 1 a = a a ph ph2 comp acomp a comp2 ρ = el aph 1 a ρ ph2 el1 comp1 acomp 1 a comp2 a a a a Z Z Z n n eff eff 2 n n eff 1 Zeff 2 ph ph1 comp acomp a n n comp1 ρ Zeff Z el eff 1 2= = n n aph2 a ρ ph1 el2 Zeff 2 Zeff 1 acomp2 acomp2 a comp1 (5.20) (5.21) where n the exponent that described the power law dependence of the photoelectric attenuation coefficient from atomic number (approximately 3-4) and ρ el are electron densities (number of electrons/ml) and is characteristic for every material. From the above relationships we observe that the values of α 1 and α 2 depend on the ratios ρ elmaterial /ρ el1 and ρ elmaterial /ρ el2 and the effective atomic numbers of the basis materials and the mixtures. Therefore, they are both dimensionless and depending on the same quantities. Assuming that the sum of the volumes of the constituent materials in the mixture is equivalent to the volume of the mixture (volume conservation), then α 1 =V 1 /V total and α 2 =V 2 /V total. For instance, for α 1 and relationships 5.20, 5.21 and 2.10 (where w 1 is the fractional electronic content), we obtain: 89

90 ρ Z Z ρ w Z Z ρ w Z Z ρ n n n n n n el eff 2 el ( w2 1) 2 el 1 1 w1 2 el V1 1= = = = n n n n n n 1= ρ Z1 Z2 ρ Z1 Z2 ρ Z1 Z2 ρ tot a w V el1 el1 el1 el1 (5.22) In principle, dual-energy CT can only accurately decompose a mixture into two materials. To decompose a mixture into three constitute materials using dual-energy CT measurements, a third piece of information must be provided to solve for three unknowns with only two spectral measurements. One way to get those 3 equations we need is to assume volume conservation, but this is not always correct. For instance the volume of salt-water mixture is not equal to the individual volumes of salt and water. Volume-conservation based algorithms for three-material decomposition can only be used for mixtures of solid materials or a solution in which one knows how the materials are mixed (i.e. have knowledge of volume displacement of the three materials when they are mixed together). A more generalized option is to use the principle of mass conservation, which declares that the sum of the masses of the three constituent materials is equivalent to the mass of the mixture.as a result, a material s mass attenuation coefficient can be expressed as a linear combination of the mass attenuation coefficients coefficients of two (or more) so-called basis materials. The advantage of a mass-conservation based algorithm is that mass is always conserved during any chemical reaction. The mass attenuation coefficient can be expressed as ( µ ρ ) = mfr ( µ ρ ) + mfr ( µ ρ ) + mfr ( µ ρ) / / ( E ) / ( E ) / ( E ) Low 1 Low1 2 Low2 3 Low3 ( µ / ρ ) = mfr ( µ / ρ ) + mfr2( µ / ρ ) + mfr3 ( µ / ρ) ( E) ( E) ( E) High 1 High1 High2 High3 (5.23) For a compound or mixture with more than one constituent elements, the mass attenuation coefficient is simply the summation of weighted mass attenuation coefficients of each constituent element. The weighting factor is the mass fraction of each constituent element. If we want to express our relationships in the 2-dimensional domain where x-axis would be the mass attenuation coefficient of the anatomical subject at 80 kvp and the y-axis would be the same quantity at 140 kvp, then if M is a vector denoted by (µ L /ρ, µ H /ρ) then the relationship would be [35]: M= mfr ( M M ) + mfr ( M M ) + M (5.24)

91 Figure 5.8: Material decomposition with mass fraction analysis The analysis will be similar with volume fractions if we consider volume conservation. Also, the so-called Energy Maps (graphs where x-axis: low kvp HU and y-axis: high kvp HU) have already been mentioned. The rationale of vectorial analysis in this case is the same and the weighting factors are the volume fractions of the basis materials in the pixels. Let us assume volume conservation for a mixture of three basis materials. Then the volume fractions of three materials can be expressed as f1+ f2+ f3 = 1 (5.25) The ρ effective of the mixture can be considered as m total / V total and therefore ρeff = f ρ + f ρ + (1 f f ) ρ (5.26) where ρ 1, ρ 2, ρ 3 are the densities for each pure basis material. ( µ / ρ ) ( µ / ρ ) ( µ / ρ ) ( µ / ρ) f µ + f µ + f µ mixture = m fr1 1+ m fr 2 2+ m fr3 3 = (5.27) ρeff µ =(mfr ( µ / ρ ) + mfr ( µ / ρ ) + mfr ( µ / ρ) ) ρ eff mixture (5.28) In [32] mass conservation is assumed in a three material decomposition method based on postreconstruction analysis, by utilizing the results of the ρ-ζ method described in relationships and relationship Postreconstruction analysis actually means that CT number or linear attenuation coefficient values are obtained from reconstructed images. The prospective of even more improved mass-conservation based algorithms for material decomposition is quite appealing because the accuracy of three-material mass-fraction decomposition is limited on current CT systems, especially for the elements with low mass 91

92 fractions. The accuracy of mass-fraction decomposition is dependent on three factors: The accuracy of the measured CT number, the accuracy of the calculated effective density, and the difference of the dual-energy ratios. The dual-energy ratio can be approximately viewed as the ratio of the mass attenuation coefficients of a chemical element (or basis material) at two X-ray tube potentials. More specifically, its significance in error propagation of computations in the dual energy algorithms can be proved mathematically. MASS DENSITY IMAGES Let us now consider the linear attenuation coefficient of a two material mixture in the following way: µ (, ) ρ ( µ / ρ) ρ ( µ / ρ) r E ds= m ( Ε) ds+ m ( Ε) ds (5.29) eff fr1 1 eff fr2 The ρ effective of the mixture, when multiplied with the mass fraction of each basis material m basis material / m total it gives us the fraction m basis material / V total which is the local (or effective) density of the basis material ρ local (r). The area density of the basis material is δ = ρ ds. local Therefore µ ( r, E) ds= ( µ / ρ ) 1( E) δ1+ ( µ / ρ ) 2( E) δ (5.30) 2 This is the relationship used in postprocessing of fast kv-switching in a two material decomposition algorithm. There, the projection data are expressed as: p Low I I0Low( E)exp ( µ / ρ) Low1( E) δ 1 ( µ / ρ) Low2( E) δ2 de + ln I 0 I0Low( E) de Low = ln = 2 (5.31) p High I I0High( E)exp ( µ / ρ) High1( E) δ 1+ ( µ / ρ) High2( E) δ 2 de = ln ln = I I ( E) de 0 High 0High (5.32) And from these relationships, δ 1 and δ 2 may be calculated before reconstruction. Reconstruction calculates ρ eff (mg/ml) of basis material (or ρ local as referred in the previous) and density maps are created. In density maps ρ eff is normalised to the corresponding pure basis material density. For instance in MD (material density) water image: ρ MAP ρ ( x, y) = 1000 ρ ρ local water water (5.33) 92

93 Effective atomic number from material decomposition analysis If material decomposition coefficients of basis materials (α 1 and α 2 ) are known, then it is proven in bibliography: Ζ eff 1 el1 2 el2 1/ n n n a1ρ el1z1 + a2ρel 2Z = 2 (5.34) aρ + a ρ VIRTUAL MONOCHROMATIC IMAGES Kalender et al. in their study [36] with third generation clinical CT scanner (Siemens Somatom DR3) tried Perspex and aluminium as basis materials but thought that water and calcium would match better soft tissue and mineralized bone in clinical studies. Kalender et al implemented the solution of equations (5.31, 5.32) by using table look up procedures. The material decomposition tables contain area density values.for each pair of measured attenuation values the respective pair of area densities are returned by table look up and interpolation. After having calculated δ 1 and δ 2, one can compute the attenuation data that would be measured with a mono-energetic x-ray source from relationship (5.30). Theory predicts that monoenergetic CT images do not exhibit spectral hardening artefacts.this was verified by Kalender et al phantom measurements [36]. Equation [5.30] is prereconstruction postprocessing for the creation of monochromatic images because it uses projection data δ 1 and δ 2 to find the projections of the monoenergetic image in first place and then the reconstruction follows. Once ρ local for each basis material in every voxel has been calculated (after reconstruction of δ = ρ ds projection data), a type of postreconstruction postprocessing (having the local meaning that the ρ eff is be taken from the already reconstructed material density images) can be used to calculate monochromatic images as: and therefore µ ( E) = ρ ( µ / ρ) ( E) + ρ ( µ / ρ) ( E) (5.35) eff 1 1 eff

94 ρ eff 1( µ / ρ) 1( E) + ρ eff 2 ( µ / ρ ) 2( E) µ w( E) HU = 1000 µ w( E) (5.36) Figure 5.9: GSI material decomposition processing It should be mentioned that although those monochromatic images are based on already reconstructed material density images, they still maintain the beam hardening elimination advantage, because the material density images have been reconstructed after dual energy projection based decomposition had taken place. In dual source CT systems, like Siemens Definition, image based decomposition methods are predominantly used. Virtual monochromatic images can be obtained with image-based methods too, as examined in published studies [37, 38] but they will lack the advantage of beam hardening elimination.the use of the appropriate algorithms that for instance take into account the increase of the effective energy in larger phantom sizes, results in more consistent CT numbers at the same monochromatic energy across different phantom sizes [37]. It should be noted though, that although the theoretical benefit of the projectionbased methods over the image based methods is valid, there are still inaccuracies of the CT numbers measured in virtual monochromatic images obtained with projection based technique, especially for dense materials and at lower monochromatic energies, as well as there is dependence on patient or phantom size [39]. This could be due to inaccuracies in the material decomposition algorithms or even due to CT artifacts over different nature.more research needs to be made on this field in order to estimate the extent to which beam 94

95 hardening is better eliminated and from what type of decomposition technique(image based or material based) this is better achieved. The difference here is that ρ eff1 and ρ eff2 will be determined from the postreconstruction observed µ L and µ H of the low and high kvp images respectively. j j µ µ µ = ρeff + ρeff, j= L, H ρ ρ 2 j (5.37) where L,H represent low and high energy respectively and 1,2 the two basis materials. Solving the two linear equations, the mass density of the two basis materials is obtained. ρ ρ µ ( µ / ρ ) µ ( µ / ρ) L Η H L 2 2 eff 1= L H H L ( µ / ρ ) 1 ( µ / ρ ) 2 ( µ / ρ ) 1 ( µ / ρ) 2 µ ( µ / ρ ) µ ( µ / ρ) H L L Η 1 1 eff 2 = L H H L ( µ / ρ ) 1 ( µ / ρ ) 2 ( µ / ρ ) 1 ( µ / ρ) 2 (5.38) The calculation of a monochromatic image at energy E is depicted in the following image: Figure 5.10: Using multi-energy imaging each pixel can be represented as a linear combination of the attenuation coefficient of two basis materials. In conventional CT, different materials with the same average attenuation cannot be distinguished. In dual-energy imaging the material dependence of each tissue is characterized and therefore true tissue characterization can be performed [11]. Specifically, the parallel lines of stable CT number are described as: ρ effiodine ( µ / ρ ) water ( E) µ ( Ε) = ρeffwater + (5.39) ( µ / ρ ) ( E) ( µ / ρ) ( E) iodine iodine 95

96 The arrow in figure 5.10 indicates the increasing CT number values, since at a particular energy for larger µ(ε) values, CT number value also increases. It is therefore obvious that at a particular energy level, different materials, may be represented by pixels that belong to a line described by the same equation, that is, have the same µ(ε) or CT number value. It can be shown that if we consider that one of the basis materials is water the CT number in the virtual monochromatic images can be expressed as a weighted average of the images at low and high energy scans, which is given by: L H CT ( E) = w( E) CT + [1 w( E)] CT (5.40) where the weighting factor is given by µ ( Ε) µ µ ( Ε) µ µ w( E) = ( Ε) H H L L H H L µ 1µ 2 µ 1 µ 2 µ 2 (5.41) Therefore, the monochromatic image at energy E is a weighted average of the low and high-energy images, where the sum of the weighting factors equals CANCELLATION IMAGES Lehmann et al (1981) [36] used an algorithm for cancellation of contrast between two materials, so that they will be no differences between them in the image but in a way that they still contrast with some third material. A basis projection image is created when the vector (A 1,A 2 ) of the basis materials equivalent lengths is projected onto a unit vector directed outwards from the basis plane origin at angle Φ,and the length of the projection(c) is displayed at every point: C = A 1 cosφ + Α 2 sinφ (5.42) The so-called material look-alike projection angle Φ forces the contrast between two known materials to zero without any knowledge of their geometric properties. 96

97 Figure 5.11: Material characteristic angles and look-alike projection angle Both material characteristic angles and the look-alike projection angle are depicted in the previous image. In this graph [40], materials B and C are embedded in a background material A, with associated characteristic directions a, b, c in the basis material plane. The logarithmic transmission of the path ray 1, namely x-rays passing through the length L of material A, is represented by the vector t 1 on the basis plane. If material B displaces a volume of material A, the logarithmic transmission of the path ray 2 will be represented by t 2. This vector sum is due to the attenuation of a thickness (L x) of material A and a thickness x of material B. In the same fashion we can associate t 3 to ray 3. Projections of t 2 and t 3 along the direction of P have the same length, thereby meaning that materials B and C appear identical. In the projection image these two materials will not contrast with each other but they will still contrast with the third material A whose projection length along P is smaller. The concept of tissue cancellation allows a broad range of applications while being able to cancel or to improve the contrast between tissues. This method has been applied and tested on clinically acquired dual energy CT data sets to evaluate its ability to improve the assessment of atherosclerosis by improving the tissue contrast [41],[42]. The cancellation algorithm of Lehmann et al.[34] is also well described in [40] and [42]. Figure 5.12: Workflow of the tissue cancelation algorithm proposed by Lehmann et al [34,42]. 97

98 5.3.5 K-EDGE IMAGING As already mentioned, in the presence of a k-edge discontinuity in the investigated energy range, the attenuation coefficient parameterization is properly modified. Contrast agents, such as gadolinium (Z=64) and iodine (Z=53) present that kind of k-edge discontinuities. The k- edge discontinuities in the corresponding atomic, photoelectric cross-sections appear at 33.2 kev for iodine and at 50.2 kev for gadolinium, well inside the energy regime relevant for medical x-ray imaging. In the case of equation (5.5), we need at least 3 energy spectra or, in the case of photon counting detectors at least 3 energy bins. In the case the number of equations (number of energy bins is inferior to the number of unknowns (dimensionality of the attenuation basis), the system of equations to be solved is under-determined and in general has many solutions. In the special case that N = 3, the number of equations equals the number of unknowns. We therefore expect a single solution. Now let us suppose a beam path containing amounts t and t I (in gr/cm 2 ) of tissue and iodine respectively. A two-beam energy-subtraction technique for selective iodine imaging is considered in [43],[44] (Kruger,Riederer and Mistretta) by utilizing the mean beam energies or monoenergetic beams. Transmission measurements T 1 = (I trans1 /I 01 ) and T 2 = (I trans2 /I 02 ) are given as: L = ln(1/ T ) = µ t+ µ Ι t L = ln(1/ T ) = µ t+ µ t H H th H I L L tl ΙL I (5.43) where µ ti and µ Ι1 are the mass attenuation coefficients of tissue and iodine respectively for the i th beam. By properly combining the above equations, one gets the iodine difference signal I free of tissue contributions: I µ th th ln T L ln T µ = t t H = µ ΙL µ IH I = µ Ι I (5.44) µ tl µ tl where µ I µ ΙΗ µ ΙL because µ tη / µ tl is almost equal to unity, since the attenuation of tissue does not change much with energy. Therefore, choosing two beams in order to obtain a large value of µ Ι, we get good iodine sensitivity, for a fixed value of t I. This can be achieved by choosing two beam energies that give us large difference of iodine attenuation coefficients. If bone is also included in the beam path, a three beams (or three energy bins for photon counting detectors) approach is required. 98

99 5.3.6 SOLUTION OF EQUATIONS TO OBTAIN A1 and A2 In prereconstruction ρ-ζ and material decomposition methods after obtaining or A 1 and A 2, α 1 and α 2 must be determined through reconstruction. However, for polychromatic beams, solving the system of high and low energy projections to obtain A 1 and A 2 is not a trivial procedure. The nonlinear relationship between A 1, A 2 and the logarithmic transmissions of the x-ray beam makes the task more complicated. In [45], 4 methods for determination of equivalent lengths A 1 and A 2 are described and compared. We will not refer to these procedures comprehensively here, since they are well described in this study. In the two non linear equations method, each of the projections (for low and high energy) are expressed as a non-linear combination of the two basis materials equivalent lengths. By using 2 calibration tables derived from transmission measurements of known values of basis materials thicknesses combinations, one determines the coefficients of these equations by a polyonomial least squares fitting algorithm. Then, by using the Newton Rapson method, the equations can be solved for A 1 and A 2. In the direct approximation method the values of A 1 and A 2 are computed directly by equations describing their non-linear relationship with projection measurements. A calibration procedure for the determination of the coefficients in the equations is necessary here too. The subregion direct approximation method takes into account the beam hardening effect The method divides the range of logarithmic transmission values into a number of subregions, each having its own beam hardening correction factors.the logarithmic transmission values in the high and low energy calibration tables are each subdivided equally into ten subregions. The iso-transmission line method is derived using the concept of effective energy of a polyenergetic spectrum. If we consider the logarithmic transmission at low and high effective energies as linear combinations of the thicknesses of the two basis materials, then the intersection of those two isotransmission lines gives the thicknessed of the two basis materials. A linear method with a non-linear beam hardening term is presented by Toshiba Medical Research Institute USA in a research of fast kv-switching in dual energy CT [33]. Because the linear term is dominant, an iterative solution to the dual energy data domain decomposition converges rapidly and is stable. In this method, two materials representing photoelectric and Compton interaction respectively are used as basis materials. µ ( Ε, x, y) µ ( Ε ) c ( x, y) + µ ( Ε ) c ( x, y) (5.45)

100 The projection data are then expressed as: gh = ln SH ( E, γ ) exp µ 1( E) c1 ( x, y) dl µ 2( E) c2( x, y) dl de l l [ ] g = ln S ( E, γ )exp µ ( E) L ( l) µ ( E) L ( l) de H H (5.46) L γ µ 1 1 µ 2 2 ln L(, γ )exp[ µ 1( ) 1( ) µ 2( ) 2( )] gl = ln S ( E, ) exp ( E) c ( x, y) dl c ( x, y) dl de g = S E E L l E L l de L = and S H,L (E,γ): energy-weighted spectra where the channel index γ where L ( l) c ( x, y) dl 1,2 1,2 l is included to account for the bow-tie filter. With the bow-tie, the spectral results depend on channel (individual x-ray sensor in the detector array). The basic idea of solving the projection data equation (5.46) is to linearize the equation and treat the rest of the pertubative beam-hardening terms that are best handled by iterative solution. These terms for each basis material depend on the difference of the attenuation coefficient of the material at any particular energy level in the energy range of interest, from the energy averaged linear attenuation coefficient of the basis material for a given channel.more details can be found in [33]. Calibration tables for calculation of A ph and A comp may also be constructed.same as before,the calibration tables can be constructed by using transmission measurements for various length combinations of materials of known α ph and α comp and then a least squares fitting procedure to determine the appropriate coefficients in the non linear equations [20,25] DUAL ENERGY CT ITERATIVE AND STATISTICAL RECONSTRUCTION Prior to the 1990 s, all work on dual-energy X-ray CT used the FBP (filtered backprojection) reconstruction method. In the early 1990 s there were a few iterative methods published for dual-energy CT reconstruction. Michael et al presented an iterative method to achieve beamhardening correction and decomposition into basis materials [46]. Markham and Fryar applied the ART algorithm [47]. These iterative approaches treat the problem as finding the solution to a system of equations. These algebraic approaches can improve the accuracy relative to FBP methods, but they do not directly address the radiation dose issue. In contrast, in statistical image reconstruction approaches, the problem is posed as finding the images that 100

101 best fit the measurements according to the (possibly nonlinear) physical model and a statistical model. Proper statistical modeling can lead to lower noise images, thereby enabling reductions in X-ray dose to the patient [48]. Recently, Clinthorne and Sukovic have investigated iterative algorithms for dual-energy and triple-energy CT reconstruction based on a weighted least-squares approach, including objectdomain constraints [49-53]. That work assumed monoenergetic measurements. Statistical approaches have been extensively investigated, particularly in the last ten years, for monoenergetic transmission measurements but there have been extensions the case of measurements with energy diversity [48]. 5.4 EVOLUTION AND TECHNICAL CHARACTERISTICS OF DECT Although dual energy CT (DECT) was first conceived in the seventies, its clinical breakthrough came later. Of course, implementations of dual energy methods were attempted early after the introduction of CT [23]. A number of applications utilizing two separate scans and postreconstruction methods (that is, data processing for spectral information acquisition based on reconstructed CT images) has been reported focusing on lung and liver, bone mineral determination and tissue characterization. In the late 80 s, the first commercial DECT (a third generation CT scanner) (SOMATOM DR) using fast-voltage-switching and prereconstruction processing was introduced by Siemens, (Forchheim, Germany), but it was not further developed. Despite its success in some applications, such as bone mineral density quantification, the potential of the technique in other clinical applications was not fully achieved due to limitations in generator powers, tube heat capacity, tube cooling, and spatial and temporal resolution of earlier CT systems. This kvp switching technique however had the limitation that the tube current could not be increased quickly enough for the low tube potential setting to achieve comparable noise levels in both the low and high kv datasets. In the 80 s, the theoretical basis of DECT (material decomposition) was already established. In 2006, Siemens introduced a revolutionary dual-source CT (DSCT). It has two X-ray source-detector pairs separate (third generation CT acquisition systems operating orthogonally and simultaneously at 90-degree offset in one gantry) [54]. Each system has its own tube, generator, detector, and control devices, while for example cooling and the image reconstruction system are shared. The two perpendicular X- ray beams image the same slice of the patient at the same time. It can operate at the 101

102 single-energy or dual-energy modes by setting two X-ray sources operating at the same or different energy levels. Its temporal resolution was remarkable 83 ms at the single-energy mode and 165 ms at the dual-energy mode. Its high temporal resolution of the single-energy mode has made possible cardiac imaging even up-to 120-bpm heart beats with minimum cardiac motion artifacts. For dual energy CT, typically 80 and 140 kv are chosen to maximize the difference of the spectra and the images are then analyzed with dedicated software (syngo Dual Energy; Siemens AG, Forchheim, Germany) to take advantage of the additional information. Fast image acquisition allows for dual-energy applications, like bone removal (Direct Angio) or lung perfusion imaging, that require short gantry rotation times and fast volume coverage. In first generation dual source CT (SOMATOM Definition), one detector (A) covers the entire scan field of view (50 cm in diameter) while the other detector (B) is restricted to a smaller, central field of view (26 cm in diameter) due to space limitations on the gantry (see figure) [55]. Each detector comprises 40 detector rows, the 32 central rows having a 0.6-mm collimated slice width and the outer rows on both sides having a 1.2-mm collimated slice width. The total coverage in the longitudinal direction (z-direction) of each detector is 28.8 mm at isocenter. By proper combination of the signals of the individual detector rows, the detector configurations of mm or mm can be realized. Using the z-flying focal spot technique (a periodic motion of the focal spot in the z-direction that allows the doubling of the sampling density), two subsequent 32-slice readings with 0.6 mm collimated slice width are combined to one 64-slice projection with a sampling distance of 0.3 mm at isocenter. In this way, each detector acquires 64 overlapping 0.6 mm slices per rotation. The shortest gantry rotation time is 0.33 s, while other gantry rotation times are 0.5 s and1.0 s [55]. Each of the two rotating envelope X-ray tubes (STRATON, Siemens Medical Solutions, Forchheim, Germany) allows up to 80-kW peak power from the two on-board generators. For DECT, one special mode is 14 Χ 1.2 mm; in this mode, the central 28 slices are illuminated by the X-ray-beam, but the whole detector is read out, which allows to measure the scatter signal in the shadow of the collimator. The detectors used are UFC scintillation detectors. In order to reconstruct images for system B, the sinogram outside the B field of view is filled with data from system A. Outside the B field of view only the 140 kv image is available. 102

103 Figure 5.13: Somatom Definition CT Scanner and its underlying technology ( Figure 5.14: (a) Somatom definition,(b) Somatom Definition Flash tube alignment. The second generation dual-source CT SOMATOM Definition Flash (128-slice CT- The two detectors have 64 physical slices, which in combination with the z-sharp leads to 128 measured slices per rotation) has a wider field of view (FOV, 33 vs. 26 cm) and a tin filter (0,5mm tin Sn) is used to filter the high-energy spectrum and to increase the image contrast and increase dose efficiency. There are several improvements in comparison to the first generation dual source CT. The field of view of detector B was increased by increasing the angle between tube A and tube B to 95. The larger field of view allows for coverage of larger anatomical areas and makes centering patients much less of an issue. Moreover, due to additional filtration, the low-energy tube can now be operated at 100 rather than 80 kvp; this markedly improves the penetration of low kvp photons, decreases cross scatter and image noise due to increased X-ray power (important especially for abdominal applications) and 103

104 makes DECT feasible in larger patients (along with the larger FOV). For instance, it is recommended that patients whose BMI is >30 should not undergo renal DECT on first generation scanners, because image noise can be high in large patients; this will lead to reduced Hounsfield unit stability due to beam hardening artefacts. The spectral separation due to filtering is improved. The result of photon shield is an increase of bone-iodine differentiation by up to 80% while reducing overall dose. Therefore, the high-quality 80/Sn 140 kv mode is ideal for the head and extremities, especially CT angiographies. The spectral separation through the Selective Photon Shield on the other hand, opens the possibility to use 100/Sn140 kv imaging with still 30% better bone-iodine contrast. Moreover, higher pitch modes are available for fast spiral scanning.(pitches greater than 3 for better temporal resolution without image distortions). The SOMATOM Definition Flash offers three different shaped filters to achieve optimum dose and spectral distributions across the scan field of view for imaging of different body regions. At 100 kv/sn140 kv the suggested ratio of the quality reference mas varies between 1.0 and 1.3 depending on the body region. Also, it is important that for the 80 kv/140 kv voltage combination, 140 kv are assigned to the A-system, because it will always have good image quality and sufficient iodine enhancement. In the mode 100 kv/sn140 kv the situation is reversed: Although the Sn140 kv image would have very good image quality, iodine enhancement would be rather low, so that the 100 kv were assigned to system A. Four different collimations are available for SOMATOM Definition Flash: 128 Χ 0.6 mm (z- Sharp), 64 Χ 0.6 mm (z-sharp), 32 Χ 0.6 mm (no z-sharp), and 40 Χ 0.6 mm (z-sharp). General Electric (Discovery CT750 HD) utilize a rapid kvp switching (dynamic switching) approach similar to the techniques developed previously. For Toshiba((Aquilion PRIME-160 slice CT scanner),dual-energy helical scanning alternates between high and low kv with each gantry rotation. The ma is also automatically adjusted for the two different energies to ensure a matched signal to noise ratio which increases the accuracy of dual energy analysis. Philips utilizes a sandwich detector technology. Using such a sandwich detector design, the low energy data is gathered from the upper detector layer and the high energy data from the lower detector layer, with photons passing through an additional filter between the two layers. GE s Discovery CT750 HD (64-section MDCT) acquires dual-energy scans with a single X- ray tube by alternating low and high kvps within milliseconds and is used to acquire data for axial and helical scanning modes. In addition, GE approached DECT by using 104

105 projection data to create useful images like pseudomonochromatic images and material density images. The data acquisition system of this CT scanner enables more than 2.5 times the data sampling in one gantry rotation compared with that enabled by the conventional 64- section CT scanner [56]. Detector primary decay and afterglow performance are critical for avoiding spectral blurring between views. In fast kv-switching the scintillator in the detector must use a very short time to acquire the X-ray photons. The acquisition time consists of three components: the rise time of the output signal of the detector, which is the time between when the X-ray source is turned on and when the detector reaches the constant value, the time when the signal is constant and the fall time of the output signal of the detector, which is the decay of the signal after the X-ray source is turned off. A short fall time is needed to ensure that there is very little information left in the detector which can be transferred to the next view. The fall time has an exponential decay and is the largest add to the acquisition time. The primary scintillation decay time constant for the Gemstone scintillator used by GE dual kv-switching system is 0.03 µs, which is 100 times faster than a GOS (Gadolinium OxySulfide-Gd 2 O 2 S) scintillator. This fast scintillation makes the Gemstone suitable for fast kv-switching. The GE Healthcare s (GEHC) scintillator material, Gemstone, is a complex rare earth based oxide, which has a chemically replicated garnet crystal structure. This lends itself to imaging that requires high light output, fast primary speed, very low afterglow, and almost undetectable radiation damage. The field of view for kv-switching Discovery CT750 HD is bigger than that of dual source CT of Siemens, since both high and low energy data sets are acquired simultaneously for axial and helical acquisitions at the full 50 cm field of view. Philips Healthcare has also been successfully operating a dual-layer detector system in a modified Brilliance 64 CT scanner. It is used as a 32-slice dual-layer scanner with 64 electronic channels (2 per each dual-layer detector element). In a single source, dual-layer detector scanner configuration, one X-ray tube is used to expose a detector consisting of two layers of scintillators. The two layers are directly on top of one another. A single CT scan is performed at a high kvp (e.g. 120 or 140 kvp). The first layer encountered by the X-ray photons absorbs most of the low-energy spectrum (by design approximately 50% of the beam), while the bottom detector layer absorbs the remaining higher energy photons. Dual layer CT scanners therefore enable separation into two different overlapping energy windows. Images are reconstructed separately from the data of the upper and lower layers.dual layer 105

106 CT enables both projection-based and attenuation-space (image-space) material decomposition. Finally, as mentioned, dual energy CTcan also be performed by scanning the same region of the patient twice, once with the kv on the X-ray tube high and once with it low. For example, for a circular scan, the first rotation is at high kv, the tube voltage is switched and then a rotation is taken a low kv. This method can be called slow kv-switching. Currently 3 of the aforementioned systems are mostly in use: 64-slice dual source CT (Definition Siemens Medical Systems; Erlangen,Germany), 128-slice dual-source CT (Definition Flash, Siemens Medical Systems) and high-definition 64-MDCT (Discovery 750 HD, GE Healthcare; Milwaukee, Winconsin, USA). The following table describes the technical characteristics of dual-energy MDCT systems. Table 5.2: Technical Specifications of dual energy MDCT systems [57] 5.5 COMPARISON OF METHODS FOR DECT IMPLEMENTATION Each of the dual energy CT configurations is characterized by its advantages and disadvantages, as well as by their own workstation environment, where the processing for clinical applications occurs. Dual energy CT performed with two subsequent scans suffers from mis-alignment artifacts due to patient movements between the two scans. Moreover, with the necessity to acquire both scans separately, the use of contrast material and its differentiation by dual-energy or spectral analysis was impossible. However, Kalender et al (1986) developed a CT scanner with a prototype apparatus for rapid kvp switching [36] as already mentioned (SOMATOM DR3). By these means, patient movement artifacts are significantly reduced because the two kvp images are acquired simultaneously. With dual source scanners there are also issues to be encountered. Special attention has to be paid to cross-scattered radiation. Cross-scattered radiation originates from the X-ray tube of the other acquisition system and enters the detector due to Compton scattering at the surface of the patient. With dual energy scanning, cross scatter can be more pronounced than 106

107 with dual source cardiac scanning. Since the amount of cross scatter is roughly proportional to the z-opening of the collimator, narrow collimations provide best quality for quantitative imaging. Another issue about the dual source CT scanners,is that the FOV of one tube is restricted limiting the clinical applications and the postprocessing of the images, while GE fast kv switching and the dual layer CT configurations utilize full 50 cm FOV. Dual-source CT scanners, with two source-detector systems, are currently used for many clinical dual-energy applications, including automatic bone removal, stone composition characterization virtual noncontrast imaging and many others. However, in helical mode, the projection data collected by the two source-detector systems are in a double-helix geometry in which the two helical trajectories have an approximately 90 degrees phase difference and the projections from the low and high energy scans are not coincident with each other. Because of this, it is challenging to perform dual-energy processing in the projection domain. Iterative methods have been proposed to solve this problem, though have not been implemented in practice. All current dual-energy processing methods available on dualsource CT scanners are based upon the low and high energy images after reconstruction (post reconstruction technique). This automatically means that the beam hardening elimination provided by projection based dual energy methods is not valid for dual source CT. This is true also for dual layer CT. For GE fast-kvp switching technique, however, this is not the case. The dual energy processing occurs before reconstruction takes place (pre-reconstruction technique). This is an advantage as far as the beam hardening elimination occurs, since the spatial and the energy dependence of CT are separated before reconstruction. Nevertheless, in order to process the data in the sinogram domain it is necessary to identically register all source-to-detector angles in low and high energy projection views of the sinogram. This registration requirement constraints the speed of scanning, especially for systems where dual energy data are acquired by two separate scans at two kvp or spectral filter conditions. Moreover, the algorithm structure of dual energy postprocessing is simpler than processing in the sinogram domain and therefore, results are expected to be obtained faster. In 2008, a study of Toshiba Medical Research institute on fast kv-switching was made on postprocessing and image quality issues in this dual energy mode [33]. Fast kv-switching as it is used nowadays, changes voltages between each projection (also called views) so that the odd (or even) projections correspond to the low (or high) tube voltage. Fast Kv-switching 107

108 has the major advantage of decreased cost.in fast kv-switching, the kvp rise and fall time between each reading reduces the spectral separation. The system design must enable rapid kvp rise/fall achieving sufficient energy separation. Thus, fast kv-switching is about a factor of 1000 to 2000 faster than slow kv-switching. Ideally, we would want the switching waveform to be a square wave (which would be the same as slow kv switching ignoring registration problems). In fact, it may be closer to a sinusoidal waveform but the energy separation between the high and low spectra is adequate Therefore, the overall kv-switching spectrum is derived by a superposition of several intermediate known spectra lying in between the nominal high and low peak voltages [33]. It is important to notice that, in comparison to dual source CT, for a constant number of projections per energy spectrum the temporal resolution is reduced; a reasonable trade off between reduced number of projections and limited temporal resolution has to be found [58]. Fast kv switching is attractive because of the high temporal registration between corresponding high and low energy projections and because of the higher cost for two tubes that is used in dual source CT systems since 2006 and of two detectors (dual layer CT). A disadvantage is the one view (projection) mis-registration between corresponding high and low energy projections, which can be treated with a certain way of matching the corresponding low and high kvp projections [33]. Another problem is the difficulty of high noise in the low energy data because it may be technically difficult to swing the ma as fast the kv [33]. It is technically more feasible to keep ma constant during fast-kv switching. Dual Layer CT (sandwich detector CT) also has several advantages, in comparison to other approaches of dual energy CT. For instance, in contrast to other techniques of dual energy CT, there is no need to redundantly expose materials with both low and high energy X-rays. Moreover, the dual-layer technique is fully registered both spatially and temporarily and this makes the technique ideal for imaging moving organs (see Fig. 5.15) like the heart. The use of a single source also obviates the cross scatter limitation of dual source techniques. Furthermore, this approach allows full 50 cm FOV imaging. In addition, though some consider dual layer CT as a dual energy method of low energy separation, this separation is generally considered adequate for the applications performed. In Fig. 5.16, the dual-layer detectors typical absorbed spectra are presented. It can be observed that the low energy spectrum (of the upper scintillation layer) has energy components which continue up to the maximal energy determined by the applied tube voltage (therefore it is not too soft as it is for dual kvp techniques which produce inferior image quality images, especially for body 108

109 regions of high attenuation such as abdomen, pelvis and large patients in general). In addition, the high energy spectrum (recorded by the lower layer) is very hard (i.e. with little low energy components) due to the strong filtration by the first layer. Figure 5.15: In a single source, dual-layer detector scanner configuration the spectral energy separation is intrinsic to the detection system, rather than at the X-ray source. This approach eliminates the time lag of sequential techniques, making it ideal for imaging moving organs, such as the heart. Dual energy material separation then enables to identify selected material as the coronary calcifications (highlighted in green) which can be separated from the iodinated blood pool. Figure 5.16: The absorption spectra of the dual-layer CT with a tube voltage of 140 kvp In [33] a table summarizing the advantages and disadvantages of different dual energy methods is presented (Table 5.2). 109

110 Table 5.3: Advantages and disadvantages of dual energy CT configurations 5.6 WORKSTATIONS FOR DECT CONFIGURATIONS As already mentioned, Gemstone Spectral Imaging (GSI) is based on projection-based material decomposition. The GSI Viewer provides visualization and quantitative analysis of the dual energy data for medical diagnostic imaging. GSI data is commonly visualized as a monochromatic image, which resembles a conventional kvp image, but with fewer artifacts. The user may interactively change the kev ( kev with an interval of 1keV) to attain the desired contrast. It is also common to visualize the data as a material basis pair. Material bases may be dynamically changed to meet the user s needs. An example of a monochromatic image and its corresponding material density images are presented in the following figure [59]. Figure 5.17: GSI noise reduced material density images:(a) monochromatic(b) iodine density (c) water density. 110

111 During the preparation of the examination in the scanning-protocol the user can simultaneously choose three different monochromatic energies from 60 to 140 kev, in which the data should be reconstructed. When the data has been reconstructed, it can be displayed in the GSI-viewer by selecting the input [60]. The ability to measure CT-values at any monochromatic energy should allow to calibrate CT-values of accuracy control phantoms but more research is needed to investigate this possibility. The GSI Viewer also calculates the effective atomic number, Z eff of dual energy data. This representation describes the data in terms of the periodic elements most closely representing its energy sensitive attenuation behaviour. The attenuation profile of the object vs kev may also be graphically depicted by a spectral HU curve. In addition, the contrast to noise ratio of multiple selected ROIs as a function of kev can also be shown. The user can quickly assess the attenuation differences between the ROIs, as well as identify the monochromatic kev which best balances the user s needs in terms of contrast and noise. As a means of combining the information, the viewer has the capability to provide the material density, or other auxiliary information, as a colour overlay on the monochromatic image. The viewer also allows the creation of scatter plots (Fig. 5.18), which can plot the values in a ROI for the various image maps against each other. This is to separate or bundle the different properties of the materials in a ROI. Also, VOI (volume of interest) creation is possible by placing constraints in the graph. The values within the limitation will be coloured in the image. There is plenty of research going on about GSI cardiac angiography. The potential for increased accuracy in coronary stenosis sizing through improved differentiation of calcified plaque and iodinated contrast lumen, the potential to do calcium scoring in a contrast scan, and exploring the use of monochromatic images for its ability to reduce beam hardening in myocardial perfusion studies are still investigated. GSI is additionally enabling research to explore the measurement and risk profiles of lipid (cholesterol) plaques [59]. 111

112 Figure 5.18: Differentiation of intraparenchymal hemorrhage and calcification (a) attenuation curve (b) scatter plot To sum up the possibilities offered, we would say that in GSI Viewer the user can: select from 101 monochromatic energy levels to optimize contrast for improved image quality. visualize a virtual non-contrast like-image from a contrast CT exam by subtracting iodine. view material density and effective atomic number images to discriminate tissue type. use image overlay tool to fuse material density & effective atomic number (Z) information on a monochromatic image. generate graphical plots based ROI 2D & 3D (VOI) analysis. It is worth noting that around 70 kev monochromatic images have lower noise and better CNR performance than 120 kvp images [56]. Moreover, the CT numbers of the VMI (virtual monochromatic) images at approximately 70 kev were equal to those of the 120 kvp image. As the X-ray energy of VMS imaging was increased, the CT numbers of the diluted contrast agents steadily decreased. This relationship between the CT number and the monochromatic X-ray energy (kilo-electron voltage) is identical to the relationship between the CT number and the polychromatic X-ray energy (kilovoltage peak) in conventional CT. The software package syngo Dual Energy, which is optionally available on the two dualsource dual energy scanners, uses two main approaches for image analysis. The first one is material decomposition, while the second is material labeling. Both methods are best understood in the CT-value diagram (xlow vs xhigh) as shown in (Fig. 5.19). 112

113 Figure 5.19: (a) Material decomposition and (b) Material labeling: While material decomposition yields two CT images containing different materials (iodine and VNC image),material labeling distinguishes two possible material mixtures that are above or below the separation line [59].CT value x 1 is the low kvp CT number value and CT value x 2 is the high kvp CT number. Instead of a material decomposition into three fixed points in the xlow/xhigh plane, syngo Dual Energy uses two body material data points (fat and soft tissue) and the slope of the iodine enhancement vector. This is possible as the infinitesimal addition of iodine to both body tissues leads to a similar and measurable enhancement vector for both tissues. Subtraction of the iodine corresponds to a parallel projection in the CT-value diagram (VNE or VNC images (virtual non enhanced or non contrast images). In syngo Dual Energy, this kind of material decomposition analysis is used to highlight iodine vs. hemorrhage in the brain (Brain Hemorrhage) to visualize perfusion defects in the lung (LungPBV), to isolate the iodine signal in a liver with fatty infiltrations or necrosis (LiverVNC), to visualize perfusion defects in the myocardium (HeartPBV) e.t.c. Details about the clinical utility of these algorithms can be found in 5.6. Therefore material decomposition algorithms are in reality analysis in the vectorial space created by basis materials.the rationale of this analysis can be found in the description of the dual energy CT algorithms and more specifically in relationship 5.25 and figure 5.8. However, since only the slope of the iodine enhancement vector is used and not the value of the iodine CT number the algorithm does not lead exactly to calculation of α 1, α 2, α 3. However, the projection on the fat-soft tissue vector gives the CT number values at low and high kvp images from which iodine has been subtracted. 113

114 General material highlighting is possible with DECT by mapping each position in the CTvalue diagram to some displayed color and intensity. As this requires a number of distinct materials of unique chemical composition and density, this approach is only useful for very specific clinical questions. In the CT-value diagram, mixtures of two noninteracting materials are always located on straight lines between the pure materials. For example, in the case of dual-energy bone removal (Fig. 5.19), the pure materials iodine or bone mineral of arbitrary concentration mix with the common matrix material blood/soft tissue. The most general approach for bone and iodine separation is to use a separation line that goes through the common matrix material; the slope of the separation line is close to the bisector between the two material mixture lines. However, the ideal choice also depends on image noise and typical iodine and bone concentrations. In syngo Dual Energy, material labeling with separation lines is used for bone subtraction in CT angiographic data sets, to visualize the composition of kidney stones, the iodine content of extremely small lung vessels and Gout vs. deposition of Calcium. In dual layer CT, images are reconstructed separately from the data of the upper (low energy E1) and lower (high energy E2) layers using a full three-dimensional filtered back projection algorithm. By combining the raw data of the two layers, standard CT images obtained from the full energy spectrum are also reconstructed and are used by the radiologists for routine diagnostic imaging (Fig. 5.20). With this image-based DECT, the raw data sets of the upper and lower layers are treated independently till after the reconstruction. The reconstructed E1 and E2 image datasets can then be combined to obtain material specific images using a post-processing software. Application of a special correction on the reconstructed images achieves stability on the HU-plane despite beam-hardening effects. Figure 5.20: A schematic illustration of the dual-layer detection system (only a few detector elements are shown). The photodiodes are parallel to the X-ray direction, attached to the sides of the two types of scintillator elements [59]. 114

115 The following figure (Fig. 5.21) shows an example of the three datasets obtained after reconstruction of a spiral neck scan performed at 140 kvp. Additional spectral information can then be obtained after mapping the data from the E1 and E2 images into a plane created from the HU of the upper-layer image vs. HU of the lower-layer image. At every image position, this HU plot displays the (E1, E2) values of every image voxel located in the reconstructed field of view. The resulting HU plot (Energy Map) is also presented in Fig If a voxel contains only one material, its position on the Energy Map will be located in a region centered on the expected HU values (E1, E2) for this material and with a size which depends on the noise in both the E1 and E2 images. For example, a voxel containing pure water should be located in a cloud centered at (0,0) HU, the width of the cloud being dependent on the noise in the dual-energy CT images. If a voxel contains two materials, its place on the plot is on a line between these two composing materials. In particular, different concentrations of a material in water appear on a line emanating from the water point, where the low concentration is closer to the water and the high concentration is further away. Figure 5.21: The three datasets obtained after reconstruction of a spiral neck scan performed at 140 kvp. Additional spectra information is then obtained after mapping the data from the E1 and E2 images into a plane created from the HU of the upperlayer image vs. HU of the lower-layer image. At every slice position, the HU plot displays the (E1, E2) values of every voxel located in the reconstructed field of view. In the energy map: iodine, calcium, air and soft tissue voxels are easily identified. The calcium line extends far in the upper right corner due to the high attenuation of the bone and calcified structures [59]. 115

116 Figure 5.22: (a) The combined full spectrum CT image and (b) the corresponding Energy Map of a water phantom containing eight identical ltubes, four containing solutions of CaCl 2 and four containing solutions of iodine in water in decreasing concentrations such that the HU# of corresponding tubes are equal. (c) A single line drawn in the Energy Map enables to separate the calcium and iodine tubes. A threshold is used for the voxel classification which defines the lower limit for the CT values that should be separated as iodine or calcium. This threshold is defined by the lower end of the separation line (yellow cross). (d) The voxels located above the separation line are displayed in blue and classified as iodine voxels while the voxels located below the separation line are displayed in yellow and classified as calcium [59]. The separation technique above is a simple separation method. With this binary approach, a voxel can be classified as one material or another material. More sophisticated separation techniques exist, which enable mixed voxel separation. Two additional algorithms are available at the Philips EBW workstation: the vectorial separation and the probability separation. Vectorial separation: This method of separating materials assumes that the CT value of each voxel may be analyzed as a composition of two materials. The CT value of each voxel is seen as a vector summation of two vectors along the corresponding material axes in the Energy Map. Probability separation: The probabilistic separation algorithm uses a statistical model to separate between the two materials. This approach is based on a probability mixture model taking into consideration the spectral response of the materials, the noise characteristics and fundamental morphological considerations. The noise is assumed to have a Gaussian distribution which is justified according to the physical analysis of the scanner. The output of this method is an estimate of the probability that each voxel is either material 1 or 116

117 material 2. Next figure shows an example (Fig. 5.23). The probability separation is commonly used for the production of VNC images. Figure 5.23: (a) Non enhanced CT scan of the upper abdomen performed with the dual-layer detector, (b) contrast enhanced CT scan of the upper abdomen of the same patient and (c) high quality virtually noncontrasted image obtained from the contrast enhanced scan using the probability separation algorithm. A small calcified plaque in the mesenteric artery (arrow) is successfully separated from the iodinated blood pool [59]. 5.7 CLINICAL APPLICATIONS OF DECT Clinical applications of Dual Energy CT have been a subject of research and discussion especially since the modern commercial DE CT scanners have been available.useful references concering those applications can be found in [59], which is a very informative book on dual energy CT and has helped a lot for the construction of this thesis,since it refers both to technical characteristics but also to available software for implementation of dual energy CT applications. Also the review article in [61] useful information about the current clinical applications on dual energy CT can be found. Specifically, the major dual energy applications studied till nowadays are the following: image blending [12,61-64], head and neck-neuroradiological [61,65-70], aorta [59,61], lower extremities and peripheral arteries [59,61,71] plaque differentiation [59,61,72-74], pulmonary applications (lung cancer,perfusion and ventilation) [59,61,75,76], myocardial perfusion and iron deposition [77,96], renal, adrenal, pancreasliver [59,61,78-89], tendons and ligaments [59,61,90,91], gout applications [59,61], virtual monochromatic images metal artifact reduction [37,38,39,56,92] and detection of posttraumatic bone marrow lesions [93]. In the following, some of these applications will be mentioned, focusing on the mostly appreciated or the mostly discussed ones in the available bibliography.however,all the aforementioned fields show promising results and sometimes coping with the limitations encountered is mostly a matter of image quality optimization and algorithmic improvement. 117

118 The most important advantages that dual energy CT may offer in clinical practice is reduced dose levels, misregistration artifacts and postprocessing time (VNE versus TNE true non enhanced) images especially in abdominal applications and dual energy bone removal versus conventional bone removal), potential for beam hardening and metal artifact elimination in some cases and quantification of subtle differences in contrast material enhancement or the presence of calcifications. There are few conditions when MRI cannot provide diagnosis (e.g. gout) but dual energy CT can, but generally MRI is a competitor and the modality of choice in some fields where dual energy CT attempts to provide diagnosis (e.g. tendons and ligaments). Blood volume maps in the case of lung or myocardium perfusion give the dual energy the advantage of functional over just anatomical information that conventional CT provides Image blending Dual energy CT uses two different tube potentials (e.g. 80kV & 140kV) to obtain two image datasets with different attenuation characteristics. The different energies significantly influence the contrast resolution and noise characteristics of the two image datasets. Instead of viewing two data series (one for each tube potential), the images are most often fused into a single image dataset using a linear mixing of the data with a 70% 140kV and a 30% 80kV mixing ratio.this dual energy fused image is known as virtual 120kVp image (0.7* *80=122) and is created to serve as a substitute of the standard 120kVp CT image. The virtual 120kVp is the best SNR in linear combinations of low and high energy images, although it may not be optimal in CNR. There are several algorithms for blending dual energy data. For instance, linear, binary, slope, moidal (a modified sigmoidal curve), normalized Gaussian. Each of the blending algorithms had at least one parameter, the adjustment of which influences the quality of the produced blended. Non-linear blending of dual energy CT data has been found to be superior to linear blending algorithms. The non-linear algorithms, especially the moidal algorithm, significantly increase the contrast resolution seen in dual energy blended images, while lowering the noise level within the image. Nonlinear blending of dual-energy CT data may provide an improvement in the contrast-to-noise ratio over linear blending and is accompanied by a visual preference for nonlinear blended images. The goal of a non-linear blending postprocessing algorithm is to maintain the contrast of the low-energy scan while achieving the noise characteristics of the high energy scan. 118

119 5.7.2 HEAD AND NECK-NEURORADIOLOGICAL For imaging of the vascular system of head and neck, DE provides two new, major applications: DE bone removal and virtual unenhanced images. Over the past few years, CT angiography has been established as a standard noninvasive imaging modality for the evaluation of the vascular system of head and neck. The evaluation of supraaortic vessels has become feasible( also in critical areas like the base of the skull) even for nonspecialized physicians. Supraaortic CT angiography (CTA) is also ideally suited for the detection of intracranial aneurysms of 3 mm and larger in cases of subarachnoidal hemorrhage. CTA is also commonly applied to evaluate stenoses or correlate findings in duplex sonography or other clinical examinations. CTA has several significant advantages over DSA (Digital Subtraction angiography). It is less time consuming, less susceptible to motion artefacts. The most important is the fact that it is less invasive. Moreover, the radiation dose at CTA has been estimated to be less than that of DSA [94]. Conventional DSA has a tendency to underestimate the degree of carotid artery stenosis because it uses a limited number of projections and can therefore fail to detect the maximum internal carotid artery stenosis. Moreover, high-quality DSA-like images can be generated with 3D CTA and maximum intensity projection (MIP) technique. However, it is a fact that CTA is characterised by limited ability to differentiate between calcified plaques and contrast material, rendering precise quantification of calcified stenoses difficult. CTA is characterised by limitations in evaluation of cerebrovascular function near the base of the skull because of difficulties in separating vessels from bony structures. Several subtraction methods of bone removal in cerebral CTA, such as simple subtraction from enhanced data to unenhanced data, have been developed for the evaluation of aneurysms at the skull base and extracranial ICA (internal carotid artery) aneurysms. Compared with conventional nonsubtracted CTA, subtraction CTA may produce a radiation dose increase because of the unenhanced preimaging mask. However, the unenhanced study is preferably obtained using a low dose and the radiation dose is still less than that for DSA. A bone removal CTA image obtained in a single contrast-enhanced CT acquisition with diagnostic image quality with a single radiation dose may have expanded clinical uses. Dualenergy CTA has the potential to be a rapid and automatic procedure with improved differentiation of bone and vessels. 119

120 DE bone removal is an automatic postprocessing algorithm which uses DE material differentiation to generate a bone mask and to subtract it from the DE-CTA dataset. In contrast to bone subtraction techniques which use bone masks generated on the basis of a first noncontrast scan and a second CTA scan, DE CTA obtains the information for bone masking from the data of one single DE scan. Misregistrations due to patient movement, e.g., swallowing and breathing, between two sequentially acquired scans are no issue in DE CTA bone removal, because both datasets are acquired simultaneously (in dual source CT). Such misregistration issues are especially great for patients with ruptured intracranial aneurysms. As a result of its dedicated postprocessing algorithms, DE bone removal makes visualization of the whole supraaortic vasculature feasible without superimposing bones and provides DSA-like images. Studies have shown an increased number of detected aneurysms using DE CTA with bone removal and VRT images compared to multislice CTA without bone removal. Especially aneurysms at the scull base can be shown very well. Moreover, recent studies of different groups have shown that the use of DE bone removal (but also matched mask bone elimination [95]) in head and neck CTA improves image quality and reduces reading time. Conventional CTA images may reveal calcifications but precise evaluation of the intraluminal aneurysmal shape is a challenging task. By comparison, the geometry of intraluminal aneurysms is clearly visible on DSA, yet calcifications can not be displayed. It can therefore be accepted that the wall and luminal information of the aneurysms could be analyzed with both DE-BR-CTA and conventional CTA. Figure 5.24: Right vertebral artery fusiform aneurysm with calcification in a 55-year-old male patient. MIP image of DE-BR-CTA (a)removed the calcification of aneurysm and revealed the distal-end stenosis (arrowhead) of the aneurysm as with DSA (b) VR image of conventional CTA (c) showed the calcification (arrow), but the stenosis is hard to see [64]. 120

121 Figure 5.25: (a) shows dense calcifications around the whole circumference of the right ICA, and these calcifications were removed after DE bone-removal post-processing (d) [64]. Despite its advantages, DE CTA is susceptible to other artifacts, which especially affect the proximal part of the supraaortic vessels, the aortic arch, and the subclavian arteries specifically as well as vessels embedded in tight bony canals. These artifacts are related to low transmission of low-energy quanta in very dense projections which occur in transversal orientation at the level of the shoulders and to minor extent also in the skull base. Moreover, dual-energy CTA has disadvantages, such as an immature algorithm that necessitates lower pitch and results in longer scanning time and excessive venous enhancement. However, the enhanced veins can be removed with the advanced software. In addition, although moderate or mild stenosis measurements may be accurate, severe stenosis can be overestimated when the stenotic part runs very close to calcified plaque. This result can be altered by applying different kernels. Application of a hard kernel might clarify the border between calcification and iodine. From above, it may be concluded that the image quality of DE-CTA and digital subtraction CTA does not have any statistical difference and the dose was much lower for DE-CTA predominantly due to elimination of the unenhanced CT scan for dualenergy CTA (only a single contrast-enhanced scan is obtained) in comparison with 121

122 digital subtraction CTA, in which both unenhanced and contrast-enhanced acquisitions are performed. Although conventional subtraction techniques for CTA seem to be accurate enough, the issue of dose reduction by DE-CTA is quite important. The amount of contrast medium necessary for DE-CTA examinations, as well as the scanning times are issues to be confronted, but the perspective is present. A primary task of cranial CT is to rule out hemorrhage or to rule out neoplasms, and this is why an unenhanced scan is usually obtained along with a contrast-enhanced scan. With syngo Dual Energy Brain Hemorrhage, a virtual non-contrast image can be generated from a contrast-enhanced dual energy scan. This application may make it possible to discard the precontrast scan in some cases.although detection of intracranial bleedingin a few studies give good results from VNE images, the contrast-to-noise ratio of the virtual non-contrast images was lower than that of conventional noncontrast images. Generally for now the virtual noncontrast reconstruction is not regarded as sufficient to replace a true noncontrast scan AORTA In many clinical centers MSCT has become the standard of reference in the diagnosis and follow-up of patients with aortic pathologies. In recent years MSCT has furthermore become important for the follow-up after endovascular aneurysm repair (EVAR). EVAR, suspected intramural hematoma and aortitis follow-up necessitate nonenhanced CT scanning besides one or two contrast-enhanced phases. In follow-up examinations after EVAR, the nonenhanced scan serves to distinguish between calcifications within the thrombosed aneurysm and endoleaks, which are defined as blood flow into the excluded aneurysm through different pathways. Using dual energy CTA, virtual-noncontrast (VNC) images can be obtained from contrast-enhanced images by subtracting the iodine information. These images have been shown to be a reasonable approximation of true noncontrast (TNC) images, since there is good agreement between TNC and VNC CT numbers measured within the aortic lumen, both adjacent to and within aortic stentgrafts, but the image quality may be slightly inferior for VNE images (more noisy). The detection of endoleaks by using VNC images is not impaired though. The single phase protocol (dual energy CT in venous phase) may lead to a further dose reduction of nearly by 41 44% compared to a dual-phase protocol (TNC phase and venous phase). It has been reported that the arterial phase can be omitted without a decrease in 122

123 diagnostic accuracy, although the standard CTA-protocol for EVAR follow-up is triphasic (nonenhanced, arterial, and venous phase). A specific dual-energy postprocessing workstation is used for image analysis (Syngo MMWP Version VA 34, Siemens Medical Solutions, Forchheim, Germany) and for the generation of other image types. In summary, the following algorithms are helpful for the fast and accurate evaluation of dual-energy datasets of the aorta: VNC images: A DE postprocessing preset called Liver VNC is used for the generation of these images ( three material decomposition. These three materials are soft tissue, iodine and fat). Color-coded datasets to map the iodine distribution: i.e., fused images, consisting of VNC or weighted average images with the overlaying iodine information from dual energy venous-phase scans. The same Liver VNC algorithm serves to generate the color-coded DECT images. Since the information of noncontrast images is included in these datasets, it is feasible to use this single dataset for the assessment of endoleaks. A further algorithm called hard plaque is used in order to differentiate between iodine and calcium.the former is colored in blue, the latter in red.this algorithm seems to have some weaknesses in the differentiation of smaller calcifications and can be used for detection of endoleaks. It should also be mentioned that, with application of bone removal by dual energy CT, direct visualisation of the aorta and branching vessels becomes feasible. To sum up, the main application of the dual-energy technique in CTA examinations of the aorta is the possibility to create VNC images. Although there are only publications available for follow-up examinations after EVAR, the diagnostic evaluation of other pathologies such as intramural hematoma and aortitis may also profit from the possibility to create VNC images without additional dose DUAL ENERGY CT IN LOWER EXTREMITY-PERIPHERAL ARTERIES CT ANGIOGRAPHY Lower-extremity computed tomographic (CT) angiography (peripheral CTA) has evolved into an accurate, noninvasive imaging modality for the evaluation of patients with peripheral arterial disease. The potential improvement that DECT could bring to lowerextremity CTA is substantial. 123

124 Dual-energy CT identification of contrast medium enhanced vessels and bone in clinical peripheral CT angiographic data sets and suppression of calcified plaque through material decomposition algorithms has become possible. The accuracy of tissue identification by the algorithms increases with higher attenuation voxels. A study of the clinical angiographic dataset revealed that the residual voxels of incompletely suppressed bone were seen in areas of low-attenuation trabecular bone and cortical bone edges because of partial volume averaging, whereas the highest attenuation cortical bone of the femoral shaft was completely suppressed. Beside bone-removal, a so-called plaque removal tool may be used in order to visualize the remaining lumen in calcified segments. The software implemented in Dual Source systems provides the option to add calcified plaques back into the MIP image. Thus, the plaques can be switched on and off in order to visualize both the residual lumen and the plaque burden in the area of a stenonis. Reported radiation doses in recent literature of dual energy CT-angiographies of the lower run-off range around 10 msv. This is comparable to standard CT-protocols [12] Plaque differentiation It is necessary for the clinical practice to not only identify plaques causing a luminal obstruction, but also to describe and characterize the different plaques that usually follow a specific distribution within the arterial vascular system. For clinical studies of plaques, it is essential to discriminate between soft tissue types such as thrombus, collagen, fat, muscle fibres as well as calcifications, in order to assess the vulnerability of plaques. Calcifed hard plaques are detected by differentiating calcium from the vessel lumen (blood/iodine), whereas for non-calcifed soft plaques, vessel lumen, adipose and surrounding tissue must be distinguished. The vulnerable plaque is considered to be a plaque with less calcification, but with a substantial part of fibrous and lipoid composition. It is associated with an increased risk of stroke. Plaque morphology is an important predictor of stroke risk and may also be a predictor of postoperative outcome after carotid endarterectomy (CEA). Although plaque morphology is not used in the decision making of whether to perform CEA or not, it plays an important role, as it is directly correlated with the risk of embolism and occlusion, thus resulting in cerebral ischaemia. Although digital subtraction angiography (DSA) still functions as the 124

125 gold standard for the assessment of the degree of stenosis, it is unable to make any predictions about plaque composition. While the detection and quantification of calcium can be done with adequate accuracy with CT, the method still falls short in characterizing the different constituents of mixed or purely noncalcified plaques, particularly in small-sized vessels and plaques. CT may be also limited to clearly distinguish the plaques from the surrounding soft tissue, a fact that is particularly true for fatty plaques in the walls of coronary arteries and the adjacent epicardial fat. Although the measured X-ray attenuation coefficient from CT depends both on the material and its density, it is represented by only one attenuation value. Therefore, different materials might show very similar attenuation with overlapping intensity ranges. This is where dual energy CT comes to give an alternative way for the assessment of the constituents of plaque. Comparison of dual energy DSCT findings with histopathology data has revealed that calcified lesions attenuated significantly more at 80 kv in both contrast and noncontrast- enhanced scans, whereas fibrous plaques attenuated more at 80 kv only in contrast enhanced scans. No differences could be found for lipid-rich plaques. In a recently published in vitro study (2010) the aim was to test whether combining two energies may significantly improve the detection of soft tissue components commonly present in arterial plaques. Correct classification of soft tissues is difficult by conventional CT since they form a closely clustered group on the linear Hounsfield scale of X-ray attenuation. The use of logistic regression to evaluate plaque differentiation, revealed that the combination of two energy levels (80 and 140 kv) significantly improved the ability to correctly classify venous thrombus vs arterial thrombus, myocardium or psoas; arterial thrombus vs myocardium or psoas; myocardium vs psoas; as well as the differentiation between fat tissue from various locations. It should be noted though,that single energy alone has been sufficient for distinguishing fat from other tissues.generally, lipid and calcium as the main components have such a high and low CT number that Dual Energy techniques are not required to evaluate these plaque components. Thus, the aim would be to differentiate mid-ct number plaque components such as fibrous tissue or thrombus which is still challenging, especially when the ROIs are small and voxels contain more than one plaque constituents. 125

126 The cancellation method is a dual energy method that can be used to cancel or to improve the contrast between tissues) is also used for the improvement of tissue constrast in atheroscelotic disease. The Dual Energy Hardplaques algorithm (syngo Dual Energy Hardplaque Display) helps to differentiate plaque from iodine by color-coding both differently. This algorithm is designed to differentiate and mark calcium and iodine rather than completely removing calciumcontaining structures from the dataset. The visual grading of calcified stenoses can be improved, because the algorithm helps to delineate plaque and lumen more exactly. Additionally, this data can be used to improve the automatic grading of stenoses by postprocessing software. The algorithm can also be used to visualize an additional contrast enhancement in calcified lesions. Figure 5.26: The syngo Dual Energy Environment with the available algorithms In conclusion, generally dual-energy CT can detect the calcium in atherosclerotic plaque, but there are difficulties in distinguishing the components of plaque. However, in the future multi-energy imaging of atherosclerotic plaque may help characterise the components of plaque in order to determine if it is stable or unstable. Also, new applications can be explored, such as using dual energy subtraction to differentiate iron from 126

127 calcium, which may allow for the differentiation between hemorrhagic and calcified plaques, which both appear bright in single-energy CT images PULMONARY APPLICATIONS One potential pulmonary application of iodine differentiation with the DE technique is to differentiate contrast material enhanced structures from the otherwise dense material in parenchymatous organs. To differentiate calcification from enhancing tissue in a solitary pulmonary nodule (SPN) or in the mediastinal lymph node is another potential application. Previous lung cancer screening trials have shown that the majority of individuals with certain risk profile will have at least one non-calcified pulmonary nodule. Chest CT is usually performed as a combination of nonenhanced and enhanced scanning. A nonenhanced scan is obtained for the detection of calcification in the SPN or in the lymph node, since the presence of calcification is one of the important findings of benignity. An enhanced scan is informative in providing the degree and pattern of enhancement with use of iodine. In particular, the degree of enhancement after iodine injection has proven to be helpful for distinguishing malignant from benign nodules. Application of the DE technique provides a virtual nonenhanced and an iodine-enhanced image from a single scanning after iodine contrast material injection by material differentiation of iodine. If we are able to detect calcification on a virtual nonenhanced image and directly measure the iodine component on an iodine-enhanced image, this technique may prevent additional nonenhanced scanning and the patient s radiation exposure will then be reduced. By using dedicated dual-energy postprocessing software (Syngo Dual Energy software; Siemens Medical Solutions), various application modes of material decomposition are available: the pulmonary blood volume (PBV) application mode for iodine perfusion and xenon ventilation maps, and the virtual noncontrast (Liver VNC) mode for removal of iodine from the image. It is obvious that if the CT number value of the pixel in the virtual nonenhanced image is subtracted from the CT number value of the pixel in the iodine enhanced image, the attenuation due to iodine content is quantified and is displayed on the so-called iodineenhanced images where the attenuation due to iodine (in HU) is displayed in a colorful way. 127

128 The iodine distribution is presented in cases when the pulmonary perfusion must be depicted. Pulmonary embolism (PE) is a very common disease, associated with significant morbidity. Multidetector CTA has emerged as the diagnostic standard for the assessment of patients with suspected PE in the past years and has replaced perfusion scintigraphy in most institutions. However, additional functional information, such as lung perfusion imaging, might be clinically useful for patient management, even though the diagnosis of PE has already been feasible with CTA. Although per definition lung perfusion is a dynamic process of pulmonary blood flow over time, imaging of the pulmonary capillary bed or blood volume is an accepted surrogate for lung perfusion. During the first pass of an intravenously injected contrast agent bolus, the distribution of the contrast agent can be considered as a good estimate of the local perfusion. Thus by visualizing the iodine distribution in the capillary bed of lung parenchyma, dualenergy CTA can be utilized for lung perfusion imaging in patients with suspected PE. PBV application of syngo Somatom for the calculation of iodine distribution in the lung parenchyma, a modified version of the so-called three-material decomposition. The lung parenchyma is color coded using gray scale 16-bit or hot metal 16-bit color coding (default setting) with different optional color scales available. The computation time of the perfusion maps by the software is negligible. Figures 5.27: First: Lung PBV application mode. Second: Lung ventilation mode Some pathologic entities such as chronic obstructive pulmonary disease (COPD) or asthma show distinct heterogeneities of lung ventilation. Therefore, imaging methods displaying the regional distribution of ventilation changes can play an important role in the management of these diseases, e.g., for an early detection of pathological changes in ventilation pattern, in the 128

129 selection of lung areas with impaired function prior to lung volume reduction surgery, or in the assessment of therapy response. Stable xenon (Xe, atomic number Z = 54, K edge: 34.6 kev) has X-ray absorption characteristics that resemble those of iodine (atomic number Z = 53) and other materials with a high atomic number. Those high-z materials share the characteristic of a relatively increased photon absorption with decreasing photon energies due an increase in photoelectric interactions ( photo effect ). It has been shown that the local xenon concentration is linearly related to the X-ray attenuation in CT and that inhalation of a gas mixture containing 30% xenon and 70% oxygen leads to a significant increase in pulmonary X-ray absorption. Based on these properties, xenon can serve as an inhalative CT contrast agent for an evaluation of regional gas transport and lung ventilation.lung ventilation imaging though is not routinely performed in clinical practice. More research about its diagnostic value and safety is necessary. Figure 5.28: Lobar perfusion defect due to a pulmonary embolism in a 72-year-old woman. (a) Color-coded perfusion map shows a wedge-shaped perfusion defect (arrows) in the right lower lobe. (b) Weighted average CT image obtained at the same level shows complete occlusion of the right lower lobar pulmonary artery (arrow) owing to an endoluminal clot MYOCARDIAL PERFUSION Myocardial perfusion imaging (MPI) has proven to be a valuable and reliable methodology in both, the diagnosis and prognosis of patients with CAD (coronary artery disease). In addition, MPI can assess the physiologic significance of a stenosis and appropriately risk-stratify patients with intermediate stenosis. The underlying rationale of perfusion imaging is to 129

130 demonstrate the hemodynamic consequence of an existing coronary artery stenosis on myocardial perfusion and function. DECT nowadays allows both, detailed assessment of coronary arteries and hemodynamic evaluation of detected coronary artery stenoses performing dynamic myocardial volume perfusion imaging of the heart. Based on a single DECT data acquisition using the routine heart perfusion blood volume (PBV) application (syngo DualEnergy, Siemens Healthcare, Erlangen, Germany) of the DECT reconstruction algorithm, DECT-based overlay of iodine distribution on virtual non-contrast (VNC) reconstructions may be obtained. The iodine maps are then superimposed onto grayscale multiplanar reformats (MPR) of the myocardium in shortand long-axis views, from which the iodine content in the voxels had been digitally subtracted using the VNC application of the dual-energy reconstruction algorithm. The resulting final images, which provide combined information on cardiac morphology and myocardial blood pool, can then be used to analyze myocardial perfusion and for the detection of myocardial ischemia based on DECT. However, cardiac imaging is routinely still performed as single energy exam. Simultaneous evaluation for coronary artery stenoses and myocardial ischemia would be desirable but may imply a relevant dose penalty RENAL APPLICATIONS In the kidneys, potential applications of dual-energy CT include the following possibilities. 1) Distinguishing hyperattenuating renal cysts from renal cell carcinoma Multidetector computed tomography (CT) is the mainstay for assessing patients with known or suspected of having renal masses. Characterization of renal masses at CT depends on the ability to determine the presence or absence of contrast enhancement and thus requires a baseline TNE data set immediately followed by a contrast material enhanced acquisition. TNE images are also necessary for detection of calcification and fat and baseline density measurement of masses. A renal mass with attenuation greater than that of water on contrast-enhanced images can pose a diagnostic dilemma and may be renal cell carcinoma or a hyperattenuating cyst that contains blood products or proteinaceous material. If no unenhanced images are obtained, it is not possible to determine whether a hyperattenuating renal mass enhances. 130

131 By comparing contrast-enhanced and true unenhanced images, a renal mass may be characterized as a hyperattenuating cyst if it does not enhance on contrast-enhanced images and it may be diagnosed as an enhancing tumor, most likely renal cell carcinoma, if it does enhance. Therefore, virtual unenhanced images generated from dual-energy CT images may be used to determine if a renal lesion enhances. To make such a determination, the attenuation of a lesion on virtual unenhanced images is compared with that on contrast-enhanced images. Tumor enhancement is defined as difference between attenuation of a mass on contrastenhanced images and its attenuation on either VNE or TNE images. True unenhanced images may be replaced by virtual unenhanced images with significant dose reduction, but further software improvements are necessary to achieve better accuracy and even more studies need to assess the limitations of vne images. There are results that show that visual VNE image quality will be slightly lower than TNE image quality. Also, subtraction of calcium from DE CT data represents an inherent technical limitation of the VNE algorithm. Calcium is not among the three materials (soft tissue, iodine and fat) analyzed in the decomposition process. This limitation can be overcome by another postprocessing algorithm that analyses calcium, iodine, and soft tissue. However, application of this algorithm requires a separate postprocessing step. 2) To identify renal calculi within contrast material filled renal collecting systems Dual-energy CT iodine-subtraction virtual unenhanced technique is capable of depicting urinary stones in iodine solutions of a diverse range of concentrations as revealed by experiments.iodine-subtraction virtual unenhanced images may allow the detection of urinary stones(especially the big ones) unless the iodine concentration value is not too high.also, itsis observed that a small collimation was associated with a higher stone visibility rate of the stones and iodine and that stone visibility rate was not affected by stone composition. 3) To characterize the composition of renal calculi For more than 20 years, renal calculi have been characterized on the basis of absolute attenuation measurements at single-energy CT. Single-energy techniques are limited by partial volume effects introduced by the rendered regions of interest, which are used to 131

132 determine the composition of calculi. Partial volume effects are especially problematic with smaller stones. The reported accuracy and sensitivity of the UA vs. non-ua differentiation using DECT varies from 88 to 100% therefore it is a promising technique for kidney stone differentiation. Since UA-containing stones are composed only of light chemical elements (H, C, N, O), they have significantly smaller Zeff and absorb X-rays differently at any given energy compared to other (non-ua-containing) stone types, whose composition includes heavy elements (P, Ca, S). DECT imaging exploits this difference in the X-ray attenuation behavior to discriminate stones of different composition. According to the algorithm utilized by the DE software tool, a kidney stone can be considered as a mixture of a hypothetical pure stone with no pores (such a stone would have a very high density and unrealistically high CT numbers) and the material that fills the pores ( urine ). In a plot of the CT numbers at 80 kv vs. the CT numbers at 140 kv (Figure 8.16), a real stone has to lie somewhere (depending on its porosity) on a line segment between the urine and the pure stone data points (their exact placement depends on the stone composition). The slopes of these segments are independent of the stone porosity ( density ). The slopes of different stone types can be determined using stones of known composition. Since UA stones are made of light chemical elements, their slope is quite different from the slopes of other (non-ua) stones, which have heavier atoms. Slopes of non-ua stones are relatively close to each other and they are represented by a single average slope corresponding to all non-ua stones. If a data point corresponding to a stone with unknown composition falls below the angle bisector (boundary line) dividing the angle between the UA and non-ua line segments, the algorithm will characterize such stone as a UA stone and assign it a predefined color code. If an unknown data point falls above the boundary line, the corresponding stone will be identified as a non-ua stone and assigned a different predefined color code. The slope of the boundary line in the low- kv vs. high-kv CT number plot that separates UA from non-ua stones depends on the spectral characteristics at high- and low-kv, and hence, varies among the DE modes available on Definition and Definition Flash scanners. 132

133 Figure 5.29: plot of the CT numbers at 80 kv vs the CT numbers at 140 kv and discrimination f UA and non UA stones. The described DE algorithm is limited and cannot discriminate different non-ua stone types. The discriminating power of the DECT technique could be improved if the high and low-energy spectra were better separated. Another limiting factor is noise which increases error bars for the data points representing the stones. For stones located close to the boundary line, the error bars may extend beyond this line. Such stones cannot be confidently classified as a UA or non-ua stone. Therefore, the noise level will determine the threshold line shown in Fig perpendicular to the boundary line. Stones whose data points fall below the threshold line cannot be properly evaluated by the algorithm and will be assigned no color. A stone with a mixed (red/blue) color could either represent a stone of mixed (UA/non- UA) composition or a misclassification caused by an artifact or excessive noise. There have been several studies concerning the effectiveness of kidney stone differentiation, giving very promising results. Moreover, there have been attempts for further discrimination of stones,beyond the simple UA-non UA differentiation with DECT CT. Dual source CT seems to have the ability to distinguish not only between calciferous stones and uric acid stones, but also among stones composed of different calcium salts. Results seem to be positive but more studies should be made to confirm the results. 133

134 5.7.9 HEPATIC APPLICATIONS Dual energy CT (DECT) has so far been investigated for hepatic imaging for the characterization of three different materials i.e. the detection of iodinated contrast media as well as the assessment hepatic fat infiltration and iron overload. Fatty liver is defined as excessive accumulation of triglycerides within the cytoplasm of hepatocytes. Sometimes fat distribution in the liver may cause diagnostic confusion by mimicking neoplastic masses. In hemochromatosis, excessive storage of iron in hepatocytes results in progressive liver damage and subsequent cirrhosis. Detection of hyperenhancing hepatic lesions at CT is important when staging or screening for hepatocellular carcinoma. Hypervascular hepatic lesions are more conspicuous at lower energies (e.g. 80kVp) than they are on high energy images (e.g. 140 kvp) when acquisition occurs in the late arterial phase of enhancement because of iodine s higher attenuation at lower energies. Characterizing the components of a hepatic tumor may help narrow the differential diagnosis. For example, fat within a hepatic tumor is suggestive of hepatocellular adenoma or hepatocellular carcinoma and calcium is suggestive of a prior infection (e.g. histoplasmosis if the lesion is entirely calcified) or a mucinous metastasis (if the lesion is partially calcified). Studies have shown that dual-energy CT may help differentiate focal fat from other low-attenuation hepatic lesions in the absence of iron deposition. Virtual unenhanced images may be used to localize the places of contrast enhancement and differentiate it from calcium. VNE images seem to be a good surrogate of TNE images and reduce the dose level of the examination. These images are based on a threematerial decomposition of iodine, soft tissue and fat. Generally,based on the few but steadily increasing number of published studies it can be concluded that the differentiation of iodine is the most, but probably also only, valuable application of DECT for hepatic imaging. DECT can be used to improve the conspicuity of hypervascular liver lesions by utilizing the higher attenuation of iodine at low kv levels. 134

135 PANCREAS There are two important applications for dual energy imaging in the pancreas. Liver VNC for iodine quantification and Body-Bone-Removal for direct angiographic visualization. With LiverVNC, the iodine content of tissues is quantified and color-coded. Therefore, faint differences in contrast material uptake that might have been missed on gray scale images are highlighted. The colour-map may be superimposed on virtual non-enhanced or regular gray scale MIP (maximum intensity projection) or MPRs. Colour overlay and gray scale image can be blended in steps of 1% from a pure colour to a pure gray scale image. Finally, by subtracting the iodine signal from the dataset, virtual non-enhanced images can be calculated to show the presence of calcifications and give baseline CT numbers. Similar post-processing options are available for Dual Energy data acquired with rapid kv-switching (GSI Viewer, General Electric). Utilizing MD, image series are available in which iodine information is either highlighted or subtracted, and iodine uptake can be quantified and colour-coded. With Body-Bone-Removal (syngo Dual Energy, Siemens), the algorithm will automatically remove bony structures from the dataset based on different spectral behaviour of iodine and calcium and will create a rotatable thick slab MIP. This gives an excellent overview about vascular invasion or compression caused by pancreatic mass. Dual energy special utility in pancreatic lesions is mainly attributed to the fact that pancreas is an area where only faint changes of tumour compared to surrounding normal pancreas can be visualised by conventional MRI or CT exams.similar issues may be encountered in the diagnosis of necrotic areas in early stages.dual energy may lead to quantification of enhancement and calcifications without additional radiation exposure by omitting the unenhanced scan. It may also quantify iodine enhancement by color coding its distribution and making it more visible.these possibilities be very time saving and of crucial diagnostic value TENDONS AND LIGAMENTS With the development of dual-energy CT there are new possibilities of imaging of these structures, because of the good delineation of collagen versus the surrounding structures like fat and bone. Possible explanation is the dense packing of the unique hydroxy-proline and hydroxy-lysine amino acids in the side chains of the collagen molecule. By their spectral 135

136 properties, collagen-containing structures can be differentiated and depicted without surrounding soft tissue. The tendons can be highlighted because of the different attenuation of the collagen versus the bony and fatty structures. It is helpful to create multiplanar reconstructions (MPR) as well as volume rendered images (VRT). Dual energy CT gives new prospective to the diagnosis of the ligamental structures without invasive methods like air or intraarticular contrast media injection. The differentiation of collagen makes it possible to depict ligaments. Though DECT seems promising for this application for differentiation of tendons, ligaments and potentially cartilage, there are still a number of problems that need further improvement at the same time. Regarding the differentiation of collagen, image noise has proved to remain a problem. The contrast to noise ratio is just too weak to make reliable diagnoses. Therefore, the diagnostic value in clinical practice is quite limited and certainly no competition to MRI. Figure 5.30: Tendons and ligaments dual energy dialogue box from a case in OLYMPION Patras 136

137 GOUT Gout is a common type of crystalline arthropathy of metabolic origin. It is triggered by the crystallization of monosodium urate (MSU) within joints which is characterized by intermittent attacks of inflammation. Other modalities like ultrasound and MRI are not very helpful for the diagnosis of gout. Plain radiographs appear normal until late in the disease of gout and are not sensitive in its diagnosis. Ultrasound has a poor sensitivity and specificity for gout as a diagnostic modality. Studies have shown MR imaging to be nonspecific in the diagnosis of gout. Although conventional CT has been reported to be superior to both MRI and ultrasonography in then detection of intra-articular tophi and erosions, none of these modalities can accurately confirm the presence of MSU deposition. Thus, a highly accurate non-invasive imaging tool to confirm the presence of gout would be desirable. Dual energy CT is a revolutionary method for gout diagnosis, utilizing material decomposition algorithms for differentiation of MSU. Scanning protocol of DECT for gout includes images of both hands, wrists, elbows, knees, ankles and feet. Calcium is a heavy, high atomic number element which has high attenuation of the low kv beam. Therefore, bone attenuation lies above the blue line and is color coded blue. MSU is composed of C, H, N, O. Therefore it has a relatively low atomic number per unit area and it attenuates the High kv beam to a greater extent. It will lie below the blue line and will be color coded green. Iodine or trabecular bone appears pink. The slope of the blue line was adjusted to separate the differential attenuation of uric acid vs. calcium.(see figure 8.19) This is actually a modified renal stone dual-energy CT protocol to confirm the presence of monosodium urate deposits within joints and within soft tissues DETECTION OF POSTTRAUMATIC BONE MARROW LESIONS Bone bruises were initially described as occult intraosseous fracture, indicating that conventional radiography and direct observation with arthroscopy could not reveal these abnormalities.magnetic resonance (MR) imaging has popularized the term bone bruise as an imaging diagnosis. Bone bruise lesions are described as areas of signal intensity reduction on T1-weighted MR images and signal intensity increase on T2-weighted MR images in the bone marrow. The depiction of bone bruises at computed tomography (CT) is hindered by the presence of overlying trabecular bone. Although bony structures can be easily removed on single-energy CT images by using different algorithms, these conventional techniques do not permit bone marrow to be visualized because the delicate trabecular structures 137

138 surrounding the bone marrow are not resolved. The same method that has been used for creation of virtual unenhanced images, can be used for creation of virtual non-calcium images. LiverVNC (Siemens syngo) algorithm with modified parameters can be used. Again what someone needs to know for the calculation of the virtual non calcium image is the slope of the calcium in the HU140-HU80 kvp space.image analysis is based on a threematerial decomposition algorithm into bone mineral, yellow marrow (which is represented as fat) and red marrow (which is represented as soft tissue). Therefore, DE CT virtual non-calcium technique subtracts calcium from cancellous bone, allowing bone marrow assessment and making posttraumatic bone bruises of the knee potentially detectable with CT. There were several cases in which, despite an equivocal visual judgment, CT numbers between normal and altered marrow showed close correlation with the MR imaging findings in the majority of tibial regions METAL ARTIFACT REDUCTION WITH MONOCHROMATIC IMAGES Virtual monochromatic images at high energies have been found to be able to reduce artifacts caused by metal implants on dualsource dual-energy CT. Optimal monochromatic energies vary between 95 and 150 kev, depending on the composition and size of the metal implant. Figure 5.31 compares two images of a pedicle screw acquired by single-energy CT at 120 kv and monochromatic images at 127 kev synthesized from a dual-source dual-energy scan for the same radiation dose. Streaking artefacts caused by the metal implant were almost completely eliminated on the monochromatic image. However, for very dense metal implants, the correction is not effective (figure 5.32). This is mainly because the metal artifacts in the presence of dense metal are caused by factors in addition to beam hardening, such as photon starvation and nonlinear partial volume averaging, which cannot be corrected by synthesizing high-energy monochromatic images. The metal artifacts are caused by photon starvation and beam hardening. Due to photon starvation, the number of photons which pass through the metallic object is less than the number of photons passing through non-metallic objects. It causes much a lower signal-to-noise ratio (SNR) in the measured projection data compared to non-metallic artifact images. Additional iterative correction has been applied to monochromatic images to further reduce metal artifacts. 138

139 Figure 5.31: Metal artifact reduction using virtual monochromatic images synthesized from dual-source dualenergy CT data using image-space techniques. A.Image shows pedicle screw in water phantom, acquired with single-energy scan at 120 kv. B. Monochromatic image at 127 kev was generated from dual-energy scan with same scanner output (volumect dose index) as used in single-energy scan. Streaking caused by metal was almost completely eliminated [38]. Figure 5.32: Metal artifact reduction using virtual monochromatic images synthesized from dual-source dualenergy CT is ineffective for dense metal objects. A. Image of dense metal implant in water phantom acquired with single-energy scan at 120 kv. B. Monochromatic image at 127 kev generated from dual-energy scan with same scanner output (volume CTdose index) as used in single-energy scan. Streaking by metal becomes worse on virtual monochromatic image [38]. From the above it becomes obvious that there are many possibilities for dual energy CT in clinical practice HOW CAN DUAL ENERGY CT GIVE IMAGES OF SIMILAR INFORMATION AS PET/CT and SPECT Imaging modalities based on x-ray transmission measurements are usually regarded as rather insensitive with respect to the detection of specific drugs, contrast materials, etc. present in 139

140 the object of interest. This is true in particular when compared to other imaging modalities such as e.g. positron-emission-tomography and is due to the fact that in the transmission case the signal coming from these samples is always superimposed on the signal resulting from the anatomic background. Conventional x-ray transmission systems based on current integration do not allow us to separate the two signals. DECT allows the selective separation of the anatomic background and contributions coming from high-z elements giving a new perspective to CT imaging and leading it to be more than just an imaging technique of anatomic information. Although PET-CT is a commonly used technique, in particular for tumor staging, a variety of difficulties limits the usefulness of this technique. Misregistration is a significant issue in PET-CT. The duration of the PET portion of a PET-CT study is longer (30 40 min) than that of the CT portion (<1 min). Therefore, PET images are acquired during free breathing, and CT images are acquired within a single breath hold. Misregistration limits the usefulness of PET-CT for the detection of small lesions, particularly in the lungs. In contrast, DECT enables perfect registration due to the almost simultaneous acquisition of 80- and 140-kVp data and thus movement artefacts are eliminated. PET-CT is an excellent tool for the demonstration of glucose metabolism, which is extremely useful in oncologic imaging. However, several causes can lead to glucose hypermetabolism, which may mimic a tumor on PET-CT images. Angiogenesis is another important feature of cancer cells that can be demonstrated by MR or CT perfusion. DECT imaging provides iodine maps that have the potential to allow an objective determination of contrast enhancement or iodine uptake independently of the anatomic background. This feature may facilitate an increased detection of lesions due to better contrast detection, which can be displayed on maximum intensity projection (MIP) and colorcoded images in a manner similar to PET-CT images. In addition, iodine maps may be used for the objective assessment of disease activity, especially in patients who have undergone a targeted antitumor treatment. The contrast agent iodine has been used in several studies to determine if any myocardial perfusion was present in the Dual Energy CT images, as already discussed in the previous. Comparing this to the sensitivity, specificity and accuracy of the SPECT images, results have shown that Dual Energy CT has the ability to perform integrative analysis of the coronary artery morphology and myocardial blood supply and is in good agreement with SPECT and ICA (invasive coronary angiography) [96]. Initial experiences suggest that dual-energy-based spectral CT imaging to evaluate myocardial perfusion is feasible and 140

141 rest-dect perfusion analysis correlates very well (90 96%) with fixed perfusion defects at 99m-Tc-Sestamibi-SPECT. In the following tables we present the dual energy CT applications approved by FDA 2007 (table 5.3) and the comparison between application availability in dual source and kv-switch scanners from [57] (2011). However, metal artifact reduction is marked as - in dual source CT, maybe because the study [38] was presented in Table 5.4: Dual Energy CT Applications approved by the FDA Dual Energy CT Applications approved by the FDA Direct subtraction of bone 2. Differentiation between plaque and contrast agent 3. Virtual unenhanced abdominal organ imaging 4. Kidney stone characterization 5. Visualization of cartillage, tendons, ligaments 6. Evaluation of lung perfusion defects 7. Heart perfusion blood volume 8. Uric acid crystal visualization 9. Lung vessel embolisation 10. Brain hemorrhage differentiation Table 5.5: Potential clinical applications of dual-energy MDCT 141

142 5.8 MULTI-ENERGY IMAGING Conventional X-ray detectors integrate the total electrical current produced in the radiation sensor and disregard the charge amplitude from individual photon detection events. The charge amplitude from each event is proportional to the photon s detected energy. During this integration, both the detector leakage current and charges resulting from X-ray detection are summed and measured and provide no information about the energy of individual photons or the dependence of the attenuation coefficients in the object. A new alternative to these detectors is photon-counting X-ray detectors that count individual X-ray photons interacting in each pixel of the detector.they have already been mentioned in of the thesis. Energy-resolved photon counting with multiple energy thresholds provides the additional capability of counting photons based on their detected energies. Such detectors acquire simultaneous measurements of the X-ray photon flux above one or more user-defined energy thresholds. These data can be used to obtain the X-ray photon flux in a set of nonoverlapping energy windows [97]. These energy resolved detectors use high speed typically solid-state, radiation sensors combined with very fast readout application specific integrated circuits (ASICs) that process individual photons. These ASICs have an electronics chain for each pixel in the detector. The current signal from the detector is integrated, amplified and shaped. The resulting pulses are processed by a set (typically two to six) of independent comparator circuits. One input to each comparator is attached to a voltage corresponding to an energy threshold and the other is attached to the output of the shaping amplifier. The output of each comparator is counted in a counting circuit. The values of the counter for each threshold and each pixel can be read out rapidly to provide the number of photons detected during the acquisition period that have energies greater than each of the energy thresholds [98]. Cadmium-based materials such as CdZnTe may serve as semiconductors for photon-counting detectors that resolve the energy of each individual photon. Therefore the separation of the spectrum into several energy bins is possible for multiple energy CT. However, this detector technology shows difficulty in coping with the high photon flux required for clinical CT. In comparison to dual-energy CT used in clinical practice, those recently developed energy-sensitive photon-counting detectors sample the material-specific attenuation curves at multiple energy levels and within narrow energy bands; the latter allows the detection of element-specific, k-edge discontinuities of the photo-electric cross 142

143 section. Multi-energy CT imaging therefore is able to concurrently identify multiple materials, each one of which has its own attenuation coefficient energy dependence, with increased accuracy. These specific data on material distribution provide information beyond morphological CT and approach functional imaging. Fig. 5.33: CdTe detection crystal and readout ASICs[97] 5.9 TISSUE CLASIFICATION USING SINGLE-ENERGY CT SCANS In single-energy CT, the historically first tissue classification method was performed by assigning the linear attenuation coefficient values into groups (for instance bone, soft tissue, etc.) delimited by threshold values. Another method currently in clinical practise assumes that each tissue is a mixture of two base materials and derived formulas for the determination of weight fractions of these two materials have been derived. There are generally examples of single energy methods to predict the chemical composition of structures in human body (for instance stone composition predictions using spiral CT and analysis of attenuation values with visual assessment of stone morphology). Those approaches were not reliable enough though BASIC REQUIREMENTS FOR DECT Dual energy analysis is quite promising as far as its medical (and not only) applications are concerned but it has some certain requirements in order to function in an optimal way. The ability of DECT to discriminate between two materials relies primarily on the separation between the high and low-energy spectra and the difference between the effective atomic numbers of the evaluated materials (so that their photoelectric absorption behavior will be quite different-for instance differentiation between a material of high and a material of low Z). 143

144 Since the photoelectric effect, which is utilized in dual energy methods is more prominent for materials with high effective atomic numbers, those materials are expected to be good candidates for dual energy CT discrimination. In order to quantify the spectral behaviour of different materials, a Dual-Energy Index (DEI) can be calculated independently as: µ µ DEI µ + µ As Hounsfield units should be related linearly with attenuation, we obtain: x80 x140 DEI x + x (5.47) (5.48) where x 80 is the CT value in HU at 80 kv tube potential and x 140 the value of the respective voxel at 140 kv. The elements that mostly make up the human body, i.e. hydrogen (1), oxygen (8), carbon (6) and nitrogen (7), have low element numbers and hence do not show a sufficient photo effect and spectral behaviour that would allow a dual energy differentiation. The DEI is zero for water, negative for light atoms and positive for all heavy atoms that are typically encountered in the human body. The DEI of a mixture of materials is between the DEIs of the original two materials. Though DEI is a measure of the spectral behaviour of materials, its clinical use is not significantly important. For instance, in the detection of urinary stones, it can be proved that its value depends on the stone density and therefore it is not the optimal DECT metric [59]. Figure 5.34: Dual-Energy Index of atoms in relation to their element number Z [99]. 144

145 The Dual energy behaviour of materials, as already shown is depicted in graphs of HU 140kVp-HU80 kvp. Materials that present a slope of a value quite different that unity show good separation with dual energy methods. We will refer to it in more detail in following chapters. Adequate spectral separation is very significant for successful spectral imaging. The smaller the spectral separation, the harder it is to discriminate between two materials, especially for materials with close atomic numbers e.g. calcium and iron. In the limit of no separation between the two spectra (single-energy limit), no material discrimination is possible if the density differences adequately offset the differences in attenuation due to atomic number. In order to achieve that kind of spectral separation in dual kv approach of dual energy CT, the voltages of 80 kvp (mean photon energy 53 kev) and 140 kvp (mean photon energy 72 kev) are used. A tube voltage lower than 80 kvp is not useful because of too much absorption of low energy photons in the human body and much image noise. On the other hand, a tube voltage higher than 140 kvp leads to poor soft tissue contrast. The higher energy spectrum is dominated by the characteristic lines of the tungsten anode, while the lower energy spectrum mainly consists of Bremsstrahlung (see Fig. 5.35). Fig. 5.35: Spectra of the Straton tube at 140 and 80 kv potential. The peaks represent the characteristic lines of the tungsten anode and the continuous spectrum is a result of Bremsstrahlung. The mean photon energies are 53 and 71 kev, respectively. The optimum spectral separation can also be achieved by appropriate filtration. For instance, The SOMATOM Definition Flash uses the new Selective Photon Shield to filter out unnecessary photons of the high energy X-ray tube. This results in a much better material separation due to much less overlap of the spectra. The filter used for increasing material 145

146 separation should consist of iodine or metals with similar absorption characteristics, such as indium, tin(sn), antimony, or tellurium [100]. Figure 5.36: Energy spectra separation with and without selective photon shield [100] Another important requirement concerns the ability of the detector to differentiate quanta of different energies. The dual energy facilities that work with integrating detectors either use separate sources with separate detectors or they are based on reading out the projection data at different time points or they use two layer detectors with different spectral sensitivities on each layer. Photon counting detectors are a new alternative since they resolve the energy of each individual photon. The possibility to visualize pathological tissues, using new X-ray imaging techniques like dual energy CT is strictly related to an accurate knowledge of the X-ray absorption coefficients, so that is another important requirement for multi-energy CT. Nowadays µ(e) values are partially derived from Monte Carlo simulation and are unfortunately known only for a little number of pathologies. Two basic requirements are necessary to experimentally define an attenuation dataset of tissues: 1) the possibility to accurately scan and analyze µ(z) values for all energies of interest in radiology (in particular, between 10 kev and 120 kev). 2) a study of the variability between samples of the same tissues obtained from different patients, in order to evaluate the inhomogeneities. Therefore, accurate datasets of µ for different materials and at different energies are very vital for determining the accurate composition of an unknown finding in CT by using dual energy analysis. NIST database of attenuation coefficients provides theoretically 146

147 calculated values, but also experimental procedures can provide attenuation coefficient information. For instance, a 2008 analysis [101] for creating such a dataset was utilized a facility based on Bragg X-ray monochromator, with selectable peak energies from 10 kev to 90 kev and biological tissues of mouse. The primary polychromatic X-ray beams are produced by a W anode tube and collimated to an LiF crystal mounted on a rotating stage. Adjusting different crystal angles, Bragg law of diffraction permits to produce quasi-monochromatic X-ray beams with selectable energies The sample and detector positions are defined by using a second rotating stage, connected to the first one, in order to collect only the X-ray beam transmitted by the sample Knowing the sample thickness x and comparing un-attenuated spectra (i.e. I 0 ) with tissue transmitted ones (i.e. I; Fig. 1), µ(e,z) values are directly derived according to Beer-Lambert law of attenuation. µ 1 I0 (, ) ln ( E E Z = ) x I ( E (5.49) ) 147

148 CHAPTER 6 THEORETICAL STUDY: THE DEPENDENCES OF X-RAY ATTENUATION PROBABILITY WITHIN MATTER In the previous chapter the requirements for successful implementation of dual energy CT were discussed. As it has become clear, the nature of the absorber defines its dual energy behaviour and therefore appropriate selection of materials makes dual energy discrimination feasible. The effective atomic number of a substance, mainly defines the energy dependence of its attenuation. In chapter 2, the concept of effective atomic number is defined and its significance in X-ray attenuation is highlighted and then the energy dependence of attenuation is investigated in order to clarify the attenuation characteristics that make some materials better candidates for dual energy discrimination than others. In the following graphs, Z effective has been obtained by the x-mudat database. In an effort to reach an approximation for the dependence of attenuation coefficients from Z effective, the mass attenuation coefficient (photoelectric, Compton and total) of several (35) materials (Table 6.1) against their Z effective for 4 different monochromatic energies (18, 65, 75 and 130 kev) has been plotted.the materials selected are pure elements, tissue-like materials and water. Table 6.1: Z effective of materials used for the graphs Material Zeffective Material Zeffective Material Zeffective Hydrogen 1 blood (whole icru) 7,74 xenon 54 Helium 2 magnesium 12 Barium 56 Lithium 3 bonecompact icru 12,31 Europium 63 polyethylene 5,53 Aluminium 13 Gadolliinum 64 polystyrene 5,74 phosporus 15 tungsten 74 nylon(type 6) 6,21 Sulfur 16 Rhenium 75 polycarbonate 6,33 calcium 20 Gold 79 adipose (icru 44) 6,47 iron 26 Mercury 80 breast tissue 7,07 copper 29 lead 82 water liquid 7,51 Gallium 31 Bismouth 83 soft tissue(icru44) 7,64 tin 50 Francium 87 brain 7,65 iodine

149 6.1 DEPENDENCE OF COMPTON EFFECT ATTENUATION FROM THE ABSORBER Compton effect mass attenuation coefficient is a expected to have a very slight dependence on chemical composition. Hydrogen is shown in figure 6.1 to have the highest Compton mass attenuation coefficient than any other material, because Z/A=1 for hydrogen, while for all other materials Z/A= and decreasing as Z increases. µ/ρ (cm 2 /gr) Compton mass attenuation coefficient (at 18 kev) µ/ρ (cm 2 /gr) Compton mass attenuation coefficient (at 65 kev) Z effective Z effective 0.35 Compton mass attenuation coefficient (at 75 kev) 0.30 Compton mass attenuation coefficient (at 130 kev) µ/ρ (cm 2 /gr) µ/ρ (cm 2 /gr) Z effective Z effective Figures 6.1: Compton mass attenuation coefficient (cm 2 /gr) versus Z effective for photon energies of 18,65,75 and 130 kev. Especially for high Z materials Compton mass attenuation coefficient is independent of Z effective. The differences in Compton mass attenuation coefficient between different elements or mixtures are weak, as it is depicted in figures 6.1, especially for pure materials of high atomic number that have been plotted. 149

150 Table 6.2: Mass electron density, Z effective and mass density for various materials For Compton scattering, mass attenuation coefficient of mixtures, the chemical composition of the mixture defines the electron density per unit mass. As seen in table 6.2, materials that have the same effective atomic numbers have slightly different Compton effect mass attenuation values at the same energy levels. These are only small differences though, so we may regard mass density as the major parameter that defines Compton linear attenuation coefficient. 6.2 DEPENDENCE OF PHOTOELECTRIC EFFECT ATTENUATION FROM THE ABSORBER 120 Photoelectric mass attenuation coefficient (18 kev) 10 Photoelectric mass attenuation coefficient (65 kev) µ/ρ (cm 2 /gr) Z effective µ/ρ (cm 2 /gr) Z effective 10 Photoelectric mass attenuation coefficient (75 kev) 3.5 Photoelectric mass attenuation coefficient(130kev) µ/ρ (cm 2 /gr) µ/ρ (cm 2 /gr) Z effective Z effective Figures 6.2: Photoelectric mass attenuation coefficient versus Z effective for photon energies 18,65,75,130 kev. 150

151 In three first 6.3 plots, discontinuities appear at higher atomic numbers and for lower and middle values of energies. Those discontinuities are due to absorption edges of materials. For instance, at 65 kev, gadolinium (Z eff = 64) has higher mass attenuation coefficient than tungsten (Z eff = 74), although the general trend is that photoelectric mass attenuation coefficient increases with increasing Z effective. This is because gadolinium has a k-edge around 50 kev. If energies lower than 18 kev had been examined, we would have found discontinuities for lower Z materials too, because materials like iron have k-edge at lower energy level. For instance at 7 kev, iron (Z=26) has higher photoelectric (and total) mass attenuation coefficient than gallium (Z=31). Absorption edges at energies higher than 1 kev are not observed for very low Z effective materials though (x-mudat gives k-edge values for elements of Z effective more than 11(sodium Na). Also, if materials of very increased Z values (which are generally not of medical interest) will have absorption edges at very high energy levels. When such absorption edges are encountered, the parameterization described in equation 5.5 is used for the attenuation coefficient and a three energy approximation must be used. Materials that pose a problem of dual energy analysis are the ones that have absorption edges above 30 kev and these are usually contrast agents. In the following, the photoelectric mass attenuation at 18, 65, 75 and 130 kev for materials of low Z effective (up to 7.74) is presented. Photoelectric mass attenuation coeffcient at 18 kev for materials with Z eff <=7.74 Photoelectric mass attenuation coefficient at 65 kev for materials with Z eff <= µ/ρ (cm 2 /gr) y = x R 2 = µ/ρ (cm 2 /gr) y = 4E-06x R 2 = Z effective Z effective µ/ρ (cm 2 /gr) Photoelectric mass attenuation coefficient at 75 kev for materials with Z eff <=7.74 y = 2E-06x R 2 = Z effective Photoelectric mass attenuation coefficient at 130 kev for materials with Z eff <=7.74 y = 3E-07x R 2 = Z effective Figures 6.3: Photoelectric attenuation coefficient (cm 2 /gr) of light materials for photon energies 18,65,75,130 kev. The exponent of the Z effective dependence is around 4. µ/ρ (cm 2 /gr) 151

152 Therefore, it seems that for low Z effective materials (Z eff < 8) the exponent of the photoelectric mass attenuation coefficient dependence of Z is approximately 4 and very slightly increasing as energy increases. It is assumed that tissue-like materials are characterized by the same or similar mass electron density (e/g). Alvarez and Macovski [20] could discriminate fat and brain tissue type materials that were chosen to have the same attenuation coefficient at a conventional CT scanning mean energy (density values were chosen so as to achieve this). In a similar way, the Z effective dependence of photoelectric mass attenuation coefficient is investigated for higher values of Z effective. Most graphs will be omitted and it will just be mentioned that for the regions between the discontinuities, the exponent n of the n Z eff for the photoelectric effect is approximately 3 for all 4 energies investigated for those materials, all with Z effective above 12 and up to 87. As an example, the following figures present the photoelectric mass attenuation coefficient of materials (12<Z eff <87) for 18 and 130 kev. 60 Photoelectric mass attenuation coefficient at 18 kev for materials with 12<= Z eff <= Photoelectric mass attenuation coefficient at 18 kev for materials with 50<= Z eff <= µ/ρ (cm 2 /gr) y = x R 2 = µ/ρ (cm 2 /gr) y = x R 2 = Z effective Z effective Figures 6.4: Photoelectric mass attenuation coefficient (cm 2 /gr) at the energy of 18 kev for materials with Z eff in the intervals and Photoelectric mass attenuation coefficient at 130 kev for materials with 12<= Z eff <= µ/ρ (cm 2 /gr) y = 3E-06x R 2 = Z effective Figure 6.5: Photoelectric mass attenuation coefficient for materials with Z eff values in the interval

153 Experimental results ( also conclude that photoelectric mass attenuation coefficient is proportional to Z n where n = 3 (approximately) for high Z materials and n is closer to 3.8 for low Z materials (like the bulk of the biological material like carbon, nitrogen and oxygen). Therefore, the exponent n is not a universal constant but depends on the effective atomic number and hence on the substance. For mixtures, the exponent n has been found to diminish with increasing Z eff but generally seems to have a marginal dependence on the photon energy [2]. Total mass attenuation coefficient seems to have a Z effective dependence similar to that of the photoelectric attenuation coefficient mainly for high Z materials. It is also characteristic that, for instance, at 18 kev, power law which is indicative of important photoelectric contribution, appears after Z eff = 12, but at a higher photon energy like 130keV, power law appears for Z eff larger than Total mass attenuation coefficient at 18 kev 12 Total mass attenuation coefficient at 65 kev µ/ρ (cm 2 /gr) µ/ρ (cm 2 /gr) Z effective Z effective 12 Total mass attenuation coefficient at 75 kev 3.5 Total mass attenuation coefficient at 130keV µ/ρ (cm 2 /gr) µ/ρ (cm 2 /gr) Z effective Z effective Figures 6.6: Total mass attenuation coefficient versus Z effective at 18,65,75 and 130 kev. The law that describes the dependence of basic attenuation mechanisms- in the radiological energy range- from atomic number has become clear though the previous graphical analysis. It is well understood that photoelectric effect is the interaction that includes the 153

154 information about the elemental composition of attenuators. Compton effect is characterised by a very weak dependence on chemical composition. 6.3 ENERGY DEPENDENCE OF ATTENUATION The next question to be answered concerns the characteristics of materials that are appropriate for optimal dual energy discrimination. More specifically it is important to determine the energy dependence of X-rays attenuation for biologically interesting (and not only) materials in order to come to a conclusion about the expected dual energy behaviour of such substances. Attenuation data used in the following analysis are obtained from x-com NIST dataset and x-mudat database. More details about the databases can be found in the appendix. Photoelectric effect attenuation energy dependence for all materials in the radiological energy range is described by a power lawµ ( E) = p 2 ph 1E, where p 2 = depending on the material and the energy region. For materials that have no absorption edges in the energy range kev, the power law has an exponent p 2 = approximately as expected from the theory. Absorption edges though, when encountered, divide the energy range into power law segments, among which the exponent may be slightly different (and usually lower than 3 unless we refer to regions past the absorption edges, where exponent approximated 3). However, the photoelectric energy dependence is still very strong for all materials. The purpose of the analysis that follows is to illustrate the energy dependence of x-ray attenuation for different materials in order to explain their strong or weak dual energy behavior. For this reason, the linear attenuation coefficient of materials was plotted at arbitrary energies within the energy range kev. Then the regions of fitting to obtain the function µ(ε) were determined either by the presence of absorption edges or in a more qualitative way at energy levels were absorption edges were not present. In this way, the regions of power law photoelectric dependence were defined and though this observation, the dual energy behaviour of materials was evaluated. p 154

155 6.3.1 IODINE ATTENUATION: PHOTOELECTRIC EFFECT DOMINATES Iodine is an element of high atomic number. Its atomic number value is 53 and its density value is 4.93 gr/cm -3. It is therefore a material of high attenuation in CT. Due to its attenuation properties, it is used as a contrast agent in various examinations. Since photoelectric attenuation is important for material discrimination, it would be interesting to investigate how it affects total iodine attenuation for spectra of low and high kvp values. In the following graphs (figure 6.7 and figures 6.8) the energy dependence of photoelectric linear attenuation coefficient of iodine in the energy range kev is displayed. From the graphs it is obvious that the photoelectric interaction is described by a power law 1 p2 µ ( E) = p E, where µ is the linear attenuation coefficient and E the photon energy. The discontinuities due to absorption edges observed divide the energy range into several segments, where the parameters p 1 and p 2 must be determined. X-mudat database provides information about absorption edges of iodine (Table 6.2). The absorption edges define specific energy intervals of power law energy dependence. Table 6.2: Absrorption edges of iodine Absorption edge Energy(keV) K L L L M Figure 6.7: Photoelectric linear attenuation coefficient with energy in the range 1-140keV. The discontinuities due to absorption edges are prominent (graph of 71 points). 155

156 Since typical CT spectra are not rich in photons of energy levels below 30 kev, in fig. 6.8 the fitting functions for energy dependence of the photoelectric linear attenuation coefficient for photons above this energy level are presented. The values of the power law exponents are calculated to be approximately a) b) Figures 6.8: Photoelectric linear attenuation coefficient of iodine in the energy range kev. Power law of exponent around 2.6 described the energy dependence in both energy intervals. It is known that the x-rays attenuation of high atomic number materials is highly related to photoelectric effect interactions. In figures 6.10 it becomes clear that, for iodine and materials of similar atomic number the contribution of photoelectric effect to total attenuation is not just important but dominant. Linear attenuation coefficient of Compton effect for iodine is presented in figure 6.9 and it is characterised by very different energy dependence than that of photoelectric effect attenuation (its value is practically stable in the radiological energy range of interest). On the other hand, total attenuation coefficient of iodine is characterised by power law energy dependence of similar exponent as for the photoelectric attenuation coefficient, throughout the whole energy range of interest (figures 6.10). Therefore, the fact that with increasing energy, rapid reduction of total attenuation coefficient occurs even for high energy photons, explains the strong dual energy behaviour of iodine. This is due to the simple observation, that, since attenuation keeps decreasing in a strong power law manner as energy increases in the whole energy range, the attenuation for high kvp spectra that contain a large amount of high energy photons will be lower than it would be if there was a plateau in the energy dependence of high energy photons attenuation (as it is for lower atomic number materials). Therefore, the difference of attenuation between low and high kvp spectra is expected to be increased. This is a fact that leads to the assumption that iodine is an appropriate dual energy imaging candidate material. The steep reduction of 156

157 attenuation with increasing energy, even for high energy (radiological) photons, as well as the k-edge of iodine at the relatively low energy level of 33.2 kev, are responsible for the dual energy behaviour of iodine. Figure 6.9: Compton linear attenuation coefficient in the energy range kev Figure 6.10: Total linear attenuation coefficient of iodine in the energy range kev and fitting functions 157

158 Materials of similar atomic number as iodine, for instance tin (Z effective =50, density 7.31gr/cm 3 ) have similar k-edges and generally similar energy dependence of total attenuation coefficient (power law of similar exponents). As a result, dual energy discrimination between iodine and tin (and generally between materials of similar atomic number) does not seem feasible. However, spectroscopic CT using a conventional X-ray tube and a photon-counting detector distinguishes contrast agents with K-edges only 4 kev apart. This opens the way for multi-contrast medium imaging. For instance, traditional triphasic imaging with iodinated contrast material could be replaced with a single acquisition after injecting iodinated contrast material and gadolinium contrast material at different times before the acquisition. Using the energy-discriminating acquisition, a virtual non-contrast image could be generated in the same way as is done with dual-energy imaging currently [38]. Figure 6.11: Total linear attenuation coefficient of tin in the energy range 1-140keV Materials of total attenuation coefficient energy dependence very similar to photoelectric a can be considered all substances of effective atomic number value larger than HIGH ATOMIC NUMBER LEADS TO SIGNIFICANT DUAL ENERGY BEHAVIOR: UP TO WHAT POINT? It was explained in the previous that high atomic number is related to important contribution of photoelectric attenuation and that this is indicative of significant dual energy behavior, because of the existence of absorption edges and the rapid reduction of attenuation coefficient as photon energy increases. It is important though, that k-edges appear at higher energy levels for higher atomic number materials and therefore may contribute to the attenuation of high kvp spectra. Lead (Pb, Z eff =82, ρ=11.4 gr/cm 3 ) is a good example. The absorption edges of lead are presented in table 6.3 and the total linear attenuation coefficient of lead is presented in figure

159 Table 6.3: Absorption edges of Lead Absorption edge Energy K L L L M M M M M Figures 6.12: Linear attenuation coefficient of lead in the energy range kev. The presence of the k-edge of lead at around 88 kev increases attenuation of high energy photons (and consequently of high kvp spectra) and therefore may lead to reduced dual energy behaviour. Therefore, it is true that high Z effective materials attenuate low kvp spectra more than they attenuate high kvp spectra, but if the effective atomic number is too high, then high energy k-edges may limit this behavior. Therefore, it may be concluded that iodine is expected to have more vivid dual energy behaviour than lead. Iodine is an ideal contrast agent for dual energy imaging because of its low k-edge energy level. Also Barium (Z=56), Gadolinium (Z=64) and Xenon (Z=54) are appropriate dual energy CT contrast agents. Gadolinium may be an even better dual energy CT contrast agent than iodine, because its k-edge is at 50.2 kev. The adequacy of photons at this energy level is even more sufficient than it is for the energy level of 33.2 kev, due to beam hardening effects that 159

160 remove lower energy photons from the beam. Therefore, it is an interesting field of research to investigate whether the use of gadolinium can replace iodine contrast agents in some dual energy CT applications. Lead is as an example of very high atomic number material but it does not have significant biological effects. While lead serves no function in our bodies, it is usually found in the body in some amount since it is so common in the environment. Low levels in adults are not thought to be harmful, but in infants and children, low levels of lead can lead to toxicity that may cause deficits in intellectual or cognitive development. It has not been reported as a material of dual energy CT interest for medical applications IRON AND CALCIUM: DOES THEIR DUALENERGY BEHAVIOR DIFFER FROM THAT OF IODINE? Iron is a metal with atomic number 26, density 7.87 g/cm -3 and one k-edge at kev. Iron is neccessary for a number of highly complex processes that continuously take place on a molecular level. Iron is required for the production of red blood cells (a process known as haematopoiesis) but it's also part of haemoglobin (that is the pigment of the red blood cells) binding to the oxygen and thus facilitating its transport from the lungs via the arteries to all cells throughout the body. It is also involved in the conversion of blood sugar to energy. Iron deficiency and iron overload (Hemochromatosis) may be the cause for significant malfunctioning of the human organism. In the following photoelectric, Compton and total linear attenuation coefficient of iron for energies in the radiological energy range are examined. a) b) 160

161 c) Figures 6.13: a)photoelectric b)compton and c) total linear attenuation coefficient of iron in the energy range 1-140keV. Total attenuation coefficient energy dependence reveals the dominance of photoelectric effect in most energies in the radiological energy range, but not in the whole range. For higher energies the power law is superseded by an exponential decay law. More specifically, the energy range kev for iron, the behaviour is described by the fitting functions in the following graphs (figures 6.14). The fact that there is no k-edge in the energy range of typical CT spectra and the (smoother than power law) exponential decay at high energies indicate that iron is expected to dual energy behavior weaker than that of iodine. As a result, iodine and iron may be discriminated by dual energy methods. Iron discrimination may have a good potential in clinical dual energy CT imaging.for instance, an application of Dual Energy CT of the heart is the quantification of iron in thalassemia patients. Also, in liver imaging, iron overload may be quantified through DECT examinations although not all studies have shown promising results. Figures 6.14: Iron total linear attenuation coefficient in the energy range kev. 161

162 Calcium is another element of importance in dual energy CT imaging. Calcium is an element of atomic number 20 and density ρ=1.55g/cm -3 and it has a k-edge at With the introduction of DECT, it is possible to reliably differentiate calcium from contrast media and thus evaluate calcifications for neuroradiological or myocardial applications as well as identify calcium based kidney stones. In the following graphs (figures 6.15), the linear attenuation coefficient of calcium in the energy range 1-140keV is presented (in the total energy range as well as the fitting functions for photons of energy larger than 4.06 kev). For energies up to around 50 kev power law dependence indicates strong photoelectric effect, while for higher energies exponential decay follows. a b c d Figures 6.15: Calcium total linear attenuation coefficient in the energy range kev and fittin functions in the energy range keV. From the graphs above it is expected that calcium will have an even weaker dual energy behavior in comparison to iron and as a consequence in comparison to iodine too. Therefore, iodine-calcium discrimination is feasible. Iron-calcium discrimination with 162

163 material decomposition and material labeling analysis seems more difficult but it may be feasible with adequate filtration for spectral separation. Power law rapid reductions of attenuation coefficient with increasing energy seems to be valid up to around 50 kev. For energies more than 55 kev up to 140 kev, first a steeper and then a smoother exponential decay describe the energy dependence of attenuation for calcium. There are no k-edges in the typical energy range of photons in CT spectra SOFT TISSUE AND OTHER MATERIALS OF LOW EFFECTIVE ATOMIC NUMBER AND DENSITY Soft tissue is characterized by a low effective atomic number that is equal to 7.35 and a low density (1.06gr/cm -3 ). In the following table, the composition of soft tissue is presented. Table 6.4: Chemical composition of soft tissue Component(Z) Weight fraction Hydrogen (1) Carbon (6) Nitrogen (7) Oxygen (8) Sodium (11) Phosforus (15) Sulfur (16) Clorine (17) Potassium (19) Figure 6.16: Total linear attenuation coefficient of soft tissue in the energy range kev 163

164 a b c Figures 6.17: Total linear attenuation coefficient of soft tissue in 3 energy intervals in the energy range 1-140keV with fitting functions. The energy dependence of soft tissue total attenuation coefficient is much different than that of iodine, calcium and iron. By observing the 6.17 graphs, it becomes clear that photoelectric effect energy region of dominance is very restricted. Power law of exponent similar to that of photoelectric effect energy dependence is observed only for energies up to around 25 kev. Above this energy level, exponential decay and for even higher energies power law of low p 2 value describe the energy dependence of attenuation with adequate accuracy. Especially the low p 2 value of the power law energy dependence for energies kev seems to be indicative of Compton effect dominance in this energy region.the region of low p 2 value power law can also be accurately fitted by a exponential decay of high decay constant value. The aforementioned behavior of soft tissue attenuation with energy explains its very weak dual energy behavior. For photons of typical x-ray beams energy dependence is 164

165 not strong enough to produce differences in attenuation between low and high kvp spectra. Moreover, information about material effective atomic number is hidden only in the attenuation of low energy photons, where photoelectric effect is of importance. There are various other materials of similar behavior that may be of interest in dual energy CT imaging. For instance, the chemical composition of brain (gray and white matte) and polycarbonate (tables 6.5 and 6.6 respectively) and their linear attenuation coefficient in the energy range kev are presented in the following. Moreover, in appendix there is a table providing information about the chemical composition of various (biological or not) low effective atomic number materials (polystyrene, nylon, polyethylene, breast tissue, blood, adipose tissue). The energy dependence of attenuation of all these materials follows the same pattern as the one described for soft tissue. Such materials are not good candidates for dual energy discrimination. Polycarbonate is a versatile, tough plastic used for a variety of applications. It is composed of hydrogen, carbon and oxygen. The fraction by weight of each element in the compound is presented in the following table. Table 6.5: Chemical composition of polycarbonate Element Weight fraction Hydrogen Carbon Oxygen Polycarbonate is a rather light material with effective atomic number 6.33 and density 1.2 gr/cm

166 Figure 6.18: Polycarbonate linear attenuation coefficient and fitting functions in the energy range 1-140keV. Grey and white matter in brain have the following chemical composition. Table 6.6: Chemical composition of grey and white matter of brain Element(Z) Weight fraction Hydrogen (1) Carbon (6) Nitrogen (7) Oxygen (8) Sodium (11) Phosphorus (15) Sulfur(16) Chlorine(17) Potassium(19) Therefore grey and white matter of brain are rich in oxygen like soft tissue. The effective atomic number of brain is 7.65 and its density is 1.04 gr/cm

167 Figures 6.19: Fitting function of the linear attenuation coefficient of brain in the energy range kev BONE: HIGH DENSITY VALUE LEADS TO INCREASED ATTENUATION Bone (compact) is characterized by effective atomic number Z eff = and density ρ=1.85g/cm -3. Its chemical composition is described in the following table (table 6.8). Table 6.7: Chemical composition of compact bone Component(Z) Weight fraction Hydrogen(1) Carbon(6) Nitrogen(7) Oxygen(8) Magnesium(12) Phosforus(15) 0.07 Sulfur(16) Calcium(20)

168 Therefore, the chemical composition of bone reveals that it is made up mostly of oxygen, carbon and calcium. The effective number value of bone is much smaller than that of iodine, yet bone is a very highly attenuating material in CT examinations due to its density. Bone removal has made the interpretation of CT examinations an easier task, especially in neuroradiological applications. Figure 6.20: Total linear attenuation coefficient of bone in the energy range kev Figures 6.21: Fitting functions of the energy dependence for bone attenuation in the energy range kev 168

169 The energy dependence of attenuation of bone lies somewhere between iodine (high Z materials) and soft tissue (low Z materials). The power law energy dependence region is more extended than that of low Z materials and is followed by exponential decay. Exponential decay is characterized by a low value of decay constant (t 1 ) for medium photon energy values and an increased value of decay constant for higher energies. This means that decay of attenuation with energy becomes weaker as energy increases. This behavior is valid for materials of similar atomic number like magnesium (12) and phosphorus (15). Attenuation of iodine and bone have quite different energy dependence and therefore their dual energy behavior allows them to be discriminated by utilizing two well separated spectra, since the exponential decay of attenuation at higher energies gives bone a dual energy behavior that is less strong than that of iodine. In the following figures (fig. 6.22) the relative relationship of mass attenuation coefficient for photoelectric and Compton effect is depicted for materials of the aforementioned 4 categories.it is observed that as effective atomic number increases,the region of dominance of photoelectric effect increases, as expected (whole energy range kev-graphs produced by x-mudat). Fig. 6.22: Photoelectric and Compton effect dominance regions for different Z effective materials 169

170 6.4 ABSORPTION EDGES AND THEIR EFFECT ON ATTENUATION From the previous analysis it is observed that the increase of attenuation due to absporption edges is not a local phenomenon that affects the attenuation at the specific energy level or of the very neighboring energy levels. Absorption edges affect the attenuation throughout an important energy range and generally their existence is a factor that makes high Z materials important attenuators. The absorption edge at 33.2 kev for iodine in fig increases the values of mass attenuation coefficients for higher energies too. For lead on the other hand, its k-dge at 88 kev increases the attenuation only for very high energy levels in the diagnostic energy range and therefore it is expected to significantly affect the attenuation of a high kvp spectrum. Figure 6.23: Iodine and Lead mass attenuation coefficients in the energy range kev In the previous, it was considered Z effective as the important quantity that defines the dual energy behavior of a material. Another important factor is the energy level of the observed k- edges of the constituent materials. Therefore, not only the Z effective of the material is important, but also the exact chemical composition of the substance is very significant. The first generally defines the photoelectric effect dominance region, the second, defines the peaks of attenuation. 170

171 Fig. 6.24: Iodine solution of relative weight iodine: Compton effect dominance region is interrupted by the iodine k-edge. Let us now consider the three different iodine solutions: Relative weight of iodine 0.004: Z effective =11, ρ=1gr/cm 3 Relative weight of iodine 0.05: Z effective =20.99, ρ=1,04gr/cm 3 Relative weight of iodine 0.5: Z effective =41.64, ρ=1,66gr/cm 3 Figure 6.25: Three different iodine solutions in water. They all exhibit the k-edge of iodine at 33.2 kev and have strong dual energy behavior. The above iodine solutions all exhibit the characteristic k-edge, therefore their attenuation is not only defined by the value of effective atomic number, but also by the exact chemical composition (presence of iodine). 171

172 Figure 6.26: Scandium has atomic number 21 and the iodine solution has effective atomic number The regions of photoelectric effect dominance are similar, but the k-edge of the solution is expected to be responsible for stronger dual energy behavior. 6.5 ENERGY DEPENDENCE OF CT NUMBER VALUES CT number by definition is a measure of material attenuation of x-rays compared to water, since its value depends on the ratio µ material / µ water. Therefore, it is expected that materials with linear attenuation coefficient that is characterized by similar energy dependence as water (like soft tissue, adipose tissue e.t.c.) will have a relatively constant CT number for different energy levels, while materials that their attenuation energy dependence is different will exhibit a significant change in CT mumber. Attenuation of all materials decrease as energy increases with exception of the absorption edges in the radiological energy range. This is not what we perceive in CT examinations though, because what is calculated is the attenuation of materials relative to the attenuation of water. In a recent technical note by Bryant, Drage and Richmond [102] which has been available on line since January 2012, graphs of CT number over the energy range 10keV to 100 kev are presented. These curves illustrate the CT number that would be obtained with monoenergetic beams at given energy levels. The curves are compared to graphs we produced by using the same NIST database, along with comments about the general behaviour of the materials of interest and potential implementations to dual energy CT practice. The curves in the following figure (Fig. 6.27) show a wide range of substances separated into three groups with different scales to preserve the detail. Over the range 10 kev 100 kev, the CT curves in group (a) comprising blood, lung, brain and muscle vary by 55 HU, 40 HU,

173 HU and 24 HU, respectively, while in group (b) breast and adipose tissue vary by nearly 150 HU and 350 HU, respectively, and finally in group (c) bone extends over about 8000 HU. Figure 6.27: Variation of the CT number with energy for some common biological substances: (a) CT number for blood, lung, brain and muscle versus photon energy, (b) CT number for adipose tissue and breast versus photon energy and (c) CT number for bone versus photon energy [39]. Adipose tissue, breast tissue, nylon, polystyrene, polyethylene, polycarbonate are all materials of effective atomic number up to approximately 7. For all of these materials, the shape of the curve describing the energy dependence of their (theoretical-monoenergetic) CT number is approximately the same. We derived curves describing this dependence and present 173

174 them in figure 6.28, for the energy range 1-140keV. The graphs are in good agreement with those of the technical note (see Figure 6.27 b). Figure 6.28: HU of adipose tissue, breast tissue, polystyrene, nylon, polyethylene, polycarbonate with energy in the energy range 1-140keV. On the other hand, brain, blood, soft tissue, ovary, lung tissue are also considered light materials (with effective atomic numbers above 7.5 and below 8) and the variation of their linear attenuation coefficient with energy is also small, but they belong to a category of materials that is characterized by the following behavior: Figure 6.29: HU of brain, soft tissue, ovary, lung and blood with energy in the energy range kev. The previous graph is in good agreement with Figure 6.27(a) from the technical note of Bryant, Drage and Richmond [102]. 174

175 From the previous graphs it becomes obvious that, although all the materials presented have very similar behavior as far as their energy dependence of their attenuation coefficient is concerned, their CT number energy dependence divides them into two groups. This is because CT number values express the attenuation of materials relative to the attenuation of water. We observe that for low energy photons where photoelectric effect is more prominent, even materials of the same group (as depicted in figures 6.28 and 6.29) have quite different CT number values. For higher energy photons though, where photoelectric effect (and as a consequence dependence from atomic number) is weaker, convergence of CT number values is observed. For instance, let us observe polycarbonate and breast tissue in figure At low energies, breast tissue has higher CT number values because its effective atomic number value is also higher (photoelectric effect dominant) than that of polycarbonate, while for higher energies polycarbonate has higher CT number values than breast tissue because of its slightly higher density (Compton effect dominant). Also blood at low energies has higher CT number values than the other materials of its group because it has the highest Z effective in the group and may be better distinguished from soft tissue or brain tissue at low energy windows. In clinical practice, it is sometimes necessary (and difficult) to clearly distinguish the plaques from the surrounding soft tissue especially for fatty plaques in the walls of coronary arteries and the adjacent epicardial fat. One of the main reasons for these shortcomings of CT is the modest contrast resolution of the modality and the relatively small attenuation differences that hinder a proper assessment, differentiation, and characterization of these various structures sharing overlapping attenuation values.theoretically, fat is easily discriminated from soft tissue even by single energy CT because of its lower CT number, but sometimes this discrimination may be hindered by the special anatomical conditions,when it may be difficult for the radiologist to perceive changes in the attenuation that are attributed to presence of adipose tissue. In such cases, some kind of discrimination followed by color coding could make the interpretation of the images an easier task. Since adipose tissue attenuation at all energies,but especially in the range 20-80keV approximately, exhibits an icreasing trend, while soft tissue attenuation is characterized by a decreasing trend after 25 kev, that could be the basis of a discrimination potential. However,x-ray spectra are usually poor in low energy photons, because such photons increase dose and do not contribute to diagnosis. Moreover, if the ROI is too small or the same voxel contains both adipose and soft tissue, exact discrimination efficiency would be expected to be poor. 175

176 The characteristic decrease in attenuation as voltage is decreased for lipid-containing tissues has been used in characterization of adrenal nodules. Also, sometimes fat distribution in the liver may cause diagnostic confusion by mimicking neoplastic masses. A difference greater than 10 HU between 140 and 80 kvp is unique to fatty infiltration [88]. The results of such studies may lead in discrimination of fat in patients with fatty liver and without iron overload. The technology of multi-bin photon counting detectors for multi-energy imaging may produce images corresponding to narrow energy bands. For instance if two images, one in an energy window kev and one at kev were obtained, a slight decrease or a slight increase of attenuation in the second image could be indicative of adipose tissue presence if CT number measurements are accurate enough. An important quantity concerning the evaluation of an image is the contrast to noise ratio value in the ROIs. Image contrast, that is, the difference between in the signal of ROI and the signal of the background, is expected to be better for specific energy intervals where the CT number difference between ROI and background is larger and therefore ROI materials may be more visible in such images. CNR is generally better for photon counting detectors as already discussed. For instance, in figure 6.30 it is seen that by choosing a low energy window contrast between soft tissue and adipose is expected to be increased. Figure 6.30: Adipose and soft tissue. Contrast between soft tissue and adipose is better for lower energy windows. More investigation for the CT number attenuation curves for clinically interesting materials that can t be discriminated in conventional CT imaging needs to be done, along with research on the promising potential of multi-energy CT imaging with photon counting detectors that may produce adequate signal even at low energy level intervals. 176

177 Dual energy spectral HU curves and monochromatic images are provided by the GSI Viewer of the GE Discovery CT750HD fast kvp switching dual energy imaging modality.an example of tissue discrimination is illustrated in the following figure [38]. This is an alternative way of illustrating and perceiving the material discrimination results, apart from color highlighting in the image. Figure 6.31: Use of spectral attenuation curve to determine simple and hemorrhagic renal cyst. A. Virtual monochromatic image synthesized from fast-kilovoltage-switching dual-energy CT. Arrows pointto hyperattenuating left renal lesion (green), hypoattenuating right renal lesion (light blue), gallbladder fluid(dark blue), and renal parenchymal enhanced by iodinated contrast material (red). Left renal lesion (green) is indeterminate and could be either enhancing mass or hyperdense cyst. B. Spectral attenuation curves measured from virtual monochromatic image for left renal lesion (green), right renal lesion (light blue), gallbladder bile (dark blue), and renal parenchyma (red) at various photon energies (kiloelectron volt, kev). Attenuation curves of both renal lesions are similar to that of gallbladder fluid, which remains relatively flat, indicating nonenhancing tissues. In contrast, attenuation curve of renal parenchyma shows sharp increase at low energies, which is characteristic of iodine-containing materials. Therefore, spectral attenuation curves obtained from virtual monochromatic images helped to determine that left hyperattenuating renal lesion is hemorrhagic or proteinaceous cyst. In the following figures, HU values versus energy for bone, iodine, calcium and iron are presented. CT numbers cannot be highetr than 3071 for the available CT scanners, so what is really presented in the graphs is 1000(µ µ w )/µ w. 177

178 Figure 6.32: The CT number of bone with energy in the energy range 1-140keV Figure 6.33: The CT number of iodine with energy in the energy range 1-140keV Figure 6.34: The CT number of calcium with energy in the energy range 1-140keV 178

179 Figure 6.35: The CT number of iron with energy in the energy range 1-140keV Iodine but also calcium and iron attenuate significantly and exhibit significant change in CT number as energy increases. In the energy range keV, the difference between the maximum and minimum HU value is for iodine, for iron, for calcium and for compact bone. It is noticeable that at low photon energies (for instance for iodine up to 18 kev approximately) there is an increase of CT number value with increasing energy. This indicates that water attenuation coefficient decreases more rapidly than attenuation coefficient of iodine in this energy region. This is also a finding from the previous analysis concerning the appropriate fitting functions for the energy dependence of attenuation coefficients and may be related to the presence of absorption edges at low energy levels for iodine. However, typical CT spectra are very poor in very low energy photons, therefore they are not of significant radiological interest. Absorption edge of iodine is observed in graph The same absorption edges are also observed in CT number versus photon energy graphs of materials solutions (for instance, in iodine in blood). Of course, the higher the concentration of a material in the solution, the more prominent its absorption edges in the graphs. Therefore, again images from multi-bin photon counting detectors can be useful in material discrimination. Supposedly we have an unknown solution of relatively high CT number that could either be a solution of iodine or a solution of calcium. Supposedly we have an image for a very narrow energy bin, for instance to energies kev and one bin for kev. Then, if the CT number of the image increases in this second image, the solution is a solution of iodine. The disadvantage of dual energy CT, that it cannot distinguish between materials of very similar attenuation curves, may be overcome this way because each material has its own attenuation signature, 179

180 that is, its absorption edges that can be identified. Moreover, CNR values for images corresponding to energy bins in the vicinity of absorption edges are expected to be increased. In the following table, we present the variation of CT number in the energy range kev for some of the materials examined in the previous in comparison to the corresponding results from [102]. The symbol (-) means not calculated in particular study. Table 6.8: Variations of theoretical CT numbers Material Bryant et al[102] Our study Variations in HU(10-100keV) Variations in HU(10-105keV) brain Soft tissue - 26 blood Cortical bone Compact bone Adipose tissue breast polycarbonate polyethylene polystyrene Muscle 24 - lung nylon ovary - 26 Therefore, materials like brain, blood, ovary, soft tissue and lung (figure 6.22) have the smallest variations of CT number within the energy range 1-100keV. Those are materials that, as far as their Z effective and their density are concerned are very close to water and as a logical consequence, CT number (as a measure of material attenuation coefficient that is normalised to water attenuation coefficient) does not exhibit great variations with energy. The attenuation coefficient for any material can be constructed linearly from its chemical formula by weight and the individual data for each of the composing elements. The data for 180

181 all 92 elements and many materials over a wide energy range can be obtained by NIST. Those theoretically generated data sets have been used by Bryant et al as well as by us in the previous analysis. Therefore, as expected, the x-ray attenuation characteristics of materials with many components are just a weighted linear combination of the characteristics of its components. 6.6 DUAL ENERGY RATIO Let us assume a three material decomposition algorithm with volume conservation and a mixture of basis materials 1 and 2 (for instance a solution of iodine (material 2) in water (material 1). Then µ Low mixture / µ High mixture is not the same for all mixtures. It can be shown that the ratio µ µ Low mixture µ µ High mixture material1low material1high is the same for all solutions, independent their concentration of solute (a three material decomposition algorithm with volume conservation is considered). Assuming volume conservation for the mixture of two materials: µ = α µ + α µ mixturel 1 1L 2 2L µ = α µ + α µ mixtureh 1 1H 2 2H µ µ α µ + ( α 1) µ α µ α µ µ µ = = = µ µ α µ + ( α 1) µ α µ α µ µ µ mixturel 2L 1 1L 2 2L 1 1L 1 2L 1L 2L mixtureh 2H 1 1H 2 2H 1 1H 1 2H 1H 2H (6.1) Figure 6.36: Linear attenuation coefficient of materials at two energies (or kvp values). In a three material decomposition algorithm mixtures of two basis materials are located on the lines that connect the two materials. Likewise for CT number values: 181

182 Figure 6.37: Three materials in the Energy map HU = α HU + α HU 1+ 2= 1 mixturel 1 mat1l 2 mat 2L HU = α HU + α HU mixtureh 1 mat1h 2 mat 2H µ µ 1000 α + α 1000 HU HU = HU HU µ µ 1000 α + α 1000 HU α α = matl1 matl2 1 2 mat 2L mixturel HU µ mat 2L wl µ wl mixtureh mat 2H math1 math mat 2H µ wh µ wh µ matl1 µ matl2 µ matl2 1000α HU µ µ µ µ math1 µ math 2 µ math α HU µ wh µ wh µ wh 1 mat 2L wl wl wl HU mat1l HU mat 2L 1 mat 2H = HU HU mat1h mat 2H (6.2) The ratio derived in equation 6.2 is called dual energy ratio and is the basis of material discrimination in dual source CT. It will be calculated experimentally for iodine and calcium in the next chapter. The important property of this ratio is its independence of the density of the mixture. Also, given that there is a linear relationship as: HU mixture low = αhu mixture high + b (6.3) where α the dual energy ratio, we obtain the following HU = HU HU = HU α HU b= (1 α) HU b mixtureh mixturel mixtureh mixtureh mixtureh α1µ 1H + α2µ 2H µ wh α 1µ 1H + (1 α 1) µ 2H µ wh = 1000( 1 α) b= 1000(1 α) b µ µ wh Hence, it depends on the constituent materials chemical composition and on the concentration of each materials in the solution. Plotting ΗU versus α 1 gives a linear relationship characteristic of the basis materials. wh (6.4) 182

183 6.7 CONCLUSIONS OF CHAPTER 6 In this chapter, the strong energy and Z effective dependence of photoelectric effect attenuation coefficient was highlighted. In fact, the exponent of the Z effective dependence was found to be of increased value for low Z effective materials. The electron density (electrons per unit volume) of a material is defined primarily by its mass density value. Compton scattering linear attenuation coefficient is therefore mostly determined by the mass density of the material (pure element or mixture). The dual energy ρ-ζ methods (like the one of Alvarez-Macovski) have the limitation that k-edges are not taken into account. It is evident from the previous analysis that materials (elements of biological significance or not, as well as tissue-like materials) could be categorized into 4 groups, in order to best describe the energy dependence of their attenuation coefficient. The groups would refer to the effective atomic number value of the materials: high, low, middle low and middle high (materials of the same category should have similar k-edges). The first group (of high Z effective materials-approximately above effective atomic number value) constitutes of materials (e.g. iodine) exhibiting energy dependence of the total attenuation coefficient, very close to that of the photoelectric attenuation coefficient in the whole energy range (1-140 kev). The energy dependence of total attenuation coefficient is described by power law in energy regions defined by absorption edges. The power law exponents range from approximately for iodine). Those are materials that generally have strong dual energy behavior (they attenuate significantly more at low kvp spectra than at high kvp spectra due to the dominant contribution of photoelectric effect and the absorption edges) and are ideal for dual energy CT applications, with the only exception of materials having k-edges at very high energy levels. The second group (of low Z effective value materials, approximately up to 11), constitutes of materials (e.g. soft tissue) whose total attenuation coefficient in the range kev may be described by the following pattern: 1. Power law of high p 2 exponent ( ) for low energies (up to approximately 20keV) 2. Exponential decay (quite rapid) for energies up to approximately kev 3. Power law with low p 2 exponent or slow exponential decay for higher energies Therefore, photoelectric attenuation seems to have a rather weak contribution to the total attenuation coefficient for energies more than kev and as a result, the energy 183

184 dependence of attenuation in the radiological energy range is weak too. Those are materials of weak dual energy behavior. The third group of middle low Z effective (approx.12-17), e.g. bone, magnesium, phosphorus) constitutes of materials that follow the pattern for the energy dependence of their total linear attenuation coefficient: 1. Power law with high p 2 exponent extending to even higher photon energies (up to approximately 35 kev for bone) than in the case of the second group of materials and 2. Regions of exponential decay in the rest of the energy range (for high photon energy values - more than approximately 85 kev- exponential decay is slow and for medium energy values it is more rapid). They differ from the second group in the fact that photoelectric effect contributes more significantly to total attenuation for medium values of photon energies. Moreover, their density values are high enough to sometimes pose the problem of discrimination from high atomic number contrast agents in conventional CT imaging (e.g. iodine solutions with bone). The absorption edges of elements in this group are generally not at energy levels that correspond to usual CT spectra photons, thus their dual energy behavior is limited mainly due to this reason, in comparison with materials that have absorption edges in the radiological range. This is true also for bone, therefore it becomes obvious why for instance bone and iodine solutions can be discriminated by dual energy methods. The fourth group middle high Z effective values (approximately 18-45), e.g. iron and calcium) constitutes of materials that have total attenuation coefficients with energy dependence closer to that of the high Z materials (first group), with the difference that for high energy photons, exponential decay appears, generally rendering their dual energy behavior less strong than the dual energy behavior of the first group. Materials like calcium and iron have a potential of dual energy discrimination from, for instance, iodine, mainly because their absorption edges are not in the radiological energy range of CT. Solutions of two materials in dual source three material decomposition CT are described by their dual energy ratio that is characteristic of the components of the mixture and independent of the density value. Although the energy dependence of linear attenuation coefficient is similar between low Z effective materials (second group-tissue and tissue-like materials), their CT number energy dependence divides them into two groups (In current study the groups were determined as 184

185 materials of Z effective < 7.5 and 7.5 < Z effective <8). For instance, adipose tissue is expected to have slighltly increasing CT number values with increasing photon energy, but the opposite is valid for soft tissue. This could be the basis of discrimination, especially if specific energy windows of multi-bin detectors are used for multi-energy imaging. Multi-energy imaging may offer a new potential to k-edge imaging as well. 185

186 CHAPTER 7 EXPERIMENTAL EVALUATION OF IODINE CALCIUM AND TISSUE LIKE MATERIALS DUAL ENERGY BEHAVIOUR 7.1. AIM OF THE EXPERIMENT Material specific dual energy behaviour has been an issue of interest in various phantom experimental studies. The experiment focused on the dual energy behaviour of iodine and calcium, elements of high interest in computed tomography. The experiment was performed in two phases: first in May 2012 (iodine experiment) and second in November 2012 (calcium experiment) by our team in Olympion hospital of Patras ( on Somatom Definition dual source CT scanner and has lead us to interesting conclusions.the aims of the experiment were the following: To estimate the changes of the X-rays attenuation for iodine (ioversol contrast agent) and calcium (calcium chloride dihydrate CaCl 2.H 2 O) solutions in 0.9% sodium chloride solution and other selected, tissue equivalent materials at 4 different kvp values (80, 100, 120, 140). To evaluate attenuation similarities between the dual energy virtual 120 kvp image (the image constructed by linear combination of images acquired from 80 and 140 kvp datasets of dual energy scanning) with the real conventional 120 kvp image. To estimate the iodine and calcium solutions vector in the Energy map (HU 140kVp-HU 80kVp space). To evaluate the results of syngo dual energy applications on the phantom. The structure and utility of Dual Energy CT Phantom, Gammex 472 (figure 7.1.) has been the prompt for the experiment. The Gammex Dual Energy CT Phantom provides users with the ability to perform Quality Assurance for Dual Energy CT analysis of Iodine and Calcium. The Phantom consists of a Solid Water disk approximately the size of an average pelvis. A matrix of 16 holes in the disk hold interchangeable rods made of materials containing 7 different concentrations each of iodine and calcium. The rods can be positioned as the 186

187 user chooses. Scanning the phantom on a periodic basis provides data useful for the QA program related to the detectability range of the Dual Energy CT scanner. Figure 7.1: Dual Energy CT Phantom, Gammex 472 and calcium and Iodine rods of various concentrations For dual energy Gammex phantom, the concentrations of the rods are the following. Table 7.1: Rod content of Dual Energy CT Phantom Rod content(mg/ml) Iodine Calcium

188 7.2 IODINE AND TISSUE-LIKE MATERIALS EXPERIMENT MATERIALS AND METHODS In the following experiment, we used the Mini CT QC Phantom used in hospital for CT quality control. It consists of a PMMA disc of a diameter of 15.25cm and thickness of 2.54 cm on a Lucite bar. In the holes, inserts of the following materials were arranged in a manner depicted in figure 7.1. Polyethylene (C 2 H 4 ) (Z eff = 5.53, ρ= 0.93 g/cm 3 ) Bone equivalent (Compact) (Ζ eff = 12.31, ρ = 1.85 g/cm 3 ) Polycarbonate (C 16 H 14 O 3 ) (Z eff = 6.33, ρ = 1.20 g/cm 3 ) Nylon (C 6 H 11 NO) (Z eff = 6.21, ρ = 1.14 g/cm 3 ) Plastic Water (Z eff = 7.51, ρ = 1.00 g/cm 3 ) Polystyrene (C 8 H 8 ) (Z eff = 5.74, ρ = 1.06 g/cm 3 ) Ioversol contrast agent solutions in water The different solutions of ioversol (iodine contrast material agent for CT examinations) in 0.9% Sodium Chloride solution(saline) covered a wide range of iodine concentrations (in mg/ml : 1.25, 2.5, 3.5, 5,7,10, 12.5, 14, 17, 25, 35, 50). The solutions were sealed in syringes of 2.5 ml volume each. The experiment required three separate arrangements of the syringes because the phantom did not provide sufficient apertures for all the ioversol solutions to be scanned at once. The material inserts and the syringes were placed as shown in figure 7.2 (the three different concentrations separated by / refer to the three contiguous parts of the experiment: part C1, part C2 and part C3). The scans where performed with single energy protocol at 80, 100, 120 and 140 kvp as well as with dual energy protocol for all C1, C2 and C3 parts of the experiment. Dual energy reconstruction produced linearly weighted (virtual 120kVp) images, constructed pixel by pixel by 30% of the 80kVp image HU value and 70% of the 140kVp image HU value. Single and dual energy scanning and reconstruction protocol parameters were identical for C1, C2 and C3 parts of the experiment and may be described as following: 188

189 Table 7.2: Single energy scanning and reconstruction protocol Voltage Convolution Slice thickness Protocol mas Pitch Increment (mm) (kvp) Kernel (mm) HeadRoutSpiral 200 H20s Table 7.3: Dual energy scanning and reconstruction protocol Voltage mas Protocol Convolution Kernel Pitch Increment (mm) Slice thickness(mm) Headangio D20f 0.55 Virtual 120kVp DE(0.3*80kVp +0.7*140kVp) Figure 7.2: Experimental arrangement. Iodine concentrations (mg/ml): Part 1 C1 (1.5, 2.5, 3.5, 5), Part 2 C2 (7, 12.5, 14, 17), Part 3 C3 (10, 25, 35, 50). 189

190 Measurements of CT number and standard deviation values (the latter as a measure of image noise) where performed by using the Image J ( tool on every selected image obtained. The criterion for the selection of images for measurements, was that they should be approximately central slices of the phantom, for more accurate measurements. ROIs were drawn manually (figure 7.3). Based on these data, image quality evaluation was attempted, based on contrast and CNR calculations. Figure 7.3: ROI selection and Image J measurements The size of the ROI for each measurement was around 25 pixels for iodine syringes and around 140 pixels for the rest of the materials. Since both our solutions and material inserts are considered homogeneous, the size of the ROI does not have a significant effect on the measurements RESULTS AND DISCUSSION MEASUREMENTS ON SINGLE AND DUAL ENERGY IMAGES In the following table, the CT number values of the materials in the inserts of the phantom are displayed. 190

191 Table 7.4: CT number & standard deviation of the materials in the rods (slice thickness 1mm-from C1 scan) Material HU 100 HU HU 140 HU DE Virtual HU 80 kvp 120kVp kvp 120 kvp kvp SE SE SE SE Air ± 5.45 ±4.19 ±3.9 ± 3.47 ±5.79 Polyethylene ± ± ± ± ±8.13 Polystyrene ± ± ± ± ±9.1 Plastic water ± ± ± ± ±7.63 Nylon ± ± ± ± ±9.23 Polycarbona te ± ± ± ± ±8.7 Background (PMMA) ±13.02 ±7,13 ±6.7 ±10.27 ±5.39 Bone ± ± ± ± ±

192 Figures 7.4: CT number at different kvp values for tha materials in the experiment. The DE Image is noted as 122 kvp because (0.3*80+0.7*140=122kVp). Table 7.5: CT number & standard deviation values of iodine solutions in the phantom (slice thickness 1 mm) 192

193 Figure 7.5: CT number of iodine solutions at different kvp values. The DE Image is noted as 122 kvp because (0.3*80+0.7*140=122kVp). The values displayed in the first table (table 7.5) are acquired from ROI measurements on the selected slices of the first part of the experiment (C1 part, but they were practically unchanged in the two following C2 and C3 parts). The slice thickness is 1mm for all measurements in the table. For plastic water in this case the noise measurement was higher than the absolute value of mean CT number measurement, which is statistically not acceptable and may be attributed to the fact that 80 kvp images are generally noisy. There are also cases where the mean CT number value shows the opposite difference than it theoretically should as kvp or concentration increases but those are differences that are always within standard deviation values range. For instance, the mean CT number value for 12.5 mg/ml iodine solutions is a bit higher than the CT number value for the 14 mg/ml iodine solution in the DE image. This difference is comparable to the noise level though. Also, for background the 120 kvp and the virtual 120 kvp image HU mean value is slightly larger than that of 140 kvp. However, those differences are also comparable to the standard deviations. 193

194 Images acquired by single and Dual energy protocols: Comments on attenuation characteristics and image noise All materials except bone and iodine solutions exhibit a small increase of CT number values while air and plastic water attenuation is characterized by stability as kvp values increase.polyethylene is represented by lower CT number values than polystyrene and both of them attenuate less than polycarbonate. Those findings are in agreement with the energy dependence of CT number presented in the graphs of chapter 6.6. As far virtual 120 kvp images are concerned, similar kvp values as for real 120 kvp images are obtained. Differences are within noise level in most cases, as far as the materials are concerned. As far CT number energy dependence for iodine solutions is concerned, some initial observations could be the following: Increased concentration leads to increased absolute values of mean CT number differences between various kvps. As kvp increases, the absolute values of CT number differences between different kvps decrease, probably because the energy range of spectral overlap is increased,less photons are in the vicinity of iodine k-edge and photoelectric effect is less important. The difference between the CT numbers of real and virtual 120 kvp images at lower concentrations is smaller than it is at higher concentrations. Especially for concentrations higher than 10 mg/ml the differences between HU real and virtual 120 kvp are not within the noise range (expect for the case of 14 mg/ml). In almost all cases the mean HU of virtual 120 kvp image has a higher value than that of real 120 kvp image (except at 3.5 mg/ml). The previous observations are depicted in Figures 7.6. The selected slices with the highest concentrations of iodine solutions from the single energy acquisition dataset (C3 acquisition-se protocol) are presented here. It is prominent that the signal of iodine solutions and bone becomes weaker as peak kilovoltage increases, while for all the other materials except plastic water and air the signal becomes slightly stronger as kvp increases. 194

195 a) b) c) d) Figures 7.6: a) 80 kvp, b) 100 kvp, c) 120 kvp, d) 140 kvp single energy protocol C3 acquisitions From the previous images, it becomes obvious that discrimination between bone and high concentration iodine solutions is not visually feasible, since especially for middle and high iodine concentrations the grey tones of iodine solution and bone look similar to the human eye. However, the attenuation dependence of iodine and bone is different and dual energy algorithms offer the possibility to utilize this difference. In an effort to identify the SE protocol that would offer best visual discrimination of iodine solutions and bone, the iodine-bone relative contrast is defined as a measure for visual discrimination of iodine solutions and bone in the image: CONTRAST HU HU sol. Iodine Bone Iodine Bone = (7.1) CTrange Then it becomes clear that iodine-bone discrimination is easier when iodine concentration is low, as it is expected. Increased kvp values lead to lower contrast between iodine and bone for concentrations mg/ml, while for concentrations 25 and 35 mg/ml this 195

196 relationship is inversed, but the increase is small as kvp increases. The lower the concentration the more rapid is the reduction of contrast as kvp value increases. Between high kvp values, the reduction or increase of contrast is smaller, for all concentrations. The concentration that is closer to bone as far as its mean CT number value is concerned, is 50 mg/ml for all kvp values except for 80 kvp where the corresponding concentration is 35 mg/ml. The highest relative contrast corresponds to 1.25 mg/ml. However for concentrations up to 17mg/ml CONTRASTIodine Bone has quite increased values. At 80 and 100 kvp a 50 mg/ml iodine solution has higher CT number values than bone, but at 120 kvp and 140 kvp it has lower CT number values than bone. For all other concentrations, iodine solutions have lower CT number values than bone. Iodine concentration (mg/ml) Table 7.6: Iodine-Bone relative Contrast values at different kvp values CONTRAST (iod-bone) 80 kvp CONTRAST (iod-bone) 100 kvp CONTRAST (iod-bone) 120 kvp CONTRAST (iod-bone) 140 kvp CONTRAST (iod-bone) DE 1,25 0,48 0,40 0,36 0,33 0,36 2,5 0,46 0,39 0,35 0,32 0,35 3,5 0,45 0,38 0,34 0,31 0,34 5 0,44 0,37 0,33 0,31 0,34 7 0,42 0,36 0,32 0,30 0, ,39 0,33 0,30 0,28 0,30 12,5 0,35 0,31 0,28 0,26 0, ,35 0,30 0,27 0,26 0, ,30 0,26 0,24 0,23 0, ,10 0,11 0,12 0,13 0, ,01 0,05 0,07 0,09 0, ,06 0,01 0,03 0,05 0,01 MIN 0,01 0,01 0,03 0,05 0,01 MAX 0,48 0,40 0,36 0,33 0,36 The values of CONTRASTIodine Bone for linearly weighted (0,3*80+0.7*140) dual energy images are of the same level as for 120 kvp in all cases and its minimum value for 50 mg/ml iodine concentration. Noise has been left out of the analysis which is generally a drawback since by changing the kvp values, the noise level is different too. 196

197 Figure 7.7: Contrast iodine-bone at different kvp values. The DE Image is noted as 122 kvp because (0.3*80+0.7*140=122kVp). SE and DE 80 kvp and 140 kvp images Image noise is reduced as peak kilovoltage values increase for single energy protocol As already mentioned HU dual = 0.3 HU HU 140 (7.2) The image noise in these dual energy images is expected to be described by the error propagation formula: σ = (0.3) σ + (0.7) σ = 0.09σ σ (7.3) dual The fact that noise differences between the 80 kvp and 140 kvp images of the dual energy protocol are much smaller than those obtained by the single energy protocol is confirmed in the following table (table 7.7). In table 7.7 the second column is the ratio of the DE 80 kvp image noise to the DE 140 kvp image noise. The maximum ratio is 2.18 and the minimum Also, it is not always the 80 kvp image that is gives higher noise values in the ROIs for the DE protocol. Relationship (7.3) is used for derivation of DE Std calculated in table 7.7 which are in good agreement with the values actually obtained from the images. Small differences may be attributed to statistical fluctuations of the measurements. It is therefore 197

198 highlighted that image noise on a weighted dual energy image exists due to error propagation resulting from postprocessing of the already reconstructed 80kVp and 140 kvp images of DE protocol. By minimizing the first part of equation 7.3 (derivative=0), someone can obtain the theoretically optimal weighting factors, given that σ 80 and σ 140 are known for the clinical issue of interest. In the following table (table 7.7) the ratio of the 80 kvp image noise to the 140 kvp image noise is presented, for all the materials in the inserts and all the iodine solutions scanned. All images are of 1mm slice thickness and are acquired by single and dual energy protocol scanning. Minimum ratio calculated is about 1.55 and maximum is about 5.79 for SE scanning (average 2.68) and for DE protocol minimum ratio is 0.8 and max ratio is 2.19 (average 1.21). Table 7.7: Std 80 kvp/std 140 kvp for all materials scanned with SE and DE protocol & error propagation Material DE Std calculated/ DE Std DE Std 80 kvp/ DE Std 140 kvp SE std 80 kvp/ SE std 140 kvp iodine 5 mg/ml 0,99 1,23 1,87 iodine 1.25 mg/ml 1,14 1,54 1,87 iodine 3.5 mg/ml 0,99 1,34 2,38 iodine 2.5 mg/ml 0,97 0,80 2,92 iodine 17 mg/ml 0,83 1,00 4,59 iodine 7 mg/ml 1,04 1,12 1,55 iodine 14 mg/ml 0,96 1,07 2,01 iodine 12.5 mg/ml 0,93 1,23 1,69 iodine 50 mg/ml 0,84 1,49 4,05 iodine 10 mg/ml 1,05 1,17 2,31 iodine 25 mg/ml 0,77 1,07 5,80 iodine 35 mg/ml 0,78 2,19 4,00 PlasticWater 1,29 0,80 2,36 Polysterene 0,94 0,92 1,91 Polyethylene 1,11 1,24 2,57 Bone 1,02 1,32 2,72 Polycarbonate 1,30 1,14 3,02 Nylon 1,03 1,27 1,99 Background 0,91 1,17 2,42 Air 0,86 1,15 1,57 AVERAGE 0,99 1,21 2,68 MIN 0,77 0,80 1,55 MAX 1,29 2,19 5,80 198

199 Dual energy weighted images are a linear combination of the CT number and the noise characteristics of 2 images, one acquired at 80 and one at 140 kvp. In order to obtain similar output of quanta from the two tubes (and therefore not very divergent noise characteristics on the corresponding images), it is important to adjust the tube current. Therefore, tube B functions at 80 kvp and 213 mas, while tube A functions at 140 kvp and 50 mas. Hence, those 80 kvp and 140kVp images are expected to be characterized by approximately the same mean HU values as the ones obtained by the single energy protocol, but the noise characteristics will be different. The 140 kvp image of the dual energy protocol will be noisier than the corresponding single energy protocol 140 kvp image, while the 80 kvp image of dual energy protocol will be approximately equally noisy to the corresponding 80 kvp image of the single energy protocol. Therefore, we should highlight the fact that by constructing the dual energy weighted images we should not expect to utilize the low noise advantages of a typical single energy protocol 140 kvp image (acquired at 200 mas). a) b) Figures 7.8: a) Dual and b) Single energy protocol 140 kvp images (1mm slice thickness). The first one is noisier. In image a, the background material noise is about 14 HU and in b about 5 HU. Mean HU values are the same for both images, about 130 HU. Moreover, it is expected that images of the same kvp and different mas are characterized by practically similar attenuation CT number measurements for all materials, since peak kilovoltage and filtering are the parameters that affect the quality of the beam. All images measured are again of 1 mm slice thickness. In table 7.8, the ratio of the mean HU values of 80 kvp DE to HU values of 80 kvp SE is close to unity for all cases. 199

200 Table 7.8: Comparison of CT numbers in single and Dual Energy protocol 80 kvp and 140 kvp images. They are practically the same. All images are of 1mm slice and the CT number values of inserts are taken from first part (C1) of scanning. Material HU 80 kvp DE/ HU 140 kvp DE/ HU 80 kvp SE HU 140 kvp SE iodine 5 mg/ml 0,98 0,93 iodine 1.5 mg/ml 1,17 1,07 iodine 3.5 mg/ml 0,97 0,89 iodine 2.5 mg/ml 0,920 0,92 iodine 17 mg/ml 1,00 0,99 iodine 7 mg/ml 0,99 0,964 iodine 14 mg/ml 0,96 0,97 Iodine 12.5 mg/ml 0,99 1,01 iodine 50 mg/ml 0,98 0,99 iodine 10 mg/ml 1,01 0,95 iodine 25 mg/ml 0,98 0,96 iodine 35 mg/ml 0,98 1,00 Plastic Water 0,82 1,33 Polysterene 0,983 1,09 Polyethylene 0,966 0,95 Bone 0,97 0,96 Polycarbonate 1,04 0,92 Nylon 1,05 0,96 Background 1,19 0,81 Air 1,01 1,00 It is also worth mentioning that changing the reconstruction thickness does not seem to have any significant effect on the mean CT number values measured. Noise on the other hand, seems to be lowest for 3 mm slice (table 7.9: average noise for the different material ROIS in the image). Background noise is highest for 1mm and lowest for 3mm slice for both 80 and 140 kvp images (SE scans). Table 7.9: C1 SE scan: average noise relationship with slice thickness Slice thickness Average 80 kvp std C1 scan Average 140 kvp std C1 scan 0,75 12,47 5, ,12 4,85 3 7,39 3,19 200

201 WEIGHTED DUAL ENERGY IMAGES: VIRTUAL 120 kvp a) b) c) Figures 7.9: Dual energy weighted images of C1, C2, C3 parts of experiment (1mm slice thickness) As already mentioned, the linearly weighted combination studied in this experiment is also referred to as virtual 120 kvp image because 80* *140=122. However, how well those images simulate the real 120 kvp images is a question under investigation. In the current thesis, we will only comment on how much the attenuation HU values of virtual kvp images are similar to the CT numbers obtained by 120 kvp real-conventional CT images. In the following table (table 7.10) the ratio of the mean CT number value of real 120 kvp to the mean CT number value of virtual 120 kvp image is derived. The images are all of 1mm slice thickness. The ratio is close to unity for almost all cases. The CT number values of DE images are always higher than the CT number values at 100 kvp and smaller than those of 140 kvp (tables 7.4 and 7.5). 201

202 Table 7.10: CT number comparison between real and virtual 120 kvp images Material HU 120 kvp HU DE virtual 120 kvp HU 120 kvp/ HU DE virtual 120 kvp iodine 5 mg/ml 151,10 155,35 0,973 iodine 1.5 mg/ml 48,33 56,95 0,849 iodine 3 mg/ml 123,99 119,14 1,041 Iodine 2.5 mg/ml 80,34 80,87 0,993 iodine 17 mg/ml 504,27 544,27 0,923 iodine 7 mg/ml 181,66 194,34 0,935 iodine 14 mg/ml 381,08 391,15 0,974 Iodine 12.5 mg/ml 362,96 393,43 0,923 iodine 50 mg/ml 1383, ,43 0,940 iodine 10 mg/ml 277,84 295,99 0,939 iodine 25 mg/ml 1007, ,42 0,955 iodine 35 mg/ml 1200, ,20 0,930 Plastic Water -6,91-9,84 0,702 Polysterene -23,37-30,40 0,769 Polyethylene -95,28-94,13 1,012 Bone 1507, ,83 0,985 Polycarbonate 107,03 97,05 1,103 Nylon 102,74 95,64 1,074 Background 124,91 123,40 1,012 Air -1002, ,06 1,002 DUAL ENERGY BEHAVIOUR OF IODINE SOLUTIONS In 1991 Raptopoulos et al. [88] performed a study on the dual energy CT discrimination of fatty infiltration and hypodense liver masses. In this study they also tested the linearity of tissue attenuation values with a phantom made of Lucite that had five tubes, four of which contained decreasing concentrations of iron dextran solutions. CT number measurements at 80 and 140 kvp were plotted for various concentrations to show the direct linear relationship between iron concentration and CT attenuation values. As expected, the slope was steeper for 80 kvp than it was for 140 kvp. Since the experiment set up in the thesis is very similar to this linearity control procedure (with the difference that we used iodine and not iron solutions), we also plotted the iodine solutions CT number values against iodine concentration. This resulted in similar results as in [88], especially for smaller iodine concentrations (Figures ). Figures have been constructed by the data from table

203 Figure 7.10: CT attenuation as a function of iron dextran concentrations for 80 and 140 kvp. Figure 7.11: CT attenuation as a function of iodine concentration for 80 and 140 kvp (SE protocol) HU kVp 100kVp 120kVp 140kVp iodine concentration(mg/ml) Figure 7.12: CT attenuation as a function of iodine concentration for the different peak kilovoltages. As kvp increases, the slope becomes smaller (SE protocol). 203

204 HU y = 32,69x + 5,387 R² = 0,958 y = 30,65x + 8,426 R² = 0, real 120Kvp virtual 120kVp iodine concentration(mg/ml) Figure 7.13: Virtual 120 kvp image gives almost the same slope as the real 120 kvp image (30.65 for the real kvp and for virtual kvp). Figure 7.14: Iodine enhancement vector (SE protocol) In figure 7.14, the plot of CT numbers at 80 versus the CT numbers at 140 kvp for various iodine concentrations is presented (Energy Map). That is the iodine enhancement vector, which is used in the algorithms of material decomposition and material labeling. The slope of the iodine vector determined in our experiment is in good agreement with the one used in dual energy algorithms, which has the value 2 [76]. Iodine enhancement vector is assumed to follow the same slope for body tissues that are characterized by very small CT number variations when the x-ray spectrum changes (for instance water, fat, soft tissue). That kind of materials lie on lines that follow a slope very close to the bisector in the HU 140 kvp - HU 80 kvp space (Energy Map). Knowledge of the material specific vectors is the milestone of dual energy CT discrimination. The material separation performance of any DECT scanner increases with the angular separation between the material axes in the Energy Map 204

205 [59]. Experiments for better specification of the material specific slopes for various materials are always useful and contribute to better performance of material decomposition algorithms. Every dual energy algorithm needs to take into account the special characteristics of the medical problem it was created for. Dual Energy Index (DEI) In tables 7.11 DEI (Dual Energy Index) as defined in chapter 5.7 is calculated for the materials in the experiment as well as the iodine solutions. In agreement to chapter 5.7, light materials have negative values of DEI while bone has a positive value DEI value and plastic water has a DEI value close to zero. Table 7.11: DEI of materials in the experiment MATERIAL DEI Bone 0,118 Polycarbonate -0,018 Nylon -0,018 Plastic water 0,001 Polystyrene 0,020 Polyethylene 0,020 Table 7.12: DEI of iodine solutions Iodine Concentration DEI (mg/ml) 1,25 0,013 2,5 0,026 3,5 0, , , ,079 12,5 0, , , , , ,202 From table 7.12 it is seen that DEI increases with increasing iodine concentration. Therefore it is not a material specific characteristic of iodine but it depends on the concentration of its solution. Thus, the iodine enhancement vector slope described 205

206 before is a more accurate and material specific measure of the dual energy behavior of a substance. Plotting DEI against iodine concentration gives a linear relationship up to 17 mg/ml. After this a tendency for plateau follows DUAL ENERGY BONE REMOVAL APPLICATION Syngo dual energy software of Siemens offers the possibility of bone removal based on a material labeling algorithm, as already discussed in previous chapter. In the following, the application of this algorithm to the present iodine phantom study will be presented and evaluated. Figure 7.15: Bone removal for C1 part of experiment Figure 7.16: C1 image before and after bone removal(0.75 mm slice thickness) 206

207 Figure 7.17: C2 image before and after bone removal (0.75mm slice thickness) Figure 7.18: C3 image before and after bone removal (0.75mm slice thickness) Head bone removal application as seen in figures removes only bony stuctures but not iodine solutions from the image. It can be observed though that in the periphery of the bone insert, there are remaining bone voxels. This could be due to blooming artifacts that may reduce the CT numbers of the periphery voxels and that is why they may be not removed by the algorithm. The problem is eliminated at higher iodine concentration images because the parameter minimum HU (in mixed image) was set to 200, while for C1 scan postprocessing it was set to Measurements inside the ROI of the removed bone give HU. The bone is removed from the linearly weighted virtual 120 kvp image (reconstruction Kernel D20f) that has slice thickness 0.75 mm as it is recommended [59]. Our measurements (comparing

208 mm DE images before and after bone removal) revealed that the mean CT number values of iodine solutions and material inserts remained practically unchanged after bone removal. The noise level also remained stable after bone removal. Bone can also be color coded blue as seen in figure Figure 7.19: C3 bone removal color coded image. 7.3 CALCIUM EXPERIMENT MATERIALS AND METHODS The experiment was performed with the same Mini QC CT Phantom as the iodine experiment. The whole procedure can be separated in three parts. PART 1 (LOW CONCENTRATION CALCIUM ONLY) Figure 7.20: Part 1 calcium experiment phantom arrangement 208

209 The first part, as we see in figure 7.20, involves only low concentrations of CaCl 2 (43.3, 83.3, 150, 200 mg/ml). The single energy and dual energy protocols are described in the following tables (tables 7.13 and 7.14). Table 7.13: Single Energy Protocol Convolution Increment Slice thickness Voltage Protocol mas Pitch Kernel (mm) (mm) HeadRoutSpi H20s ral Table 7.14: Dual Energy Protocol Voltage mas Protocol Convolution Increment Slice thickness Pitch Kernel (mm) (mm) Virtual 120kVp Headangio D20f 0.55 DE(0.3*80kVp +0.7*140kVp) PART 2 (HIGH CONCENTRATION CALCIUM AND IODINE) This part of the experiment included scanning of syringes with 250 and 300 mg/ml CaCl 2 as well as ioversol solutions of 12.5 mg/ml and 17 mg/ml iodine concentrations (figure 7.21). The single and dual energy protocols used in scan 2 are also given by the tables 7.14 and Dual energy abdomen scanning was also performed in this part of the experiment due to our intention to apply the urirany stones discrimination application of syngo dual energy to the phantom. The protocol is described in the following table (table 7.16). 209

210 Figure 7.21: Part 2 calcium experiment phantom arrangement Table 7.15: Abdomen protocol Voltage mas Protocol Convolution Kernel Pitch Increment (mm) Slice thickness (mm) Virtual 120 kvp DE - (0.3*80kVp +0.7*140kVp) Dual Energy Abdomen D30f a) b) Figures 7.22: a) Dual energy Abdomen image of phantom with high calcium and iodine concentrations b) Dual Energy Headangio for high concentrations of calcium and iodine solutions 210

211 PART 3 (LOW CONCENTRATION CALCIUM AND IODINE) The last part of the experiment involves only two dual energy scans virtual 120 kvp images were reconstructed). One with HeadAngio Protocol (slice thickness 0.75 and increment 0.5, reconstruction Kernel D20f and one with Abdomen dual energy protocol (slice 1.5mm, increment 1mm and reconstruction Kernel D30f). The images in this part of the experiment were reconstructed for dual energy applications. The arrangement of the phantom syringes was as shown in figure Figure 7.23: Part 3 calcium experiment phantom arrangement MEASUREMENTS Measurements for the calcium experiment were performed in similar manner as in iodine experiment. In figures 7.24 we present the selection of ROI for bone, background, CaCl 2 and iodine solutions in the dual energy image of high CaCl 2 and iodine concentrations (part 2 of experiment). In the same way, measurements were made for all dual and single energy protocol images in the experiment. The sizes of the ROIs were around 30 pixels for the syringes and 240 pixels for the bone and background. The size of the pixel does not significantly affect the standard deviation in the ROI because of the homogeneity of the materials. 211

212 Figures 7.24: ROI selection and Image J measurements for DE Head Protocol Image with high concentrations of Ca and iodine solutions (slice thickness 1mm) RESULTS AND DISCUSSION MEASUREMENTS IN SINGLE AND DUAL ENERGY IMAGES In the following tables, the CT number values and standard deviations of the ROI measurements for all CaCl 2 are presented as well as for bone, background and iodine solutions. The measurements were restricted to image slices of 1mm and Head Single and dual energy Protocol. The images of other slice thickness values as well as the dual energy images of the abdomen protocol were reconstructed only because they were recommended in the bibliography [59] for syngo dual energy applications. By making measurements for head 1 mm slices we obtain the same experiment conditions as in the iodine experiment described. Table 7.16: Single and Dual energy HU Material 80 kvp SE 80 kvp 100 kvp SE 100 kvp HU StdDev HU StdDev 43.3 mg/ml sol Ca 69,39 16,60 61,15 11, mg/ml sol Ca 108,97 10,23 89,23 8, mg/ml sol Ca 271,83 10,74 219,28 4, mg/ml sol Ca 334,66 12,81 270,75 7, mg/ml sol Ca 443,85 22,17 356,88 16, mg/ml sol Ca 441,58 17,50 356,00 12,14 212

213 Bone 2034,4 22, ,35 13,45 Background 98,87 10,63 116,04 7,66 Material DE 120 kvp SE 120 kvp (0.3*80kVp+0.7*140kVp) HU StdDev HU DE StdDev 43 mg/ml sol Ca 52,76 9,73 58,22 10,56 83 mg/ml sol Ca 77,69 5,71 77,98 6, mg/ml sol Ca 195,23 5,65 203,25 7, mg/ml sol Ca 231,96 8,13 246,81 6, mg/ml sol Ca 310,45 16,36 333,20 11, mg/ml sol Ca 307,52 10,19 327,19 7,76 Bone 1510,93 11, ,82 11,91 Background 126,32 5,62 101,99 8,48 Material 140 kvp SE 140 kvp HU ΗU=HU140-HU80 SE HU StdDev StdDev 43 mg/ml sol Ca 48,33 11,54-21,06 20,22 83 mg/ml sol Ca 71,75 3,55-37,22 10, mg/ml sol Ca 175,44 6,10-96,39 12, mg/ml sol Ca 208,22 7,01-126,44 14, mg/ml sol Ca 278,47 15,71-165,38 27, mg/ml sol Ca 273,35 10,49-168,23 20,40 Bone 1389,69 9,08-644,71 24,38 Background 131,01 4,17 32,14 11,42 Calcium solutions attenuate less at higher kvp as bone and iodine solutions also do. In figures 7.25 this attenuation reduction becomes obvious for both calcium and iodine solutions (images from part 2 of experiment). 213

214 c) a) b) c) d) Figure 7.25: a) 80 kvp b) 100 kvp c) 120 kvp d) 140 kvp images of part 2 of experiment (1 mm slice thickness). Syringes at right and left inserts in the phantom are iodine solutions. Up and in the center we have calcium solutions. Figure 7.26: CT number of calcium solutions at different kvp values 214

215 For higher concentrations the difference of mean CT number value between real and virtual 120 kvp images is of higher value. In almost all cases though, the noise level accounts for the differences, especially for low concentrations. Increased concentration of calcium solutions leads to increased absolute HU differences between different kvp values and the differences are reduced between images of increased kvp values. As in the iodine experiment in relationship (7.1), the contrast (calcium-bone) was also defined. Contrast Iodine Bone = HU sol Ca HU CT Range Bone Material Table 7.17: Contrast (calcium-bone) CONTRAST Calcium-bone 80 kvp CONTRAST Calcium-bone 100 kvp 43.3 mg/ml sol Ca 0,480 0, mg/ml sol Ca 0,470 0, mg/ml sol Ca 0,430 0, mg/ml sol Ca 0,415 0, mg/ml sol Ca 0,388 0, mg/ml sol Ca 0,389 0,329 Material CONTRAST CONTRAST Calcium-bone 120 kvp Calcium-bone 140 kvp 43.3 mg/ml sol Ca 0,356 0, mg/ml sol Ca 0,350 0, mg/ml sol Ca 0,321 0, mg/ml sol Ca 0,312 0, mg/ml sol Ca 0,293 0, mg/ml sol Ca 0,294 0,273 Material CONTRAST Calcium-bone DE 43.3 mg/ml sol Ca 0, mg/ml sol Ca 0, mg/ml sol Ca 0, mg/ml sol Ca 0, mg/ml sol Ca 0, mg/ml sol Ca 0,

216 Figure 7.27: Relative contrast (calcium-bone) for the different kvp values. The values in table 7.17 are similar to the values contrast (iodine-bone) for low concentration iodine solutions. Again, higher concentrations and increased kvp values are accompanied with smoother contrast reduction (fig.7.27). COMPARISON OF REAL AND VIRTUAL 120kVp IMAGES Table 7.18: Comparison of real and virtual 120kVp images Calcium solution DE 120 kvp HU 120kVp/ (0.3*80kVp+0.7*140kVp) SE HU HU DE HU 43 mg/ml sol Ca 52,76 58,22 0, mg/ml sol Ca 77,69 77,98 0, mg/ml sol Ca 195,23 203,25 0, mg/ml sol Ca 231,96 246,81 0, mg/ml sol Ca 310,45 333,2 0, mg/ml solca 307,52 327,19 0,940 Real and virtual 120 kvp images, according to the criteria of table 7.18 seem to be quite similar, as far as the CT number values are concerned. Virtual 120 kvp images though, seem to overestimate the attenuation of all calcium solutions. In the following table, we present the difference of CT number values for all the materials studied in the experiment. Increased concentrations of both iodine and calcium solutions 216

217 generally give larger values of CT number differences between real and virtual 120 kvp images. Table 7.19: Difference (absolute value) of CT number between real and virtual 120 kvp Material HU at HU difference/ HU DE 120 kvp CT range iodine 1.25 mg/ml 48,33 56,95 0,0021 iodine 2.5 mg/ml 80,34 80,87 0,0001 iodine 3 mg/ml 123,99 119,14 0,0012 iodine 5 mg/ml 151,1 155,35 0,00102 iodine 7 mg/ml 181,66 194,34 0,0031 iodine 10 mg/ml 277,84 295,99 0,0044 iodine 12.5 mg/ml 362,96 393,43 0,0074 iodine 14 mg/ml 381,08 391,15 0,0025 iodine 17 mg/ml 504,27 544,27 0,0098 iodine 25 mg/ml 1007, ,42 0,0116 iodine 35 mg/ml 1200, ,2 0,0219 iodine 50 mg/ml 1383, ,43 0, ,3 mg/ml sol Ca 52,76 58,22 0, ,3 mg/ml sol Ca 77,69 77,98 0, mg/ml sol Ca 195,23 203,25 0, mg/ml sol Ca 231,96 246,81 0, mg/ml sol Ca 310,45 333,2 0, mg/ml sol Ca 307,52 327,19 0,0048 Plastic Water -6,91-9,84 0,0007 Polysterene -23,37-30,4 0,00171 Polyethylene -95,28-94,13 0,0003 Bone 1507, ,83 0,0055 Polycarbonate 107,03 97,05 0,0024 Nylon 102,74 95,64 0,0017 Background 124,91 123,4 0,0004 Air -1002,5-1000,06 0,0006 DUAL ENERGY BEHAVIOUR OF CALCIUM SOLUTIONS The plots following were produced with the same rational as in iodine solutions. The plots should all coincide at (0,0) but there is as small deviation, due to statistical errors. 217

218 Figure 7.28: Linearity of HU values with density of solutions is confirmed for the case of calcium too (SE protocol). Figure 7.29: Calcium solutions at different kvp valies. The higher the kvp value, the smaller the slope (SE protocol). Figure 7.30: The slope for real and virtual kvp images is almost the same (1.18 for dual energy image and for real 120 kvp image). 218

219 a) b) c) 219

220 d) Figures 7.31: Energy map for iodine and calcium (a: single energy protocol, b: dual energy protocol). Notice that their slopes are not the same and that gives the opportunity for dual energy discrimination. Any mixture closer to the iodine vector can be classified as iodine solution and any material closer to the calcium vector can be classified as calcium solution. In imagse c and d (SE protocol), it is obvious that worse spectral separation leads to worse dual energy contrast SYNGO APPLICATIONS ON CALCIUM EXPERIMENT Calcium and iodine solutions may sometimes be displayed with similar CT number values on conventional 120 kvp images. PART 1 Head bone removal was applied to images of Headangio protocol of the first experiment part (part 1: Calcium solutions only) (figures 7.32 and 7.33). Figure 7.32: Head bone removal for part 1 of experiment As observed in figure 7.32, the calcium solutions up and in the center were not detected by the algorithm because their concentrations (83.3 and 43.3 mg/ml respectively) are low and 220

221 their CT number values in the averaged image are smaller than 150 HU which has been set as minimum value for the algorithm. Therefore their voxels have not been postprocessed. Hardplaques off tool has been selected because it removes calcium from the dataset, while bone removal algorithm on its own does not. Figure 7.33: Head bone removal before and after color coding (calcium only-part 1). Blue overlay has been superimposed on the averaged dual energy image. A weakness of the algorithm performance in the periphery of the calcium or bone area can be observed in figure The most possible explanation would be that the posprocessing averaging of voxels in the periphery reduces the CT number of the voxels located there and hinders their identification by the algorithm. PART 2 In the second part of the experiment we have higher calcium concentrations in the phantom as well as iodine solutions of 12.5 and 17 mg/ml at the right and left side of the images respectively. Head bone removal was applied again, with and without display of Hardplaques (here, Calcium solutions). The results are depicted in the following images: 221

222 Figure 7.34: Head bone removal hard plaques on. Calcium solutions are perceived as hard plaque components and are not removed by the algorithm, but bone is removed. Figure 7.35: Head bone removal hard plaques off. Calcium solutions are now color coded blue in the image. 222

223 Figure 7.36: Hardplaques on and off In addition to the head bone removal application, the abdomen DE protocol images acquired in the second part of the calcium experiment were utilized for urinary stone discrimination application. There was no urinary stone in the image and the light materials were excluded from discrimination due to the high minimum value set in the dialog box (200 HU). The maximum value was set lower than the default (default: 3071 HU) to exclude bone voxels from discrimination. All syringes (both iodine and calcium) were color coded blue, which means that the algorithm recognized them as high Z materials. Figure 7.37: Kidney stone discrimination: iodine and calcium voxels have been colored. Bone has been less affected. 223

224 PART 3 In part 3 of the calcium experiment, all syringes are filled with calcium solutions (up: 200 mg/ml, right: 150mg/ml and left: 83.3 mg/ml) and in the center we have an iodine solution of 7 mg/ml). In the DE head image the CT numbers of calcium solutions are very similar to that of iodine solution as it can be seen in the following table. Table 7.21: DE head 0.75mm image: solutions of iodine and calcium have similar CT number values DE head 0.75 mm slice Solutions HU Std 200 mg/ml sol Ca 254,06 8, mg/ml sol Ca 200,1 7,92 7 mg/ml iodine 205,28 9,43 In the following image it can be seen that the DE Head Bone removal algorithm can effectively discriminate between iodine and calcium solutions. The 200 and 150 mg/ml calcium solutions are color coded blue, while the iodine solution in the centre is not. Figures 7.38: Syngo Head Bone removal: the low concentration iodine solution on the left is not postprocessed by the algorithm. A few calcium voxels in the up and in the right syringe have not been color-coded probably because the algorithm is not very effective for low concentrations. 224

225 7.4 COMPARISON OF DUAL ENERGY RATIOS WITH RESULTS FROM CURRENT BIBLIOGRAPHY Kelcz et al [103] were the first to show that noise in dual-energy-processed material-specific images, and hence the ability of dual-energy CT to discriminate between two materials, depends on the difference between the dual-energy ratios of the materials. Here, the dualenergy ratio represents a density-independent material-specific parameter. The dual-energy ratio can be obtained experimentally by measuring the low and high-energy CT numbers (CTlow and CThigh, respectively) for several different densities of a given material, determining the slopes of the lines relating CT number to material density, and calculating the ratio of these slopes (slopelow / slopehigh) (or by determining the slope of the material vector in the Energy Map as above). The difference between the dual-energy ratios of two materials is determined by the separation between the high and low-energy spectra and the effective atomic numbers of the evaluated materials and is called dual energy contrast. The smaller the spectral separation, the harder it is to discriminate between the materials, especially when they have close atomic numbers (e.g. calcium and iron). In study [104] the dual energy ratios of iodine and calcium were derived for dual source CT acquisitions with and without additional tin filtration, in order to evaluate the material discrimination efficiency. The same will be done for the data of the experiment and the results will be compared. In study [104], the dual-energy ratios for calcium and iodine were measured using small and large (30 and 40 cm lateral dimension, respectively) anthropomorphic thorax phantoms (Cardio Phantom, QRM). The 10 cm cardiac insert of the phantomwas replaced with a waterfilled cylinder containing a custom frame made from polystyrene foam. The frame was used to hold five 3-ml syringes filled with different known concentrations of iodine and five cylinders with different known concentrations of calcium. The syringes and the calcium cylinders were approximately 10 mm in diameter. The iodine solutions were prepared by diluting iodine contrast medium (iohexol, Omnipaque 350, GE Healthcare) with water and had iodine concentrations ranging from 3.5 to 17.5 mg/cm 3. The density of calcium in the cylinders ranged from 50 to 900 mg/cm 3. The small thorax phantom was scanned using 80 and 140 kv with and without tin, and the large phantom was scanned using 100 and 140 kv with and without tin, all in dual energy mode. For every dual-energy image set (high and low-kv pair), the mean CT number in each calcium and iodine sample was measured and used to determine the slopes of the lines relating 225

226 the CT numbers to material density, which were determined using linear regression and divided to obtain the dual-energy ratio. In the following table (Table 7.22), the results of study [104] are presented (only for the small thorax phantom and without the additional filtration), along with the results of the thesis experiment. The agreement is quite good. Table 7.22: Dual energy ratios and dual energy contrast MATERIAL Study of Primak et al-80 and 140 kvp without additional filtration Thesis experiment 80 and 140 kvp without additional filtration IODINE DUAL ENERGY RATIO CALCIUM DUAL ENERGY RATIO DUAL ENERGY CONTRAST The problem of the definition of DE ratio is that it exaggerates the dual energy performance when the DE ratios are high, especially when they are increased by added filtration [105]. For instance if we assume two DE ratios 5.5 and 5, they give smaller angle between the two material vectors than two materials of DE ratios 1 and 0.5 (1 degree in the first case and 18,43 degrees in the second case). Figure 7.39:Limitation of dual energy contrast 226

227 7.5 CONCLUSIONS OF CHAPTER 7 The energy dependence of iodine attenuation coefficient is characterized by power law decay throughout the whole radiological energy range, while for calcium after some energy point, this dependence seems to be described by an exponential decay. Moreover, their absorption edges are at different energy levels. Therefore, calcium and iodine could not have the exact same dual energy behaviour, since their characteristics lead to an overall different energy dependence of their attenuation. This expected behavior was confirmed in the experiment of this chapter.also, the different dual energy behavior of iodine and bone was confirmed. In the experiment of this chapter, it was also confirmed that materials like polystyrene, polyethylene, polycarbonate, nylon, PMMA all have slightly increasing CT number values with increasing photon energy. However, iodine solutions, calcium solutions and bone have decreasing CT number values with increasing photon energy. The differences of CT number values between different kvp values are dependent on the concentration of the solution, therefore the measure of dual energy ratio may be used for material discrimination, since it is independent of solution density value. Dual energy contrast is increased with increased spectral separation. 227

228 CHAPTER 8 DISCUSSION AND OPEN ISSUES The current thesis attempted to provide a general aspect of the principles that Dual Energy Computed Tomography is based on and of the methods for its clinical implementation. Since the thesis is relevant to the physical properties of dual energy CT, it is important to highlight the contribution of the interactions dominating in radiological energies, to the dual energy behavior of the material. It became clear that Compton effect linear attenuation coefficient is mainly dependent on mass density of irradiated materials, while the dependence on the exact chemical composition is very weak. It is expressed by slight differences in mass electron density (e/g), between low and high atomic number elements (it is generally smaller for high atomic number elements). For mixtures, the exact value of the mass electron density depends on the relative weight of each component in the mixture but the differences are very small. For photoelectric effect, the dependence on Z effective is very strong and also absorption edges characterize the photoelectric attenuation of the material under interest. Considering low Z effective tissue-like materials that constitute of light components, it was concluded that (µ/ρ) ph is proportional to 4 Ζ eff, while for materials including high Z elements (like contrast agents), absorption edges make dual energy ρ-ζ methods inaccurate in radiological energies, hence a three-energy approach is required. In an effort to depict the specific characteristics of materials that make them appropriate or inappropriate candidates for dual energy CT, it was pointed out that for iodine, photoelectric attenuation is dominant throughout the whole radiological range, while for soft tissue-like materials the dominance of photoelectric attenuation is very restricted. The energy dependence of bone attenuation lies somewhere in between and therefore it can be discriminated from iodine by dual energy algorithms. The attenuation energy dependence of calcium and iron are more like that of iodine, but at high energies the exponential decay of total attenuation coefficient with energy and the absence of absorption edges in the radiological range of interest, makes their dual energy behaviour less vivid and therefore iodine has the possibility to be discriminated from calcium or iron. 228

229 The most important conclusion of the experiments, is that it confirms the independence of dual energy ratio from solution concentration.the calculated values of dual energy ratio for iodine and calcium solutions and the dual energy ratio of bone reveal the potential of their dual energy CT discrimination, as predicted theoretically. Also, tissue-like materials in the experiment, were confirmed to exhibit the slight increase of CT number values with increasing energy. There are several open issues for future research in the field of dual energy CT. According to research in the bibliography and personal comprehension of the subject, some of the open issues can be summarized as following: Image quality assessment of blended, virtual non enhanced and virtual monochromatic images. For instance, it is an open issue to assess the image quality and diagnostic accuracy of virtual non contrast images created by the Brain Hemorrhage algorithm of syngo and understand if they can be used to detect intracranial bleeding. Up to now, it is still under question whether VNE images created by this algorithm are too noisy to be considered satisfactory in some cases. Also, virtual monochromatic images are a new potential that may offer beam hardening free images or images that have similar or even improved quality than the conventional 120 kvp image. Optimal conditions for adequate CNR virtual monochromatic images and their diagnoistic accuracy should be verified experimentally. Establishment of the reduced dose level advantages that can be offered by dual energy CT examinations. For instance, virtual non enhanced images against true non enhanced images or dual energy bone removal techniques over DSA or other CTA bone removal techniques. Since in CT reduction of dose is a major issue, the establishment of dual energy CT should be based on its advantages in this field. Improvement of x-ray spectra separation. It has already been discussed that increased x-ray spectra separation decreases the noise level of material specific images and the performance of the algorithms is significantly improved. Additional filtering of the high kvp beam may lead to better separation and reduced dose levels. Experimental evaluation of appropriate filtering for several clinical issues is an interesting field of study. Multi-energy imaging. The new promising application is imaging an object at more than 2 non overlapping energy windows by using energy resolved photon counting detectors. Material specific k-edges may be identified in this way and energy windows 229

230 that enhance CNR between materials of interest can be chosen, with a single x-ray exposure. Moreover, multi-contrast agent imaging could be performed, since photon counting detectors may discriminate contrast agents with k-edges only 4 kev apart. The requirement for faster counting detectors and electronics and elimination of artefacts (like ring artefacts) is still an open issue, as well as clinical and experimental evaluation of photon counting detectors. Research for optimum dual energy contast agents. Gadolinium with a k-edge of 50.2 kev may be a better contrast agent than iodine for dual energy CT, because typical CT spectra are abundant in photons at energy level near its k-edge. Moreover, smaller concentrations of gadolinium may be required in examinations because of its higher atomic number. Iterative methods have been developed to enable projection domain dual processing, but have not been implemented yet in clinical practice. Generally, algorithmic improvements for the task of material selective imaging are still a field of research. Algorithmic optimization and comprehension of the dual energy behaviour of an even wider variety of materials is important and may be applied to occasions different than medical imaging, for instance material differentiation for safety checking or for soil sample analysis e.t.c. 230

231 APPENDICES APPENDIX 1: X-COM AND X-mudat databases XCOM is a NIST (National Institute of Standards and Technology) database provided on the Physical Reference Data Web page from which values of x-ray cross sections can be obtained. The XCOM program can generate cross sections on a standard energy grid (spaced approximately logarithmically), or on a grid selected by the user, or for a mix of both grids, at energies between 1 kev and 100 GeV. The program provides total cross sections and attenuation coefficients as well as partial cross sections for the following processes: incoherent scattering, coherent scattering, photoelectric absorption, and pair production in the field of the atomic nucleus and in the field of the atomic electrons. For compounds, the quantities tabulated are partial and total mass interaction coefficients, which are equal to the product of the corresponding cross sections times the number of target molecules per unit mass of the material. The reciprocals of these interaction coefficients are the mean free paths between scatterings, between photo-electric absorption events, or between pair production events. The sum of the interaction coefficients for the individual processes is equal to the total attenuation coefficient. Total attenuation coefficients without the contribution from coherent scattering are also given, because they are often used in gamma-ray transport calculations. The interaction coefficients and total attenuation coefficients for compounds or mixtures are obtained as sums of the corresponding quantities for the atomic constituents. The weighting factors, that is, the fractions by weight of the constituents, are calculated by XCOM from the chemical formula entered by the user. For mixtures, however, the user must supply the fractions by weight of the various components. The incoherent (Compton) scattering cross sections in [106] were obtained from a combination of the Klein-Nishina formula and nonrelativistic Hartree-Fock incoherent scattering functions. Radiative and double Compton-scattering corrections were also included.. The photoelectric cross sections were obtained by Scofield [107]. Scofield's results extend only up to 1.5 MeV. At higher energies, where the photoelectric cross section is quite small, a semi-empirical formula from Ref. [108] connects Scofield's values at 1.5 MeV to the asymptotic high-energy limit calculated by Pratt [109]. The x-mudat tool is also based on NIST database. In particular, the sources it uses are described in references [110],[111]. Six absorbing materials can be set up individually. Each 231

232 material can be composed of components chosen from the elements and further from a number of compounds and mixtures of dosimetric interest. Data for mass attenuation, mass energy transfer and mass energy absorption coefficients in a photon energy range of 1 kev to 50 MeV can be retrieved. The x-mu dat tool environment APPENDIX 2: ENERGY DEPENDENCE OF SOFT-TISSUE LIKE MATERIAL IN THE RADIOLOGICAL RANGE OF INTEREST 232