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

Abstract

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.

Calibration of a Heterogeneous Brain Model Using a Subject-Specific Inverse Finite Element Approach

“…There are also several limitations associated with the MRE-based approach. Firstly, although brain heterogeneity was represented as a function of tissue stiffness and not tissue type, the implementation was still isotropic as brain MRE measurements typically assume material isotropy, though methods for extracting anisotropic properties are being developed ( Romano et al, 2012 ; Tweten et al, 2015 ; McGarry et al, 2020 ; Smith et al, 2020 ). Secondly, it was assumed that the relative stiffnesses obtained from the micron-level displacements used in MRE were linear with strain, and that the heterogeneity observed in MRE was applicable for higher levels of deformation.…”

Viscoelasticity Imaging of Biological Tissues and Single Cells Using Shear Wave Propagation

“…Retrieved mechanical parameter distributions, corresponding to each subzone distribution, are finally averaged to form the final solution. This reconstruction method has been applied to phantoms, brain [176,203,264,265] and breast [266,267] data, and has proven its capacity to reconstruct multiple variables at various actuation frequencies using elastic and viscoelastic physical models (compressible elastic [268], compressible viscoelastic [269], and nearly incompressible viscoelastic [176, 184, 203, 231, 264-266, 268, 270-272]). Additionally, poroelastic models have been introduced for accurate consideration of the biphasic nature of entangled solid-liquid structures in biological tissues [168,184,211,270,271,273]).…”

“…This constitutes a direct measurement of the anisotropy impact in isotropic models. Such observation was quantified using a finite element formulation of a heterogeneous, nearly incompressible, and transverse isotropic model providing benchmark displacement fields for inversion testing [265].…”

Quantitative effects of off‐resonance related distortion on brain mechanical property estimation with magnetic resonance elastography

“…The complex‐valued shear modulus, G*, was assigned to the simulation as G* = 2.11 + i 0.86 kPa for gray matter and as G* = 2.53 + i 1.14 kPa for white matter, with subcortical structures assigned values as reported by Johnson et al 41 A finite element solution of the governing equations for steady‐state vibration of a viscoelastic material was used to compute whole‐brain displacement data for this geometry and distribution of properties. Displacement boundary conditions were assigned from the measured MRE displacements on the exterior brain surface to produce realistic simulated displacement fields 42,43 …”

“…Displacement boundary conditions were assigned from the measured MRE displacements on the exterior brain surface to produce realistic simulated displacement fields. 42,43 The output of the simulation is a set of complex-valued displacement amplitude fields at 1.25 mm resolution. From these simulated displacements, we created a set of complex objects representing a typical MRE dataset with displacement from four phase offsets in each of the three cardinal directions encoded in the phase of the object, and with a common magnitude from the original input image.…”