Page 44 - Summer2019
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Modeling Therapeutic Ultrasound
scanner. The sound speed and absorption coefficient can then
be inferred from the mass density, albeit with relatively large umasound IV
uncertainties (Mast, 2000). When using MR images, the differ- transducer
ent organs within the body must first be segmented, and then
values for the tissue properties are assigned (these values are a needle
usually taken from previous measurements reported in the  hYd|’°Ph0nE
literature made using ex vivo tissue samples). Perhaps unsur- .
prisingly, uncertainties in the geometry and properties of the ‘ _,
body (particularly the sound speed) form a significant source , l ‘V’ V . ’ i
of error in model-based predictions made for ultrasound ther- _ ‘. '
apy (Robertson et al., 2017b).
3D-printed skull segment
Model Validation
Checking whether a computer program gives the correct Figures. Measurementaf the ucaustic field behind 113-D-printed skull
answer under different circumstances is known as model segment (cznrzr) usinga fecused Mltrusmmd transducer (left) and a
validation. Errors can come from any of the four preceding needle hydmphane (right) in a water tank.
steps in the circle of model development, including invalid  
assumptions made when developing the governing equa-
tions, the wrong choice of grid parameters in the numerical characteristics of the ultrasound transducer, the acoustic
model, mistakes in the computer code or rounding and properties of the medium, the geometry and position of
overflow errors, and inaccuracies in the acoustic material any scattering objects, and the spatial locations at which
properties or source conditions. The validation of numeri- the pressure is measured. Errors in any of these will lead to
cal models is an important part of the software design life discrepancies between the model and measurement. One
cycle, particularly in the context of therapeutic ultrasound approach is to use simple geometries and standardized
where software may be used to derive treatment parameters materials with well-known properties. For example, phan-
or influence clinical decisions. toms with precisely known geometries can be created using
3-D printing as seen in Figure 3 (Robertson et al., 2017b).
Model accuracy is generally tested in several stages, including Unfortunately, performing quantitative validation measure-
(1) performing a convergence test; ments using more realistic biological specimens such as ex
(2) comparing with analytical solutions, for example, the vivo skull samples remains a difficult task.
scattering of a plane mve by a sphere;
(3) quantitatively comparing the predicted acoustic field The second challenge is obtaining accurate, absolute mea-
against well-controlled laboratory experiments; surements of acoustic pressure. It cannot be assumed that a
(4) quantitatively comparing with experiments conducted measurement is the ground truth because there are many fac-
using ex vivo tissue or animal models; and tors that give rise to measurement uncertainties. Variations can
(5) comparing against the outcome of clinical treatments occur in the transducer output due to fluctuations in the sup-
in patients, for example, comparing the volume of plied voltage, the electrical impedance, or changes inthe water
ablated tissue after a treatment using high-intensity temperature. Errors can also arise from the alignment and
focused ultrasound. positioning of the source and receiver, misalignment of scan-
For therapeutic ultrasound, there are a limited number of rel- axes, a.nd interference from acoustic reflections.
evant analytical solutions, and it is often diflicult to quantify Perhaps most importantly, the properties of the hydrophone
model accuracy (or the origins of any discrepancies) using used ca.n have a significant influence on the measurement. For
clinical data. Consequently, the bulk of model validation is example, the finite size of the hydrophone detector element
performed using experimental measurements. ca.n give rise to spatial averaging effects, particularly for the
tightly focused fields used in ultrasound therapy. Moreover,
When performing experimental validation, there are two for some hydrophones, the frequency-dependent sensitiv-
main challenges. The first is precisely replicating the experi- ity is nonuniform i.n both magnitude and phase, which can
mental setup in the computer simulation, for example, the resultin significant pressure errors if not properlydeconvolved
42 | AA:auIIiI:l‘I'b:Iay| Summer 2019

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