Comparison between two different full-wave methods for the computation of nonlinear ultrasound fields in inhomogeneous and attenuating tissue

Nonlinear propagation is important in many diagnostic and therapeutic applications of medical ultrasound. The design of equipment and protocols for nonlinear modalities is facilitated by the simulation of the nonlinear ultrasound field. However, many existing simulation tools have difficulties of dealing with realistic features like tissue inhomogeneity, power law losses, or steered beams. Recently, two full-wave simulation methods for nonlinear ultrasound have been developed that are able to deal with these features. Those methods are known as the Iterative Nonlinear Contrast Source method (INCS; an integral equation method) and k-Wave (a pseudospectral time domain method). This paper assesses the accuracy of both methods by comparing their spatial and spectral results for two test configurations. In both configurations, a square piston excites a three-cycle Gaussian-modulated tone burst with a center frequency of 1 MHz and a source pressure of 750 kPa. The medium in the first configuration is homogeneous and has a speed of sound, density of mass and parameter of nonlinearity equal to that of water, and a power law attenuation with an exponent 1.5 and a magnitude of 0.75 dB/cm at 1 MHz. In the second configuration, the medium has been made inhomogeneous by putting a hollow cylinder (speed of sound equal to 1540 m/s) and a solid sphere (parameter of nonlinearity equal to 1) in the course of the radiated beam. In both cases, the results obtained with INCS and k-Wave are in excellent agreement, with maximum local differences in the order of 0.5-0.6 dB in the significant parts of the field. Because both methods are computationally quite different, it is improbable that these both suffer from the same systematic error. Hence it is established that both methods are correct and highly accurate, and are suitable tools for performing precise simulations and generating accuracy benchmarks.