A fast full-wave solver for calculating ultrasound propagation in the body

Haqshenas, Seyyed R.; Gélat, Pierre; Wout, Elwin van ’t; Betcke, Timo; Saffari, Nader

doi:10.1016/j.ultras.2020.106240

Cited by 20 publications

(12 citation statements)

References 43 publications

(66 reference statements)

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“… 61,88 The BEM employs the Green's function of the Helmholtz equation to reformulate the volumetric wave problem into a boundary integral equation at the interfaces of piecewise homogeneous domains embedded in free space. 62 Benchmarks 3, 5, and 7 were modeled with the Poggio–Miller–Chew–Harrington–Wu–Tsai (PMCHWT) formulation, 63 benchmarks 4 and 6 were solved with a multi-trace formulation, 64 and a nested version of the PMCHWT formulation solves benchmarks 8 and 9. The numerical discretization leads to a dense system of linear equations, whose computational footprint is reduced through hierarchical matrix compression.…”

Section: Modelsmentioning

confidence: 99%

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

Aubry

Bates

Boehm

et al. 2022

The Journal of the Acoustical Society of America

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Computational models of acoustic wave propagation are frequently used in transcranial ultrasound therapy, for example, to calculate the intracranial pressure field or to calculate phase delays to correct for skull distortions. To allow intercomparison between the different modeling tools and techniques used by the community, an international working group was convened to formulate a set of numerical benchmarks. Here, these benchmarks are presented, along with intercomparison results. Nine different benchmarks of increasing geometric complexity are defined. These include a single-layer planar bone immersed in water, a multi-layer bone, and a whole skull. Two transducer configurations are considered (a focused bowl and a plane piston operating at 500 kHz), giving a total of 18 permutations of the benchmarks. Eleven different modeling tools are used to compute the benchmark results. The models span a wide range of numerical techniques, including the finite-difference time-domain method, angular spectrum method, pseudospectral method, boundary-element method, and spectral-element method. Good agreement is found between the models, particularly for the position, size, and magnitude of the acoustic focus within the skull. When comparing results for each model with every other model in a cross-comparison, the median values for each benchmark for the difference in focal pressure and position are less than 10% and 1 mm, respectively. The benchmark definitions, model results, and intercomparison codes are freely available to facilitate further comparisons.

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Section: Modelsmentioning

confidence: 99%

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

Aubry

Bates

Boehm

et al. 2022

The Journal of the Acoustical Society of America

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“…Here, the elements are considered to be smaller than one fourth of the wavelength ( λ /4), and the focal size is also considered to be λ /8. In calculating the pressure field, the time step is of order 10 −9 s, and the time of solving the transient equation is of order 9 × 10 −6 s. For the temperature field, the solution time is considered to be of order 10 −3 s. The difference in the two‐time scales used is attributed to multi‐physical numerical modeling, in which the acoustic wave takes about 1 μs (50–60 μs in this study) to reach the desired region 21,22,35–37 . Thermal meshing is shown in Figure 1C.…”

Section: Methodsmentioning

confidence: 99%

Numerical study of high‐intensity focused ultrasound (HIFU) in fat reduction

MORTAZAVI

Mokhtari‐Dizaji

2023

Skin Research and Technology

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Introduction:This study aimed to investigate the effect of fat-layer thickness and focal depth on the pressure and temperature distribution of tissue. Methods:Computer simulations were performed for the skin-fat layer models during high-intensity focused ultrasound (HIFU) treatment. The acoustic pressure field was calculated using the nonlinear Westervelt equation and coupled with the Pennes bioheat transfer equation to obtain the temperature distribution. To investigate the effect of the thickness of the fat layer on pressure and thermal distributions, the thickness of the fat layer behind the focal point (z = 13.5 mm) changed from 8 to 24 mm by 2 mm step. The pressure and temperature distribution spectra were extracted. Results:The simulated results were validated using the experimental results with a 98% correlation coefficient (p < 0.05). There was a significant difference between the pressure amplitude and temperature distribution for the 8-14 mm thickness of the fat layer (p < 0.05). By changing the focal point from 11.5 to 13.5 mm, the maximum acoustic pressure at the focal point increased 66%, and the maximum temperature was 56%, respectively. Conclusion:Considering the specific treatment plan for each patient, according to the skin and fat layer thicknesses, can help prevent side effects and optimize the treatment process of HIFU.

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“…As an example of OSRC preconditioning, the PMCHWT formulation for a single object becomes

[\begin{matrix} 0 & V_{NtD, 1}^{prefix-} \\ V_{DtN, 1}^{prefix-} & 0 \end{matrix}] [\begin{matrix} prefix- K_{0} prefix- K_{1} & V_{0} + \frac{σ_{0}}{σ_{1}} V_{1} \\ D_{0} + \frac{σ_{1}}{σ_{0}} D_{1} & T_{0} + T_{1} \end{matrix}] [\begin{matrix} ϕ \\ ψ \end{matrix}] = [\begin{matrix} 0 & V_{NtD, 1}^{prefix-} \\ V_{DtN, 1}^{prefix-} & 0 \end{matrix}] [\begin{matrix} γ_{D}^{+} p_{inc} \\ γ_{N}^{+} p_{inc} \end{matrix}]

which is equivalent to a block‐diagonal preconditioner for a permuted PMCHWT formulation 67 and with direct extensions to multiple domains 68 . Furthermore, the OSRC operators can be used as a combination parameter for the combined single‐trace formulations (35)–(37) as well 57,69,70 …”

Section: Preconditioningmentioning

confidence: 99%

“…which is equivalent to a block-diagonal preconditioner for a permuted PMCHWT formulation 67 and with direct extensions to multiple domains. 68 Furthermore, the OSRC operators can be used as a combination parameter for the combined single-trace formulations ( 35)-( 37) as well.…”

Section: Osrc Preconditioningmentioning

confidence: 99%

“…Here, at least four elements per wavelength are used (

n_{h} = 4

). Even though this is on the lower side of common choices for the mesh width, 78 a Galerkin method with P1 elements is sufficiently accurate at a sphere 67 . For comparison, the benchmarks at 1 MHz were performed with eight elements per wavelength as well, without yielding different conclusions for this study.…”

Section: Benchmarkingmentioning

confidence: 99%

See 1 more Smart Citation

Benchmarking preconditioned boundary integral formulations for acoustics

Wout

Haqshenas

Gélat

et al. 2021

Numerical Meth Engineering

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The boundary element method (BEM) is an efficient numerical method for simulating harmonic wave propagation. It uses boundary integral formulations of the Helmholtz equation at the interfaces of piecewise homogeneous domains. The discretization of its weak formulation leads to a dense system of linear equations, which is typically solved with an iterative linear method such as GMRES. The application of BEM to simulating wave propagation through large-scale geometries is only feasible when compression and preconditioning techniques reduce the computational footprint. Furthermore, many different boundary integral equations exist that solve the same boundary value problem. The choice of preconditioner and boundary integral formulation is often optimized for a specific configuration, depending on the geometry, material characteristics, and driving frequency. On the one hand, the design flexibility for the BEM can lead to fast and accurate schemes. On the other hand, efficient and robust algorithms are difficult to achieve without expert knowledge of the BEM intricacies. This study surveys the design of boundary integral formulations for acoustics and their acceleration with operator preconditioners. Extensive benchmarks provide valuable information on the computational characteristics of several hundred different models for multiple reflection and transmission of acoustic waves.

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A fast full-wave solver for calculating ultrasound propagation in the body

Cited by 20 publications

References 43 publications

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

Numerical study of high‐intensity focused ultrasound (HIFU) in fat reduction

Benchmarking preconditioned boundary integral formulations for acoustics

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