Treeby Bradley E, Wise Elliott S, Kuklis Filip, Jaros Jiri, Cox B T
Department of Medical Physics and Biomedical Engineering, University College London, Gower Street, London WC1E 6BT, United Kingdom.
Centre of Excellence IT4Innovations, Faculty of Information Technology, Brno University of Technology, Božetěchova 2, Brno, 612 00, Czech Republic.
J Acoust Soc Am. 2020 Oct;148(4):2288. doi: 10.1121/10.0002177.
A full-wave model for nonlinear ultrasound propagation through a heterogeneous and absorbing medium in an axisymmetric coordinate system is developed. The model equations are solved using a nonstandard or k-space pseudospectral time domain method. Spatial gradients in the axial direction are calculated using the Fourier collocation spectral method, and spatial gradients in the radial direction are calculated using discrete trigonometric transforms. Time integration is performed using a k-space corrected finite difference scheme. This scheme is exact for plane waves propagating linearly in the axial direction in a homogeneous and lossless medium and significantly reduces numerical dispersion in the more general case. The implementation of the model is described, and performance benchmarks are given for a range of grid sizes. The model is validated by comparison with several analytical solutions. This includes one-dimensional absorption and nonlinearity, the pressure field generated by plane-piston and bowl transducers, and the scattering of a plane wave by a sphere. The general utility of the model is then demonstrated by simulating nonlinear transcranial ultrasound using a simplified head model.
建立了一个用于轴对称坐标系中非线性超声在非均匀吸收介质中传播的全波模型。使用非标准或k空间伪谱时域方法求解模型方程。轴向空间梯度采用傅里叶配置谱方法计算，径向空间梯度采用离散三角变换计算。时间积分采用k空间校正有限差分格式。该格式对于均匀无损介质中沿轴向线性传播的平面波是精确的，并且在更一般的情况下显著减少了数值色散。描述了该模型的实现，并给出了一系列网格尺寸的性能基准。通过与几个解析解的比较对该模型进行了验证。这包括一维吸收和非线性、平面活塞和碗形换能器产生的压力场以及平面波被球体的散射。然后通过使用简化头部模型模拟非线性经颅超声来证明该模型的通用性。
