Wall Shear Stress Topological Skeleton Independently Predicts Long-Term Restenosis After Carotid Bifurcation Endarterectomy

Umberto Morbiducci, Valentina Mazzi, Maurizio Domanin, Giuseppe De Nisco, Christian Vergara, David A. Steinman, Diego Gallo

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)2936-2949
JournalAnnals of Biomedical Engineering
Issue number12
Publication statusPublished - 2020


  • Computational fluid dynamics
  • Fixed points
  • Intima-media thickness
  • Manifolds
  • Wall shear stress divergence

ASJC Scopus subject areas

  • Biomedical Engineering


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