King, Matthew J;
Gutleb, Timon S;
Treeby, BE;
Cox, BT;
(2025)
Modelling power-law ultrasound absorption using a time-fractional, static memory, Fourier pseudo-spectral method.
The Journal of the Acoustical Society of America (JASA)
, 157
(3)
pp. 1761-1771.
10.1121/10.0035937.
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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.
| Type: | Article |
|---|---|
| Title: | Modelling power-law ultrasound absorption using a time-fractional, static memory, Fourier pseudo-spectral method |
| Location: | United States |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1121/10.0035937 |
| Publisher version: | https://doi.org/10.1121/10.0035937 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Med Phys and Biomedical Eng |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10206316 |
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