Fast simulation of second harmonic ultrasound fields

Numerical modeling of nonlinear (NL) ultrasound (US) beam propagation plays a key role in designing state-of-art medical US systems due to the improvements in image quality coming from the use of second harmonic overtones. Describing the combined effects of diffraction, absorption and nonlinearity, the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation is the most commonly used model to address this simulation problem. This work introduces an algorithm capable of providing good estimations of pressure profiles at arbitrary depth without requiring stepping techniques. Our proposal consists in a perturbative approach to the solution of the KZK equation cast in a discrete Fourier–Bessel domain applicable to axisymmetric propagation from circular transducers. The resulting algorithm is capable of simulating NL US fields with significant computational savings and an accuracy at least comparable to other standard approaches to the same problem. Comparing our algorithm to the output of a publicly available NL KZK solver, significant cost reductions and performance improvements were recorded.