Fast finite element methods for focused ultrasound applications
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
University of Cambridge
Department of Engineering
Department of Engineering
Abstract
Description
This thesis presents the development of a three-dimensional, time-domain, fast
finite element solver for focused ultrasound (FUS) applications.
FUS is a rapidly evolving medical technology used for tissue heating, ablation,
and neuromodulation. In recent years, interest in FUS has grown significantly,
especially for the treatment of cancers and brain diseases. Effective
patient-specific treatment planning can be supported by accurate simulations.
However, this poses a challenge from a computational standpoint since the ratio
of the domain size to the wavelength is typically large, therefore
computationally demanding. This is made even more challenging for nonlinear
models such as the Westervelt model, commonly used in high-intensity focused
ultrasound (HIFU) treatments, as higher harmonics need to be resolved.
To address this challenge, a three-dimensional, time-domain acoustic solver for
FUS applications is developed. The solver is based on the high-order finite
element method and the explicit Runge-Kutta method. It is well known that
low-order finite element methods suffer from pollution errors, especially for
high-frequency problems. However, it is demonstrated that with high-order finite
elements, the pollution error is significantly reduced. Moreover, the
availability of modern open-source finite element software, such as FEniCSx,
eases the implementation of high-order finite element methods. A mass-lumped
finite element scheme is implemented, which, combined with the explicit
Runge-Kutta method avoids the need to solve a linear system of equations. To
further accelerate the solver, a fast finite element integration algorithm is
employed. In particular, an algorithm with the lowest known computational cost
complexity is implemented, namely the sum-factorisation algorithm. Furthermore,
the algorithm is carefully implemented to ensure optimal performance. The solver
is implemented for both CPU and GPU architectures. On both architectures, it is
shown that the finite element integration implementations achieve a good
fraction of peak hardware performance. Additionally, it is shown that the solver
exhibits excellent parallel scalability. Contrary to common perceptions, it is
demonstrated that a high-order finite element method is well-suited for
realistic acoustic simulation for focused ultrasound applications. The novel
contributions in this thesis include the development of a high-order finite
element method with a fast finite element integration algorithm.
The solver is validated against other acoustic wave solvers for several
benchmark problems. Overall, it is shown that the developed solver is fast,
accurate, scalable, and is suitable for large-scale linear and nonlinear
time-domain acoustic simulations.
Ministry of Higher Education Malaysia Scholarship, University of Cambridge Physics Department
Ministry of Higher Education Malaysia Scholarship, University of Cambridge Physics Department