Modeling and numerical simulation of the bubble cloud dynamics in an ultrasound field for burst wave lithotripsy - 2.0000946.pdf

Modeling and numerical simulation of the bubble cloud dynamics in an ultrasound field

for burst wave lithotripsy

Kazuki Maeda

, Tim Colonius

, Adam Maxwell

, Wayne Kreider

, and

Michael Bailey

Citation:

Proc. Mtgs. Acoust.

35

, 020006 (2018); doi: 10.1121/2.0000946

View online:

https://doi.org/10.1121/2.0000946

View Table of Contents:

https://asa.scitation.org/toc/pma/35/1

Published by the

Acoustical Society of America

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Volume

35

http://acousticalsociety.org/

176th Meeting of Acoustical Society of America

2018 Acoustics Week in Canada

Victoria, Canada

5-9 Nov 2018

Biomedical Acoustics: Paper 2pBAa5

Modeling

and

numerical

simulation

of

the

bubble

cloud

dynamics

in

an

ultrasound

field

for

burst

wave

lithotripsy

Kazuki

Maeda

Mechanical

Engineering,

University

of

Washington,

Seattle,

WA,

98115;

kazuki.e.maeda@gmail.com

Tim

Colonius

California

Institute

of

Technology,

Pasadena

,

CA

;

colonius@caltech.edu

Adam

Maxwell,

Wayne

Kreider

and

Michael

Bailey

University

of

Washington,

Seattle

,

WA

;

amax38@u.washington.edu,

wkreider@uw.edu,

mbailey@uw.edu

Modeling and numerical simulation of bubble clouds induced by intense ultrasound waves are

conducted to quantify the effect of cloud cavitation on burst wave lithotripsy, a proposed non-invasive

alternative to shock wave lithotripsy that uses pulses of ultrasound with an amplitude of O(1) MPa and a

frequency of O(100) kHz. A unidirectional acoustic source model and an Eulerian-Lagrangian method are

developed for simulation of ultrasound generation from a multi-element array transducer and cavitation

bubbles, respectively. Parametric simulations of the spherical bubble cloud dynamics reveal a new scaling

parameter that dictates both the structure of the bubble cloud and the amplitude of the far-field, bubble-

scattered acoustics. The simulation further shows that a thin layer of bubble clouds nucleated near a

kidney stone model can shield up to 90% of the incoming wave energy, indicating a potential loss of

efficacy during the treatment due to cavitation. Strong correlations are identified between the far-field,

bubble-scattered acoustics and the magnitude of the shielding, which could be used for ultrasound

monitoring of cavitation during treatments. The simulations are validated by companion experiments in

vitro.

Published by the Acoustical Society of America

© 2018 Acoustical Society of America. https://doi.org/10.1121/2.0000946

Proceedings of Meetings on Acoustics, Vol. 35, 020006 (2018)

Page 1

1. INTRODUCTION

This paper provides a brief summary and overview of recent progress in modeling, numerical simulation,

and experiments on cavitation bubble clouds that are nucleated in the human body during treatment using

Burst Wave Lithotripsy (BWL) [1], a method of lithotripsy that uses pulses of high-intensity, focused ultra-

sound at a frequency of

O

(100)

kHz and an amplitude of

O

(1

−

10)

MPa to break kidney stones [7]. BWL is

an alternative to standard shockwave lithotripsy (SWL) [8], which uses much higher amplitude shock waves

delivered at a typically much lower rate. In both SWL and BWL, the tensile component of the pressure can

nucleate cavitation bubbles in the human body. For SWL, cavitation is a significant mechanism in stone

communition, but also causes tissue injury. By contrast, little is yet known about cavitation in BWL. A

series of our studies has successfully identified the effects of cavitation on BWL; although they may be less

injurious than cavitation in SWL, bubble clouds in BWL can scatter a large portion of the incoming wave

energy that would otherwise be transmitted into the stone and thereby potentially cause loss of efficacy of

stone comminution. The latest study reported in our article published in

The Journal of the Acoustical Socity

of America

[6] suggests that the activities of cavitation in the human body and the resulting energy shielding

could be identified by ultrasound monitoring in realtime during the treatment. We will review the results

and their implication for future work.

2. MODELING AND NUMERICAL FRAMEWORK

Our initial experiment identified that diffuse bubble clouds with a size of

O

(1)

mm are formed near the

focal region during the passage of the burst wave in a water tank [5]. They are highly distinct from denser

and larger bubble clouds observed in SWL. For simulation of the clouds in BWL, two numerical tools are

developed: a model of ultrasound generation from a medical transducer [2], and a method of simulating

clouds of cavitation bubbles in the focal region [3]. For the former, an analytical expression was derived

to express acoustic source distribution on an arbitrary curvature of two-dimensional surface that generates

a wave propagating in a favorable direction. For the latter, an Eulerian-Lagrangian method was introduced,

in which the liquid phase is descritized on structured grids and bubbles are treated as spherical cavities that

volumetrically oscillate at the sub-grid scale. The numerical framework enables large-scale simulation of

the ultrasound-induced cavitation growth and collapse of individual bubbles, their mutual interactions, and

the resulting bubble-scattered acoustic waves with and without a kidney stone.

3. ENERGY SHIELDING

A canonical study of the dynamics of isolated, spherical bubble clouds induced by intense ultrasound

waves suggests that even diffuse bubble clouds in BWL can scatter a large portion of the incoming wave

energy, and this can lead to loss of efficacy of stone comminution [4]. In order to quantify the energy

shielding in the presence of a kidney stone, a combined numerical and experimental study has recently

been conducted [6]. Figure 1 shows an overview of the study. In the experiment (Fig. 1a), 10 cycles of

a burst wave with a peak maximum amplitude of 7 MPa and a frequency of 335 kHz was focused from

a multi-element array medical transducer (Fig. 1b) on a cylindrical model kidney stone made of epoxy

resin. A high-speed camera was used to capture bubble clouds nucleated in the proximal surface of the

stone and bubble-scattered acoustic waves were measured by the transducer array that was used to generate

the burst wave. In high speed images, we observed a thin layer of bubble clouds nucleated on the proximal

surface of the stone (1c). The simulation successfully reproduced the experimental bubble clouds (Fig. 1d).

Figure (1e) shows the correlation between the scattering factor,

F

, and the shielding factor,

S

, obtained

from simulations with various values of the thickness and the initial void fraction of bubble clouds,

β

0

. The

scattering factor is a function of the maximum value of the imaging functional,

I

, a metric introduced to

K. Maeda et al.

Modeling and simulation of the bubble cloud dynamics for BWL

Proceedings of Meetings on Acoustics, Vol. 35, 020006 (2018)

Page 2

Figure 1: Overview of the study of the energy shielding of kidney stones by cavitation bubble clouds

in BWL. (a) shows the schematic of the experimental setup. (b) shows the multi-element array medical

transducer. (c) and (d) show images of representative bubble clouds observed during the passage of the

burst wave from the high-speed imaging and the the simulation, respectively. The height and diameter of

the stone are 10 and 6.25 mm. (e) shows the correlation between the scattering factor and the shielding

factor obtained from simulations with various values of the thickness and the initial void fraction of

bubble clouds,

β

0

. The figures are reproduced from [6].

quantify the amplitude of the back-scattered acoustic waves from the bubbles and the stone.

F

is defined as

F

=

max[

I

]

max[

I

ref

]

,

(1)

where

I

ref

is the reference value of imaging functional without bubbles. Therefore,

F

quantifies the en-

hancement/decay of the scattered acoustic waves due to the presence of bubbles. The shielding factor is

defined as

S

= 1

−

P

P

ref

,

(2)

where

P

is the total work done by the acoustic energy to the stone during each simulation.

P

ref

is the

reference value of

P

obtained in the case without bubbles. Note that

S

= 0

and

S

= 1

indicate no shielding

and perfect shielding (no energy transmission into the stone), respectively. Notably, the plot indicates a

strong positive correlation between the shielding factor and the scattering factor over the global range of

the data points, independent of the initial condition of bubbles. The shielding factor grows with increasing

the scattering factor and reaches

S

≈

0

.

9

at

F

≈

4

. The result indicates that up to 90% of the energy of

the incident burst wave can be absorbed/scattered by bubbles that would otherwise be transmitted into the

K.

Maeda

et al.

Modeling

and

simulation

of

the

bubble

cloud

dynamics

for

BWL

Proceedings

of

Meetings

on

Acoustics,

Vol.

35,

020006

(2018)

Page

3

stone, and this can lead to significant loss of efficacy of stone comminution. An important implication of

the correlation between the scattering factor and the shielding factor is that one may identify the magnitude

of the strong energy shielding by measuring the scattered acoustic waves without directly observing the

bubble clouds; cavitation and the shielding can be monitored during treatment using BWL. Extension of

the numerical and experimental setups to model an

in vivo

environment is desirable to further quantify the

energy shielding in practical conditions of BWL.

4. CONCLUSION AND OUTLOOK

This series of combined numerical and experimental studies successfully identified the dynamics of

cavitation bubble clouds in BWL and quantified the energy shielding of kidney stones by the bubbles, the

latter of which may cause loss of efficacy of stone comminution. Recent work suggests that the magnitude

of the energy shielding can be identified by scattered ultrasound waves. The results motivate future work

to monitor and possibly control cavitation, and mitigate the energy shielding in real-time during clinical

treatment. Such a strategy may lead to further precise, efficient, and safe methods of stone commminution

for improved outcomes of BWL.

ACKNOWLEDGMENTS

This work was supported by the National Institutes of Health under grants P01-DK043881 and K01-

DK104854.

REFERENCES

1

K. Maeda.

Simulation, Experiments, and Modeling of Cloud Cavitation with Application to Burst Wave

Lithotripsy

. PhD thesis, California Institute of Technology, 2018.

2

K. Maeda and T. Colonius. A source term approach for generation of one-way acoustic waves in the euler

and navier-stokes equations.

Wave Motion

, 75:36–49, 2017.

3

K. Maeda and T. Colonius. Eulerian–lagrangian method for simulation of cloud cavitation.

Journal of

Computational Physics

, 371:994 – 1017, 2018.

4

K. Maeda and T. Colonius. Bubble cloud dynamics in an ultrasound field.

to appear in Journal of Fluid

Mechanics

, 2019. arXiv preprint arXiv:1805.00129.

5

K. Maeda, W. Kreider, A. Maxwell, B. Cunitz, T. Colonius, and M. Bailey. Modeling and experimental

analysis of acoustic cavitation bubbles for burst wave lithotripsy.

Journal of Physics: Conference Series

,

656(1):012027, 2015.

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K. Maeda, A. D. Maxwell, T. Colonius, W. Kreider, , and M. Bailey. Energy shielding by cavitation bubble

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The Journal of the Acoustical Society of America

, 144(5), 2018.

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A. Maxwell, B. Cunitz, W. Kreider, O. Sapozhnikov, R. Hsi, J. Harper, M. Bailey, and M. Sorensen.

Fragmentation of urinary calculi in vitro by burst wave lithotripsy.

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, 193(1):338–

344, 2015.

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Y. Pishchalnikov, O. Sapozhnikov, M. Bailey, J. Williams Jr, R. Cleveland, T. Colonius, L. Crum, A. Evan,

and J. McAteer. Cavitation bubble cluster activity in the breakage of kidney stones by lithotripter shock-

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Modeling and simulation of the bubble cloud dynamics for BWL

Proceedings of Meetings on Acoustics, Vol. 35, 020006 (2018)

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