Choice of coordinate system for left ventricular FE-mesh generation

Abstract

Given the ellipsoid shape of the left ventricle (LV), prolate spheroidal coordinates are often adopted to construct a finite element (FE) -mesh of the left ventricle. However, a Cartesian reference frame is needed to define these coordinates. The aim of this study was therefore to examine whether the fitting of a FE-mesh to the LV-surfaces is influenced by the choice of cardiac cycle phase used to define the frame of reference. In 6 MRI datasets of pig hearts the LV borders were manually segmented at end-diastole (ED) and at end-systole (ES). Based on these segmentations, 3 reference systems were defined using the ED contours (EDRF), the ES contours (EDRF) and the average of the two (AVRF). In each reference system, FE-meshes of the LV-surfaces were fitted to the segmentation data of both the ES- and ED-phase. The root mean square Euclidean distance (RMSE) between the data points and their radial projections was assessed as a measure of the goodness of fit. The RMSE over the entire fitted surface was < 1 mm in all cases. The average RMSE between corresponding points on the meshes in the different reference frames was 0.06 mm. Comparison of the RMSE showed no significant difference between the three choices of reference frames. Based on these results, no preferred reference frame was found and the resulting meshes are independent of the frame chosen.Keywordsfinite elementleft ventriclemesh fittingprolate spheroidcoordinate system