Rationale behind the Iterative Nonlinear Contrast Source method

Modern medical echoscopy increasingly relies on imaging modalities that exploit the features of nonlinear ultrasound. The development of these modalities and corresponding dedicated transducers requires accurate simulations of pulsed nonlinear acoustic wave fields in realistic biomedical situations. This involves nonlinear media with frequency power law attenuation and spatially dependent acoustic properties. Simulations frequently concern strongly steered beams, hundreds of wavelengths long, and their grating lobes. The Iterative Nonlinear Contrast Source (INCS) method is a full-wave method that has been developed for this purpose. It treats the nonlinear term in the Westervelt equation as a contrast source that operates, alongside other source terms, in a homogeneous linear ‘background’ medium. The background Green’s function is known analytically, and convolution with the source terms yields an integral equation. This is solved iteratively to obtain the nonlinear pressure field. The convolution over the four-dimensional computational domain is performed with FFT’s, and a grid with only two points per wavelength suffices due to prior filtering of the involved quantities. The present talk elaborates on the characteristic steps of the INCS method, i.e. the contrast source formulation and the filtered convolution. Comparisons with other methods will be made, and recent developments will be presented.