The shock-induced collapse of a pre-existing nucleus near a solid surface in the focal region of a lithotripter is investigated. The entire flow field of the collapse of a single gas bubble subjected to a lithotripter pulse is simulated using a high-order accurate shock- and interface-capturing scheme, and the wall pressure is considered as an indication of potential damage. Results from the computations show the same qualitative behavior as that observed in experiments: a re-entrant jet forms in the direction of propagation of the pulse and penetrates the bubble during collapse, ultimately hitting the distal side and generating a water-hammer shock. As a result of the propagation of this wave, wall pressures on the order of 1 GPa may be achieved for bubbles collapsing close to the wall. The wall pressure decreases with initial stand-off distance and pulse width and increases with pulse amplitude. For the stand-off distances considered in the present work, the wall pressure due to bubble collapse is larger than that due to the incoming shockwave; the region over which this holds may extend to ten initial radii. The present results indicate that shock-induced collapse is a mechanism with high potential for damage in shockwave lithotripsy.

1.
NIH
, “
Kidney stones in adults
,” on the WWW, URL: http://kidney.niddk.nih.gov (Last viewed April 21,
2008
).
2.
R. F.
Paterson
,
D. A.
Lifshitz
,
J. E.
Lingeman
,
A. P.
Evan
,
B. A.
Connors
,
N. S.
Fineberg
,
J. C.
Williams
, and
J. A.
McAteer
, “
Stone fragmentation during shock wave lithotripsy is improved by slowing the shock wave rate: Studies with a new animal model
,”
J. Urol. (Baltimore)
168
,
2211
2215
(
2002
).
3.
W.
Eisenmenger
, “
The mechanisms of stone fragmentation in ESWL
,”
Ultrasound Med. Biol.
27
,
683
693
(
2001
).
4.
R. O.
Cleveland
and
O. A.
Sapozhnikov
, “
Modeling elastic wave propagation in kidney stones with application to shock wave lithotripsy
,”
J. Acoust. Soc. Am.
118
,
2667
2676
(
2005
).
5.
M.
Lockandwalla
and
B.
Sturtevant
, “
Fracture mechanics model of stone comminution in ESWL and implications for tissue damage
,”
Phys. Med. Biol.
45
,
1923
1940
(
2000
).
6.
S.
Zhu
,
F. G.
Preminger
, and
P.
Zhong
, “
The role of stress waves and cavitation in stone comminution in shock wave lithotripsy
,”
Ultrasound Med. Biol.
28
,
661
671
(
2002
).
7.
A. J.
Coleman
,
J. E.
Saunders
,
L. A.
Crum
, and
M.
Dyson
, “
Acoustic cavitation generated by an extracorporeal shockwave lithotripter
,”
Ultrasound Med. Biol.
13
,
69
76
(
1987
).
8.
L. A.
Crum
, “
Cavitation microjets as a contributory mechanism for renal calculi disintegration in ESWL
,”
J. Urol. (Baltimore)
140
,
1587
1590
(
1988
).
9.
A.
Philipp
and
W.
Lauterborn
, “
Cavitation erosion by single laser-produced bubbles
,”
J. Fluid Mech.
361
,
75
116
(
1998
).
10.
Y.
Tomita
and
A.
Shima
, “
Mechanisms of impulsive pressure generation and damage pit formation by bubble collapse
,”
J. Fluid Mech.
169
,
535
564
(
1986
).
11.
M. S.
Plesset
and
R. B.
Chapman
, “
Collapse of an initially spherical vapour cavity in the neighbourhood of a solid boundary
,”
J. Fluid Mech.
47
,
283
290
(
1971
).
12.
Y. A.
Pishchalnikov
,
O. A.
Sapozhnikov
,
M. R.
Bailey
,
J. C.
Williams
,
R. O.
Cleveland
,
T.
Colonius
,
L. A.
Crum
,
A. P.
Evan
, and
J. A.
McAteer
, “
Cavitation bubble cluster activity in the breakage of kidney stones by lithotripter shockwaves
,”
J. Endourol.
17
,
435
446
(
2003
).
13.
M.
Tanguay
, “
Computation of bubbly cavitating flow in shock wave lithotripsy
,” Ph.D. thesis,
California Institute of Technology
, Pasadena, CA (
2004
).
14.
L.
Rayleigh
, “
On the pressure developed in a liquid during the collapse of a spherical cavity
,”
Philos. Mag.
34
,
94
98
(
1917
).
15.
T. J.
Matula
,
P. R.
Hilmo
,
M. R.
Bailey
, and
L. A.
Crum
, “
In vitro sonoluminescence and sonochemistry studies with an electrohydraulic shock-wave lithotripter
,”
Ultrasound Med. Biol.
28
,
1199
1207
(
2002
).
16.
E.
Johnsen
, “
Numerical simulation of non-spherical bubble collapse
,” Ph.D. thesis,
California Institute of Technology
, Pasadena, CA (
2007
).
17.
A.
Vogel
,
W.
Lauterborn
, and
R.
Timm
, “
Optical and acoustic investigations of the dynamics of laser-produced cavitation bubbles near a solid boundary
,”
J. Fluid Mech.
206
,
299
338
(
1989
).
18.
C. D.
Ohl
and
R.
Ikink
, “
Shock-wave-induced jetting of micron-size bubbles
,”
Phys. Rev. Lett.
90
,
214502
(
2003
).
19.
A.
Philipp
,
M.
Delius
,
C.
Scheffczyk
,
A.
Vogel
, and
W.
Lauterborn
, “
Interaction of lithotripter-generated shock waves with air bubbles
,”
J. Acoust. Soc. Am.
93
,
2496
2509
(
1993
).
20.
G. N.
Sankin
,
W. N.
Simmons
,
S. L.
Zhu
, and
P.
Zhong
, “
Shock wave interaction with laser-generated single bubbles
,”
Phys. Rev. Lett.
95
,
034501
(
2005
).
21.
C. H.
Chang
and
M. S.
Liou
, “
A robust and accurate approach to computing compressible multiphase flow: Stratified flow model and AUSM+-up scheme
,”
J. Comput. Phys.
225
,
840
873
(
2007
).
22.
X. Y.
Hu
,
B. C.
Khoo
,
N. A.
Adams
, and
F. L.
Huang
, “
A conservative interface method for compressible flows
,”
J. Comput. Phys.
219
,
553
578
(
2006
).
23.
R. R.
Nourgaliev
,
T. N.
Dinh
, and
T. G.
Theofanous
, “
Adaptive characteristics-based matching for compressible multifluid dynamics
,”
J. Comput. Phys.
213
,
500
529
(
2006
).
24.
X. Y.
Hu
and
N. A.
Adams
, “
Shock-induced collapse of bubbles in liquid
,” in
Proceeding of the 26th International Symposium on Shock Waves
, Goettingen, Germany (
2007
).
25.
A. R.
Jamaluddin
, “
Free-Lagrange simulations of shock-bubble interaction in extracorporeal shock wave lithotripsy
,” Ph.D. thesis,
University of Southampton
, Southampton, UK (
2005
).
26.
S.
Nagrath
,
K.
Jansen
,
R. T.
Lahey
, Jr.
, and
I.
Akhatov
, “
Hydrodynamics simulation of air bubble implosion using a level set approach
,”
J. Comput. Phys.
215
,
98
132
(
2006
).
27.
E.
Johnsen
and
T.
Colonius
, “
Implementation of WENO schemes for compressible multicomponent flow problems
,”
J. Comput. Phys.
219
,
715
732
(
2006
).
28.
C. C.
Church
, “
A theoretical study of cavitation generated by an extracorporeal shock wave lithotripter
,”
J. Acoust. Soc. Am.
86
,
215
227
(
1989
).
29.
A. J.
Coleman
and
J. E.
Saunders
, “
A survey of the acoustic output of commercial extracorporeal shock wave lithotripters
,”
Ultrasound Med. Biol.
15
,
213
227
(
1989
).
30.
P. A.
Thompson
,
Compressible-Fluid Dynamics
(
McGraw-Hill
,
New York
,
1972
).
31.
R. O.
Cleveland
,
M. R.
Bailey
,
N.
Fineberg
,
B.
Hartenbaum
,
M.
Lokhandwalla
,
J. A.
McAteer
, and
B.
Sturtevant
, “
Design and characterization of a research electrohydraulic lithotripter patterned after the Dornier HM3
,”
Rev. Sci. Instrum.
71
,
2514
2525
(
2000
).
32.
P.
Zhong
,
C. J.
Chuong
, and
G. M.
Preminger
, “
Propagation of shock waves in elastic solids caused by cavitation microjet impact. II: Application in extracorporeal shock wave lithotripsy
,”
J. Acoust. Soc. Am.
94
,
29
36
(
1993
).
33.
K. M.
Shyue
, “
An efficient shock-capturing algorithm for compressible multicomponent problems
,”
J. Comput. Phys.
142
,
208
242
(
1998
).
34.
F.
Harlow
and
A.
Amsden
, “
Fluid dynamics
,” LANL Monograph Technical Report No. LA-4700,
Los Alamos National Laboratory
.
35.
J. P.
Cocchi
,
R.
Saurel
, and
J. C.
Loraud
, “
Treatment of interface problems with Godunov-type schemes
,”
Shock Waves
5
,
347
357
(
1996
).
36.
R.
Abgrall
, “
How to prevent pressure oscillations in multicomponent flow calculations: A quasi conservative approach
,”
J. Comput. Phys.
125
,
150
160
(
1996
).
37.
J. S.
Jiang
and
C. W.
Shu
, “
Efficient implementation of WENO schemes
,”
J. Comput. Phys.
126
,
202
228
(
1996
).
38.
E. F.
Toro
,
M.
Spruce
, and
M.
Spears
, “
Restoration of the contact surface in the HLL-Riemann solver
,”
Shock Waves
4
,
25
34
(
1996
).
39.
A. J.
Coleman
,
M. J.
Choi
,
J. E.
Saunders
, and
T. G.
Leighton
, “
Acoustic emission and sonoluminescence due to cavitation at the beam focus of an electrohydraulic shock wave lithotripter
,”
Ultrasound Med. Biol.
18
,
267
281
(
1992
).
40.
J. J.
Quirk
and
S.
Karni
, “
On the dynamics of a shock-bubble interaction
,”
J. Fluid Mech.
318
,
129
163
(
1996
).
41.
S.
Fujikawa
and
T.
Akamatsu
, “
Effects of the non-equilibrium condensation of vapour on the pressure wave produced by the collapse of a bubble in a liquid
,”
J. Fluid Mech.
97
,
481
512
(
1980
).
42.
R.
Hickling
and
M. S.
Plesset
, “
Collapse and rebound of a spherical bubble in water
,”
Phys. Fluids
7
,
7
14
(
1964
).
43.
A.
Shima
,
Y.
Tomita
, and
K.
Takahashi
, “
The collapse of a gas bubble near a solid wall by a shock wave and the induced impulsive pressure
,”
Proc. Inst. Mech. Eng.
198C
,
81
86
(
1984
).
44.
M.
Kameda
and
Y.
Matsumoto
, “
Shock waves in a liquid containing small gas bubbles
,”
Phys. Fluids
8
,
322
335
(
1996
).
45.
M.
Kameda
,
N.
Shimaura
,
F.
Higashino
, and
Y.
Matsumoto
, “
Shock waves in a uniform bubbly flow
,”
Phys. Fluids
10
,
2661
2668
(
1998
).
You do not currently have access to this content.