Simulating focused ultrasound propagation through heterogeneous biomedical materials with volume-surface integral equation methods and hierarchical matrix compression

Focused ultrasound has gained importance in cancer therapy and neuromodulation because it offers a non-invasive treatment that can reach malignant tissue at high precision. Fast and accurate simulation tools are essential to improve safety guidelines and patient-specific treatment planning. The goal is guiding sufficient acoustic energy toward the focus to achieve ablation while sparing healthy tissue in the beam path. We have already achieved realistic simulations with our open-source OptimUS library using the Boundary Element Method (BEM). The BEM is a powerful algorithm to simulate high-frequency acoustics in unbounded domains that scatter at objects with high material contrasts, like soft tissue and bone, and only needs surface meshes at material interfaces. However, the BEM is limited to scatterers with constant density and speed of sound. To investigate the influence of bone heterogeneities on the focus aberrations, we developed a Volume Integral Equation and coupled it with the BEM. To improve computational efficiency and reduce memory footprint, we developed a hierarchical matrix compression technique for the dense system matrices. Our innovations allow for simulating ultrasound scattering at ribcage models for transcostal ultrasound and transmission through skull slabs for transcranial ultrasound at operating frequencies and with material data taken from biomedical images.