Wall Shear Stress (WSS) topological skeleton, composed by fixed points and the manifolds linking them, reflects the presence of blood flow features associated to adverse vascular response. However, the influence of WSS topological skeleton on vascular pathophysiology is still underexplored. This study aimed to identify direct associations between the WSS topological skeleton and markers of vascular disease from real-world clinical longitudinal data of long-term restenosis after carotid endarterectomy (CEA). Personalized computational hemodynamic simulations were performed on a cohort of 13 carotid models pre-CEA and at 1 month after CEA. At 60 months after CEA, intima-media thickness (IMT) was measured to detect long-term restenosis. The analysis of the WSS topological skeleton was carried out by applying a Eulerian method based on the WSS vector field divergence. To provide objective thresholds for WSS topological skeleton quantitative analysis, a computational hemodynamic dataset of 46 ostensibly healthy carotid bifurcation models was considered. CEA interventions did not completely restore physiological WSS topological skeleton features. Significant associations emerged between IMT at 60 months follow-up and the exposure to (1) high temporal variation of WSS contraction/expansion (R² = 0.51, p < 0.05), and (2) high fixed point residence times, weighted by WSS contraction/expansion strength (R² = 0.53, p < 0.05). These WSS topological skeleton features were statistically independent from the exposure to low WSS, a previously reported predictor of long-term restenosis, therefore representing different hemodynamic stimuli and potentially impacting differently the vascular response. This study confirms the direct association between WSS topological skeleton and markers of vascular disease, contributing to elucidate the mechanistic link between flow disturbances and clinical observations of vascular lesions.

The degeneration of the arterial wall at the basis of the ascending thoracic aortic aneurysm (ATAA) is a complex multifactorial process, which may lead to clinical complications and, ultimately, death. Individual genetic, biological or hemodynamic factors are inadequate to explain the heterogeneity of ATAA development/progression mechanisms, thus stimulating the analysis of their complex interplay. Here the disruption of the hemodynamic environment in the ATAA is investigated integrating patient-specific computational hemodynamics, CT-based in vivo estimation of local aortic stiffness and advanced fluid mechanics methods of analysis. The final aims are (1) deciphering the ATAA spatiotemporal hemodynamic complexity and its link to near-wall topological features, and (2) identifying the existing links between arterial wall degeneration and hemodynamic insult. Technically, two methodologies are applied to computational hemodynamics data, the wall shear stress (WSS) topological skeleton analysis, and the Complex Networks theory. The same analysis was extended to the healthy aorta. As main findings of the study, we report that: (1) different spatiotemporal heterogeneity characterizes the ATAA and healthy hemodynamics, that markedly reflect on their WSS topological skeleton features; (2) a link (stronger than canonical WSS-based descriptors) emerges between the variation of contraction/expansion action exerted by WSS on the endothelium along the cardiac cycle, and ATAA wall stiffness. The findings of the study suggest the use of advanced methods for a deeper understanding of the hemodynamics disruption in ATAA, and candidate WSS topological skeleton features as promising indicators of local wall degeneration.

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.