Computation of ultrasound propagation in a population of nonlinearly oscillating microbubbles including multiple scattering.

In contrast-enhanced echography, the simulation of nonlinear propagation of ultrasound through a population of oscillating microbubbles imposes a computational challenge. Also, the numerical complexity increases because each scatterer has individual properties. To address these problems, the Iterative Nonlinear Contrast Source (INCS) method has been extended to include a large population of nonlinearly responding microbubbles. The original INCS method solves the Westervelt equation in a four-dimensional spatiotemporal domain by generating increasingly accurate field corrections to iteratively update the acoustic pressure. The field corrections are computed by the convolution of a nonlinear contrast source with the Green's function of the linear background medium. Because the convolution integral allows a coarse discretization, INCS can efficiently deal with large-scale problems. To include a population of microbubbles, these are considered as individual contrast point sources with their own nonlinear response. The field corrections are computed as before, but now, in each iteration, the temporal signature of each contrast point source is computed by solving the bubble's Marmottant equation. Physically, each iteration adds an order of multiple scattering. Here, the performance of the extended INCS method and the significance of multiple scattering is demonstrated through various results from different configurations.