Characterization of surface motion patterns in highly deformable soft tissue organs from dynamic Magnetic Resonance Imaging

In this work, we present a pipeline for characterization of bladder surface dynamics during deep respiratory movements from dynamic Magnetic Resonance Imaging (MRI). Dynamic MRI may capture temporal anatomical changes in soft tissue organs with high-contrast but the obtained sequences usually suffer from limited volume coverage which makes the high resolution reconstruction of organ shape trajectories a major challenge in temporal studies. For a compact shape representation, the reconstructed temporal data with full volume coverage are first used to establish a subject-specific dynamical 4D mesh sequences using the large deformation diffeomorphic metric mapping (LDDMM) framework. Then, we performed a statistical characterization of organ shape changes from mechanical parameters such as mesh elongations and distortions. Since shape space is curved, we have also used the intrinsic curvature changes as metric to quantify surface evolution. However, the numerical computation of curvature is strongly dependant on the surface parameterization (i.e. the mesh resolution). To cope with this dependency, we propose a non-parametric level set method to evaluate spatio-temporal surface evolution. Independent of parameterization and minimizing the length of the geodesic curves, it shrinks smoothly the surface curves towards a sphere by minimizing a Dirichlet energy. An Eulerian PDE approach is used for evaluation of surface dynamics from the curve-shortening flow. Results demonstrate the numerical stability of the derived descriptor throughout smooth continuous-time organ trajectories. Intercorrelations between individuals' motion patterns from different geometric features are computed using the Laplace-Beltrami Operator (LBO) eigenfunctions for spherical mapping.