Lagrangian wall shear stress structures and near-wall transport in high-Schmidt-number aneurysmal flows

Abstract

The wall shear stress (WSS) vector field provides a signature for near wall convective transport, and can be scaled to obtain a first order approximation of the near wall fluid velocity. The near wall flow field governs mass transfer problems in convection dominated open flows with high Schmidt number, in which case a flux at the wall will lead to a thin concentration boundary layer. Such near wall transport is of particular interest in cardiovascular flows whereby hemodynamics can initiate and progress biological events at the vessel wall. In this study we consider mass transfer processes in pulsatile blood flow of abdominal aortic aneurysms resulting from complex WSS patterns. Specifically, the Lagrangian surface transport of a species released at the vessel wall was advected in forward and backward time based on the near wall velocity field. Exposure time and residence time measures were defined to quantify accumulation of trajectories, as well as the time required to escape the near wall domain. The effect of diffusion and normal velocity was investigated. The trajectories induced by the WSS vector field were observed to form attracting and repelling coherent structures that delineated species distribution inside the boundary layer consistent with exposure and residence time measures. The results indicate that Lagrangian wall shear stress structures can provide a template for near wall transport.

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

“…A normal to wall distances of δn = 15µm, 0.7µm, 1µm, and 1µm are chosen in this study, which are within δ c in the AAA, carotid artery, cerebral aneurysm, and coronary aneurysm models, respectively. The significance of this choice is discussed in our previous study [1].…”

“…The relevance of this measure could be explained as follows. As discussed in [23,1], the WSS vector can be scaled to obtain the near-wall fluid velocity, and because displacements of fluid in the concentration boundary layer are small over each cardiac cycle, the time-averaged WSS vector field dominates transport. Therefore, in regions of low TAWSS vector magnitude (high RRT) the near-wall species are displaced to smaller extent, implying higher near-wall stagnation.…”

“…In order to quantify near-wall stagnation, WSSET [1] is computed for each triangular surface element as the accumulated amount of time that all the WSS trajectories spend p. 6 inside that element, with proper normalizations…”

“…We have previously demonstrated emergence of Lagrangian coherent structures (LCS) computed from WSS (WSS LCS) and how they relate to the near-wall transport in AAAs [1]. The WSS LCS were computed by integrating a high resolution of surface tracers and identifying p. 7 the distinct material lines formed.…”

“…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] leads to complex WSS distributions [4] and interesting near-wall flow structures [1]. Thrombosis in the left ventricle [49], aortic dissection [41], stented arteries [28], and flow diverter treated cerebral aneurysms [43] represent other applications of complex transport potentially affecting local thrombosis.…”