Finite Deformation Guided Nonlinear Filtering for Multiframe Cardiac Motion Analysis

Abstract

Abstract. In order to obtain sensible estimates of myocardial kinematics based on biomechanics constraints, one must adopt appropriate material, deformation, and temporal models. Earlier efforts, although not concurrently adopted within the same framework, have shown that it is essential to carefully consider the fibrous structure of the myocardium, the large geometric deformation of the cardiac wall movement, the multiframe observations over the cardiac cycle, and the uncertainties in the system modeling and data measurements. With the meshfree particle method providing the platform to enforce the anisotropic material property derived from the myofiber architecture, we present the first effort to perform multiframe cardiac motion analysis under finite deformation conditions, posed as a nonlinear statistical filtering process. Total Lagrangian (TL) formulation is adopted to establish the myocardial system dynamics under finite deformation, which is then used to perform nonlinear state space prediction (of the tissue displacement and velocity) at each time frame, using the Newton-Raphson iteration scheme. The system matrices of the state space equation are then derived, and the optimal estimation of the kinematic state is achieved through TL-updated recursive filtering. Results from synthetic data with ground truth and canine cardiac image sequence are presented.

Estimation of Cardiac Electrical Propagation from Medical Image Sequence

“…The dense cardiac motion fields, including displacements, velocities and accelerations throughout the myocardium, can then be estimated from those coarse measurements with a priori constraints [2,3,4,5], for which biomechanical models have been the popular choices because of their physics meaningfulness. A recent effort is particularly related to our current work [6].…”

Physiome Model Based State-Space Framework for Cardiac Kinematics Recovery

“…In order to properly use the patient measurements and compromise with the prior physiome model, a statistical framework is required to couple them together. Equation (5) can be rewritten as a state-space updating equation [6]:…”

“…where T is the transformation matrix related to the fiber orientations, and R is the matrix responsible for the transformation between the strain tensor components and the engineering strain tensor components [6].…”

“…The displacement-based total Lagrangian (TL) system dynamics of the heart under finite deformation can be written in the following form [6]:…”

“…Expressing the cardiac dynamics in a state-space representation, with the physiome model providing a priori predictive cardiac kinematics, patient specific kinematic estimates can be obtained in minimum-mean-square-error (MMSE) sense by updating the model predictions with measurements from images and other means. With the use of the physiome model, the predictions are more meaningful and potentially more accurate compared with the strategies which are only based on BM model and image-derived passive force [6]. Experiments have been performed on synthetic data to show the importance of utilizing the physiome model, and also performed on canine MR image sequences to show its possible practical applications.…”