Dublin Institute of Technology ARROW@DIT Other resources School of Manufacturing and Design Engineering 2005-01-01 Experimental and Numerical Investigation of Therapeutic Ultrasound Angioplasty Graham P. Gavin Dublin Institute of Technology, graham.gavin@dit.ie M.S. J. Hashmi Dublin City University Garrett B. McGuinness Dublin City University Follow this and additional works at: http://arrow.dit.ie/engschmancon Part of the Biomedical Engineering and Bioengineering Commons, and the Mechanical Engineering Commons Recommended Citation Gavin, Graham P. and Hashmi, M.S.J and McGuinness, Garrett B.: Experimental and Numerical Investigation of Therapeutic Ultrasound Angioplasty, PhD, Dublin City University, Dublin, Ireland, 2005 This Theses, Ph.D is brought to you for free and open access by the School of Manufacturing and Design Engineering at ARROW@DIT. It has been accepted for inclusion in Other resources by an authorized administrator of ARROW@DIT. For more information, please contact yvonne.desmond@dit.ie, arrow.admin@dit.ie, brian.widdis@dit.ie. This work is licensed under a Creative Commons Attribution- Noncommercial-Share Alike 3.0 License
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Table of Contents ) 456 # # = @@ A B @C A C! C@C@ 7 C@C@ & 0) 047 ** = * *. :, *, = # ) - *3 " # D *- ;E 5 : F & ) 8 249.* @ G.. = # ) *,..* : # ) *,... = # *-., " 77 *F.,* *F.,. " *1
.,, : *G.,3 :.*.,3*.*.,3. #.,.,3, #.,.,-.3.,-* :.3.,-. =.G.3 : &,..3* <,..3. #,3.3, =,D.33 #,D.- B #" 7 7,1.-* :,1.-. :,G.-,,G.D < 3+ & :) ; ; 9043,* # 3*,. " 77# 33,.* " 33,.. # 3D,., 7 3D,.,*! 3F
3G -+,.3 = -+,.3* -, -D D+ D,,.- B D-,, < F. & 9) & 3:423 ; ; 3* F, 3. : F- 3.* ) F- 3.. = 5 FF 3, 7 7 %' 1+ 3,* 1+ 3,. 13 33 %'; A 7 7 G+ 3- < GF & ) + ; ; 2740 1 < -* G1 -. : #7 7 *++ -.* : #: *++ -.. : : #
7 7 *+. -., < #: *+. -.3 ; : # *+3 -.- <: # *+D -, / ;#7 7 *** -,* / ;: *** -,. ) **, -,, **, -,3 **3 -,- 7 7 < $ **3 -,D ; **3 -,F </ #7 7 *,* -3 =B< : 7 7 *,3-3* # B< : *,3-3. B *,F -3, B *-* -- < *-D & 1) ; 0 34032 ; D* *-F D. 7 7 *-1 D, : : *D. D3 " 7 7 # : : *DD D- " 7 7 B *F3
D-* = *F3 D-. # < *FD DD < *FG & 3) &< ; = 074077 F* = *1+ F. <; *1. F, ;B *1F 8 > 4
8 < & 0) 047 B**.++,. B**.++3 +D3. B*. : ><?& # 3 B*. : ><DD+? < 3 & ) 8 249 B.* < # *+ B..! *. B., " ) *3 B.3 $.+ B.3.+ B.- <.. B.D $.- B.F # 7.1 B.1 #,+ B.G,* B.*+,, B.**
,- B.*. =,F & :) ; ; 9043 B,* &5 3, B,. & 3- B,, 0 31 B,3 # / 31 B,- # 31 B,D < +,-! -* B,F =< +D! -. B,1-3 B,G -- B,*+ -F B,** -F B,*. -1 B,*, +D -G B,*3 D* B,*- D* B,*D D. B,*F B,*1 D3 D3 B,*G DF B,.+ +D D1
B,.* +,- D1 B,.. DG B,., F+ B,.3 F* & 9) & 3:423 ; ; B3* FD B3. B3, < FD F1 B33 FG B3- / FG B3D 1* B3F 1. B31 %'*+ 1, B3G 1- B3*+ %'*+ 1F B3** %' 1G B3*. # %'.11 G. B3*, %' G, B3*3
%'.11 G3 B3*- %'.F, G- B3*- %',+, GD & ) + ; ; 2740 1 < B-* *+* B-. *+.HD+D *+, B-. *+.H,+, *+, B-, : *+ *+F B-, : +D *+1 B-, : +,- *+G B-3 ) %I-4'9? **+ B-3 ) %I-4' **+ B-- **D B-D )
+J,+/ 0 **F B-F ) *-J,+/ 0 %',+KD+K G+K **1 B-1 ) *1J.1/ 0 %',+K,+, *4-4 **G B-G ) *1J.1/ 0 %',+K.D,.1,,+, *.+ B-*+.,- / 0 **1J,+, %',.K34 3-4 -4 *.. B-** = **1J,+, %',.K % L*-'3-4 *., B-*. = **1J,+, %'3DK % L..-'3-4 *.3 B-*, =%' %L.11' *.D
B-*3 =%L3-4' %L.11' *.F B-*- =%L3-4' %L,+,' *.1 B-*D =%L3-4' %L.F,' *.G B-*F = ) +,- *,, B-*1 <! B< : *,D B-*G B-.+ < # B< : 7 7 *+ *,1 %' *+ D3-K%'.,-/ 0 *,G B-.* = ) +,- *+ *3+ B-.. = ) +,- *- *3* B-., = % ' >+C?
*+ *3, B-.3 = % ' >+C? *+ *-.,- / 0 *33 B-.- = % ' >+;? *+ *-.,- / 0 *3- B-.D % ' *- -*K %'.,-/ 0 *3F B-.F %'% '.3D %'*,+ K%'..-/ 0 : MD.N *31 B-.1 = % ' : MD.N *3G B-.G =' : MD.N' % LD-2%'' %O*.' *-+ B-,+ *-. B-,* %'+,- %)L.,-/ 0 %'L**2'*-. B-,. = % '
%+,- '.,-/ 0 *-, B-,, % L 1+2%'' +,- *-3 B-,3 = % ' %*+ '.,-/ 0 *-- & 1) ; 0 34032 ; BD* +,- *-G BD. %'*+.11 *D+ BD, +,- 5 1 *D* BD3 & *D3 BD- ; %L.' %.+3+-+!' *D- BDD = *D- BDF *DF BD1 #
*D1 BDG ;.+3+-+! +,- *! *DG BD*+ ; +,- *! *DG BD** ;.+3+-+! +,-.! *F+ BD*. ; +,-.! *F* BD*, +,- *F. BD*3.+! +,- *F. BD*-.+! *+ *F, BD*D *+ *-D- *F- BD*F *+ *FF
8! & ) 8 249.* #.D.. 7.D & :) ; ; 9043,* " ) 3. & 9) & 3:423 ; ; 3* = 1-3. = 1G & ) + ; ; 2740 1 < -* =#! ; B) *+-
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) * +, -. / 012 34 5 0 2!6$ u ) u ) u ) a F ) 0*2!7$
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! 6 = " 7 7 $ $ $ &: $ B : <6/.++-'=>!$ = ## B< < " # $ $ $ & : $ B : <6 / '' ' * *? @A@% >.++- = = " # $ $$ &: $B: <6/ % BB >*>? &'>.++-! : < " # $ $$ &: $B: <6/ % BC >*>? &'>.++3 = < & " # $ $ $ & : $ B : <6 / * +?@D" @ >.++3
= " 7 # )$ $ $ &: $ B : <6/ > ' *@@E >.++- " 7 # )$ $ $ & : $ B : <6 / > + *@>.++-
'@=@ >F >
& 0 1.1 Cardiovascular Disease 7 / E %=@' *DF =@ M*N&.+.+.- M*N = %=/ ' " % "' %3.4' *- M.N ) # / # #.++3 P,D13 M,N.++,,G4 B **M3N=.+4 7 +JD3 B**.++3 =@.34 %D*1,*+++++ ' " %--D,*+++++ 'M3N
Figure 1.1a: Principal causes of death in Ireland for all ages in 2003, Irish Heart Foundation, Reports and Position Statements [4] Figure 1.1b: Principal causes of death in Ireland in 2004 in the 0-64 age category, Irish Heart Foundation, Reports and Position Statements [4] = M-
DN & MFN 1.2 Minimally Invasive Procedures & B*. M1G% *+'N E ) M*+**N < *GF1 " <.++* -F*+++.DD4 *G1FM,N # Q B*. 7 M*.N ) 5 B MD*,N
+ * & B*. : >< R? Figure 1.2b: Image of the distal end of a Medtronic S660 over-thewire coronary stent, image courtesy of Medtronic Vascular Ltd. # D+4.+,+4 M*3N
1.3 Complicated Atherosclerotic Plaques ) Q M*-*DN 7 ) )M*F*1N ) M*GN < ) ) ) M.+N # 5 )M.*N ) 55 ) # 1.4 Therapeutic Ultrasound Angioplasty " ) ) : 0M..N
) M.,N ) M.3%.,'.-.DN ) ) MF.*.F.1N : @A %$ '.++- B S %< =" <#' =R < " )M.GN= %.++-' B # %B#' " < %.++-'M.G,+N : ) < )
1.5 Research Objectives and Methodology 5 # ) # # B )
& 2.1 Vascular Disease # ) B.*M,*N! # ) M-N 7 M,,N # 0 MD,*N
B.*< # : # 7 / M,*N% : M,.N'
# M,3,-,D% D'N M,FN Q ) MD,1N )MD,1N ) ) ) B..MDN )) M,1N ) B..MDN E ) ) MDN M*GN
40 Thrombus Calcification Complicated Lesion: haemorrhage, ulceration, thrombosis Age in Years 30 Plaque Core Plaque Cap Fibrous Plaque? 20 Fatty Streak 10 B..! <MDN% = M,GN' 2.2 Complicated Atherosclerotic Plaques T ) 2.2.1 Mechanical Properties of Atherosclerotic Plaques < / M3+3*3.N
5 ) )) <MD.+N ) < %)' - H- # %' % ' % ' 5 B., ) ) ) ) % ' ) 0.000 Strain -0.50-0.45-0.40-0.35-0.30-0.25-0.20-0.15-0.10-0.05 0.00-50.000-100.000 Hard Medium Healthy Soft Stress kpa) -150.000-200.000-250.000-300.000-350.000 Figure 2.3: Uniaxial radial compression data for various types of plaques. Adapted from Topoleski and Salunke [6] using digitising extraction software xyextract ) AM*FN.D ) < %*. ' U %G '%- '
) ) ) )., ) )) ) ) < MD.+N M3,333-3DN ) 5 AM*FN 2.2.2 Complications Associated with Present Procedures 1+4 M*-N : hypocellular: containing less than the normal number of cells = ) )) = ) < 5 M3FN
7 ) M**313G% D'N= M**N 5 ) M.+3FN # ) 2.3 Therapeutic Ultrasound Delivered via Wire Waveguide ) M.,N = A0 % # M-+N' ) M-*-.N )M.,N 2.3.1 Introduction *GF+ <M.3%.,'N *G1+ <;
! 5 < M.*.-.DN & < 2.3.2 Ultrasound Generation ) ) )& <M.-N;M.*.DN 0 0 V 0;< & A W %W' 7 = Q ) *+++ M-,N )? ) M-,N" B.3 +J-K ) *++ / 0 # ) 0 ) ) M-3N
M.-N B % ) ' % ' # M-3N # B M-3N < ) < B.3 ) M--N / M-3N7 *-+K ) *++/ 0 # M.3%.,'.-.DN 2.3.3 Minimal Invasive Delivery of Ultrasound : %X*D++ ' %Y+,- ' 7
-? =? + < + - *=+ B.3$ B.3 ; M.*N
B *-B%X+- ' M-DN #MFN M-*N M-*N.+ <M3FN*F 5 2.3.4 Mechanical Effects of Wire Waveguide Tip Displacement # M-+N 5 Q ) M-F-1-GD+N# B.- 2.3.4.1 Direct Contact Ablation ; MD*N
Wire waveguide in catheter Direct Contact Ablation Cavitation Pressure Waves Acoustic Streaming Distal Tip Vibration 0 150 µm) @ 18 45 khz Figure 2.5: Schematic of ultrasonic wire waveguide in catheter and the regions surrounding the longitudinal vibrating distal-tip where disruptive mechanisms can occur. ) ) 5 M-.N # ) ) ) M.DN
2.3.4.2 Acoustic Pressure Waves and Cavitation # M-1D.NE = ) &M-FN.3,= M-F-1D,N 9B 0M.,N 5 ) 2.3.4.3 Acoustic Streaming B.DM-1-GN 2.3.5 Testing of Ultrasound Delivered via Wire Waveguide Q%' %' 7
2.3.5.1 Mechanical Performance Evaluation #MFN.+/0 %-+4 ' +FD.+ 1G " %' B 1J.-7 D,-K ***K.* ) M-3N: M.*-*N..
@ 6 B.D$ #! M-1N.*#.+/ 0 #MFN
Acoustic Horn Tip Power 8 11 15 18 23 25 Watts) Waveguide Tip Displace. p-p m) 63.5 76 83 89 102 111..7 Author Rosenschein et al [21] Frequency of Operation khz) Distal Peak-topeak Displacement µm) 20 150 ± 25 Ariani et al [7] 20 63.5-111 Demer et al [51] 20 50 ± 25 Makin et al[62] 22.5 200/ 130 Wire Data Aluminium Alloy Wire 1.6mm No Ball Tip Titanium Wire.72mm 2mm Ball-Tip Titanium Wire.5mm 2mm Ball-Tip Titanium Wire 1.98/2.46 mm Ball-Tip : MD.N..-/ 0.++K *,+K 33- *G1 DD+.3D B.F.3D *,+K *..-+ :
;M.*N 17
16000 14000 12000 Pressure Pa) 10000 8000 6000 4000 2000 0 0 50 100 150 200 250 Distance mm) B.F# : MD.N% R ' 2.3.5.2 Clinical Evaluation # MFN7 Q B.1.* E M.*D3N
<M-.N *G-/0 -+,34 ) M-*N B.G B Q ) M-DN
200 Disruption of thrombi Average Disruption Time Sec) 180 160 140 120 100 80 60 40 20 0 5 10 15 20 25 Power Watts) B.1# %L-+' #MFN% R
Pressure Volume Curve 2.50 2.00 Pre 1 Pre 2 Post 1 Post 2 Pressure atm) 1.50 1.00 0.50 0.00 3.00E+02 5.00E+02 7.00E+02 9.00E+02 Volume 100 microlitres/ division) 1.10E+03 B.G % ' % ' M-*N% R ' 2.4 Theoretical Mechanics Background % ' % ' 2.4.1 Steady-state vibration of a uniform rod
B.*+5!$G!!$$ ).*MD-N ) ωx ωl ωx u x, t) = bcos + tan sin )sinωt %.*' c c c %CHH$ ).* ).. f n ) l % ' c f nc = n 4 GB@I@JK %..' l
B.*+ G # < MD,N
< ) )., %L*,-F' %L+.3D1Z' ) nc l n = %.,' 4 f 2.4.2 Acoustic Pressure Field around an Oscillating Sphere MD.N# : MD+N ).3B.** % 2 R cosθ 2 2 Pmax = 2π ρrf d 0 2 r %.3' ) C
P r 2R Direction of Motion B.** #! M-1N
2.4.3 Cavitation B 7 &M-FN ).- T 2 Pmax = %.-' 2ρc # M-3N.,7 [. ).+J,+/0B.*. ) )*++/ 0 B.*. ).+3-/ 0 2.4.4 Acoustic Streaming # M-1-GN B.D A7 M-GN M-1N
Cavitation Threshold 1.E+08 1.E+07 18-45 khz Intensity W/cm^2) 1.E+06 1.E+05 1.E+04 1.E+03 1.E+02 1.E+01 B) " # 1.E+00 1.E-01 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 Frequency Hz) B.*.= # M-3N% R '
2.5 Finite Element Analysis of Ultrasound Transmission in Wire Waveguides 7 ) B! ) MDDN 2.5.1 Material Properties ) 9?: %+' %' MDD DFN ) %c' ).D E c = %.D' ρ ) MD1N 2.5.2 Mesh Density
: 5 ) ) : ) = ) MDDN 2.5.3 Damping MDDDFN6MDGN
2.6 Summary = ) ) A ) ) 7 "< ) #? # &
& :!! "#$ %% &"" 3.1 Introduction to Apparatus Design )< 5 5 5 0 ),* 5 B,*
,*" ) Performance Characteristic Specification Justification Frequency of Operation 20-30 khz Typical values used in clinical applications in the literature [7, 21, 51] Wire waveguide diameter 0.35mm -1.0mm Access to peripheral and coronary arteries, similar to standard guidewire dimensions and those reported in the literature [51] Wire waveguide distal-tip displacement Up to 100m peakto-peak Typical values used in clinical applications in the literature [7, 21, 51] Wire waveguide length Up to 500mm Allow for the testing of a range of lengths
=0 8 @ = =: & @ " 7 7 # @ B) =9 <4 + @ = * @ E =1 6 + # = # < B,*& 5
3.2 Ultrasonic Wire Waveguide Apparatus Design and Development <*-+S &" S%3* ; =" <#' 3.2.1 Ultrasonic generator and converter %G-+@ '..-/0ID4MF+N ) ) B,. ) # ) [ )% ' A= ) M-3N
A8& A & @B@ @ B,. &" $ 0 %0 '..-/ 0 B,,MF+N
3.2.2 Acoustic Horn 5 E %&S: - ' *++2 )..- / 0 0 MF*N B,3 ) MF+N B,- 3.2.3 Wire Waveguide Design! %!' B 7 : R %GD+G;B 7! 3D1+G' < MF.F,N 3.2.3.1 NiTi Wire Waveguide -D47 %X3,47 '7 %#' *+ + =MF3N / *D- + =
MF3N! *+ +D +,- *+ +D +,- ) : 9? Q) < +?4 = B,, 0 " =
4 B,3 # / & - B,-# # / = Tensile testing of NiTi wire waveguide < +,- +D 5 Q*' 9? : % '.',' 7 / R /.+T7. [ %.+ + =' +,- B,D MF.F,F-N
& MF,N % ' 9? XF-$ % +14' # D++: % ' # D4E 9? X,+$ % ' +D B,F % L1-4' *+4 +*D4 %Y+14' 9? F-$E *3++: Material density of NiTi waveguide # )! AVR < : T D331[, 9??! MF-N
3.2.4 Connection of wire waveguide to acoustic horn ) #..-/0 ) $ ID4 ) 1.40E+09 1.20E+09 1.00E+09 Austenitic Transformation Martensitic Stress Pa) 8.00E+08 6.00E+08 4.00E+08 2.00E+08 0.00E+00 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 Strain B,D< +,-!
1.80E+09 1.60E+09 1.40E+09 Stress Pa) 1.20E+09 1.00E+09 8.00E+08 6.00E+08 Cycle 1 Cycle 2 Cycle 3 4.00E+08 2.00E+08 0.00E+00 0 0.02 0.04 0.06 0.08 0.1 0.12 Strain
B,F= +D! ) 0 ) 3.2.4.1 Evaluation of wire waveguide connection method # *+ +D +,- ) MF+N B,1 B *-,+
*- B,G & > - " B,1 J
- 4 & ; ; B,G # Q ;
Single side set-screw. *+ :. B,*+B,** B,** B %,- 3- ' %D+ 1+ ' # & F+ %A S; = >D+*?' B,*. %L-' 7 B,*, %L*-' B B,*, *+ % ' +D +,-
B,*+ 4A - #: ; ; 0 * B,**
45 Time to Failure Single Side Set-screw) 40 35 30 Time Seconds) 25 20 15 10 5 0 0 0.35 0.6 1.0 Wire Waveguide Diameter mm) B,*.
A A & 4 A A A B,*, +D
+,- +D & 7 ) E Double side set-screw B,*3,*- %L-' B,*D #%L*-' B +,-
B,*3 4A #1 ; ; 4A B,*-
60 Time to Failure Double Side Set-screw) 50 40 Time Seconds) 30 20 10 0 0 0.35 0.6 1.0 Wire Waveguide Diameter mm) B,*D
+,- +D *+ E Axial set-screw D+ :, B,*F,*1 %L-' B,*G # # %L*3' B,.+ %L*', E B,*1 *+ %L,',++ +,- +D D+
B,*F A & 4A A A A 0# A A B,*1 *+
+,- +D B,.* %A R ; = >D+*?'E B,.3 B 3.2.5 Final apparatus design and housing & # B,.. 5 # 5 # 5? B,., B,++ B,.3 +,-
350 Time to Failure Axial Crimped Set-screw) 300 250 Time Seconds) 200 150 100 50 0 0 0.35 0.6 1.0 Wire Waveguide Diameter mm) B,*G @ 6A ; < 46A B,.+ +D
< #: A @ B,.* +,- # % '
B,.. Figure 3.21: Detailed drawing of ultrasonic wire waveguide apparatus
&! ; B,.,
350 Time to Failure in Housing 300 250 Time Seconds) 200 150 100 50 0 0 0.35mm 0.35mm with sleeve 0.6mm 1.0mm Connection Method B,.3
3.3 Summary #! 5 *+,++ *+ # 7 +D +,- G+ +,- # = D ) ) = 3-
& 9 #'#$ %% &"" 4.1. Introduction ) =, 5 ) )
4.2. Direct peak-to-peak displacement measurement ) = B3* 4.2.1. Displacement measurement technique " ) E B3. 7 E B3. G<A L'A B3, %<< ' %@ >@$ =3++?'= % #< &' 5 1+
; ; 6+ + A & &A A B3* = + = 6! 6! + = 4 C 4 C B3.<
7 5 4.2.2. Calibration of Objective Lenses = %T ;R >< :?' 7 5 = B B33 5 3+ & 7 5 3+.+ D+ *++ 2 5.- B 3-.+K.+K *GG1K %\' +*1K < D+K -G1.%\+.,K '*++K GG13K %\+..K ' %\ +.,K ' D+K GGF4 %,\' I +DGK
6+ & & B3, =
B33.+*++ 10 Histogram of Displacement Measurement 9 Number of Measurements 8 7 6 5 4 3 2 1 0 19.5 19.6 19.7 19.8 19.9 20 20.1 20.2 20.3 20.4 20.5 Displacement m) B3-/.+K % *GG1K \+*1K '
4.3. Wire Waveguide Distal-Tip Peak-to-Peak Displacements " 5 3+ B3D B3F *+ B *+ *+ +D +,- B,.3 4.3.1. Effect of input power dial settings *+ B31 < E.-1.- 1-K
; + B3D
B3F
Distal-Tip Displacement µm p-p) 90 80 70 60 50 40 30 20 10 0 1 1.5 2 2.5 3 Input Power Dial-Setting Length =298mm Length = 278mm Length = 258mm Length = 228mm B31 *+ *-...-.-
4.3.2. Effects of Wire Waveguide Length J **1,+, - *+ *- B3G.1,,3K.D, -.K # %.-1 *11 ' %.11.*1 ' B3G ) & ) " %' ) 3* ).,- / 0 3* f nc = GC@9@M@NK %3*' 4 l n
90 Output peak-to-peak Displacement µm) 80 70 60 50 40 30 20 100 150 200 250 300 Wire Length mm) B3G7 **1,+, *- 3*= ).,-/ 0 n Analytical Experimental Percentage Lengths mm) Lengths mm) Error %) 0 0 - - 2 72.4 - - 4 144.8 146.8 6 217.2 218 0.36 8 289.6 288 0.55
) F. F+ ).,-/ 0 / ) ).* ) " B3*+ & 0 *- %GC',.K # 3.
90 Power Setting = 1.5 Output peak-to-peak Displacement µm) 80 70 60 50 40 30 y = -0.0071x + 32.224 Analytical Non- Resonant Lengths Linear Line AA) 20 0 50 100 150 200 250 300 Wire Length mm) B3*+7 **1,+, ) : ) /
...-.-*+ B3**& 3. *-...-.- *+ :...-.- 3*K 33-K 3DK
Output peak-to-peak Displacement µm) 110 100 90 80 70 60 50 40 30 20 Power Setting = 2 Power Setting = 2.25 Power Setting = 2.5 Linear Trend 2) Linear Trend 2.25) Linear Trend 2.5) 0 50 100 150 200 250 300 Wire Length mm) B3**7 **1,+, 3.= Power Setting Linear Fit y-intercept R-Squared of Linear Fit Exponential Fit y-intercept R-Squared of Exponential Fit 1.5 32.224 0.75 32.269 0.75 2 41.114 1 41.237 0.99 2.25 44.781 0.75 44.863 0.75 2.5 45.781 0.75 45.861 0.75 4.4. Displacement results along length of wire waveguide " ) 3. %'
%GC' %G' ωx ωl ωx u x, t) = bcos + tan sin )sinωt %3.' c c c.11 B ).,-/0,.K B 3*..11,,*+D*F1.-* F+*3,.*-.11 B ).11,+,.F, # B3*,# *-,.K.11 B3*3 0 %.11.*,*31 ' %.-, *F1 '.F,,+, B3*-
.F,,+,.11 E ),-
Internal Displacements p-p) 35 30 Displacement m) 25 20 15 10 5 0 0 50 100 150 200 250 300 Distance mm) B3*.#.11 5,.K.,-/ 0! %'
B3*, G.K D,*FK -3K
Displacements p-p) along wire waveguide 35 30 Displacements m p-p) 25 20 15 10 5 0 0 50 100 150 200 250 300 Distance mm) B3*3.11 *-% L,.K '
Displacements p-p) along wire waveguide 40 Experimental 273mm Experimental 288mm Displacements p-p) 35 30 25 20 15 10 5 0 0 50 100 150 200 250 300 Distance mm) B3*-.F, *-% L,.K '
Displacements p-p) along wire waveguide 40 Experimental 303mm Experimental 288mm Displacements p-p) 35 30 25 20 15 10 5 0 0 50 100 150 200 250 300 Distance mm) B3*-,+, *-% L,.K '
4.5. Summary 7 7 / ).,-/0 B &
& ) #%% * 5.1 Introduction = 3 E ) 7 =. ) Q! # B
=. B ) = 3 E < : MD.N )< 5.2 Modal Analysis of Wire Waveguide #
5.2.1 Modal Analysis Method B-* #! <9<R : %1*'5 & A0 MFDN ) 2 [ K]{ φ } = ω [ M ]{ φ } %-*' i i i [K ] L { φ i } L % ' ω L )% ω 2 ' i i [M ] L
8 +,,+,+,+ B-*
5.2.2 Effects of Mesh Density on Modal Analysis of Wire Waveguide B-. ). 3) %3.'MFFN 0 0 : % ' %' %' %H'MDDN : ),+, *+ +D +,- 9?! = 3 5.2.3 Sensitivity Analysis of Material Properties B 9? @ 9? I-4 = 3 = 3
B-. *+.HD+D. B-. *+.H,+, 3
5.2.4 Results of Modal Analysis ),+, -*)+,+/0 ) ) B-, ) B %*H*+' ) ) *H- B *+ B-, * H*+ ) 7 ) *H.++ ).HD+D B-.. 3 *+ -, B-,B-, +D +,-
-*= #! ; B),+, Resonant Frequency Analytical Resonant Frequency Solution Hz) 1 2812.7 2813.5 Numerical Resonant Frequency Predictions Hz) % Error) 1.0mm 0.6mm 0.35mm 0.03%) 2 8438.11 8440.53 0.03%) 3 14063.53 14067.6 0.03%) 4 19688.94 19694.74 0.03%) 5 25314.35 25321.96 0.03%) 2813.5 0.03%) 8440.53 0.03%) 14067.57 0.03%) 19694.65 0.03%) 25321.77 0.03%) 2813.5 0.03%) 8440.52 0.03%) 14067.56 0.03%) 19694.62 0.03%) 25321.71 0.03%) B.HG+G +D, 3 < +,-.H*.*. 3
3 5.2.5 Summary of Modal Analysis -* ) ) ++,4 ) B-3 9? I-4 ) 5 )
Frequency Hz) 30000 25000 20000 15000 10000 5000 1st Resonant Frequency 2nd Resonant Frequency 3rd Resonant Frequency 4th Resonant Frequency 5th Resonant Frequency 0 1 1 1 3 1 5 1 10 1 50 1 100 1 200 1 303 2 606 Mesh Density r y) B-,: *+,+,
Frequency Hz) 30000 25000 20000 15000 10000 5000 1st Resonant Frequency 2nd Resonant Frequency 3rd Resonant Frequency 4th Resonant Frequency 5th Resonant Frequency 0 1 1 1 3 1 5 1 10 1 50 1 100 1 303 2 909 Mesh Density r y) B-,: +D,+,
Frequency Hz) 30000 25000 20000 15000 10000 5000 1st Resonant Frequency 2nd Resonant Frequency 3rd Resonant Frequency 4th Resonant Frequency 5th Resonant Frequency 0 1 1 1 3 1 5 1 10 1 50 1 100 1 303 2 1212 Mesh Density r y) B-,: +,-,+,
30000 25000 1st Resonant Frequency 5th Resonant Frequency Frequency Hz) 20000 15000 10000 5000 0 71.25-5%) 75 78.75 +5%) Young's Modulus Gpa) B-3 ) %I-4'9? L,+, 30000 25000 1st Resonant Frequency 5th Resonant Frequency Frequency Hz) 20000 15000 10000 5000 0 6127.5-5%) 6450 6772.5 +5%) Density kg/m^3) B-3 ) %I-4' L,+,
5.3 Harmonic Response Analysis of Wire Waveguide # ) MDFN ) ) ) = 3 ) 5.3.1 Harmonic response method # ) MDFN [ M ] u) + [ C] u) + [ K] u) = F a ) %-.' [M ] L [K ] L a F ) L
[C] L u ) u ) u ) L [ C] = β )[ K] %-,' β ) ζ ) ) f ) ζ β ) = %-3' πf B-- # 3. 0 5 G!!$$ )
5.3.2 Distal-tip response of wire waveguides over a range of frequencies ) +,+/0 ) : *+ +D +,- ) 5.3.3 Distal-tip response of wire waveguides over a range lengths = 3 : **1,+, - *+ +D +,- ).,-/ 0 ) 5.3.4 Displacement response along length of wire waveguides " % ' ).,-/ 0 = 3
5.3.5 Wire Waveguides with Spherical Distal-tip Geometry / M.-.-N7 = 5.3.6 Results from harmonic response analysis B-D )+J,+/ 0,+K,+, *4 ) ) MD-N B-F *+,+K D+K G+K E *4 ) =, ).,-/0 = 3 B-1
7 ) B-G 5 ) J = 3 B )
8 +,,-.#,+,+ B--
8.00E-04 Distal-tip peak-to-peak displacement m) 7.00E-04 6.00E-04 5.00E-04 4.00E-04 3.00E-04 2.00E-04 1.00E-04 0.00E+00 Diameter = 0.35mm Diameter = 0.6mm Diameter = 1.0mm 0 5000 10000 15000 20000 25000 30000 Frequency Hz) B-D )+J,+/ 0,+K,+, *4
5.00E-04 Distal-tip peak-to-peak displacement m) 4.50E-04 4.00E-04 3.50E-04 3.00E-04 2.50E-04 2.00E-04 1.50E-04 1.00E-04 5.00E-05 Input = 30m p-p) Input = 60m p-p) Input = 90m p-p) 0.00E+00 15000 18000 21000 24000 27000 30000 Frequency Hz) B-F *+ )*-J,+/ 0,+K D+K G+ K,+, *4
Distal-tip peak-to-peak displacement m) 2.00E-04 1.80E-04 1.60E-04 1.40E-04 1.20E-04 1.00E-04 8.00E-05 6.00E-05 4.00E-05 2.00E-05 Damping = 1% Damping = 2% Damping = 3% Damping = 4% Damping = 5% 0.00E+00 18000 20000 22000 24000 26000 28000 Frequency Hz) B-1 *+ )*1J.1/ 0,+K,+, *4-4
Distal-tip peak-to-peak displacement m) 3.00E-04 2.50E-04 2.00E-04 1.50E-04 1.00E-04 5.00E-05 Length = 303mm Length = 283mm Length = 263mm 0.00E+00 18000 19000 20000 21000 22000 23000 24000 25000 26000 27000 28000 Frequency Hz) B-G *+ )*1J.1/ 0,+K.D,.1,,+, *4
B-*+ ).,-/0 *+ **1J,+, -,.K *+ *- %34 3-4 -4 ' 3-4 B-** MF,N % ' B-*..- 3DK Q
Damping = 4% Distal-tip peak-to-peak Displacement µm) 100 Damping = 4.5% Damping = 5% 80 60 40 20 0 100 150 200 250 300 Wire Length mm) B-*+ *+.,-/ 0 **1 J,+,,.K 34 3-4 -4
Distal-tip peak-to-peak Displacement µm) 100 80 60 40 20 Numerical Experimental 0 100 150 200 250 300 Wire Length mm) B-**= *+ **1 J,+,,. K % L*-' 3-4
Distal-tip peak-to-peak Displacement µm) 100 80 60 40 20 Numerical Experimental 0 100 150 200 250 300 Wire Length mm) B-*.= *+ **1 J,+, 3D K % L..-' 3-4
B-*, *+.11,.K.,-/0 ).*# 3-4 B -*3 %'.11,.K.,-/0 3-4 #.11 B-*, %,.K %'' 0# -*1 : 7 B-*3.1K %'# 0.1:
Phase Numerical Analytical Phase Degrees) 180 160 140 120 100 80 60 40 20 0 0 50 100 150 200 250 300 Distance mm) Internal Displacements p-p) 35 Displacement m) 30 25 20 15 10 5 0 0 50 100 150 200 250 300 Distance mm) 6.0E+07 Stress 5.0E+07 4.0E+07 Stress Pa) 3.0E+07 2.0E+07 1.0E+07 0.0E+00 0 50 100 150 200 250 300 Distance mm) B-*,= % ' *+ %L.11 '
Phase 90.00 45.00 Phase Degrees) 0.00 0 50 100 150 200 250 300-45.00-90.00 Internal Waveguide Displacements p-p) 35 Numerical Experimental 30 Displacement p-p m) 25 20 15 10 5 0 0 50 100 150 200 250 300 Distance mm) 6.E+07 Internal Waveguide Stress 5.E+07 Stress Pa) 4.E+07 3.E+07 2.E+07 1.E+07 0.E+00 0 50 100 150 200 250 300 Distance mm) B-*3= % L3-4' *+ %L.11 '
Phase 90 Phase Degrees) 45 0 0 50 100 150 200 250 300-45 -90 Internal Waveguide Displacements p-p) 40 Numerical Experimental 35 Displacement p-p) m) 30 25 20 15 10 5 0 0 50 100 150 200 250 300 Distance mm) 6.E+07 Internal Waveguide Stress 5.E+07 Stress Pa) 4.E+07 3.E+07 2.E+07 1.E+07 0.E+00 0 50 100 150 200 250 300 Distance mm) B-*-= % L3-4' *+ %L,+, '
Phase 90 45 Phase Degrees) 0 0 50 100 150 200 250 300-45 -90 45 40 Internal Waveguide Displacements p-p) Numerical Experimental Displacem ent p-p) m ) 35 30 25 20 15 10 5 0 0 50 100 150 200 250 300 Distance mm) Internal Waveguide Stress 7.E+07 6.E+07 5.E+07 Stress Pa) 4.E+07 3.E+07 2.E+07 1.E+07 0.E+00 0 50 100 150 200 250 300 Distance mm) B-*D= % L3-4' *+ %L.F, ' ) %' B *+..!
-+-:! =, B-*-,+, ) %' <,D1: -3,: < B-*D.F, ) -..: D3D: *+.F, 3*! # M-3N % ' =,3 B -*F ) +,- -++ *+ *- ) )< MD-N < -3
5.3.7 Summary of Harmonic Analysis of Wire Waveguide # 5!
Distal-Tip Displacement m) 120 100 80 60 40 20 No distal-tip 1.0mm Ball-tip 1.5mm Ball-tip 0 22000 22500 23000 23500 24000 24500 25000 25500 26000 Frequency Hz) B-*F= ) +,- %L-++ ' *++K 3-4 5.4 Coupled Fluid-Structure Model of Wire Waveguide
< : MD.N ) 5.4.1 Acoustic Fluid-Structure Method MD1N) % ) -.' < [ M ] u) + [ K ] u) = F ) + [ R] P) S S S %--' T B M ] P) + [ K ] P) = F ) ρ [ R] u) [ F F F 0 P ) P ) L. M&NL ) ) -- ) ) ) -D
= M ρ 0 R S T 0 M F u K S + P 0 R u F = K F P F S F %-D' B #.G%. 3 ' %B<' # # *.G%. 3 ' B-*1 % & % ' 7 P = + %-F' max 2 2 P R PI
A < A B-*1<! B< : 5.4.2 Fluid-structure model of spherical distal-tip # +,- -++ *+ *- %X*-1+ *' %X*+-+, 'MF1N
+,- *+ B -*G MD+N B-.+ %' *+ # >+C? >+;? *+*- B-.*B-.. ) *- 0
< $ % < $<% ; ; < $; % B-*G < # B< : 7 7 *+
5 > B-.+ %' *+ D3-K.,-/ 0
Distal-Tip Displacement p-p m) 180 160 140 120 100 80 60 40 20 No Distal Fluid 100m With Distal Fluid 100m With Distal Fluid 150m 0 22000 22500 23000 23500 24000 24500 25000 25500 26000 Frequency Hz) B-.*= ) +,-%L-++' *+ *++K*-+K%'
Distal-Tip Displacement p-p m) 140 120 100 80 60 40 20 No Distal Fluid With fluid 100m With fluid 150m 0 22000 22500 23000 23500 24000 24500 25000 25500 26000 Frequency Hz) B-..= ) +,- %L-++ ' *- *++K *-+K %' %>+C?' % ' +,- *+ B-., ) -1MD+N*+ %D3-2 ')%.,- / 0'
P max 2 R cosθ 2 2 = 2π ρrf d 0 %-1' 2 r *1-+++ 7.-7 [. B.*. ) -GM-FN.11/ ) *++.++M-3-1N T 2 Pm = %-G' 2ρc B-.3 >+C? B -.- >+;? *+ *- %'
200000 180000 160000 64.5m Numerical 64.5m Analytical 140000 Pressure Pa) 120000 100000 80000 60000 40000 20000 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Distance from distal-tip mm) B-.,= >+C? *+ D3-K.,-/0
350000 64.5m, 1.0mm tip 300000 95m, 1.0mm tip Pressure Pa) 250000 200000 150000 100000 51m, 1.5mm tip 76m, 1.5mm tip Cavitation Threshold 2.5W/cm^2) 50000 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Distance mm) B-.3= >+C? *+ *-.,-/ 0 = %.-7 [. '
Pressure Pa) 350000 300000 250000 200000 150000 100000 64.5m, 1.0mm tip 95m, 1.0mm tip 51m, 1.5mm tip 76m, 1.5mm tip Cavitation Threshold 2.5W/cm^2) 50000 0 0 0.5 1 1.5 2 2.5 3 Distance mm) B-.-= >+;? *+ *-.,-/ 0 = %.-7 [. '
B-.D, +,- *- -*2 < MD.N & B-.F B-.F : MD.NB-.1 *. *: : MD.N,! # D-2 B -.G 5 &
B-.D % ' *- -*K.,-/ 0
B-.F %'.3D *,+K..-/ 0 : MD.N
20000 18000 16000 Experimental, Makin [62] Numerical 14000 Pressure Pa) 12000 10000 8000 6000 4000 2000 0 0 20 40 60 80 100 Distance mm) B-.1= : MD.N
' Pressure [Pa] '
B-.G= ' : MD.N' % LD-2 %'' %O*. ' & 5.4.3 Fluid-structure model of wire waveguide with no distal-tip # +,- B-,+B-,* **.D--1+2 B-,. B-,,
# *+ B -,3 *+ D+ 2.-7 B -,+ ) [. M-3N
B-,* %'+,- %)L.,-/ 0 L**2 ' 160000 140000 120000 11µm 26µm 55µm 80µm Pressure Pa) 100000 80000 60000 40000 20000 0 0.0 0.5 1.0 1.5 2.0 Distance from distal-tip mm) B-,.= %+,- '.,-/ 0
B-,, % L1+2 %'' +,-
350000 68um p-p) Pressure Pa) 300000 250000 200000 150000 100000 54ump-p) 27ump-p) Cavitation Threshold 2.5W/cm^2) 50000 0 0 0.5 1 1.5 2 2.5 3 3.5 4 Distance mm) B-,3= %*+ '.,-/ 0= %.-7 [. '
5.5 Summary # 3-4 ) % ' : MD.N )
& 1 " /#$ % % &"" 6.1 Introduction & *+ =,! +,- = -
6.2 Tapered Wire Waveguide #! *+ +,- B D* 7 = %*+.,+<7 <= E " <#'! =,,*+ & *+ +,- *+.11 BD. = 3! +,- % ' # +,- BD, : MD.N +3
3 01 3 0# #: BD* +,-
80 70 Distal-Tip Displacement µm p-p) 60 50 40 30 20 10 0 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Input Power Dial Setting BD. *+.11
BD, +,- 5 1
6.3 Model Materials = %' MF1N< %@#' MF1FG% MDN'N ) & =; $= " =%E/'..+3+ -+!M1+N= % ' BD3 5 <MD.+N& ;&;= = / /.+T7.[ BD- -+! B DD 9? D+: F+: )<MD.+NB.,%*3' 3*D:
9? * *+++: M1* 1.% D'3G1,N
&&! &- BD3&
Strain -0.09-0.08-0.07-0.06-0.05-0.04-0.03-0.02-0.01 0 0-2,000,000-4,000,000 Stress Pa) -6,000,000-8,000,000-10,000,000-12,000,000-14,000,000-16,000,000 Calc. Carb. 1 Calc. Carb. 2 20kN Calc. Hydr. 40kN Calc. Hydr. 50kN Calc. Hydr. -18,000,000 BD-; %L.' %.+3+-+!'
0 Strain -0.09-0.08-0.07-0.06-0.05-0.04-0.03-0.02-0.01 0-1,000,000 Stress Pa) -2,000,000-3,000,000-4,000,000-5,000,000-6,000,000 Slope = 60 MPa R 2 = 0.9776 Slope = 70 MPa R 2 = 0.9742 Calc. Carb. 1 Calc. Carb. 2 Linear Calc. Carb. 2) Linear Calc. Carb. 1) BDD=
6.4 Testing Ultrasonic Wire Waveguide Apparatus on Model Materials =, BDFBD1 %.$ %.'.G!.O $.. +-! B [ BDGBD*+ %.'*! BD** BD*..! #,-.1. [ -* [ -+!
Fc Fr Fa Specimen Slider/ Holder Nylon) Table-top Steel) W =mg N) Waveguide and horn BDF
BD1#