Modeling of nonlinear medical diagnostic ultrasound

In this PhD Thesis, a numerical method is described that accurately predicts the pulsed acoustic pressure field generated by a medical diagnostic phased array transducer in a nonlinear acoustic medium. The method is called the Iterative Nonlinear Contrast Source (INCS) method, and it is capable of handling a large-scale, threedimensional domain of interest, in the order of 100 wavelengths in each spatial dimension and 100 periods in the temporal dimension. Unlike many existing methods, the method is based on a full-wave approach and it does not employ an implicit or explicit plane wave approximation. Starting from a set of two nonlinear first-order field equations and a two nonlinear constitutive equations, we show that the nonlinear acoustic field may be approximated with a second-order wave equation which is a lossless form of the Westervelt equation including source terms. The Westervelt equation may be solved efficiently by means of the INCS method. In this method, the nonlinear wave problem is formally solved by a Neumann iterative solution, in which the nonlinear term in the Westervelt equation acts as a nonlinear contrast source and provides iterative corrections to the linear approximation of the nonlinear wave problem. The linear step in the Neumann scheme is solved by a spatiotemporal convolution integral of the (primary or contrast) source with the Green's function of the linear background medium. For the evaluation of the convolution integral as a discrete convolution sum on a spatiotemporal grid, the Green's function and the (primary or contrast) source are filtered and windowed in all spatiotemporal dimensions, allowing for their coarse discretization at the Nyquist limit of two points per wavelength/period for the maximum frequency of interest. This approach is referred to as the Filtered Convolution (FC) method. The resulting discretized convolution sum is efficiently evaluated using a Fast Fourier Transform (FFT) method. Results for various one-dimensional and three-dimensional wave problems show that in all cases the INCS method produces accurate results. A validation experiment with a rectangular transducer also shows that the measured nonlinear acoustic field is reproduced very well with the INCS method. Because of its accuracy, reliability and the general validity of its solution, we conclude that the INCS method can be used as a benchmark model for weak to moderate nonlinear distortion, as it occurs in medical diagnostic ultrasound