This work aims to validate a time domain numerical model for the short pulse finite amplitude sound beam propagation, radiated by a plane piston, in biological tissue. As it has been shown by Tavakkoli and Cathignol [J. Acoust. Soc. Am. 104, 1998], the method of fractional operators is well suited to account for the different effects: diffraction (Ld), absorption (La), and nonlinear distortion (Ln). The normal particle velocity and the acoustical pressure are calculated plane by plane, at each point of a two dimensional spatial grid, from the surface of the circular transducer to a specified distance. The complete nonlinear evolution equation is simply derived by a superposition of elementary operators corresponding to the "one effect equation". The surface displacement field of the transducer, measured in water with a laser interferometer, is used as source condition in the fractional step algorithm. The absorption law is measured in the 1 MHz to 10 MHz range in a tissue-mimicking liquid (1,3-Butandiol). The calculations of the acoustical pressure in the near and far field zones in time-domain representation are presented together with time and spectral comparisons between theoretical and experimental pressure waveform on axis.
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机译：这项工作旨在验证生物组织中由平面活塞辐射的短脉冲有限振幅声束传播的时域数值模型。正如Tavakkoli和Cathignol所证明的那样[J. co Soc。是。 [第104页，1998年]，分数算子的方法非常适合解决不同的影响：衍射（Ld），吸收（La）和非线性失真（Ln）。在二维空间网格的每个点上，从圆形换能器的表面到指定距离，逐平面计算法向粒子速度和声压。通过与“一个效应方程”相对应的基本算子的叠加，可以简单地得出完整的非线性演化方程。在分数阶跃算法中，使用激光干涉仪在水中测量的换能器的表面位移场用作源条件。在组织模拟液体（1,3-丁二醇）中，吸收定律的测量范围为1 MHz至10 MHz。给出了时域表示中近场和远场区域中声压的计算以及轴向和理论上的和实验压力波形之间的时间和频谱比较。
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