On the calculation of principle curvatures of the left-ventricular surfaces

A local description of the shape of the left ventricle is relevant in assessing the process of adverse ventricular remodeling, associated with most cardiac pathologies, and in monitoring reverse remodeling by therapy. To quantify local shape of the left ventricle, one can calculate the curvature of its epicardial or endocardial surface. The 3D geometry of the heart and especially the ventricles, can typically be described using finite element meshes. From a mathematical point of view these meshes provide a local parametrization of the surface in the 3-dimensional space. We discuss the analytic derivation of the principle curvatures of the left-ventricular surfaces given their smooth finite-element meshes and apply this derivation to assess the regional shape of the normal porcine left ventricle.