Experimental and Numerical Investigation of Therapeutic Ultrasound Angioplasty

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1 Dublin Institute of Technology Other resources School of Manufacturing and Design Engineering Experimental and Numerical Investigation of Therapeutic Ultrasound Angioplasty Graham P. Gavin Dublin Institute of Technology, M.S. J. Hashmi Dublin City University Garrett B. McGuinness Dublin City University Follow this and additional works at: 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 It has been accepted for inclusion in Other resources by an authorized administrator of For more information, please contact This work is licensed under a Creative Commons Attribution- Noncommercial-Share Alike 3.0 License

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6 Acknowledgements & : ;: : 9 $ : $</ <: : = " ) <: : = " : 6 > 5?

7 Table of Contents ) 456 # # A A C! C@C@ 7 C@C@ & 0) 047 ** = * *. :, *, = # ) - *3 " # D *- ;E 5 : F & ) 8 G.. = # ) *,..* : # ) *,... = # *-., " 77 *F.,* *F.,. " *1

8 .,, : *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

9 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, %'; A 7 7 G+ 3- < GF & ) + ; ; < -* G1 -. : #7 7 *++ -.* : #: * : : #

10 7 7 *+. -., < #: * ; : # * <: # *+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) ; ; D* *-F D. 7 7 *-1 D, : : *D. D3 " 7 7 # : : *DD D- " 7 7 B *F3

11 D-* = *F3 D-. # < *FD DD < *FG & 3) &< ; = F* = *1+ F. <; *1. F, ;B *1F 8 > 4

12 8 < & 0) 047 B**.++,. B**.++3 +D3. B*. : ><?& # 3 B*. : ><DD+? < 3 & ) B.* < # *+ B..! *. B., " ) *3 B.3 $.+ B.3.+ B.- <.. B.D $.- B.F # 7.1 B.1 #,+ B.G,* B.*+,, B.**

13 ,- 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

14 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

15 %'.11 G3 B3*- %'.F, G- B3*- %',+, GD & ) + ; ; < 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 )

16 +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,+, %',.K *.. B-** = **1J,+, %',.K % L*-'3-4 *., B-*. = **1J,+, %'3DK % L..-'3-4 *.3 B-*, =%' %L.11' *.D

17 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?

18 *+ *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-,. = % '

19 %+,- '.,-/ 0 *-, B-,, % L 1+2%'' +,- *-3 B-,3 = % ' %*+ '.,-/ 0 *-- & 1) ; ; BD* +,- *-G BD. %'*+.11 *D+ BD, +,- 5 1 *D* BD3 & *D3 BD- ; %L.' %.+3+-+!' *D- BDD = *D- BDF *DF BD1 #

20 *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

21

22 8! & ) * #.D.. 7.D & :) ; ; 9043,* " ) 3. & 9) & 3:423 ; ; 3* = 1-3. = 1G & ) + ; ; < -* =#! ; B) *+-

23 !"#$ % % % &% % ' % & &

24 ) * +, -. / !6$ u ) u ) u ) a F ) 0*2!7$

25 8 P ) 9 P ) [R]... : ; << :

26 ! 6 = " 7 7 $ $ $ &: $ B : <6/.++-'=>!$ = ## B< < " # $ $ $ & : $ B : <6 / '' ' * >.++- = = " # $ $$ &: $B: <6/ % BB >*>? &'>.++-! : < " # $ $$ &: $B: <6/ % BC >*>? &'>.++3 = < & " # $ $ $ & : $ B : <6 / * >.++3

27 = " 7 # )$ $ $ &: $ B : <6/ > ' *@@E >.++- " 7 # )$ $ $ & : $ B : <6 / > + *@>.++-

28 >F >

29 & Cardiovascular Disease 7 / E %=@' *DF =@ M*N& M*N = %=/ ' " % "' %3.4' *- M.N ) # / # #.++3 P,D13 M,N.++,,G4 B **M3N= JD3 B**.++3 =@.34 %D*1,*+++++ ' " %--D,*+++++ 'M3N

30 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-

31 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

32 + * & 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

33 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

34 ) M.,N ) M.3%.,'.-.DN ) ) MF.*.F.1N %$ '.++- B S %< =" <#' =R < " )M.GN= %.++-' B # %B#' " < %.++-'M.G,+N : ) < )

35 1.5 Research Objectives and Methodology 5 # ) # # B )

36 & 2.1 Vascular Disease # ) B.*M,*N! # ) M-N 7 M,,N # 0 MD,*N

37 B.*< # : # 7 / M,*N% : M,.N'

38 # M,3,-,D% D'N M,FN Q ) MD,1N )MD,1N ) ) ) B..MDN )) M,1N ) B..MDN E ) ) MDN M*GN

39 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 ) Mechanical Properties of Atherosclerotic Plaques < / M3+3*3.N

40 5 ) )) <MD.+N ) < %)' - H- # %' % ' % ' 5 B., ) ) ) ) % ' ) Strain Hard Medium Healthy Soft Stress kpa) 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 '%- '

41 ) ) ) )., ) )) ) ) < MD.+N M3,333-3DN ) 5 AM*FN Complications Associated with Present Procedures 1+4 M*-N : hypocellular: containing less than the normal number of cells = ) )) = ) < 5 M3FN

42 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 Introduction *GF+ <M.3%.,'N *G1+ <;

43 ! 5 < M.*.-.DN & < 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

44 M.-N B % ) ' % ' # M-3N # B M-3N < ) < B.3 ) M--N / M-3N7 *-+K ) *++/ 0 # M.3%.,'.-.DN Minimal Invasive Delivery of Ultrasound : %X*D++ ' %Y+,- ' 7

45 -? =? + < + - *=+ B.3$ B.3 ; M.*N

46 B *-B%X+- ' M-DN #MFN M-*N M-*N.+ <M3FN*F Mechanical Effects of Wire Waveguide Tip Displacement # M-+N 5 Q ) M-F-1-GD+N# B Direct Contact Ablation ; MD*N

47 Wire waveguide in catheter Direct Contact Ablation Cavitation Pressure Waves Acoustic Streaming Distal Tip Vibration 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

48 Acoustic Pressure Waves and Cavitation # M-1D.NE = ) &M-FN.3,= M-F-1D,N 9B 0M.,N 5 ) Acoustic Streaming B.DM-1-GN Testing of Ultrasound Delivered via Wire Waveguide Q%' %' 7

49 Mechanical Performance Evaluation #MFN.+/0 %-+4 ' +FD.+ 1G " %' B 1J.-7 D,-K ***K.* ) M-3N: M.*-*N..

50 @ 6 B.D$ #! M-1N.*#.+/ 0 #MFN

51 Acoustic Horn Tip Power Watts) Waveguide Tip Displace. p-p m) Author Rosenschein et al [21] Frequency of Operation khz) Distal Peak-topeak Displacement µm) ± 25 Ariani et al [7] Demer et al [51] ± 25 Makin et al[62] / 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 *..-+ :

52 ;M.*N 17

53 Pressure Pa) Distance mm) B.F# : MD.N% R ' Clinical Evaluation # MFN7 Q B.1.* E M.*D3N

54 <M-.N *G-/0 -+,34 ) M-*N B.G B Q ) M-DN

55 200 Disruption of thrombi Average Disruption Time Sec) Power Watts) B.1# %L-+' #MFN% R

56 Pressure Volume Curve Pre 1 Pre 2 Post 1 Post 2 Pressure atm) E E E E+02 Volume 100 microlitres/ division) 1.10E+03 B.G % ' % ' M-*N% R ' 2.4 Theoretical Mechanics Background % ' % ' Steady-state vibration of a uniform rod

57 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

58 B.*+ G # < MD,N

59 < ) )., %L*,-F' %L+.3D1Z' ) nc l n = %.,' 4 f 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

60 P r 2R Direction of Motion B.** #! M-1N

61 2.4.3 Cavitation B 7 &M-FN ).- T 2 Pmax = %.-' 2ρc # M-3N.,7 [. ).+J,+/0B.*. ) )*++/ 0 B.*. ).+3-/ Acoustic Streaming # M-1-GN B.D A7 M-GN M-1N

62 Cavitation Threshold 1.E+08 1.E 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 '

63 2.5 Finite Element Analysis of Ultrasound Transmission in Wire Waveguides 7 ) B! ) MDDN Material Properties ) 9?: %+' %' MDD DFN ) %c' ).D E c = %.D' ρ ) MD1N Mesh Density

64 : 5 ) ) : ) = ) MDDN Damping MDDDFN6MDGN

65 2.6 Summary = ) ) A ) ) 7 "< ) #? # &

66 & :!! "#$ %% &"" 3.1 Introduction to Apparatus Design )< ),* 5 B,*

67 ,*" ) Performance Characteristic Specification Justification Frequency of Operation 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

68 =0 = =: " 7 7 B) =9 <4 = E =1 6 + # = # < B,*& 5

69 3.2 Ultrasonic Wire Waveguide Apparatus Design and Development <*-+S &" S%3* ; =" <#' Ultrasonic generator and converter %G-+@ '..-/0ID4MF+N ) ) B,. ) # ) [ )% ' A= ) M-3N

70 A8& B,. &" $ 0 %0 '..-/ 0 B,,MF+N

71 3.2.2 Acoustic Horn 5 E %&S: - ' *++2 )..- / 0 0 MF*N B,3 ) MF+N B, Wire Waveguide Design! %!' B 7 : R %GD+G;B 7! 3D1+G' < MF.F,N NiTi Wire Waveguide -D47 %X3,47 '7 %#' *+ + =MF3N / *D- + =

72 MF3N! *+ +D +,- *+ +D +,- ) : 9? Q) < +?4 = B,, 0 " =

73 4 B,3 # / & - B,-# # / = Tensile testing of NiTi wire waveguide < +,- +D 5 Q*' 9? : % '.',' 7 / R /.+T7. [ %.+ + =' +,- B,D MF.F,F-N

74 & 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

75 3.2.4 Connection of wire waveguide to acoustic horn ) #..-/0 ) $ ID4 ) 1.40E E E+09 Austenitic Transformation Martensitic Stress Pa) 8.00E E E E E Strain B,D< +,-!

76 1.80E E E+09 Stress Pa) 1.20E E E E+08 Cycle 1 Cycle 2 Cycle E E E Strain

77 B,F= +D! ) 0 ) Evaluation of wire waveguide connection method # *+ +D +,- ) MF+N B,1 B *-,+

78 *- B,G & > - " B,1 J

79 - 4 & ; ; B,G # Q ;

80 Single side set-screw. *+ :. B,*+B,** B,** B %,- 3- ' %D+ 1+ ' # & F+ %A S; = >D+*?' B,*. %L-' 7 B,*, %L*-' B B,*, *+ % ' +D +,-

81 B,*+ 4A - #: ; ; 0 * B,**

82 45 Time to Failure Single Side Set-screw) Time Seconds) Wire Waveguide Diameter mm) B,*.

83 A A & 4 A A A B,*, +D

84 +,- +D & 7 ) E Double side set-screw B,*3,*- %L-' B,*D #%L*-' B +,-

85 B,*3 4A #1 ; ; 4A B,*-

86 60 Time to Failure Double Side Set-screw) Time Seconds) Wire Waveguide Diameter mm) B,*D

87 +,- +D *+ E Axial set-screw D+ :, B,*F,*1 %L-' B,*G # # %L*3' B,.+ %L*', E B,*1 *+ %L,',++ +,- +D D+

88 B,*F A & 4A A A A 0# A A B,*1 *+

89 +,- +D B,.* %A R ; = >D+*?'E B,.3 B Final apparatus design and housing & # B,.. 5 # 5 # 5? B,., B,++ B,.3 +,-

90

91 350 Time to Failure Axial Crimped Set-screw) Time Seconds) Wire Waveguide Diameter mm) 6A ; < 46A B,.+ +D

92 < #: B,.* +,- # % '

93 B,.. Figure 3.21: Detailed drawing of ultrasonic wire waveguide apparatus

94 &! ; B,.,

95 350 Time to Failure in Housing Time Seconds) mm 0.35mm with sleeve 0.6mm 1.0mm Connection Method B,.3

96 3.3 Summary #! 5 *+,++ *+ # 7 +D +,- G+ +,- # = D ) ) = 3-

97 & 9 #'#$ %% &"" 4.1. Introduction ) =, 5 ) )

98

99 4.2. Direct peak-to-peak displacement measurement ) = B3* Displacement measurement technique " ) E B3. 7 E B3. G<A L'A B3, %<< ' %@ >@$ =3++?'= % #< &' 5 1+

100 ; ; 6+ + A & &A A B3* = + = 6! 6! + = 4 C 4 C B3.<

101 Calibration of Objective Lenses = %T ;R >< :?' 7 5 = B B & D+ * B 3-.+K.+K *GG1K %\' +*1K < D+K -G1.%\+.,K '*++K GG13K %\+..K ' %\ +.,K ' D+K GGF4 %,\' I +DGK

102 6+ & & B3, =

103 B33.+*++ 10 Histogram of Displacement Measurement 9 Number of Measurements Displacement m) B3-/.+K % *GG1K \+*1K '

104 4.3. Wire Waveguide Distal-Tip Peak-to-Peak Displacements " 5 3+ B3D B3F *+ B *+ *+ +D +,- B, Effect of input power dial settings *+ B31 < E K

105 ; + B3D

106 B3F

107 Distal-Tip Displacement µm p-p) Input Power Dial-Setting Length =298mm Length = 278mm Length = 258mm Length = 228mm B31 *+ *

108 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

109 90 Output peak-to-peak Displacement µm) Wire Length mm) B3G7 **1,+, *- 3*= ).,-/ 0 n Analytical Experimental Percentage Lengths mm) Lengths mm) Error %)

110 ) F. F+ ).,-/ 0 / ) ).* ) " B3*+ & 0 *- %GC',.K # 3.

111 90 Power Setting = 1.5 Output peak-to-peak Displacement µm) y = x Analytical Non- Resonant Lengths Linear Line AA) Wire Length mm) B3*+7 **1,+, ) : ) /

112 ...-.-*+ B3**& 3. * *+ : *K 33-K 3DK

113 Output peak-to-peak Displacement µm) Power Setting = 2 Power Setting = 2.25 Power Setting = 2.5 Linear Trend 2) Linear Trend 2.25) Linear Trend 2.5) 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 Displacement results along length of wire waveguide " ) 3. %'

114 %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*-

115 .F,,+,.11 E ),-

116 Internal Displacements p-p) Displacement m) Distance mm) B3*.#.11 5,.K.,-/ 0! %'

117 B3*, G.K D,*FK -3K

118 Displacements p-p) along wire waveguide Displacements m p-p) Distance mm) B3*3.11 *-% L,.K '

119 Displacements p-p) along wire waveguide 40 Experimental 273mm Experimental 288mm Displacements p-p) Distance mm) B3*-.F, *-% L,.K '

120 Displacements p-p) along wire waveguide 40 Experimental 303mm Experimental 288mm Displacements p-p) Distance mm) B3*-,+, *-% L,.K '

121 4.5. Summary 7 7 / ).,-/0 B &

122 & ) #%% * 5.1 Introduction = 3 E ) 7 =. ) Q! # B

123 =. B ) = 3 E < : MD.N )< 5.2 Modal Analysis of Wire Waveguide #

124 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

125 8 +,,+,+,+ B-*

126 5.2.2 Effects of Mesh Density on Modal Analysis of Wire Waveguide B-. ). 3) %3.'MFFN 0 0 : % ' %' %' %H'MDDN : ),+, *+ +D +,- 9?! = Sensitivity Analysis of Material Properties B 9? I-4 = 3 = 3

127 B-. *+.HD+D. B-. *+.H,+, 3

128 5.2.4 Results of Modal Analysis ),+, -*)+,+/0 ) ) B-, ) B %*H*+' ) ) *H- B *+ B-, * H*+ ) 7 ) *H.++ ).HD+D B-.. 3 *+ -, B-,B-, +D +,-

129 -*= #! ; B),+, Resonant Frequency Analytical Resonant Frequency Solution Hz) Numerical Resonant Frequency Predictions Hz) % Error) 1.0mm 0.6mm 0.35mm 0.03%) %) %) %) %) %) %) %) %) %) %) %) %) %) %) B.HG+G +D, 3 < +,-.H*.*. 3

130 Summary of Modal Analysis -* ) ) ++,4 ) B-3 9? I-4 ) 5 )

131 Frequency Hz) st Resonant Frequency 2nd Resonant Frequency 3rd Resonant Frequency 4th Resonant Frequency 5th Resonant Frequency Mesh Density r y) B-,: *+,+,

132 Frequency Hz) st Resonant Frequency 2nd Resonant Frequency 3rd Resonant Frequency 4th Resonant Frequency 5th Resonant Frequency Mesh Density r y) B-,: +D,+,

133 Frequency Hz) st Resonant Frequency 2nd Resonant Frequency 3rd Resonant Frequency 4th Resonant Frequency 5th Resonant Frequency Mesh Density r y) B-,: +,-,+,

134 st Resonant Frequency 5th Resonant Frequency Frequency Hz) %) %) Young's Modulus Gpa) B-3 ) %I-4'9? L,+, st Resonant Frequency 5th Resonant Frequency Frequency Hz) %) %) Density kg/m^3) B-3 ) %I-4' L,+,

135 5.3 Harmonic Response Analysis of Wire Waveguide # ) MDFN ) ) ) = 3 ) Harmonic response method # ) MDFN [ M ] u) + [ C] u) + [ K] u) = F a ) %-.' [M ] L [K ] L a F ) L

136 [C] L u ) u ) u ) L [ C] = β )[ K] %-,' β ) ζ ) ) f ) ζ β ) = %-3' πf B-- # G!!$$ )

137 5.3.2 Distal-tip response of wire waveguides over a range of frequencies ) +,+/0 ) : *+ +D +,- ) Distal-tip response of wire waveguides over a range lengths = 3 : **1,+, - *+ +D +,- ).,-/ 0 ) Displacement response along length of wire waveguides " % ' ).,-/ 0 = 3

138 5.3.5 Wire Waveguides with Spherical Distal-tip Geometry / M.-.-N7 = 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

139 7 ) B-G 5 ) J = 3 B )

140 8 +,,-.#,+,+ B--

141 8.00E-04 Distal-tip peak-to-peak displacement m) 7.00E E E E E E E E+00 Diameter = 0.35mm Diameter = 0.6mm Diameter = 1.0mm Frequency Hz) B-D )+J,+/ 0,+K,+, *4

142 5.00E-04 Distal-tip peak-to-peak displacement m) 4.50E E E E E E E E E-05 Input = 30m p-p) Input = 60m p-p) Input = 90m p-p) 0.00E Frequency Hz) B-F *+ )*-J,+/ 0,+K D+K G+ K,+, *4

143 Distal-tip peak-to-peak displacement m) 2.00E E E E E E E E E E-05 Damping = 1% Damping = 2% Damping = 3% Damping = 4% Damping = 5% 0.00E Frequency Hz) B-1 *+ )*1J.1/ 0,+K,+, *4-4

144 Distal-tip peak-to-peak displacement m) 3.00E E E E E E-05 Length = 303mm Length = 283mm Length = 263mm 0.00E Frequency Hz) B-G *+ )*1J.1/ 0,+K.D,.1,,+, *4

145 B-*+ ).,-/0 *+ **1J,+, -,.K *+ *- % ' 3-4 B-** MF,N % ' B-*..- 3DK Q

146 Damping = 4% Distal-tip peak-to-peak Displacement µm) 100 Damping = 4.5% Damping = 5% Wire Length mm) B-*+ *+.,-/ 0 **1 J,+,,.K

147 Distal-tip peak-to-peak Displacement µm) Numerical Experimental Wire Length mm) B-**= *+ **1 J,+,,. K % L*-' 3-4

148 Distal-tip peak-to-peak Displacement µm) Numerical Experimental Wire Length mm) B-*.= *+ **1 J,+, 3D K % L..-' 3-4

149 B-*, *+.11,.K.,-/0 ).*# 3-4 B -*3 %'.11,.K.,-/0 3-4 #.11 B-*, %,.K %'' 0# -*1 : 7 B-*3.1K %'# 0.1:

150 Phase Numerical Analytical Phase Degrees) Distance mm) Internal Displacements p-p) 35 Displacement m) Distance mm) 6.0E+07 Stress 5.0E E+07 Stress Pa) 3.0E E E E Distance mm) B-*,= % ' *+ %L.11 '

151 Phase Phase Degrees) Internal Waveguide Displacements p-p) 35 Numerical Experimental 30 Displacement p-p m) 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 Distance mm) B-*3= % L3-4' *+ %L.11 '

152 Phase 90 Phase Degrees) Internal Waveguide Displacements p-p) 40 Numerical Experimental 35 Displacement p-p) m) 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 Distance mm) B-*-= % L3-4' *+ %L,+, '

153 Phase Phase Degrees) Internal Waveguide Displacements p-p) Numerical Experimental Displacem ent p-p) m ) 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 Distance mm) B-*D= % L3-4' *+ %L.F, ' ) %' B *+..!

154 -+-:! =, B-*-,+, ) %' <,D1: -3,: < B-*D.F, ) -..: D3D: *+.F, 3*! # M-3N % ' =,3 B -*F ) +,- -++ *+ *- ) )< MD-N < -3

155 5.3.7 Summary of Harmonic Analysis of Wire Waveguide # 5!

156

157 Distal-Tip Displacement m) No distal-tip 1.0mm Ball-tip 1.5mm Ball-tip Frequency Hz) B-*F= ) +,- %L-++ ' *++K Coupled Fluid-Structure Model of Wire Waveguide

158 < : MD.N ) 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

159 = 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

160 A < A B-*1<! B< : Fluid-structure model of spherical distal-tip # +,- -++ *+ *- %X*-1+ *' %X*+-+, 'MF1N

161 +,- *+ B -*G MD+N B-.+ %' *+ # >+C? >+;? *+*- B-.*B-.. ) *- 0

162 < $ % < $<% ; ; < $; % B-*G < # B< : 7 7 *+

163 5 > B-.+ %' *+ D3-K.,-/ 0

164 Distal-Tip Displacement p-p m) No Distal Fluid 100m With Distal Fluid 100m With Distal Fluid 150m Frequency Hz) B-.*= ) +,-%L-++' *+ *++K*-+K%'

165 Distal-Tip Displacement p-p m) No Distal Fluid With fluid 100m With fluid 150m Frequency Hz) B-..= ) +,- %L-++ ' *- *++K *-+K %' %>+C?' % ' +,- *+ B-., ) -1MD+N*+ %D3-2 ')%.,- / 0'

166 P max 2 R cosθ 2 2 = 2π ρrf d 0 %-1' 2 r * [. B.*. ) -GM-FN.11/ ) *++.++M-3-1N T 2 Pm = %-G' 2ρc B-.3 >+C? B -.- >+;? *+ *- %'

167 m Numerical 64.5m Analytical Pressure Pa) Distance from distal-tip mm) B-.,= >+C? *+ D3-K.,-/0

168 m, 1.0mm tip m, 1.0mm tip Pressure Pa) m, 1.5mm tip 76m, 1.5mm tip Cavitation Threshold 2.5W/cm^2) Distance mm) B-.3= >+C? *+ *-.,-/ 0 = %.-7 [. '

169 Pressure Pa) m, 1.0mm tip 95m, 1.0mm tip 51m, 1.5mm tip 76m, 1.5mm tip Cavitation Threshold 2.5W/cm^2) Distance mm) B-.-= >+;? *+ *-.,-/ 0 = %.-7 [. '

170 B-.D, +,- *- -*2 < MD.N & B-.F B-.F : MD.NB-.1 *. *: : MD.N,! # D-2 B -.G 5 &

171 B-.D % ' *- -*K.,-/ 0

172 B-.F %'.3D *,+K..-/ 0 : MD.N

173 Experimental, Makin [62] Numerical Pressure Pa) Distance mm) B-.1= : MD.N

174 ' Pressure [Pa] '

175 B-.G= ' : MD.N' % LD-2 %'' %O*. ' & Fluid-structure model of wire waveguide with no distal-tip # +,- B-,+B-,* **.D--1+2 B-,. B-,,

176 # *+ B -,3 *+ D B -,+ ) [. M-3N

177 B-,* %'+,- %)L.,-/ 0 L**2 ' µm 26µm 55µm 80µm Pressure Pa) Distance from distal-tip mm) B-,.= %+,- '.,-/ 0

178 B-,, % L1+2 %'' +,-

179 um p-p) Pressure Pa) ump-p) 27ump-p) Cavitation Threshold 2.5W/cm^2) Distance mm) B-,3= %*+ '.,-/ 0= %.-7 [. '

180 5.5 Summary # 3-4 ) % ' : MD.N )

181 & 1 " /#$ % % &"" 6.1 Introduction & *+ =,! +,- = -

182 6.2 Tapered Wire Waveguide #! *+ +,- B D* 7 = %*+.,+<7 <= E " <#'! =,,*+ & *+ +,- *+.11 BD. = 3! +,- % ' # +,- BD, : MD.N +3

183 # #: BD* +,-

184 80 70 Distal-Tip Displacement µm p-p) Input Power Dial Setting BD. *+.11

185 BD, +,- 5 1

186 6.3 Model Materials = %' MF1N< %@#' MF1FG% MDN'N ) & =; $= " =%E/' !M1+N= % ' BD3 5 <MD.+N& ;&;= = / /.+T7.[ BD- -+! B DD 9? D+: F+: )<MD.+NB.,%*3' 3*D:

187 9? * *+++: M1* 1.% D'3G1,N

188 &&! &- BD3&

189 Strain ,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+-+!'

190 0 Strain ,000,000 Stress Pa) -2,000,000-3,000,000-4,000,000-5,000,000-6,000,000 Slope = 60 MPa R 2 = Slope = 70 MPa R 2 = Calc. Carb. 1 Calc. Carb. 2 Linear Calc. Carb. 2) Linear Calc. Carb. 1) BDD=

191 6.4 Testing Ultrasonic Wire Waveguide Apparatus on Model Materials =, BDFBD1 %.$ %.'.G!.O $.. +-! B [ BDGBD*+ %.'*! BD** BD*..! #,-.1. [ -* [ -+!

192 Fc Fr Fa Specimen Slider/ Holder Nylon) Table-top Steel) W =mg N) Waveguide and horn BDF