Identification of Transversely Isotropic Material Properties from Cardiac Magnetic Resonance Elastography

Abstract

Myocardial stiffness is an important determinant of cardiac function, and significant increases in global stiffness are thought to be associated with some forms of diastolic heart failure. Although magnetic resonance elastography (MRE) has been used to estimate isotropic stiffness in the heart, myocardium has anisotropic material properties with greatest stiffness along the fibre direction. This thesis investigated two methods for determining global transversely isotropic material properties from MRE displacement fields using the finite element model update (FEMU) method and the optimised virtual fields method (VFM). A geometrically accurate finite element model of a canine left ventricle (LV) was developed and fibre directions measured from histology were interpolated at element locations. The model was used to simulate harmonic steady-state motion in Abaqus (Chapter 3). The simulated displacements for the LV model were used to validate the boundary value FEMU method for a transversely isotropic material model (Chapter 4). Identifiability of transversely isotropic material properties was assessed in both the LV model and MRE displacement fields measured from an isotropic phantom. While the FEMU method was able to identify all parameters, this iterative method was computationally expensive and required selection of noisy pixel data as boundary conditions. A second method, the optimised VFM (Chapters 5 and 6), was implemented, which does not require the application of boundary conditions. The VFM was tested with a cantilever beam model, the canine LV model and isotropic phantom MRE data. Two transversely isotropic material model formulations were implemented with the VFM to estimate three and five material properties, respectively. The VFM approach was found to achieve good results but was largely dependent on the loading conditions. Young’s moduli and Poisson’s ratio were less accurately estimated than when applying the FEMU method. In conclusion, this thesis utilised two inversion methods, the FEMU method and optimised VFM, to estimate transversely isotropic material properties from simulated and experimental MRE displacements. The thesis illustrates the challenges of identifying anisotropic material properties from MRE, including the dependence on the loading conditions. Future work should include MRE experiments with an anisotropic phantom to further validate the optimised VFM as an inversion method.