UCL Discovery
UCL home » Library Services » Electronic resources » UCL Discovery

Accelerating frequency-domain numerical methods for weakly nonlinear focused ultrasound using nested meshes

Groth, SP; Gelat, P; Haqshenas, SR; Saffari, N; van 't Wout, E; Betcke, T; Wells, GN; (2021) Accelerating frequency-domain numerical methods for weakly nonlinear focused ultrasound using nested meshes. The Journal of the Acoustical Society of America , 150 (1) pp. 441-453. 10.1121/10.0005655.

[thumbnail of 10.0005655.pdf] Text
10.0005655.pdf - Published version
Access restricted to UCL open access staff until 21 January 2022.

Download (2MB)

Abstract

The numerical simulation of weakly nonlinear ultrasound is important in treatment planning for focused ultrasound (FUS) therapies. However, the large domain sizes and generation of higher harmonics at the focus make these problems extremely computationally demanding. Numerical methods typically employ a uniform mesh fine enough to resolve the highest harmonic present in the problem, leading to a very large number of degrees of freedom. This paper proposes a more efficient strategy in which each harmonic is approximated on a separate mesh, the size of which is proportional to the wavelength of the harmonic. The increase in resolution required to resolve a smaller wavelength is balanced by a reduction in the domain size. This nested meshing is feasible owing to the increasingly localised nature of higher harmonics near the focus. Numerical experiments are performed for FUS transducers in homogeneous media to determine the size of the meshes required to accurately represent the harmonics. In particular, a fast volume potential approach is proposed and employed to perform convergence experiments as the computation domain size is modified. This approach allows each harmonic to be computed via the evaluation of an integral over the domain. Discretising this integral using the midpoint rule allows the computations to be performed rapidly with the FFT. It is shown that at least an order of magnitude reduction in memory consumption and computation time can be achieved with nested meshing. Finally, it is demonstrated how to generalise this approach to inhomogeneous propagation domains.

Type: Article
Title: Accelerating frequency-domain numerical methods for weakly nonlinear focused ultrasound using nested meshes
DOI: 10.1121/10.0005655
Publisher version: https://doi.org/10.1121/10.0005655
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Medical Sciences > Div of Surgery and Interventional Sci
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Medical Sciences > Div of Surgery and Interventional Sci > Department of Surgical Biotechnology
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Mechanical Engineering
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10132383
Downloads since deposit
1Download
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item