Quantification of the non-planarity of the human carotid bifurcation

The carotid bifurcation has been a region of particular interest due to its predilection for clinically significant atherosclerosis. It has been shown that the vessel geometry is a major determinant of the local haemodynamic properties which are believed to be associated with the location of atherosclerotic lesions. Current knowledge of the geometry of the carotid bifurcation is insufficient and restricted to basic geometric parameters. To provide some means of quantifying the degree of complexity of the 3D shape of the bifurcation, we made an initial attempt by evaluating the non-planarity of an arterial bifurcation based upon the singular value decomposition theorem. In this paper we present our results obtained on the right carotid bifurcations of six normal subjects, each of whom was scanned twice using the 2D time-of-flight MR sequence. The acquired 2D cross sectional images were processed by using our in-house software which comprises 2D segmentation, 3D reconstruction and smoothing. The centroids of each transverse slices were determined and used as input data for the non-planarity analysis. Our results using the singular value decomposition method have demonstrated discernible differences in non-planarity among individuals. Comparisons with the planarity definition proposed by other investigators suggest that the singular value decomposition method offers more information about the linearity and planarity of the bifurcation. However, it is also realised that a single measure of non-planarity can never fully characterise a bifurcation owing to the great variety of geometries.