Development Of A Hybrid Finite Difference Solution Of The Westervelt Equation Using the Fast Nearfield Method As A Boundary Condition For Focused Sources: or Microbubble Nuclei Interaction with Histotripsy Shockwaves

摘要

Theoretical models of therapeutic ultrasound expand the understanding of the mechanisms of treatment, and expedite the development of regulatory standards. For focused ultrasound therapies that rely on thermal mechanisms to generate lesions, only modeling of the incident sound field needs is sufficient. Modeling of microbubble clouds formed through shock scattering for histotripsy requires computation of both the incident and scattered fields. The objective of this study was to utilize a finite-difference time-domain (FDTD) method to compute both fields. A fine computation grid is required to resolve the shocked field at the focus. In the nearfield, where nonlinearity is negligible, a fine resolution computation is unnecessary and adds significant computational time. A hybrid method model was developed that employs an analytic solution to compute the nearfield, and the FDTD method to compute the field at the focus. The Fast Nearfield Method (FNM) was used to compute the nearfield solution using Gaussian quadrature integration. A FDTD method was used to solve the Westervelt equation at the focus, using the FNM solution as the source boundary condition. Computed fields agree with previously reported insonations when the FNM method calculation is set to half the focal distance. Thus, this hybrid technique allows reliable calculation of the focal pressure while reducing the FDTD computational domain by a factor of two. Implications of the model will be discussed, and the extension of the model to scattering of histotripsy pulses from spherical microbubbles will be presented.