Estimation of transversely isotropic material properties from magnetic resonance elastography using the optimised virtual fields method

Abstract

Magnetic resonance elastography (MRE) has been used to estimate isotropic myocardial stiffness. However, anisotropic stiffness estimates may give insight into structural changes that occur in the myocardium as a result of pathologies such as diastolic heart failure. The virtual fields method (VFM) has been proposed for estimating material stiffness from image data. This study applied the optimised VFM to identify transversely isotropic material properties from both simulated harmonic displacements in a left ventricular (LV) model with a fibre field measured from histology as well as isotropic phantom MRE data. Two material model formulations were implemented, estimating either 3 or 5 material properties. The 3-parameter formulation writes the transversely isotropic constitutive relation in a way that dissociates the bulk modulus from other parameters. Accurate identification of transversely isotropic material properties in the LV model was shown to be dependent on the loading condition applied, amount of Gaussian noise in the signal, and frequency of excitation. Parameter sensitivity values showed that shear moduli are less sensitive to noise than the other parameters. This preliminary investigation showed the feasibility and limitations of using the VFM to identify transversely isotropic material properties from MRE images of a phantom as well as simulated harmonic displacements in an LV geometry.

Real‐time MR elastography for viscoelasticity quantification in skeletal muscle during dynamic exercises

“…Higher deviations can occur, for example, in the GAST, where the mean fiber pennation angle is 32°, giving rise to approximately 15% FT contribution to ST waves. Taking additional scans such as diffusion tensor imaging would allow us to avoid assumptions about the local coordinate system; however, diffusion tensor imaging cannot be combined with MRE in real time. A further limitation is that we did not quantify muscle activity by electromyography or by measuring the load applied to the fixation plate.…”

Towards Material Testing 2.0. A review of test design for identification of constitutive parameters from full‐field measurements

“…The second type concerns applications involving more sophisticated constitutive equations. Anisotropic elasticity for composite materials [45][46][47] and wood, [48] elasticity or hyperlasticity of elastomers [49,50] and biological materials, [51][52][53][54] elastoplasticity of plain metals [55][56][57][58][59][60][61] or welds, [62] are typical examples. The use of the VFM to characterize some materials which are less widely used in mechanical engineering, such as paperboard [63] or polymeric foams, [64] has also been reported in recent papers.…”

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.…”