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

• Published in: Physics of fluids (1994) Vol. 36; no. 6
• Main Authors: Mazzi, Valentina, Gallo, Diego, Calò, Karol, Steinman, David A., Morbiducci, Umberto
• Format: Journal Article
• Language: English
• Published: Melville American Institute of Physics 01.06.2024
• Subjects: Blood vessels; Computational fluid dynamics; Disturbances; Fields (mathematics); Flow distribution; Hemodynamics; Shear stress; Stability; Topology; Vorticity; Wall flow; Wall shear stresses
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/5.0209003

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.