Wall Shear Stress Topological Skeleton Analysis in Cardiovascular Flows: Methods and Applications

A marked interest has recently emerged regarding the analysis of the wall shear stress (WSS) vector field topological skeleton in cardiovascular flows. Based on dynamical system theory, the WSS topological skeleton is composed of fixed points, i.e., focal points where WSS locally vanishes, and unsta...

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Bibliographic Details
Published in:Mathematics (Basel) 2021-04, Vol.9 (7), p.720
Main Authors: Mazzi, Valentina, Morbiducci, Umberto, Calò, Karol, De Nisco, Giuseppe, Lodi Rizzini, Maurizio, Torta, Elena, Caridi, Giuseppe Carlo Alp, Chiastra, Claudio, Gallo, Diego
Format: Article
Language:English
Subjects:
Blood flow
computational fluid dynamics
Disease
divergence
Dynamic systems theory
Dynamical systems
Eigenvalues
Endothelium
Fields (mathematics)
fixed points
Hemodynamics
manifolds
Pathophysiology
Post-production processing
Shear stress
System theory
Topology
Wall shear stresses
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Summary:A marked interest has recently emerged regarding the analysis of the wall shear stress (WSS) vector field topological skeleton in cardiovascular flows. Based on dynamical system theory, the WSS topological skeleton is composed of fixed points, i.e., focal points where WSS locally vanishes, and unstable/stable manifolds, consisting of contraction/expansion regions linking fixed points. Such an interest arises from its ability to reflect the presence of near-wall hemodynamic features associated with the onset and progression of vascular diseases. Over the years, Lagrangian-based and Eulerian-based post-processing techniques have been proposed aiming at identifying the topological skeleton features of the WSS. Here, the theoretical and methodological bases supporting the Lagrangian- and Eulerian-based methods currently used in the literature are reported and discussed, highlighting their application to cardiovascular flows. The final aim is to promote the use of WSS topological skeleton analysis in hemodynamic applications and to encourage its application in future mechanobiology studies in order to increase the chance of elucidating the mechanistic links between blood flow disturbances, vascular disease, and clinical observations.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9070720