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Time-domain simulation of ultrasound propagation in a tissue-like medium based on the resolution of the nonlinear acoustic constitutive relations

机译：超声波在组织样介质中传播的时域模拟   基于非线性声学本构关系的分辨率

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摘要

A time-domain numerical code based on the constitutive relations of nonlinearacoustics for simulating ultrasound propagation is presented. To modelfrequency power law attenuation, such as observed in biological media, multiplerelaxation processes are included and relaxation parameters are fitted to bothexact frequency power law attenuation and empirically measured attenuation of avariety of tissues that does not fit an exact power law. A computationaltechnique based on artificial relaxation is included to correct thenon-negligible numerical dispersion of the numerical method and to improvestability when shock waves are present. This technique avoids the use of highorder finite difference schemes, leading to fast calculations. The numericalcode is especially suitable to study high intensity and focused axisymmetricacoustic beams in tissue-like medium, as it is based on the full constitutiverelations that overcomes the limitations of the parabolic approximations, whilesome specific effects not contemplated by the Westervelt equation can be alsostudied. The accuracy of the method is discussed by comparing the proposedsimulation solutions to one-dimensional analytical ones, to $k$-space numericalsolutions and also to experimental data from a focused beam propagating in afrequency power law attenuation media.
机译：提出了一种基于非线性声学本构关系的时域数值模拟方法。为了模拟诸如在生物介质中观察到的频率幂定律衰减，包括多个松弛过程，并且将松弛参数拟合到精确的频率幂定律衰减和根据经验测量的各种组织的衰减，这些衰减不符合确切的幂定律。包含了基于人工松弛的计算技术，可以校正数值方法的不可忽略的数值离散，并在存在冲击波时提高稳定性。该技术避免了使用高阶有限差分方案，从而实现了快速计算。数值代码特别适用于研究组织状介质中的高强度和聚焦轴对称声束，因为它基于完全本构关系，克服了抛物线近似的局限性，同时还可以研究Westervelt方程未考虑的某些特定效果。通过将所提出的仿真解决方案与一维解析解决方案，$ k $空间数值解决方案以及在频率幂律衰减介质中传播的聚焦束的实验数据进行比较，讨论了该方法的准确性。

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