A heterogenous, time harmonic, nearly incompressible transverse isotropic finite element brain simulation platform for MR elastography

In this study, we describe numerical implementation of a heterogenous, nearly incompressible, transverse isotropic (NITI) finite element (FE) model with key advantages for use in MR elastography of fibrous soft tissue. MR elastography (MRE) estimates heterogenous property distributions from MR-measured harmonic motion fields based on assumed mechanical models of tissue response. Current MRE property estimation methods usually assume isotropic properties, which cause inconsistencies arising from model-data mismatch when anisotropy is present. In this study, we use a NITI model parameterized by a base shear modulus, shear anisotropy, tensile anisotropy, and an isotropic bulk modulus, which describes the mechanical behavior of tissues with aligned fiber structures well. Property and fiber direction heterogeneity are implemented at the level of FE Gauss points, which allows high-resolution diffusion tensor imaging (DTI) data to be incorporated easily into the model. The resulting code was validated against analytical solutions and a commercial FEM package, and is suitable for incorporation into nonlinear inversion MRE algorithms. Simulations of MRE in brain tissue with heterogeneous properties and anisotropic fiber tracts, which produced wavefields similar to experimental MRE, were generated from anatomical, DTI and MRE image data, allowing investigation of MRE inversion performance in a realistic setting where the ground truth and underlying mechanical behavior are known. Two established isotropic inversion algorithms - nonlinear inversion (NLI) and local direct inversion (LDI) - were applied to simulated MRE data. Both algorithms performed well in simple isotropic homogenous cases; however, heterogeneity cased substantial artifacts in LDI arising from violation of local homogeneity assumptions. NLI was able to recover accurate heterogenous displacement fields in the presence of measurement noise. Isotropic NLI inversion of simulated anisotropic data (generated using the NITI model) produced maps of isotropic mechanical properties with undesirable dependence on the wavefield. Local anisotropy also caused wavefield-dependent errors of 7% in nearby isotropic structures, compared to 10% in the anisotropic structures.