Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method
Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method
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DOI：
10.1121/1.4712021
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发表时间：
2012-06-01
影响因子：
2.4
通讯作者：
Cox, B. T.
中科院分区：
文献类型：
--
作者：
Treeby, Bradley E.;Jaros, Jiri;Cox, B. T.
非线性超声在组织真实介质中的传播模拟具有广泛的实际应用。然而，这是一个计算困难的问题，因为与声波波长相比，计算域的尺寸很大。在这里，使用k空间伪谱方法来减少精确模拟每个波长所需的网格点数量。该模型基于一阶耦合声学方程，该方程适用于具有幂律吸收的非均匀介质中的非线性波传播。这些是从流体力学方程推导出来的，包括一个压力-密度关系，它结合了非线性、幂律吸收和介质非均质性的影响。考虑对流非线性和幂律吸收的附加项被表示为空间梯度，使它们能够有效地进行数值编码。然后使用k空间伪谱技术将控制方程离散化，其中使用傅里叶配置方法计算空间梯度。与传统的有限差分方法相比，这提高了梯度计算的精度，从而减少了对密集计算网格的要求。通过几个数值实验，包括临床超声探头光束模式的三维模拟，证明了所开发模型的准确性和实用性。(C) 2012美国声学学会。[http://dx.doi.org/10.1121/1.4712021]
The simulation of nonlinear ultrasound propagation through tissue realistic media has a wide range of practical applications. However, this is a computationally difficult problem due to the large size of the computational domain compared to the acoustic wavelength. Here, the k-space pseudospectral method is used to reduce the number of grid points required per wavelength for accurate simulations. The model is based on coupled first-order acoustic equations valid for nonlinear wave propagation in heterogeneous media with power law absorption. These are derived from the equations of fluid mechanics and include a pressure-density relation that incorporates the effects of nonlinearity, power law absorption, and medium heterogeneities. The additional terms accounting for convective nonlinearity and power law absorption are expressed as spatial gradients making them efficient to numerically encode. The governing equations are then discretized using a k-space pseudospectral technique in which the spatial gradients are computed using the Fourier-collocation method. This increases the accuracy of the gradient calculation and thus relaxes the requirement for dense computational grids compared to conventional finite difference methods. The accuracy and utility of the developed model is demonstrated via several numerical experiments, including the 3D simulation of the beam pattern from a clinical ultrasound probe. (C) 2012 Acoustical Society of America. [http://dx.doi.org/10.1121/1.4712021]