Cardiac Motion and Elasticity Characterization with Iterative Sequential $\mathcal{H}_\infty$ Criteria

Abstract

Robustness is of paramount importance in cardiac wall motion estimation and myocardial tissue elasticity characterization, especially for clinical applications. Given partial, noisy, image-derived measurements on the cardiac kinematics, we present an integrated robust estimation framework for the joint recovery of dense field cardiac motion and material parameters using iterative sequential \(\mathcal{H}_\infty\) criteria. This strategy is particulary powerful for real-world problems where the types and levels of model uncertainties and data disturbances are not available a priori. Constructing the myocardial dynamics equations from biomechanics principles, at each time step, we rely on techniques from \(\mathcal{H}_\infty\) filtering theory to first generate estimates of heart kinematics with suboptimal material parameter estimates, and then recover the elasticity property given these kinematic state estimates. These coupled iterative steps are repeated as necessary until convergence. We demonstrate the accuracy and robustness of the strategy through experiments with both synthetic data of varying noises and magnetic resonance image sequences.