The Promise of Wall Shear Stress Topological Analysis for Cardiovascular Flow Characterization

Although interest in cardiovascular flow topology dates back at least to the 1970s, its application to clinically relevant problems gained momentum in the early 2000s, when Ethier et al. used topological analysis?including singular points (also known as critical or fixed points)?to characterize flow and wall shear stress (WSS) patterns in bypass grafts. Since then, topological analysis of WSS and near-wall flow has been broadly applied to coronary and carotid artery disease, cerebral and aortic aneurysms, and cardiothoracic flows. In this paper, we illustrate the theory and recent developments in the practice of topological analysis, including the detection and classification of WSS and surface vorticity fixed points, and the topological constraints underlying them; identification of the manifolds (expansion/contraction regions) connecting fixed points; and the links between these topological features and vascular mechanobiology. Based on an objective literature review focusing on work published since 2020, we identified and tabulated more than 50 peer-reviewed research articles, which highlight the growth of WSS topological analysis in the last five years. A narrative summary of studies is provided to demonstrate the tangible promise of topological analysis for understanding, treating, and even predicting the clinical outcomes of cardiovascular diseases. Current challenges and future perspectives are also highlighted.