Meshless deformable models for LV motion analysis

We propose a novel meshless deformable model for in vivo cardiac left ventricle (LV) 3D motion estimation. As a relatively new technology, tagged MRI (tMRI) provides a direct and noninvasive way to reveal local deformation of the myocardium, which creates a large amount of heart motion data which requiring quantitative analysis. In our study, we sample the heart motion sparsely at intersections of three sets of orthogonal tagging planes and then use a new meshless deformable model to recover the dense 3D motion of the myocardium temporally during the cardiac cycle. We compute external forces at tag intersections based on tracked local motion and redistribute the force to meshless particles throughout the myocardium. Internal constraint forces at particles are derived from local strain energy using a moving least squares (MLS) method. The dense 3D motion field is then computed and updated using the Lagrange equation. The new model avoids the singularity problem of mesh-based models and is capable of tracking large deformation with high efficiency and accuracy. In particular, the model performs well even when the control points (tag intersections) are relatively sparse. We tested the performance of the meshless model on a numerical phantom, as well as in vivo heart data of healthy subjects and patients. The experimental results show that the meshless deformable model can fully recover the myocardium motion in 3D.