title: A k-space method for large-scale models of wave propagation in tissue.
abstract: Large-scale simulation of ultrasonic pulse propagation in inhomogeneous tissue is important for the study of ultrasound-tissue interaction as well as for development of new imaging methods. Typical scales of interest span hundreds of wavelengths; most current two-dimensional methods, such as finite-difference and finite-element methods, are unable to compute propagation on this scale with the efficiency needed for imaging studies. Furthermore, for most available methods of simulating ultrasonic propagation, large-scale, three-dimensional computations of ultrasonic scattering are infeasible. Some of these difficulties have been overcome by previous pseudospectral and k-space methods, which allow substantial portions of the necessary computations to be executed using fast Fourier transforms. This paper presents a simplified derivation of the k-space method for a medium of variable sound speed and density; the derivation clearly shows the relationship of this k-space method to both past k-space methods and pseudospectral methods. In the present method, the spatial differential equations are solved by a simple Fourier transform method, and temporal iteration is performed using a k-t space propagator. The temporal iteration procedure is shown to be exact for homogeneous media, unconditionally stable for "slow" (c(x) < or = c0) media, and highly accurate for general weakly scattering media. The applicability of the k-space method to large-scale soft tissue modeling is shown by simulating two-dimensional propagation of an incident plane wave through several tissue-mimicking cylinders as well as a model chest wall cross section. A three-dimensional implementation of the k-space method is also employed for the example problem of propagation through a tissue-mimicking sphere. Numerical results indicate that the k-space method is accurate for large-scale soft tissue computations with much greater efficiency than that of an analogous leapfrog pseudospectral method or a 2-4 finite difference time-domain method. However, numerical results also indicate that the k-space method is less accurate than the finite-difference method for a high contrast scatterer with bone-like properties, although qualitative results can still be obtained by the k-space method with high efficiency. Possible extensions to the method, including representation of absorption effects, absorbing boundary conditions, elastic-wave propagation, and acoustic nonlinearity, are discussed.
authors.affiliation: Applied Research Laboratory, Pennsylvania State University, University Park, PA 16802, USA. mast@sabine.acs.psu.edu
authors.forename: T D
authors.initials: TD
authors.lastname: Mast
authors.forename: L P
authors.initials: LP
authors.lastname: Souriau
authors.forename: D L
authors.initials: DL
authors.lastname: Liu
authors.forename: M
authors.initials: M
authors.lastname: Tabei
authors.forename: A I
authors.initials: AI
authors.lastname: Nachman
authors.forename: R C
authors.initials: RC
authors.lastname: Waag
mesh_terms: D000273:Adipose Tissue / Q000000981:diagnostic imaging; D000465:Algorithms; D001698:Biomedical Engineering; D006801:Humans; D008954:Models, Biological; D012542:Scattering, Radiation; D014463:Ultrasonography / Q000706:statistics & numerical data*