{'fraction_non_alphanumeric': 0.021013597033374538, 'fraction_numerical': 0.0, 'mean_word_length': 5.639344262295082, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Numerical modeling of ultrasound propagation in heterogeneous media using a mixed domain method

A mixed domain method (MDM) is presented in this paper for modeling one-way linear/nonlinear wave propagation in biological tissue with arbitrary heterogeneities, in which sound speed, density, attenuation coefficients, and nonlinear coefficients are all spatial varying functions. The MDM is based on solving a Westervelt-like equation. We validated the algorithm by studying a number of one-dimensional and two-dimensional problems. Overall, this study demonstrates that the MDM is a computationally efficient and accurate method when used to model wave propagation in biological tissue with relatively weak heterogeneities. We also proposed methods to improve the algorithm for moderately heterogeneous media.