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.

Centre of Excellence IT4Innovations Faculty of Information Technology Brno University of Technology Bozetechova 2 Brno 612 00 Czech Republic

Department of Applied Physics University of Eastern Finland 70211 Kuopio Finland

Department of Bioengineering Imperial College London Exhibition Road London SW7 2AZ United Kingdom

Department of Biomedical Engineering and Department of Electrical and Computer Engineering University of Utah Salt Lake City Utah 84112 USA

Department of Electrical Engineering Stanford University Stanford California 94305 USA

Department of Medical Physics and Biomedical Engineering University College London Gower Street London WC1E 6BT United Kingdom

Department of Radiology Stanford University Stanford California 94305 USA

Department of Surgical Biotechnology Division of Surgery and Interventional Science University College London London NW3 2PF United Kingdom

Earth Science and Engineering Department Imperial College London London United Kingdom

Foundation for Research on Information Technologies in Society Zurich Switzerland

Graduate Program in Acoustics The Pennsylvania State University University Park Pennsylvania 16802 USA

Institute for Mathematical and Computational Engineering School of Engineering and Faculty of Mathematics Pontificia Universidad Católica de Chile Santiago Chile

Institute of Geophysics Swiss Federal Institute of Technology Zürich Sonneggstrasse 5 8092 Zürich Switzerland

Joint Department of Biomedical Engineering University of North Carolina at Chapel Hill Chapel Hill North Carolina 27599 USA and North Carolina State University Raleigh North Carolina 27695 USA

Physics for Medicine Paris National Institute of Health and Medical Research UMR 8063 Paris France

Radiology and Clinical Neurosciences Departments Cumming School of Medicine University of Calgary Calgary Alberta Canada

Technical University of Denmark Kongens Lyngby Denmark

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See supplementary material at https://www.scitation.org/doi/suppl/10.1121/10.0013426 for a table form of the model summaries given in Sec. III and summaries of the complete set of intercomparison results. SuppPub1.xlsx gives an alternate table form of the model summaries given in Sec. III. SuppPub2.zip provides summaries of the comparison results (including metrics, field plots, axial profiles, and difference plots) for each model compared against FOCUS (for benchmarks 1 and 2) and KWAVE (for benchmarks 1–9). The .zip file contains separate pdf files for each model and for each benchmark, as a well as a summary of the cross-comparison metrics. The raw data files and matlab codes to process the results are also freely available (Refs. 8 and 11). DOI

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