Stochastic Finite Element Framework for Cardiac Kinematics Function and Material Property Analysis

A stochastic finite element method (SFEM) based framework is proposed for the simultaneous estimation of cardiac kinematics functions and material model parameters. While existing biomechanics studies of myocardial material constitutive laws have assumed known kinematics, and image analyses of cardiac kinematics have relied on chosen constraining models (mathematical or mechanical), we believe that a probabilistic strategy is needed to achieve robust and optimal estimates of kinematics functions and material parameters at the same time. For a particular a priori patient-dependent constraining material model with uncertain parameters and a posteriori noisy observations, stochastic differential equations are combined with the finite element method. The material parameters and the imaging/image-derived data are treated as random variables with known prior statistics in the dynamic system equations of the heart. In our current implementation, extended Kalman filter (EKF) procedures are adopted to linearize the equations and to provide the joint estimates. Because of the periodic nature of the cardiac dynamics, we conclude experimentally that it is possible to adopt this physical-model based optimal estimation approach to achieve converged estimates. Results from canine MR phase contrast images with linear elastic model are presented.