[Paper Review] Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

Jean‐François Aubry, Oscar Bates+20 more|arXiv (Cornell University)|Feb 9, 2022

Ultrasound Imaging and Elastography4 citations

TL;DR

This paper presents a standardized benchmark suite for transcranial ultrasound simulation, evaluating 11 different computational models using compressional wave propagation through skull phantoms of increasing complexity. The intercomparison reveals excellent agreement across models, with median differences of less than 10% in focal pressure and less than 1 mm in focal position, validating the reliability of numerical simulations for clinical applications such as focused ultrasound therapy and phase correction.

ABSTRACT

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), 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.

Motivation & Objective

• To establish a standardized benchmark framework for evaluating computational models of transcranial ultrasound propagation.
• To assess the consistency and accuracy of different numerical methods used in transcranial ultrasound simulation.
• To identify sources of variability in simulation results across diverse modeling tools and techniques.
• To support best practices in computational modeling for focused ultrasound therapy and intracranial pressure prediction.
• To provide freely accessible benchmarks, data, and code to enable replication and future validation of new solvers.

Proposed method

• The study defines nine benchmark problems of increasing geometric complexity, including planar and multi-layered skull models and a full skull, all immersed in water.
• Two transducer configurations—focused bowl and plane piston—are used, resulting in 18 total benchmark permutations.
• Eleven different modeling tools are employed, representing diverse numerical methods: finite-difference time-domain, angular-spectrum, pseudospectral, boundary-element, and spectral-element methods.
• Each model computes the acoustic pressure field, with results compared using metrics such as focal position, focal size, and pressure magnitude.
• Cross-comparisons are performed between all model pairs to quantify inter-model agreement across all benchmarks.
• All benchmark definitions, simulation results, and intercomparison code are made publicly available for reproducibility and extension.

Experimental results

Research questions

• RQ1 How do different numerical models of compressional wave propagation perform when simulating ultrasound through transcranial bone structures of varying complexity?
• RQ2 What level of agreement can be achieved between diverse modeling tools in predicting the focal pressure field within the brain after skull transmission?
• RQ3 How do differences in numerical methods and implementation choices affect key simulation metrics such as focal position and pressure magnitude?
• RQ4 To what extent do model discrepancies vary with geometric complexity and transducer configuration?
• RQ5 Can a standardized benchmark framework reduce uncertainty and improve confidence in computational predictions for transcranial ultrasound therapies?

Key findings

• The intercomparison shows median differences of less than 10% in focal pressure and less than 1 mm in focal position across all benchmarks when comparing any model against any other.
• Good agreement is observed particularly for the position, size, and magnitude of the acoustic focus after propagation through the skull.
• Larger discrepancies are observed in the full-field metrics, primarily between the transducer and the skull, due to differences in near-field wave behavior.
• The results demonstrate strong consistency across a wide range of numerical techniques, including finite-difference, spectral, and boundary-element methods.
• The benchmark definitions, simulation results, and intercomparison code are publicly available, enabling replication and future validation of new modeling tools.
• The study provides a foundation for future intercomparisons, including elastic wave models and simulations using patient-specific CT-derived material parameters.