JASA MS #TU12-12223 Response to Reviewers
We thank the reviewers for their careful reading of our manuscript
submitted to JASA, “Experimentally validated multiphysics
computational model of focusing and shock wave formation in an
electromagnetic lithotripter”, and the many constructive
suggestions offered to improve the paper. We answer specific
comments below, point by point, but start with some general
information on modifications made to the manuscript:
(1)
(2)
Figure (Fig. 11 in the first submission) contains updated
geometric data on the lens cut that corresponds to the
configuration that was experimentally tested. (Minor
changes with respect to data used in first draft computational
model).
Though we are not aware of any previous numerical study
that validated computation of refraction of acoustic waves in
a lens and subsequent nonlinear front steepening, we have
extended the scope of the study to more clearly reflect the
multiphysics nature of the computational model by
presentation of the penetration of the focused shock wave
into a kidney stone simulant. A simple damage model is
incorporated into the elasticity equations to qualitatively
model fracture progression in the stone simulant.
Reviewer #1
Review Comment:
The authors present results from a modeling study where a
multiphysics shock-capturing solver is used to propagate an
acoustic/shock wave generated by an electromagnetic lithotripter.
Experimentally measured pressures are in very nice agreement
with the model. Overall, this is a clearly written and carefully
constructed numerical study. Perhaps the only shortcoming is the
scope of the paper--there aren't really any new observations or
interesting physics going on here. This is purely a modeling
exercise. The only real novelty is the creative way in which the
equations of elasticity and the Euler equations are hybridized in
time in order to accurately capture the refraction of waves in the
solid lens. Here too, though, I'm not certain the method is very
general--it seems to rely on an ad hoc switching between the
elastic/fluid equations after a certain time. Despite this, I believe
the paper can be published, with minor corrections, in JASA, as it
nicely demonstrates a technique which ought to be useful in future
work on wave focusing in HIFU/lithotripsy/hisotripsy/etc.
Author Response:
As presented in general comments above, the computational model
solves linear elasticity, Euler compressible fluid flow,
heterogeneous elasticity with a simple stone fracture model. The
authors would put forward that this does indeed constitute a
multiphysics computation. With respect to the switching between
equations, this was done purely due to reduce computational run
time; the overall framework accommodates general linkage
between spatial domains in which different physics are solved.
Review Comment:
Cavitation is blamed for the shortened tensile pulse in the
experiment compared to the model. This is a reasonable
hypothesis, but could be made much stronger with additional
observations from the experiments. Cavitation, if present, could be
easily detected using the same FOPH but measuring the sound
some ~100 microsec. later when any cavitation bubbles generated
would collapse. If the authors cannot corroborate this, the
conclusion that cavitation is the source of the discrepancy should
be weakened and other possible sources of error in the modeling
considered.
Author Response:
We do indeed observe cavitation from the FOPH measurements.
The phrasing in the manuscript has been changed to document this
experimental observation. Cavitation is commonplace in these
experiments (as seen in the references), and the focus of the
manuscript is on the refraction/shock formation, hence we do not
include the raw FOPH data showing cavitation. A full study
including cavitation effects is the object of follow-on work.
Review Comment:
The authors should explain why averaging over 4 samples (section
A) is appropriate. I would think that either (a) the measurements
are very repeatable, in which case no averaging is needed, or (b)
the measurements contain noise/uncertainties that need to be
averaged out, but in which case 4 samples does not sound like a
sufficient number. The authors should at least show what effect
averaging has on their data through the use of error bars in the
plots.
Author Response:
Error bars have been included where applicable.
An explanatory sentence has been added to the manuscript
addressing why 4 samples were used. The measurements do
contain some noise but we’ve found that averaging 4 samples is
enough for comparison against the model. The averaging increases
the signal to noise ratio by approximately 4-7 dB. While using
more samples might improve this further we don’t feel it’s
necessary for the measurements and comparisons being made here.
Reviewer #2
Review Comment:
Light green color in Figs. 8 and 11 are difficult to see. I would
suggest to replace green by black color.
Author Response:
These plots have been replaced with black substituted for green.
Review Comment:
I am not so sure about the appropriateness of using the term
multiphysics. Technically speaking, the authors remain within one
branch of physics- acoustics, and the only debatable
"multiphysics" aspect relates to taking or not taking into account
shear stresses. I do not think that the use of term multiphysics can
be justified simply because the governing equations are different.
For instance, is the term multiphysics OK to use when Euler's
equations are replaced by Navier-Stokes (viscosity is turned on and
off)? Probably not. Typically, multiphysics refers to modeling of
two or more sufficiently different physical processes that affect
each other, such as, for example, chemical kinetics and fluid
mechanics. In respect to modeling an electromagnetic lithotripter
the true multiphysics would be, for example, modeling eddy
currents induced in the membrane during the discharge of the highvoltage capacitor and taking into account fluid dynamics to
simulate the motion of the membrane in the liquid. It seems that
one needs to be somewhat cautious not to overuse the term to the
point when the terminology does not mean much. If we follow the
authors' rationale, modeling of shock wave interaction with kidney
stones should be called multiphysics, as the modeling typically
uses the same two sets of equations (linear elasticity and Euler
equations) as the authors used in this manuscript. I would suggest
removing the word multiphysics from the title and the text of the
manuscript.
Author Response:
We hope that the inclusion of a model which simultaneously solves
the linear elasticity equations, the Euler equations, and the
elasticity equations with a damage variable within arbitrary subsets
of the computational domain helps to alleviate this concern. We
now model the interaction over time between the elastic solids and
the fluid surrounding them instead of relying on a simple switch at
one point in time. We feel that modeling the stress distributions in
the solids, the fluid dynamics of the water, and the interaction
continuously over time justifies the use of the term multiphysics.
Review Comment:
1. Page 3, second paragraph "In an EM lithotripter an acoustic
pulse is formed by an electro-magnetic actuator and is focused by
an acoustic lens or parabolic reflector."
Correct to read: "... is usually focused ... " as the Eisenmenger selffocusing EM lithotripter uses neither acoustic lens nor parabolic
reflector; it uses a spherically shaped electromagnetic actuator
[Eisenmenger et al.: The first clinical results of "wide-focus and
low-pressure" ESWL, UMB 28: 769-774 (2002).]
2. Page 3, last sentence: "Some reasons for the successful efficacy
of the HM3 include the wider beam width and cavitation resulting
from the long tensile portion of the pulse."
I would soften this
speculation: "...likely include..." Although some results appear to
support this speculation I am not so sure this statement is 100%
proven. For one thing, head-to-head comparisons of HM3 and EM
lithotripters often showed no degradation in stone breakage
efficiency in laboratory in vitro tests.
3. Make a reference to item 24 in the reference list when the
acronym CLAWPACK first appears in the text (the first paragraph
on page 5).
4. In the third paragraph on Page 8, "..., t+ t-;,
respectively,.." change to read "t+ and t-;, respectively"
5. In the third paragraph on Page 8, "The rise time, tr, is calculated
as the time from when the leading compressive wave increases
from 10% to 90% of the peak pressure." Consider rephrasing to
read "The rise time, tr, is calculated as the time for the leading
compressive wave to increase from 10% to 90% of the peak
pressure."
7. The first sentence on Page 14: "The Euler equations model
sound wave propagation and fluid flow in compressible inviscid
fluids and are used here to model the transition of the focused
acoustic pulse through water which includes a nonlinear steepening
effect."
Consider rephrasing to read "The Euler equations
describe sound wave propagation and fluid flow in compressible
inviscid fluids and are used here to model ..."
9. The first paragraph on page 20: "...15.8 kV input is well
captured by the model." Consider adding "except ~10% difference
in P+".
11. The last sentence on page 26: "This will allow for
direct comparisons of lens modifications on kidney stone fracture."
Consider: "This will allow for direct comparisons of the effect of
lens modifications on kidney stone fracture."
12. Page 28, reference 15: capitalized KZK as this acronym stands
for three names: Khokhlov, Zabolotskaya, and Kuznetsov.
Author Response:
The authors are very grateful for the reviewer’s effort to ensure
more cursive phrasing in the manuscript, and the suggested
revisions are now included in the manuscript.
Review Comment:
6. Page 11: Provide references for the used equations.
Author Response:
References have been added for the elasticity equations.
Review Comment:
8. Page 19, the end of the second paragraph: "In these latter images
it is apparent that the duration of the tensile portion of the pulse
(t−) is less in experiment than in the model. This may be
due to cavitation interference in the FOPH measurements which
can lead to tensile wave shortening.29-31 Also, the computation
does not include cavitation, so any effect on the remainder of the
pulse from wave-induced cavitation is not modeled."
In addition
to the references 29-31 there are also other works specifically
devoted to this issue, e.g. "Cavitation selectively reduces the
negative-pressure phase of lithotripter shock pulses," ARLO 6 (4):
280-286 (2005).
Author Response:
The suggested reference is now included.
Review Comment:
10. The first paragraph on page 21: "...which are typical of the
source voltages used in the medical procedure." Provide reference
or remove this and the other phrase in the last sentence of the same
paragraph "...for the most relevant input voltages..."
Author Response:
A reference was added to corroborate these statements (Egilmez,
et. al. 2007).