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g; The circle of model development can be used as a gen-
'‘E i,._.,, V /— I . eral framework to guide developers. Equally, it can be
§ ‘~\ - 7 g employed by end users to ask, Is this model appropriate
g '4 for my application? For exa.mple, considering each of the
5‘ five components, questions arise.
§ (1) Do the model equations capture enough of the phys-
§ — ~ ' ics to simulate the phenomenon of interest?
A (2) Is the chosen numerical method stable, efficient, and
3 "W~Ij~-"vi accurate? What are the convergence properties?
E Wilma  (3) Is the computer code fast, fault tolerant, portable,
E  ‘ ' ' " ‘; ’ Va H-...<.—. scalable, well-documented, and easy-to-use? Is it
Q 1 ‘\   regulatory compliant?
E  /> 2 ——-%—- M ‘W (4) What are the model inputs? Are they material prop-
3 1 ‘~’/ 1‘ 77777 K" "W erties, physical constants, or tuning parameters, and
E _ - -':\:,;;,,1,,>,m(_,m,, are they easy to measure or specify? What is the sen-
sitivity of the model to errors in the inputs? What
3 ” d‘ WNW“ settings do I need to use to ensure accurate results?
E l / L I (5) Has the model been validated against analytical solu-
vé / tions, experimental measurements, or clinical data?
§ 5; Do I have confidence in using the model to make
§ \\ b clinical predictions?
Lg  - In this article, each component of the circle of model
E \\ "__ development is discussed in more detail as a general
\ l"’"”“"“' mm" framework for the development of software for model-
Figure 1. Predicted distortion of the acoustic field from a therapeutic ing therapeutic ultrasound in the human body. Like many
ultrasound transducer firra liver target when the beam path is occluded endeavors in modern science, adequately addressing all
by the ribs (bottom). The spatially varying acoustic properties for the five components requires a team of people with a wide
simulation (middle) are derived from cryosection images from the breadth of expertise. This includes physical acoustics,
Visible Human Project run by the US National Library of Medicine numerical methods, computer science, software engineer-
(map). The predicted ultrasound field is calculated using the open-source ing, ultrasound metrology, and medical imaging. I.n many
k-Wave Toolbox (Jaros et al., 2016). cases, input from regulatory experts, clinicians, and other
  end users will also be needed.
(1) deriving equations that describe the underlying physics; 1
(2) choosing a suitable algorithm (numerical method) to 9°V5mi“9
solve these equations; ’ eql-‘atl°"5 \
(3) implementing the numerical scheme as computer code; I.’
(4) :ii_efining inputs to the model, for example, the spatial 5 vafidation numerica| 2
iscretization and material properties; and methods
(5) validating the model (numerically and experimentally). \ t
The process is often iterative (Figure 2, dashed line) and
is repeated until the model predictions agree with the model computer
experimental observations (the level of agreement required inputs code
depends on the context). For ultrasound therapy, it is criti- 4 <—/ 3
cal that each component in the circle of model development
is carefully considered before models are used to assist in Figure 2. The circle of model development showing the five key
calculations and predictions because any deficiencies could components that should be considered when developing scientific
have serious ramifications for patient safety. software. See text fizr explanation.
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