title: Mapped Chebyshev pseudo-spectral method for simulating the shear wave propagation in the plane of symmetry of a transversely isotropic viscoelastic medium.
abstract: Shear wave elastography is a versatile technique that is being applied to many organs. However, in tissues that exhibit anisotropic material properties, special care must be taken to estimate shear wave propagation accurately and efficiently. A two-dimensional simulation method is implemented to simulate the shear wave propagation in the plane of symmetry in transversely isotropic viscoelastic media. The method uses a mapped Chebyshev pseudo-spectral method to calculate the spatial derivatives and an Adams-Bashforth-Moulton integrator with variable step sizes for time marching. The boundaries of the two-dimensional domain are surrounded by perfectly matched layers to approximate an infinite domain and minimize reflection errors. In an earlier work, we proposed a solution for estimating the apparent shear wave elasticity and viscosity of the spatial group velocity as a function of rotation angle through a low-frequency approximation by a Taylor expansion. With the solver implemented in MATLAB, the simulated results in this paper match well with the theory. Compared to the finite element method simulations we used before, the pseudo-spectral solver consumes less memory and is faster and achieves better accuracy.
authors.affiliation: Department of Physiology and Biomedical Engineering, Mayo Clinic College of Medicine, Rochester, MN, 55905, USA. qiangbo@gmail.com.|The Nielsen Company, Oldsmar, FL, 34677, USA. qiangbo@gmail.com.
authors.forename: Bo
authors.initials: B
authors.lastname: Qiang
authors.affiliation: Department of Civil and Environmental Engineering, Department of Bioengineering, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA, 15261, USA.|School of Engineering and Computing Sciences, Durham University, South Road, Durham, DH1 3LE, UK.
authors.forename: John C
authors.initials: JC
authors.lastname: Brigham
authors.affiliation: Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI, 48824, USA.
authors.forename: Robert J
authors.initials: RJ
authors.lastname: McGough
authors.affiliation: Department of Physiology and Biomedical Engineering, Mayo Clinic College of Medicine, Rochester, MN, 55905, USA.
authors.forename: James F
authors.initials: JF
authors.lastname: Greenleaf
authors.affiliation: Department of Physiology and Biomedical Engineering, Mayo Clinic College of Medicine, Rochester, MN, 55905, USA.|Department of Radiology, Mayo Clinic College of Medicine, Rochester, MN, 55905, USA.
authors.forename: Matthew W
authors.initials: MW
authors.lastname: Urban
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004548:Elasticity; D033081:Shear Strength; D013816:Thermodynamics; D013997:Time Factors; D014783:Viscosity
keywords: Perfectly matched layer; Pseudo-spectral method; Shear wave; Transversely isotropic; Viscoelastic