Modeling and simulation of nonlinear wave propagation in ultrasound i...

Nonlinear ultrasound imaging has become increasingly important in medical but also industrial areas, as it makes the ultrasound beam analysis more accurate and enhances the quality of images. We develop a three dimensional model for nonlinear ultrasound imaging and a numerical algorithm to simulate pressure waveforms based on the KZK-equation. In our case we model the propagation of three dimensional sound beams in water for a rectangular source. With an eigensystem approach for the Laplacian operator on a rectangular domain and an operator splitting method the effects of nonlinearity and diffraction can efficiently be taken into account. To demonstrate the accuracy of the developed model it has been implemented in MATLAB and simulated results are compared to acoustic output measurements performed by a hydrophone.