Heterogeneous Angular Spectrum Method for Trans-Skull Imaging and Focusing.

Ultrasound, alone or in concert with circulating microbubble contrast agents, has emerged as a promising modality for therapy and imaging of brain diseases. While this has become possible due to advancements in aberration correction methods, a range of applications, including adaptive focusing and tracking of the microbubble dynamics through the human skull, may benefit from even more computationally efficient methods to account for skull aberrations. Here, we derive a general method for the angular spectrum approach (ASA) in a heterogeneous medium, based on a numerical marching scheme to approximate the full implicit solution. We then demonstrate its functionality with simulations for (human) skull-related aberration correction and trans-skull passive acoustic mapping. Our simulations show that the general solution provides accurate trans-skull focusing as compared to the uncorrected case (error in focal point location of 1.0 ± 0.4 mm vs 2.2 ± 0.7 mm) for clinically relevant frequencies (0.25-1.5MHz), apertures (50-100 mm), and targets, with peak focal pressures approximately 30 ± 17% of the free field case, with the effects of skull attenuation and amplitude shading included. In the case of source localization, our method leads to an average of 75% error reduction (from 2.9 ± 1.8 mm to 0.7 ± 0.5 mm) and 40-60% increase in peak intensity, evaluated over the range of frequencies (0.4-1.2 MHz), apertures (50-100 mm), and point source locations (40 mm by 50 mm grid) as compared to the homogeneous medium ASA. Overall, total computation times for both focusing and point source localization of the order milliseconds (166 ± 37 ms, compared with 44 ± 4 ms for the homogeneous ASA formulation) can be attained with this approach. Collectively our findings indicate that the proposed phase correction method based on the ASA could provide a computationally efficient and accurate method for trans-skull transmit focusing and imaging of point scatterers, potentially opening new possibilities for treatment and diagnosis of brain diseases.