Analytic calculation of shear wave signals in an incompressible, transversely isotropic material

Elastic properties of materials can be measured by observing shear wave propagation following localized, impulsive excitations and comparing the spatiotemporal signals with signals calculated using a mechanical model of the material. These calculations are difficult in anisotropic materials because of the complex relations among the material symmetries, propagation directions, and wave polarizations. This study presents a new analytic model of wave propagation in an incompressible transversely isotropic (ITI) material, which is a commonly used model for anisotropic biological tissues such as skeletal muscle. The model solves the Cauchy equation of motion in the spatial and temporal Fourier domains by separating the system response function that relates the excitation force and shear wave signal into two terms corresponding to shear horizontal and shear vertical shear wave polarizations. Sample results are reported for an ITI material with model parameters similar to parameters measured in in vivo muscle and for model parameters determined by fitting the model to experimentally measured shear wave speeds in in vivo muscle. Calculation times for the analytic model are significantly shorter compared to similar calculations based on finite element simulations or Green's function calculations, and thus, the analytic model is well-suited for iterative fitting of model parameters.