Research School of Engineering, College of Engineering and Computer Science, The Australian National University, Canberra ACT 0200, Australia.
J Acoust Soc Am. 2012 Jun;131(6):4324-36. doi: 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.
通过组织逼真介质模拟非线性超声传播具有广泛的实际应用。然而，由于计算域的大小与声波长相比非常大，因此这是一个计算上困难的问题。此处，使用 k 空间伪谱方法来减少每个波长所需的网格点数，以实现准确的模拟。该模型基于适用于具有幂律吸收的非均匀介质中非线性波传播的耦合一阶声学方程。这些方程源自流体力学方程，并包含一个压力-密度关系，其中包括非线性、幂律吸收和介质非均匀性的影响。计入对流非线性和幂律吸收的附加项表示为空间梯度，这使得它们在数值上易于编码。然后，使用 k 空间伪谱技术对控制方程进行离散化，其中使用傅里叶共位置法计算空间梯度。与传统有限差分方法相比，这提高了梯度计算的准确性，从而放宽了对密集计算网格的要求。通过几个数值实验，包括从临床超声探头的光束模式的 3D 模拟，展示了所开发模型的准确性和实用性。
