Multiharmonic algorithms for contrast-enhanced ultrasound
Journal:
arXiv
Published Date:
Apr 17, 2025
Abstract
Harmonic generation plays a crucial role in contrast-enhanced ultrasound,
both for imaging and therapeutic applications. However, accurately capturing
these nonlinear effects is computationally very demanding when using
traditional time-domain approaches. To address this issue, in this work, we
develop algorithms based on a time discretization that uses a multiharmonic
Ansatz applied to a model that couples the Westervelt equation for acoustic
pressure with a volume-based approximation of the Rayleigh--Plesset equation
for the dynamics of microbubble contrast agents. We first rigorously establish
the existence of time-periodic solutions for this Westervelt-ODE system. We
then derive a multiharmonic representation of the system under time-periodic
excitation and develop iterative algorithms that rely on the successive
computation of higher harmonics under the assumption of real-valued or complex
solution fields. In the real-valued setting, we characterize the approximation
error in terms of the number of harmonics and a contribution owing to the
fixed-point iteration. Finally, we investigate these algorithms numerically and
illustrate how the number of harmonics and presence of microbubbles influence
the propagation of acoustic waves.
