Tillett Jason C, Daoud Mohammad I, Lacefield James C, Waag Robert C
Department of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14627, USA.
J Acoust Soc Am. 2009 Sep;126(3):1231-44. doi: 10.1121/1.3158857.
A previously described two-dimensional k-space method for large-scale calculation of acoustic wave propagation in tissues is extended to three dimensions. The three-dimensional method contains all of the two-dimensional method features that allow accurate and stable calculation of propagation. These features are spectral calculation of spatial derivatives, temporal correction that produces exact propagation in a homogeneous medium, staggered spatial and temporal grids, and a perfectly matched boundary layer. Spectral evaluation of spatial derivatives is accomplished using a fast Fourier transform in three dimensions. This computational bottleneck requires all-to-all communication; execution time in a parallel implementation is therefore sensitive to node interconnect latency and bandwidth. Accuracy of the three-dimensional method is evaluated through comparisons with exact solutions for media having spherical inhomogeneities. Large-scale calculations in three dimensions were performed by distributing the nearly 50 variables per voxel that are used to implement the method over a cluster of computers. Two computer clusters used to evaluate method accuracy are compared. Comparisons of k-space calculations with exact methods including absorption highlight the need to model accurately the medium dispersion relationships, especially in large-scale media. Accurately modeled media allow the k-space method to calculate acoustic propagation in tissues over hundreds of wavelengths.
一种先前描述的用于大规模计算组织中声波传播的二维k空间方法被扩展到三维。三维方法包含了二维方法的所有特性，这些特性使得能够准确且稳定地计算传播。这些特性包括空间导数的谱计算、在均匀介质中产生精确传播的时间校正、交错的空间和时间网格以及完美匹配的边界层。空间导数的谱评估通过三维快速傅里叶变换来完成。这个计算瓶颈需要全对全通信；因此，并行实现中的执行时间对节点互连延迟和带宽很敏感。通过与具有球形不均匀性的介质的精确解进行比较，评估了三维方法的准确性。通过将用于实现该方法的每个体素近50个变量分布在一组计算机上，进行了大规模的三维计算。比较了用于评估方法准确性的两个计算机集群。k空间计算与包括吸收在内的精确方法的比较突出了准确建模介质色散关系的必要性，特别是在大规模介质中。精确建模的介质允许k空间方法计算组织中数百个波长上的声传播。
