A revised and expanded unified theory linking wall shear stress and vorticity topologies to enable the interpretation of cardiovascular flow disturbances

Deciphering the complex interactions at the blood vessel-wall interface remains a key challenge in hemodynamics research. Wall shear stress (WSS) is recognized as a signature for near-wall velocity dynamics, while vorticity represents a fundamental structure of fluid motion. In this work, we revise and extend a recently proposed unifying theoretical approach that sought to connect the topological features of surface vorticity (SV) and WSS [Mazzi, Gallo, Calò, Steinman, and Morbiducci, “Linking wall shear stress and vorticity topologies: Toward a unified theory of cardiovascular flow disturbances,” Phys. Fluids 36(6), 61905 (2024)], the latter recently gaining momentum as a predictor of vascular disease. By revising a partially erroneous interpretation of the link between WSS and SV fixed points (focal points on the luminal surface where these fields vanish), we demonstrate here that every WSS fixed point is also a SV fixed point, and vice versa, though their nature and stability may differ. Building upon the previous study, we establish a robust theoretical classification of the possible combinations of WSS and SV fixed points, based on their nature and stability, and mechanistically connect them to near-wall fluid structures. These structures can further be distinguished by the presence or absence of vorticity diffusion flux normal to the wall, depending on local vorticity kinematics. High-resolution computational fluid dynamics simulations on intracranial aneurysm models validate these theoretical insights. This unifying framework offers a clear taxonomy describing the mechanistic relationship between near-wall flow disturbances and intravascular hemodynamics, providing a deeper understanding of how local shear forces are influenced by near-wall fluid structures, while also paving the way for a clearer interpretation of the role of near-wall hemodynamics in vascular pathophysiology.