Fast algorithm for nonlinear acoustics and high-intensity focused ultrasound modeling

Abstract

The inhomogeneous characteristics of biological media and the nonlinear nature of sound propagation at high-intensity focused ultrasound (HIFU) regimes make accurate modeling of real HIFU applications a challenging task in terms of computational time and resources. A fast, dynamically adaptive time-domain method that drastically reduces these pitfalls is presented for the solution of multidimensional HIFU problems in complex geometries. The model, based on lifted interpolating second-generation wavelets in a collocation approach, consists of the coupled solution of the full-wave nonlinear equation of sound with the bioheat equation for temperature computation. It accounts for nonlinear acoustic propagation, arbitrary frequency power law for attenuation, multiple reflections, and backscattered fields. The characteristic localization of wavelets in both space and wave number domains allows for accurate simulations of strong material inhomogeneities and steep nonlinear processes at a reduced number of collocation points, while the natural multiresolution analysis of wavelets decomposition introduces automatic grid refinement in regions where localized structures are present. Compared to standard finite-difference or spectral schemes on uniform fine grids, this method shows significant savings in computational time and memory requirements proportional with the dimensionality of the problem. [Work supported by U.S. Army Medical Research Acquisition Activity through the University.]