An Angular Spectrum Method for Nonlinear Propagation in Heterogeneous Tissue with Immersed Sources for Ultrasound

Abstract

A modified angular spectrum method (ASM) is developed for three-dimensional nonlinear acoustic propagation through heterogeneous tissue, targeting transcranial and therapeutic ultrasound. First, a consistent obliquity correction is applied to both the linear and nonlinear operators of the split-step update. The attenuation and dispersion filter carries a per-mode k/kz factor on the full wavenumber-frequency grid, so each component accumulates absorption and phase over its true path length dz/cos(theta), while the Burgers coefficient is scaled by the power-weighted mean beam obliquity. Second, the retarded-time Burgers update is discretized with a second-order Kurganov-Tadmor central-upwind flux using MUSCL reconstruction and SSP-RK2 time integration, composed with diffraction and attenuation through Strang splitting with adaptive CFL sub-cycling, resolving fully developed shocks without the temporal refinement that the CFL coupling imposes on FDTD. Third, a plane-by-plane source-injection scheme decomposes deeply curved bowl transducers into axial slices injected at their correct propagation depths, preserving the aperture-dependent shock-formation distance. Phase-and-amplitude screens derived from skull CT data model transcranial aberration and insertion loss, and three enhanced absorbing-boundary treatments reduce boundary reflections by a factor of 2.4. Analytical validation reproduces the baffled-piston far-field pattern to 0.014 RMS and the focused-piston focal pressure to within 2.3 percent. In a transcranial benchmark through an ex vivo human skull, the ASM matches the Fullwave 2 focal-plane intensity to 1.1 percent RMS and predicts a 5.4 dB through-skull insertion loss. For a bowl transducer (R = 80 mm, f0 = 1 MHz), the ASM matches the Fullwave 2 focal depth to within 2.3 percent with 9x less memory and 2.9x less wall time.