Non-invasive acoustic monitoring of transcranial focused ultrasound therapy faces significant barriers due to skull-induced attenuation that severely limits high-frequency acoustic wave transmission. Reliance on MR-based imaging makes FUS therapy less flexible. We introduce the Heterogeneous Angular Spectrum Parametric Array (HASPA) framework, an innovative approach that exploits nonlinear acoustic phenomena to achieve high-resolution brain therapy monitoring by detecting lower-frequency signals generated by the parametric array effect that readily penetrate skull tissue. HASPA solves the Westervelt equation for nonlinear acoustics through perturbation methods integrated with computationally efficient angular spectrum techniques for heterogeneous media. By leveraging weak nonlinearity assumptions and the near-equivalence of primary acoustic fields, our approach enables complete reconstruction of the original therapeutic beam. The methodology comprises two key components: (1) a forward propagation model that simulates both primary and parametric acoustic fields, accounting for tissue heterogeneity and (2) an inverse reconstruction (iHASPA) algorithm that recovers high-frequency therapeutic field distributions from experimentally accessible low-frequency parametric measurements. This addresses a critical gap in focused ultrasound real-time, non-invasive acoustic assessment of brain therapies. Work supported by NSF CMMI Award 1933158.
Dash et al. (Wed,) studied this question.