This paper proposes a new numerical framework to simulate ultrasound wave propagation in 3D viscoelastic heterogeneous media based on the elastodynamic wave equation including a 3D second-order time-domain perfectly matched layer formulation. A finite difference discretization of this formulation is presented, along with a stability analysis. The resulting model is capable of simulating 3D shear and longitudinal acoustic waves for arbitrary source geometries and excitations, together with arbitrary initial and boundary conditions. A simulation example is provided to show the application of our proposed method for tissue elastography imaging. Specifically, the propagation of shear waves from a localized lesion to the surrounding normal tissue is examined.

中文翻译：

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3D 粘弹性非均匀介质中声学传播的模拟及其在医用剪切波弹性成像中的应用

本文提出了一种新的数值框架来模拟超声波在 3D 粘弹性非均质介质中的传播，该框架基于包括 3D 二阶时域完美匹配层公式的弹性动力学波动方程。提出了该公式的有限差分离散化以及稳定性分析。生成的模型能够模拟任意源几何形状和激励的 3D 剪切和纵向声波，以及任意初始和边界条件。提供了一个模拟示例来展示我们提出的组织弹性成像方法的应用。具体来说，检查从局部病变到周围正常组织的剪切波的传播。