Determining Anisotropic Myocardial Stiffness from Magnetic Resonance Elastography: A Simulation Study

Although magnetic resonance elastography (MRE) has the potential to non-invasively measure myocardial stiffness, myocardium is known to be anisotropic and it is not clear whether all material parameters can be uniquely determined from MRE data. In this study, we examined the determinability of anisotropic stiffness parameters using finite element analysis (FEA) simulations of harmonic steady state wave behavior. Two models were examined: (i) a cylindrical and (ii) a canine left ventricular geometry with realistic fiber architecture. A parameter sweep was carried out, and the objective function, which summed the error between reference displacements and displacements simulated from MRE boundary data and material parameters, was plotted and determinability assessed from the Hessian. Then, given prescribed boundary displacements from the ground truth simulation with added Gaussian noise, an anisotropic material parameter optimization was run 30 times with different noise in order to investigate the effect of noise on determination of material parameters. Results show that transversely isotropic material parameters can be robustly determined using this method.