Evolution of the Iterative Nonlinear Contrast Source method for simulating nonlinear ultrasound: From still water to sparkling water

For many medical ultrasound modalities, the inherent nonlinearity of acoustic waves cannot be neglected or is even of prime importance. The original Iterative Nonlinear Contrast Source (INCS) method was developed to accurately simulate the nonlinear propagation of a pulsed ultrasound beam in a large, three-dimensional domain. As a key step, the nonlinear term in the relevant wave equation is considered to describe a contrast source in the linearized background medium. Convolution of the contrast term with Green’s function of the linear background yields the nonlinear field contribution. The resulting integral equation is solved by an iterative scheme. The INCS approach was subsequently extended by introducing contrast sources that account for other realistic medium properties, like frequency-dependent attenuation and inhomogeneity of tissue. The most recent extension is the inclusion of microbubble contrast agents. To model the propagation of an ultrasound wave through a large population of microbubbles, each microbubble is represented as a point contrast source. The strength of each point source depends on the bubble radius, which is obtained by solving each bubble’s individual Rayleigh–Plesset equation. In this presentation, the versatility of INCS will be demonstrated by discussing results that have been obtained for various types of contrast sources.