Identification of Transversely Isotropic Properties from Magnetic Resonance Elastography Using the Optimised Virtual Fields Method

Magnetic resonance elastography (MRE) has been used to estimate myocardial stiffness. However, inversion methods typically introduce unrealistic assumptions. 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 added Gaussian noise and isotropic phantom MRE data. Two material model formulations were implemented, estimating three and five material properties. In the LV model, mean estimated moduli were more accurate from the five-parameter estimation than the three-parameter estimation. In the isotropic phantom experiment, where the material was assigned an arbitrary fibre orientation, results accurately revealed an isotropic material (\(G_{\mathrm {12}}\) = \(G_{\mathrm {13}}\)) and estimated shear moduli were close to reference values. This preliminary investigation showed the feasibility and limitations of the VFM to identify transversely isotropic material properties from MRE.