Linking wall shear stress and vorticity topologies: Toward a unified theory of cardiovascular flow disturbances

Abstract

Broadening current knowledge about the complex relationship at the blood-vessel wall interface is a main challenge in hemodynamics research. Moving from the consideration that wall shear stress (WSS) provides a signature for the near-wall velocity dynamics and vorticity is considered the skeleton of fluid motion, here we present a unified theory demonstrating the existing link between surface vorticity (SV) and WSS topological skeletons, the latter recently emerged as a predictor of vascular disease. The analysis focused on WSS and SV fixed points, i.e., points where the fields vanish, as they play a major role in shaping the main vector field features. The theoretical analysis proves that: (i) all SV fixed points on the surface must necessarily be WSS fixed points, although with differences in nature and stability and (ii) a WSS fixed point is not necessarily a SV fixed point. In the former case, WSS fixed points are the consequence of flow patterns where only shear contributes to vorticity; in the latter case, WSS fixed points are the consequence of flow impingement to/emanation from the vessel wall. Moreover, fluid structures interacting with the wall characterized by zero or non-zero rotational momentum generate WSS fixed points of different nature/stability. High-fidelity computational fluid dynamics simulations in intracranial aneurysm models confirmed the applicability of the theoretical considerations. The presented unified theory unambiguously explains the mechanistic link between near-wall flow disturbances and the underlying intravascular flow features expressed in terms of vorticity, ultimately facilitating a clearer interpretation of the role of local hemodynamics in vascular pathophysiology.