Doo-Sabin Surface Models with Biomechanical Constraints for Kalman Filter Based Endocardial Wall Tracking in 3D+T Echocardiography

In this paper, a 3D left ventricle (LV) tracking framework utilizing Doo-Sabin subdivision surface models is extended with biomechanically constrained state transitions. First, an isoparametric finite element analysis (FEA) method for Doo-Sabin surface models is provided. The isoparametric FEA produces a stiffness matrix for a given endocardial model directly, eliminating inconvenient remodeling/meshing procedures commonly conducted prior to FEA. The computed model might lead to inaccurate deformation modes during the tracking due to hypothesized model shape and FEA parameters. Accordingly, we introduce a statistical model improvement approach for modifying the model shape and its stiffness matrix using experimentally observed endocardial surface variations. Finally, the state prediction stage of the Kalman tracking framework is formulated to perform constrained tracking. Comparative analyses show that the biomechanical constraints can significantly improve the endocardium tracking accuracy of the models with high control node resolutions.