A framework for simulating ultrasound imaging based on first order nonlinear pressure-velocity relations

An ultrasound imaging framework modeled with the first order nonlinear pressure-velocity relations (NPVR) and implemented by a half-time staggered solution and pseudospectral method is presented in this paper. The framework is capable of simulating linear and nonlinear ultrasound propagation and reflections in a heterogeneous medium with different sound speeds and densities. It can be initialized with arbitrary focus, excitation and apodization for multiple individual channels in both 2D and 3D spatial fields. The simulated channel data can be generated using this framework, and ultrasound image can be obtained by beamforming the simulated channel data. Various results simulated by different algorithms are illustrated for comparisons. The root mean square (RMS) errors for each compared pulses are calculated. The linear propagation is validated by an angular spectrum approach (ASA) with a RMS error of 3% at the focal point for a 2D field, and Field II with RMS errors of 0.8% and 1.5% at the electronic and the elevation focuses for 3D fields, respectively. The accuracy for the NPVR based nonlinear propagation is investigated by comparing with the Abersim simulation for pulsed fields and with the nonlinear ASA for monochromatic fields. The RMS errors of the nonlinear pulses calculated by the NPVR and Abersim are respectively 2.4%, 7.4%, 17.6% and 36.6% corresponding to initial pressure amplitudes of 50 kPa, 200 kPa, 500 kPa and 1 MPa at the transducer. By increasing the sampling frequency for the strong nonlinearity, the RMS error for 1 MPa initial pressure amplitude is reduced from 36.6% to 27.3%.