We propose a novel meshless deformable model for in vivo cardiac left ventricle (LV) 3D motion estimation from tMRI. As a relatively new technology, tagged MRI (tMRI) provides a direct and noninvasive way to reveal local deformation of the myocardium. Many previous research on tMRI are on 2D displacement and strain analysis. It is imperative to reconstruct the motion of a whole LV volume from deformed tagging lines in a few slices in cardiac disease research and diagnosis. We compute the external forces at the tag intersections based on tracked local motion and redistribute the forces to meshless particles throughout the myocardium. Internal constraint forces at particles are derived from local strain energy using Moving Least Squares (MLS). The dense 3D motion field is then computed and updated using the Lagrange equation. The meshless deformable model is capable of tracking 3D deformations with high accuracy and efficiency. In particular, the model outperforms previous methods when the tag intersections are relatively sparse. The experimental results on both a numerical phantom and in vivo healthy and patient heart data show that the meshless deformable model can fully recover the myocardium motion in 3D.
