Heterogeneous angular spectrum method for trans-skull imaging and focusing

Ultrasound has emerged as a promising modality for therapy and imaging of brain diseases. Existing methods for the correction of skull-related distortions (aberration) require significant computation, which hampers their use in real-time applications, including adaptive focusing and tracking of bubble dynamics when used with microbubble contrast agents. Unfortunately, the angular spectrum (AS) method, which is the most computationally efficient focusing/beamforming method, does not intrinsically account for heterogeneity in the propagation medium. Here, we present a full solution for the AS in a heterogeneous medium, and an analytical solution for the special case of a stratified medium. Simulations of trans-skull acoustic propagation were performed for passive acoustic mapping (PAM) and focal aberration correction. Results show the general solution provides accurate trans-skull focusing as compared to the homogeneous case (error 0.65 ± 0.27 mm) for clinically relevant frequencies (0.5 to 1.5 MHz). Source localization error was reduced by 70% (from 2.89 ± 1.76 mm to 0.68 ± 52 mm), and computation of the corrections required milliseconds (166 ± 37 ms, compared with 44 ± 4 ms; the analytical stratified solution is at least 54% faster than the full correction). The proposed phase correction method may provide a computationally efficient method for improved trans-skull focusing and imaging for real-time applications.