A k-space method for acoustic propagation using coupled first-order equations in three dimensions.
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.
Tillett
Jason C
JC
Department of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14627, USA.
Daoud
Mohammad I
MI
Lacefield
James C
JC
Waag
Robert C
RC
D000042:Absorption; D000162:Acoustics; D000465:Algorithms; D003198:Computer Simulation; D005583:Fourier Analysis; D006801:Humans; D008954:Models, Biological; D008962:Models, Theoretical; D011312:Pressure; D012815:Signal Processing, Computer-Assisted; D013997:Time Factors