Mapped Chebyshev pseudo-spectral method for simulating the shear wave propagation in the plane of symmetry of a transversely isotropic viscoelastic medium

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.