Relative identifiability of anisotropic properties from magnetic resonance elastography

Abstract

Although magnetic resonance elastography (MRE) has been used to estimate isotropic stiffness in the heart, myocardium is known to have anisotropic properties. This study investigated the determinability of global transversely isotropic material parameters using MRE and finite-element modeling (FEM). A FEM-based material parameter identification method, using a displacement-matching objective function, was evaluated in a gel phantom and simulations of a left ventricular (LV) geometry with a histology-derived fiber field. Material parameter estimation was performed in the presence of Gaussian noise. Parameter sweeps were analyzed and characteristics of the Hessian matrix at the optimal solution were used to evaluate the determinability of each constitutive parameter. Four out of five material stiffness parameters (Young's modulii E and E , shear modulus G and damping coefficient s), which describe a transversely isotropic linear elastic material, were well determined from the MRE displacement field using an iterative FEM inversion method. However, the remaining parameter, Poisson's ratio, was less identifiable. In conclusion, Young's modulii, shear modulii and damping can theoretically be well determined from MRE data, but Poisson's ratio is not as well determined and could be set to a reasonable value for biological tissue (close to 0.5).

Advances and Future Direction of Magnetic Resonance Elastography

“…Recently, Miller et al studied the relative detectability of tissue anisotropic properties from MRE 73 . In this work, a FEM-based inversion method was proposed in which anisotropic material properties were estimated by iteratively minimizing the ground truth and the estimated displacement resulted by the material properties under iteration.…”

Mechanical Properties of White Matter Tracts in Aging Assessed via Anisotropic MR Elastography

“…An early two-parameter approach that models shear modulus parallel and perpendicular to the fiber direction was initially applied to study breast (Sinkus et al, 2005) and skeletal muscle (Green et al, 2013); this approach does not capture the potential tensile anisotropy of brain tissue. Conversely, an orthotropic, nine-parameter model was applied to WM and the corticospinal tract specifically (Romano et al, 2012(Romano et al, , 2014; due to the large number of coefficients of dramatically different magnitudes, estimating these parameters accurately is difficult from traditional MRE data (Miller et al, 2018a(Miller et al, , 2018b. Recently, a three-parameter, nearly-incompressible, transversely-isotropic material model was proposed that comprises a substrate shear modulus and two anisotropy parameters that represent the differences in Young's modulus and shear modulus relative to the assumed fiber direction.…”

Quantifying stability of parameter estimates for in vivo nearly incompressible transversely-isotropic brain MR elastography

“…Some MRE tissues of interest consist of tracts of aligned fibers, such as muscle and brain white matter, which are likely to produce an anisotropic mechanical response. This reality has motivated the development of anisotropic MRE methods [13][14][15][16][17] that can return direction-dependent mechanical properties of tissue. Here, predictive stability measures are important due to the directional dependence of the stress-strain relationship; some wave fields generate stresses completely independent of specific anisotropic stiffness parameters, thus making their estimation inaccurate or even impossible [18].…”