Stochastic finite element framework for simultaneous estimation of cardiac kinematic functions and material parameters

Abstract

A stochastic finite element framework is presented for the simultaneous estimation of the cardiac kinematic functions and material model parameters from periodic medical image sequences. While existing biomechanics studies of the myocardial material constitutive laws have assumed known tissue kinematic measurements, and image analysis efforts on cardiac kinematic functions have relied on fixed constraining models of mathematical or mechanical nature, we illustrate through synthetic data that a probabilistic joint estimation strategy is needed to achieve more robust and accurate analysis of the kinematic functions and material parameters at the same time. For a particular a priori constraining material model with uncertain subject-dependent parameters and a posteriori noisy imaging based observations, our strategy combines the stochastic differential equations of the myocardial dynamics with the finite element method, and the material parameters and the imaging data are treated as random variables with known prior statistics. After the conversion to state space representation, the extended Kalman filtering procedures are adopted to linearize the equations and to provide the joint estimates in an approximate optimal sense. The estimation bias and convergence issues are addressed, and we conclude experimentally that it is possible to adopt this biomechanical model based multiframe estimation approach to achieve converged estimates because of the periodic nature of the cardiac dynamics. The effort is validated using synthetic data sequence with known kinematics and material parameters. Further, under linear elastic material model, estimation results using canine magnetic resonance phase contrast image sequences are presented, which are in very good agreement with histological tissue staining results, the current gold standards.