A mathematical model to simulate acoustic field propagation in layered structures with undulating boundaries is presented. The model is based on solving the Helmholtz partial differential equation for each medium and defines physically possible refracted paths from an emitting source to a desired receiving point. The presented model considers each layer as a homogeneous and linear medium with a different acoustical impedance compared to its adjacent layers.

The model is then further used in the development of and adaptive beamforming technique to compensate for the phase aberration induced by each layer. Application of the proposed model and the suggested adaptive beamforming method is discussed for the case of trans-skull adaptive focusing via ultrasound phased arrays in both HIFU and imaging modes. The human skull is a multilayered acoustical barrier consisting of cortical versus trabecular bone layers. If conventional phased array beamforming techniques are used for ultrasonic trans-skull focusing, strong phase aberration and attenuation induced by the skull lead to deformation and shifting, or even a total destruction of the intended focal spot. In the imaging mode, such distortions result in significant degradation of the image quality, loss of spatial resolution, and displacement or even disappearance of targets in the resulting sonogram.

Simulated and experimental results of applying the suggested adaptive focusing method through human skull phantoms are presented. Correction of up to 2.5 cm focal point displacement at up to 10 cm depth under the skull phantoms is demonstrated. Quantitative assessment of the method in a variety of temporal focusing scenarios is also reported. Overall temporal deviation on the order of a few nanoseconds, observed between the simulated and experimental results, confirms the validity of the method.