Wall shear stress exposure time: a Lagrangian measure of near-wall stagnation and concentration in cardiovascular flows
- 597 Downloads
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.
KeywordsAdvection–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.
- Davies PF (1995) Flow-mediated endothelial mechanotransduction. Physiol Rev 75(3):519–560Google Scholar
- Lévêque M (1928) Les lois de la transmission de chaleur par convection. Ann Mines 13:201–239Google Scholar
- Meng W, Yu F, Chen H, Zhang J, Zhang E, Dian K, Shi Y (2009) Concentration polarization of high-density lipoprotein and its relation with shear stress in an in vitro model. BioMed Research International 695838–695838:2009Google Scholar
- Peiffer V, Sherwin SJ, Weinberg PD (2013) Does low and oscillatory wall shear stress correlate spatially with early atherosclerosis? A systematic review. Cardiovasc Res 99(2):242–250Google Scholar
- Seo JH, Abd T, George RT, Mittal R (2016) A coupled chemo-fluidic computational model for thrombogenesis in infarcted left ventricles. Am J Physiol-Heart Circ Physiol. 10.1152/ajpheart.00855.2015Google Scholar
- Tricoche X, Scheuermann G, Hagen H (2001) Continuous topology simplification of planar vector fields. In: Proceedings of the conference on Visualization’01, pp 159–166Google Scholar
- Updegrove A, Wilson NM, Merkow J, Lan H, Marsden AL, Shadden SC (2016) Simvascular—an open source pipeline for cardiovascular simulation. Ann Biomed Eng (in press)Google Scholar