Meshless deformable models for LV motion and strain computation from TMRI

OF THE DISSERTATION Meshless Deformable Models for LV Motion and Strain Computation from TMRI by Xiaoxu Wang Dissertation Director: Dimitris N. Metaxas Tagged MRI(TMRI) provides a direct and noninvasive way to reveal the in-wall deformation of the myocardium. Due to the through-plane motion, the 3D trajectories and strain of material points cannot be calculated directly from 2D TMRI images. With the intersections of three orthogonal tagging planes as cue points, we build a meshless volumetric deformable model to track the displacement of every material point in the heart wall. Meshless deformable models describe an object as point clouds inside of the object boundary. Each material point in the object is represented as a parameterized function of its coordinates in the model coordinate system, and the model is deformed by updating these parameters. The similarity transformation of each point is computed by assuming its neighboring points are doing the same transformation. The deformation is computed iteratively when the cue points match the target locations in the consecutive image frame. The 3D strain field is computed from the 3D displacement field with Moving Least Squares (MLS). We validate the performance of meshless deformable models with a numerical phantom and demonstrate that the meshless method outperform the finite element method (FEM). Meshless deformable models can track the trajectories of any material