Guillaume Landry
UUNIVERSITAIRE PERS MAASTRICHT P M
1
ρ
2
60 "Monte Carlo" AND brachytherapy Number of publications 50 40 30 20 10 0 1980 1985 1990 1995 2000 2005 2010 Publication year
μ ρ μ ρ μ ρ μ ρ μ ρ μ ρ μ ρ μρ μρ
μ ρ μ ρ μ μ μρμ ρ
( μ ρ)
3
ρ
= = μ ( ρ) ρ
σ σ σ ( ) =
ρ ρ ρ ρ ρ ρ
ρ μ ρ ρ
ρ
μρ Δ Δ Δ =
φ φ τρ φ τρ φ
ρ ρ Δ Δ =
Δ ρ ρ ρ ρ Δ ρ ρ ρ ρ Δ = ρ ρ ρ
ρ ρ Δ Δ ρ ρ ρ ρ Δ ρ ρ
ρ ρ ρ Δ = ρ Δ ρ
4
μ ( μ ρ) = ( ) ρ = ( μ ) μ ρ ( ) μ ( ρ) μ ρ ( ) μ ρ
( ) = = μ ρ ρ ρ ρ ρ
σσ
ρ
μ ρ μ ρ
μ ρ ( μ ρ) ( μ ρ) Ψ Ψ ( μ ρ)
( μ ρ) μ ρ σδ
Δ = ( ) ( ) ( ) Δ
μ ρ
μ ρ
5
ρ ρ
ρ
= ( ) ( ) ( ) μ ( ) ( ) μ ρ
ρ 1.0 normalized number of photons / a.u. 0.8 0.6 0.4 0.2 80 kv 120 kv 140 kv 0.0 20 40 60 80 100 120 140 photon energy / kev
ρρ ρ ρ
ρρ
ρ ρρ ρ ρ ρ ρ ρ ρ = ρ ρ
ρ ρ ρ ρ ρ ρ ρ ρ = ( ) ( ) ρ ρ ρ ρ
μμ μμ
ρ ρ ρ ρ ρ ρ relative electron density 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 Calibration phantom theory simulation 0.2 5 6 7 8 9 10 11 12 13 14 effective atomic number ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ
relative electron density 0.98 0.96 0.94 0.92 Breast and prostate phantoms theory simulation corrected simulation 0.90 6.0 6.5 7.0 7.5 8.0 effective atomic number ρ ρ ρ ρ ρ ρ ρ ρ
ρ ρ
1.0 103 Pd D seg w,m /Dref w,m 0.9 0.8 0.7 TG43 SECT 3 tissues SECT 7 tissues DECT ideal DECT noise adipose hi Z adipose m Z adipose lo Z breast A30G70 breast A70G30 female tissue gland hi Z gland m Z gland lo Z lung muscle hi Z muscle m Z muscle lo Z rib skin hi Z skin m Z skin lo Z 0.6 1.4 1.3 1.2 103 Pd TG43 SECT 3 tissues SECT 7 tissues DECT ideal DECT noise D seg m,m /Dref m,m 1.1 1.0 adipose hi Z adipose m Z adipose lo Z breast A30G70 breast A70G30 female tissue gland hi Z gland m Z gland lo Z lung muscle hi Z muscle m Z muscle lo Z rib skin hi Z skin m Z skin lo Z 0.9 0.8
1.05 125 I 1.00 D seg w,m /Dref w,m 0.95 0.90 TG43 SECT 3 tissues SECT 7 tissues DECT ideal DECT noise 0.85 1.20 125 I water adipose hi Z adipose m Z adipose lo Z bladder full bladder empty lung male soft tissue muscle hi Z muscle m Z muscle lo Z prostate A prostate C rectum rib 1.15 1.10 D seg m,m /Dref m,m 1.05 1.00 0.95 0.90 0.85 0.80 water adipose hi Z adipose m Z adipose lo Z bladder full bladder empty lung male soft tissue ρ ρ ρ ρ ρ ρ ρ ρ muscle hi Z muscle m Z muscle lo Z prostate A prostate C rectum rib
1.10 tissue separation with noise skin lo Z, m Z, hi Z gl. hi Z, muscle lo Z, m Z, hi Z relative electron density 1.05 1.00 0.95 adip. m Z br. a30g70 adip. hi Z br. a70g30 fem. tis. gl. m Z gl. lo Z adip. hi Z 0.90 5.5 6.0 6.5 7.0 7.5 effective atomic number ρ ρ
ρ ρ
μ ρ μ( )= ρ ( )+ ( ) τρ σ ρσ ρ τρ σ ρ σ ρ μ μ ( ρ )= ρ ω ( ) ( )+ ( ) ω ( ( ) ( ) )= ( ) ( ) ρ μ μ μ = μ μ μ μ = μ μ = ρ ω ( ) ( )+ ( ) = ω ( ) ( ) = ω ( ) ( )
μ μ μ = μ μ μ ρ μ ρ ρ μ ρ = +
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ρ ρ ρ ρ ρ
μ μ ρ ρ
= ρ ρ ρ ρ ρ
A B ρ ρ
μ = + μ μ
μμ ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ
relative electron density 1.6 1.4 1.2 1.0 0.8 0.6 0.4 12 atomic number 11 10 9 8 7 measured simulated ρ ρ Z Z A Z Z Z B Z ρ ρ ρ ρ ρ ρ C Z 6 Z
μμ ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ
ρ ρ ρ ρ ρ ρ
7
ρ ρ ρ ρ ρ
ρ ρ ρ
ρ ρ
μρ ρ ρ ρ ρ ρ ρ ρ
ρ ρ ρ ρ ρ ρ
ρ Z
A standard deviation of muscle insert 1.6 1.4 1.2 1 0.8 0.6 0.4 muscle Z eff half dose 1mm stand. dose 1mm double dose 1mm max dose 1mm 0.2 0.01 D30f Q30f\1 Q30f\3 Q30f\5 D30f Q30f\1 Q30f\3 Q30f\5 reconstruction method reconstruction method ρ ρ ρ ρ ρ B standard deviation of muscle insert 0.07 0.06 0.05 0.04 0.03 0.02 e half dose 1mm stand. dose 1mm double dose 1mm max dose 1mm
ρ ρ ρ ρ
ρ ρ
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ρ ρ μ μ
ρ ρ ρ ρ ρ μρ μ = ρ ( )+ ( )+ ( )
μ ρ + + ( ) μ μ μ μ μ μ ( ) ( μ μ ) μ + + + + μ μ μ μ μ = + ω = β ω β ω β μ
μ μ
ρρ β ρ ρ ρρ β ρ ρ = = μ ( μ ) + μ ( μ )= ρ + + = ( ) ρ ( + + )+ ( + + ) ρ
μ ρ β μ β β
TSM RTM SPECTRAL METHOD DECT Gammex Scan HU inserts 80kVp and HU inserts 140kVp DECT Gammex Scan HU inserts 80kVp and HU inserts 140kVp CT Scanner Spectra Detector response NIST X-ray linear attenuation coefficients Correction for attenuation through phantom Stoichiometric parameters k 1,kVp and k 2,kVp HU tissues 80kVp and HU tissues 140kVp Model parameters A kvp,b kvp,c kvp,m + HU measured 80kVp and HU measured 140kVp } {{ } Z eff Model parameters A kvp,b kvp,c kvp,m + HU measured 80kVp and HU measured 140kVp } {{ } Z eff HU measured 80kVp and HU measured 140kVp } {{ } Z eff μ μ + +
μ
μ μ μ μ
1 0.9998 0.9996 0.9994 R 2 0.9992 0.999 0.9988 0.9986 0.9984 RTM TSM 0.9982 3 3.2 3.4 3.6 3.8 4 β β β β β β β β β
μ μ
μ μ
μ μ μ 80kVp /μ 140kVp 1.03 1.02 1.01 1 0.99 Gammex 467 CIRS phantom reference tissues TSM incl. lungs TSM excl. lung RTM 0.98 0.97 0.96 6 6.5 7 7.5 8 Z eff
μ μ
μ
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ρ ρ ρ ρ
β
ρ ρ = ω ω ω ρ ρ ρ
ρ soft tissues skeletal tissues 80 soft tissues 60 50 skeletal tissues % weight 60 40 20 C O P Ca % weight 40 30 20 10 0 6 7 8 9 0 11 12 13 14 Z eff Z eff
1.1 soft tissues 1.8 skeletal tissues Z eff /Z eff,water 1 Z eff /Z eff,water 1.7 1.6 head abdomen thorax 0.9 1.5 0.8 1.4 0.9 0.95 1 1.05 1.1 1.2 1.4 1.6 1.8 e / e,water e / e,water
σ
fits table ρ μ μ μ μ
Z eff 14 12 10 human tissues skeletal tissues 8 soft tissues 6 1.0 1.1 1.2 1.3 μ /μ 80kVp 140kVp ρ ρ ρ
ρ ρ ρ ρ ρ ρ ρ ρ
σ σ σ
Z
ρ ρ ρ
ρ ρ
RMS error on %C assignment RMS error on %C assignment RMS error on %C assignment 40 30 20 10 0 Adipose lo Z Adipose mean Z 30 25 20 15 10 5 0 CTDI vol =20 mgy Adipose lo Z Adipose mean Z Adipose hi Z bone marrow yellow 30 25 20 15 10 5 0 Adipose lo Z Adipose mean Z Adipose hi Z bone marrow yellow yellow/red marrow CTDI vol =20 mgy Gland lo Z yellow/red marrow Gland mean Z bone marrow red brain fluid CTDI vol =20 mgy Adipose hi Z bone marrow yellow yellow/red marrow bone marrow red brain fluid adrenal gland small intestine wall bone marrow red brain fluid lymph brain, white Muscle lo Z brain, grey thyroid Muscle mean Z Muscle hi Z blood whole Skin lo Z Skin mean Z Skin hi Z connective tissue cartilage whole column C4 incl cart C4 excl cart cranium mandible cortical bone ρ head thorax lymph Muscle lo Z heart1 heart2 aorta Muscle mean Z Muscle hi Z Gland hi Z heart3 trachea blood whole herart blood filled abdomen Skin lo Z Skin mean Z Skin hi Z connective tissue cartilage sternum urine bile lymph pancreas Prostate A testis Muscle lo Z stomach kidney1 liver1 kidney2 Muscle mean Z Muscle hi Z ovary kidney3 liver2 spleen blood whole liver3 Skin lo Z Skin mean Z Skin hi Z connective tissue cartilage Bladder full Bladder empty SECT DECT SECT DECT D6 inc cart whole column D6 excl cart humerus sphe head humerus whole spec ribs 2 6 clavicle humerus total humerus cyl shaft ribs 10 cortical bone SECT DECT sacrum male whole column femur sph head femur con troch sacrum female innominate male femur total innominate female femur cyl shaft cortical bone
RMS error on %C assignment RMS error on %C assignment RMS error on %C assignment 40 30 20 10 0 Adipose lo Z Adipose mean Z 30 25 20 15 10 5 0 CTDI vol =80 mgy Adipose lo Z Adipose mean Z Adipose hi Z bone marrow yellow 30 25 20 15 10 5 0 Adipose lo Z Adipose mean Z Adipose hi Z bone marrow yellow yellow/red marrow CTDI vol =80 mgy Gland lo Z yellow/red marrow Gland mean Z bone marrow red brain fluid CTDI vol =80 mgy Adipose hi Z bone marrow yellow yellow/red marrow bone marrow red brain fluid adrenal gland small intestine wall bone marrow red brain fluid lymph brain, white Muscle lo Z brain, grey thyroid Muscle mean Z Muscle hi Z blood whole Skin lo Z Skin mean Z Skin hi Z connective tissue cartilage whole column C4 incl cart C4 excl cart cranium mandible cortical bone ρ head thorax lymph Muscle lo Z heart1 heart2 aorta Muscle mean Z Muscle hi Z Gland hi Z heart3 trachea blood whole herart blood filled abdomen Skin lo Z Skin mean Z Skin hi Z connective tissue cartilage sternum urine bile lymph pancreas Prostate A testis Muscle lo Z stomach kidney1 liver1 kidney2 Muscle mean Z Muscle hi Z ovary kidney3 liver2 spleen blood whole liver3 Skin lo Z Skin mean Z Skin hi Z connective tissue cartilage Bladder full Bladder empty SECT DECT SECT DECT D6 inc cart whole column D6 excl cart humerus sphe head humerus whole spec ribs 2 6 clavicle humerus total humerus cyl shaft ribs 10 cortical bone SECT DECT sacrum male whole column femur sph head femur con troch sacrum female innominate male femur total innominate female femur cyl shaft cortical bone
RMS error on %O assignment RMS error on %O assignment RMS error on %O assignment 40 30 20 10 0 Adipose lo Z Adipose mean Z 30 25 20 15 10 5 0 CTDI vol =20 mgy Adipose lo Z Adipose mean Z Adipose hi Z bone marrow yellow 30 25 20 15 10 5 0 Adipose lo Z Adipose mean Z Adipose hi Z bone marrow yellow yellow/red marrow CTDI vol =20 mgy Gland lo Z yellow/red marrow Gland mean Z bone marrow red brain fluid CTDI vol =20 mgy Adipose hi Z bone marrow yellow yellow/red marrow bone marrow red brain fluid adrenal gland small intestine wall bone marrow red brain fluid lymph brain, white Muscle lo Z brain, grey thyroid Muscle mean Z Muscle hi Z blood whole Skin lo Z Skin mean Z Skin hi Z connective tissue cartilage whole column C4 incl cart C4 excl cart cranium mandible cortical bone ρ head thorax lymph Muscle lo Z heart1 heart2 aorta Muscle mean Z Muscle hi Z Gland hi Z heart3 trachea blood whole herart blood filled abdomen Skin lo Z Skin mean Z Skin hi Z connective tissue cartilage sternum urine bile lymph pancreas Prostate A testis Muscle lo Z stomach kidney1 liver1 kidney2 Muscle mean Z Muscle hi Z ovary kidney3 liver2 spleen blood whole liver3 Skin lo Z Skin mean Z Skin hi Z connective tissue cartilage Bladder full Bladder empty SECT DECT SECT DECT D6 inc cart whole column D6 excl cart humerus sphe head humerus whole spec ribs 2 6 clavicle humerus total humerus cyl shaft ribs 10 cortical bone SECT DECT sacrum male whole column femur sph head femur con troch sacrum female innominate male femur total innominate female femur cyl shaft cortical bone
RMS error on %O assignment RMS error on %O assignment RMS error on %O assignment 40 30 20 10 0 Adipose lo Z Adipose mean Z 40 30 20 10 0 CTDI vol =80 mgy Adipose lo Z Adipose mean Z Adipose hi Z bone marrow yellow 40 30 20 10 0 Adipose lo Z Adipose mean Z Adipose hi Z bone marrow yellow yellow/red marrow CTDI vol =80 mgy Gland lo Z yellow/red marrow Gland mean Z bone marrow red brain fluid CTDI vol =80 mgy Adipose hi Z bone marrow yellow yellow/red marrow bone marrow red brain fluid adrenal gland small intestine wall bone marrow red brain fluid lymph brain, white Muscle lo Z brain, grey thyroid Muscle mean Z Muscle hi Z ρ blood whole Skin lo Z Skin mean Z Skin hi Z connective tissue cartilage whole column C4 incl cart C4 excl cart cranium mandible cortical bone head thorax lymph Muscle lo Z heart1 heart2 aorta Muscle mean Z Muscle hi Z Gland hi Z heart3 trachea blood whole herart blood filled abdomen Skin lo Z Skin mean Z Skin hi Z connective tissue cartilage sternum urine bile lymph pancreas Prostate A testis Muscle lo Z stomach kidney1 liver1 kidney2 Muscle mean Z Muscle hi Z ovary kidney3 liver2 spleen blood whole liver3 Skin lo Z Skin mean Z Skin hi Z connective tissue cartilage Bladder full Bladder empty SECT DECT SECT DECT D6 inc cart whole column D6 excl cart humerus sphe head humerus whole spec ribs 2 6 clavicle humerus total humerus cyl shaft ribs 10 cortical bone SECT DECT sacrum male whole column femur sph head femur con troch sacrum female innominate male femur total innominate female femur cyl shaft cortical bone
Carbon Carbon Oxygen Oxygen
Hydrogen Hydrogen Nitrogen Nitrogen
Oxygen ρ Oxygen
ρ ρ
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ρ ρ
ρ ρ ρ ρ ρ ρ ρ = +ρ 2 1.8 ρ = 1.178 ρ e - 0.177 1.6 ρ 1.4 1.2 1 0.8 0.8 1 1.2 1.4 1.6 1.8 2 ρ e ρρ
ω = = ω ( ) ω ( ) ω ω ω ω ω ω ω
2 D r 2 1.5 1 Reference All H All C All O Muscle ρ = 1.05 g/cm 3 0.5 2 0 0 20 40 60 80 r (mm) Muscle 0.06 1.5 RMSE 0.04 0.02 D r 2 1 0.5 H = 5 % H = 6 % H = 7 % H = 8 % H = 9 % H = 10 % Reference 0 0 2 4 6 8 10 12 [H] (%) 0 0 20 40 r (mm) 60 80 0.03 0.02 Muscle Adipose Skin Gland RMSE 0.01 0 4 8 12 16 [H] %
ρ ρ β ( β ) = ρ β β ( β ) β β ρ ρ ρ
ρ ρ ρ
ρ