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

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.