Cardiac dynamic analysis using hierarchical shape models and Gaussian curvature recovery: an integrated approach

We present in this paper a scheme to analyze the left ventricle motion over a cardiac cycle through the integration of the hierarchical surface fitting and the point correspondence estimation. The hierarchical surface fitting is a coarse-to-fine analysis scheme and has been successfully applied to cine-angiographic cardiac images. In this study, the hierarchical surface fitting and motion analysis is applied to a set of CT images with real volumetric nature. We also incorporate an additional global deformation, long axis bending, into the shape model to reflect the curved nature of the left ventricle long axis. With the dense volumetric data, we are able to implement higher order spherical harmonics in the analysis of the local deformations. The fitted surface allows us a complete recovery of the Gaussian curvature of the shape. The estimation of the point correspondence is accomplished through the analysis of the first fundamental form and the Gaussian curvature computed from the fitted shape assuming conformal motion. The overall coarse-to-fine hierarchical analysis and the parametric nature of the fitted surface enable us to compute the Gaussian curvature analytically and gain a clear and complete description of the left ventricle dynamics based on the shape evolution over the cardiac cycle. Results based on a set of CT data of 16 volumes show that this hierarchical surface fitting and motion analysis scheme is promising for cardiac analysis.