Geometry and flow properties affect phase shift between pressure and shear stress waves in blood vessels

Haifeng Wang, Timm Krüger, Fathollah Varnik

Research output: Contribution to journalArticlepeer-review


The phase shift between pressure and wall shear stress (WSS) has been associated with vascular diseases such as atherosclerosis and aneurysms. The present study aims to understand the effects of geometry and flow properties on the phase shift under the stiff wall assumption, using an immersed-boundary-lattice-Boltzmann method. For pulsatile flow in a straight pipe, the phase shift is known to increase with the Womersley number, but is independent of the flow speed (or the Reynolds number). For a complex geometry, such as a curved pipe, however, we find that the phase shift develops a strong dependence on the geometry and Reynolds number. We observed that the phase shift at the inner bend of the curved vessel and in the aneurysm dome is larger than that in a straight pipe. Moreover, the geometry affects the connection between the phase shift and other WSS-related metrics, such as time-averaged WSS (TAWSS). For straight and curved blood vessels, the phase shift behaves qualitatively similarly to and can thus be represented by the TAWSS, which is a widely used hemodynamic index. However, these observables significantly differ in other geometries, such as in aneurysms. In such cases, one needs to consider the phase shift as an independent quantity that may carry additional valuable information compared to well-established metrics.
Original languageEnglish
Article number378
Issue number11
Early online date23 Oct 2021
Publication statusE-pub ahead of print - 23 Oct 2021


  • phase shift
  • Wall Shear Stress
  • pressure
  • pulsatile blood flow
  • hemodynamics


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