Modelling power-law ultrasound absorption using a time-fractional, static memory, Fourier pseudo-spectral method
Year: 2025
Type: article
Abstract: We describe and implement a numerical method for modelling the frequency-dependent power-law absorption of ultrasound in tissue, as governed by the first order linear wave equations with a loss taking the form of a fractional time derivative. The (Caputo) fractional time derivative requires the full problem history, which is contained within an iterative procedure. The resulting numerical method requires a fixed (static) memory cost, irrespective of the number of time steps. The spatial domain is treated by the Fourier spectral method. Numerically. comparisons are made against a model for the same power-law absorption with loss described by the fractional-Laplacian operator. One advantage of the fractional time derivative over the fractional-Laplacian operator is the local treatment of the power-law, allowing for a spatially varying frequency power-law.
DOI: 10.1121/10.0035937
Authors: Matthew J. King, Timon S. Gutleb, B. E. Treeby, B. T. Cox
Institutions: University College London, University of Leeds
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1313000435, k-Wave: An open-source toolbox for the time-domain simulation of acoustic wave fields, Spectral element methods for fractional differential equations, with applications in applied analysis and medical imaging, G6018169193, G6539321339, WHOLE-BODY, HIGH RESOLUTION, 3D, SMALL ANIMAL PHOTOACOUSTIC AND ULTRASOUND COMPUTED TOMOGRAPHY SYSTEM
OpenAlex ID: W4408408608