State-Space Analysis of Cardiac Motion With Biomechanical Constraints

Quantitative estimation of nonrigid motion from image sequences has important technical and practical significance. State-space analysis provides powerful and convenient ways to construct and incorporate the physically meaningful system dynamics of an object, the image-derived observations, and the process and measurement noise disturbances. In this paper, we present a biomechanical-model constrained state-space analysis framework for the multiframe estimation of the periodic cardiac motion and deformation. The physical constraints take the roles as spatial regulator of the myocardial behavior and spatial filter/interpolator of the data measurements, while techniques from statistical filtering theory impose spatiotemporal constraints to facilitate the incorporation of multiframe information to generate optimal estimates of the heart kinematics. Physiologically meaningful results have been achieved from estimated displacement fields and strain maps using in vivo left ventricular magnetic resonance tagging and phase contrast image sequences, which provide the tag-tag and tag-boundary displacement inputs, and the mid-wall instantaneous velocity information and boundary displacement measures, respectively.