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

Abstract

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms suitable in regions of complex hemodynamics that are traditionally difficult to quantify, yet encountered in many disease scenarios. Keywords: advection-diffusion; blood flow; hemodynamics; near-wall transport; residence time; shear stress; p. 2 IntroductionBiomechanical interactions between blood flow and the vessel wall are central to the initiation and progression of most cardiovascular diseases. Indeed, the majority of computational and experimental investigations into blood flow seek to understand how local flow mechanics relates to disease progression in or on the vessel wall. Blood flow conditions in diseased vessels are usually spatially and temporally complex and are challenging to characterize [51,50], even without reference to the coupled biochemical or biophysical processes driving disease progression. Nonetheless, the role of blood flow mechanics in the "near-wall" region is of utmost importance since this is where such couplings are most profound. In the near-wall region, blood flow serves to impart mechanical stresses on the vessel wall, as well as regulate the local transport of reactive material between the tissue and fluid domains. It is this latter mechanism that motivates the work presented herein.A compelling scenario involving the interaction between blood flow and the vessel wall is atherosclerosis, which is a leading cause of death worldwide. Atherosclerosis occurs mainly in locations of disturbed blood flow patterns [9,47]. The local transport of several substances near and at the vessel wall are known to influence atherosclerosis progression [56]. For example, previous studies have looked into transport of low density lipoproteins (LDL) [17,20,30,14], high density lipoproteins (HDL) [40,24], oxygen [16,27], nitric oxide (NO) [45,35], monocytes [12,14], and adenine triphosphate ATP and adenine diphosphate ADP [13,15,8] as important mass transport processes involved in atherosclerosis.Intravascular thrombosis is another compelling pathology associated with most cardiovascular diseases where near-wall transport becomes important [7,25]. The trajectories of individual platelets and the accumulation and residence time of chemical solutes including ADP, thrombin, and various blood factors control clot formation. These solutes, and especially in activated form, are generated at the vessel wall or from bound platelets. Complex hemodynamics and flow stagnation are often associated with prothrombotic conditions. For example, intraluminal thrombus in abdominal aortic aneurysm (AAA) [57,54] complicates disease progression, and is thought to be strongly coupled to flow stagnation and recirculation. The chaotic flow field in AAAs [3] Near-wall transport can either be (i) explicitly modeled for a specific transport problem, or (ii) inferred from appropriate hemodynamics meas...

Coronary artery plaque growth: A two‐way coupled shear stress–driven model

“…As expected, an increase in plaque growth expands this backflow region. Such regions may have important implications for near‐wall accumulation of atherogenic biochemicals and cells . Moreover, changes in WSS fixed points and manifolds may be visualized downstream of the stenosis as the plaque grows.…”

“…First, low WSS is known to induce inflammatory endothelial cell (EC) behavior, which promotes the atherogenic processes in plaque development. Second, low WSS has been shown to be correlated with near‐wall biochemical accumulation and stagnation, which may promote atherosclerosis. Based on similar observations, Zohdi developed a very simple ODE model to simulate WSS‐driven plaque growth .…”

Finite element modeling of near‐wall mass transport in cardiovascular flows

“…The similarity in qualitative surface concentration patterns for different diffusion coefficients suggests that near‐wall convection patterns dominate surface concentration distribution in high–Péclet‐number mass transport problems. Recently, Arzani et al computed Lagrangian coherent structures (LCS) in the wall shear stress (WSS) vector field to study near‐wall convective transport and demonstrated how the attracting WSS LCS correspond to high surface concentration patterns. Although WSS LCS have been suggested for high‐Schmidt‐number ( and higher) mass transport, we have shown that high surface concentration localization patterns are robust with respect to changes in mass diffusivity and therefore the Schmidt number.…”

Quantification of near‐wall hemodynamic risk factors in large‐scale cerebral arterial trees

“…However, reliable mechanical properties and vessel thickness measurements of all arterial blood vessels are necessary before attempting more rigorous 3D fluid‐structure interaction simulations for large sections of the cerebral vasculature. In addition, near‐wall hemodynamic risk analysis can be extended to more WSS components such as Lagrangian processing of the WSS vector field …”

“…In addition, near-wall hemodynamic risk analysis can be extended to more WSS components such as Lagrangian processing of the WSS vector field. 3,72 Another future improvement concerns the use of non-Newtonian blood flow rheology. 73 This step would be critical for blood vessels less than 100 μm in diameter.…”