Biomechanics and Modeling in Mechanobiology

, Volume 16, Issue 3, pp 787–803 | Cite as

Wall shear stress exposure time: a Lagrangian measure of near-wall stagnation and concentration in cardiovascular flows

  • Amirhossein ArzaniEmail author
  • Alberto M. Gambaruto
  • Guoning Chen
  • Shawn C. Shadden
Original Paper


Near-wall transport is of utmost importance in connecting blood flow mechanics with cardiovascular disease progression. The near-wall region is the interface for biologic and pathophysiologic processes such as thrombosis and atherosclerosis. Most computational and experimental investigations of blood flow implicitly or explicitly seek to quantify hemodynamics at the vessel wall (or lumen surface), with wall shear stress (WSS) quantities being the most common descriptors. Most WSS measures are meant to quantify the frictional force of blood flow on the vessel lumen. However, WSS also provides an approximation to the near-wall blood flow velocity. We herein leverage this fact to compute a wall shear stress exposure time (WSSET) measure that is derived from Lagrangian processing of the WSS vector field. We compare WSSET against the more common relative residence time (RRT) measure, as well as a WSS divergence measure, in several applications where hemodynamics are known to be important to disease progression. Because these measures seek to quantify near-wall transport and because near-wall transport is important in several cardiovascular pathologies, surface concentration computed from a continuum transport model is used as a reference. The results show that compared to RRT, WSSET is able to better approximate the locations of near-wall stagnation and concentration build-up of chemical species, particularly in complex flows. For example, the correlation to surface concentration increased on average from 0.51 (RRT) to 0.79 (WSSET) in abdominal aortic aneurysm flow. Because WSSET considers integrated transport behavior, it can be more suitable in regions of complex hemodynamics that are traditionally difficult to quantify, yet encountered in many disease scenarios.


Advection–diffusion Blood flow Hemodynamics Near-wall transport Residence time Shear stress 



The authors are thankful to Nathan M. Wilson for providing the coronary aneurysm data. This work was supported by the National Science Foundation (Grant No. 1354541).

Compliance with ethical standards

Conflict of interest

The authors have no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of California BerkeleyBerkeleyUSA
  2. 2.Department of Mechanical EngineeringUniversity of BristolBristolUK
  3. 3.Department of Computer ScienceUniversity of HoustonHoustonUSA

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