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

Abstract

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.

Influence of left-ventricular shape on passive filling properties and end-diastolic fiber stress and strain

“…Streeter and Hanna (1973). The left-ventricular free wall has also been observed to be less curved than predicted by an ellipsoid model (Claus et al, 2008), which may also lead to a more homogeneous contraction force of the myocytes. It is not certain though that passive ED fiber strain or contraction force is really homogeneous distributed in the beating left ventricle.…”

Standardized Delineation of Endocardial Boundaries in Three-Dimensional Left Ventricular Echocardiograms

“…Nevertheless, the trends observed before consensus still hold true. At ED, the highest distance errors were again at segments 17,1,7,13,6,12,16 and at ES at the apical cap (segment 17), the mid anterior wall (segment 7) and basal anteroseptum (segment 2).…”

“…After all three experts had submitted their tracings, 3D shapes ( Figure 7) were generated from the nine 2D contours in ED and ES by interpolation [10,13]. The shapes were represented by a 3D mesh with a resolution of about 40-by-80 points (longitudinal x circumferential).…”

Real-time 3D interactive segmentation of echocardiographic data through user-based deformation of B-spline explicit active surfaces

“…Manual contouring was done using an in-house developed software package (Speqle3D, KU Leuven) dedicated to 3D visualization and manual delineation of LV boundaries [34]. This software package is implemented in MATLAB (The Mathworks Inc., Natick, MA).…”