WALL SHEAR STRESS TOPOLOGICAL SKELETON IDENTIFICATION IN CARDIOVASCULAR FLOWS: A PRACTICAL APPROACH

The observed co-localization of “disturbed” hemodynamics and atherosclerotic lesion prevalence has led to the identification of low and oscillatory Wall Shear Stress (WSS) as a biomechanical localizing factor for vascular dysfunction. However, recent evidences have underlined how consideration of only “low and oscillatory” WSS may oversimplify the complex hemodynamic milieu to which the endothelium is exposed. In this context, recent studies have highlighted the relevance of WSS fixed points, and the stable and unstable manifolds that connect them. These WSS topological features have a strong link with flow features like flow stagnation, separation, and recirculation, which are usually classified as “disturbed” flow. Technically, a fixed point of a vector field is a point where the vector field vanishes, while unstable/stable vector field manifolds identify contraction/expansion regions linking the fixed points. The set of fixed points and their connections form the topological skeleton of a vector field. The presence of WSS fixed points and of WSS contraction/expansion regions, highlighted by WSS manifolds, might induce focal vascular responses relevant for, e.g., early atherosclerosis, or, aneurysm rupture. For these reasons, the topological skeleton analysis of the WSS vector field is of great interest and motivates the study present herein. Lagrangian techniques have been recently proposed to identify WSS manifolds but have certain practical limitations. A Eulerian approach has also been suggested, but only for 2D analytical fields. Here we propose and demonstrate the use of a simple Eulerian approach for identifying WSS topological skeleton on 3D surfaces.