An Optimization Framework to Personalize Passive Cardiac Mechanics

Personalized cardiac mechanics modeling is a powerful tool for understanding the biomechanics of cardiac function in health and disease and assisting in treatment planning. However, current models are limited to using medical images acquired at a single cardiac phase, often limiting their applicability for processing dynamic image acquisitions. This study introduces an inverse finite element analysis (iFEA) framework to estimate the passive mechanical properties of cardiac tissue using time-dependent medical image data. The iFEA framework relies on a novel nested optimization scheme, in which the outer iterations utilize a traditional optimization method to best approximate material parameters that fit image data, while the inner iterations employ an augmented Sellier's algorithm to estimate the stress-free reference configuration. With a focus on characterizing the passive mechanical behavior, the framework employs structurally based anisotropic hyperelastic constitutive models and physiologically relevant boundary conditions to simulate myocardial mechanics. We use a stabilized variational multiscale formulation for solving the governing nonlinear elastodynamics equations, verified for cardiac mechanics applications. The framework is tested in myocardium models of biventricle and left atrium derived from cardiac phase-resolved computed tomographic (CT) images of a healthy subject and three patients with hypertrophic obstructive cardiomyopathy (HOCM). The impact of the choice of optimization methods and other numerical settings, including fiber direction parameters, mesh size, initial parameters for optimization, and perturbations to optimal material parameters, is assessed using a rigorous sensitivity analysis. The performance of the current iFEA is compared against an assumed power-law-based pressure-volume relation, typically used for single-phase image acquisition.