Modeling shock-wave fields generated by a diagnostic-type transducer

Abstract

New applications of ultrasound imaging may benefit from increased in situ pressure levels. However strong nonlinear propagation effects have not been studied in detail for fields generated by diagnostic transducers. Here we compare two modeling approaches for predicting shock formation in fields generated by a curvilinear imaging probe (C5-2). The field was simulated in two ways: 1) a 3D full-diffraction model based on the Westervelt equation, with a boundary condition defined on a cylindrical surface; 2) an axially symmetric parabolic model based on the KZK equation to define a flat, circular equivalent source. For both models, boundary conditions are adjusted to match low-power axial pressure measurements in the focal lobe of the beam. Simulations and measurements were performed for operation of 40, 64, and 128 central probe elements, and a wide range of clinically relevant output levels was considered. Comparison of focal waveforms shows that the KZK model can predict the amplitudes of fully developed shocks within 5% for 64 and 128 active elements, and within 15% for 40 elements. The full 3D calculations provide better agreement with experiments (within 3%) but require significantly more computational resources. [Work supported by RSF 14-12-00974 and a scholarship of the president of Russia.]