The iterative nonlinear contrast source method for simulating ultrasound propagation through a polydisperse microbubble population

Multiple scattering of sound by a population of particles attracts scientific interest for many decades. In contrast-enhanced echography, the simulation of ultrasound propagation through a dense cloud of nonlinearly oscillating microbubbles imposes a numerical challenge. This is particularly the case for polydisperse concentrations in which each scatterer has individual and independent properties. To address this problem, the Iterative Nonlinear Contrast Source (INCS) method has been adapted. Originally, this solved the Westervelt equation by letting its nonlinear term represent a contrast source in a “linearized” medium, and iteratively updating the pressure by computing the 4D spatiotemporal convolution between this source and the Green’s function. Because convolution allows a coarse discretization, INCS is suitable to deal with large-scale problems. In this talk, microbubbles are regarded as nonlinearly responding point sources that act as contrast sources. The total scattered pressure is computed iteratively, as in the original method, but now in each iteration the temporal signature of the contrast sources is calculated by solving every bubble’s own Marmottant equation. Physically, each iteration accounts for an order of multiple scattering. Numerical results will also be presented, demonstrating that INCS can accurately and efficiently simulate ultrasound propagation through a 3D population of polydisperse nonlinear microbubbles.