Dependence of leukocyte capture on instantaneous pulsatile flow

Abstract

Atherosclerosis, an artery disease, is currently the leading cause of death in the United States in both men and women. The first step in the development of atherosclerosis involves leukocyte adhesion to the arterial endothelium. It is broadly accepted that blood flow, more specifically wall shear stress (WSS), plays an important role in leukocyte capture and subsequent development of an atherosclerotic plaque. What is less known is how instantaneous WSS, which can vary by up to 5 Pa over one cardiac cycle, influences leukocyte capture. In this paper we use direct numerical simulations (DNS), performed using an in-house code, to illustrate that leukocyte capture is different whether as a function of instantaneous or time-averaged blood flow. Specifically, a stenotic plaque is modeled using a computational fluid dynamics (CFD) solver through fully three-dimensional Navier-Stokes equations and the immersed boundary method. Pulsatile triphasic inflow is used to simulate the cardiac cycle. The CFD is coupled with an agent-based leukocyte capture model to assess the impact of instantaneous hemodynamics on stenosis growth. The computed wall shear stress agrees well with the results obtained with a commercial software, as well as with theoretical results in the healthy region of the artery. The analysis emphasizes the importance of the instantaneous flow conditions in evaluating the leukocyte rate of capture. That is, the capture rate computed from mean flow field is generally underpredicted compared to the actual rate of capture. Thus, in order to obtain a reliable estimate, the flow unsteadiness during a cardiac cycle should be taken into account.

Keywords: Direct numerical simulation; Hemodynamics; Instantaneous flow; Leukocyte capture; Time-averaged flow.

Figure 1:

Geometry of the stenoses used in the simulations: (a) cross-section along the artery axis for the axisymmetric geometry. The color shades denote the different stenosis heights h: h = 0.1D, h = 0.2D, h = 0.3D. (b) Visualization of the three-dimensional stenosis in the case h = 0.2D. Only half of the circular wall is shown. The other half is smooth.

Figure 2:

Flow field during a cardiac cycle: (a) cardiac cycle: instantaneous bulk velocity; mean bulk velocity. (b) Mean flow field averaged over a cardiac cycle. (c)–(f) Instantaneous flow fields: (c) t/T = 6/32 , (d) t/T = 14/32 , (e) t/T = 18/32 , (f) t/T = 30/32 . The scales of the axes in the figures are different to show the details of the flow past the stenosis.

Figure 3:

Velocity profiles at 1.615 mm (x/D ≈ 0.55) upstream the MLA (a–d), at the MLA (e–h), and 1.615 mm downstream the MLA (i–l) at different instants during the cardiac cycle: ■ t/T = 0; • t/T = 1/4; ▴ t/T = 1/2; ▾ t/T = 3/4. Line represents the COMSOL simulation; symbols represent our in-house code results. The shaded region represents the shape and position of the plaque in the coronary.

Figure 4:

Wall shear stress along the artery: (a)$\overline{WSS}$, as a function of the streamwise coordinate: DNS, theoretical value for a circular pipe, according to eq. (13); (b) instantaneous wall shear stress: t/T = 6/32, t/T = 14/32, t/T = 18/32, t/T = 30/32; time-averaged $\overline{WSS}$ ; value of WSS above which leukocytes cannot adhere, WSS = 1.2 Pa. (c) root mean square value of WSS normalized by the healthy value WSS₀.

Figure 5:

Neutrophil capture R due to the WSS. (a) Capture rate throughout the cardiac cycle: t/T = 6/32, t/T = 14/32, t/T = 18/32, t/T = 30/32; time-averaged $\overline{R(WSS)}$. (b) Comparison between using rate of capture from the mean shear, $R(\overline{WSS})$, () and the actual mean rate of capture, $\overline{R(WSS)}$, ().

Figure 6:

Mean rate of capture $\overline{R(WSS)}$ for different types of leukocytes: neutrophil, monocyte, lymphocyte. (a) per unit concentration ρ_i (where i indicates the type of leukocytes); (b) actual capture rate.

Figure 7:

Neutrophil capture rate for different stenosis heights: mean rate from instantaneous shear stress $\overline{R(WSS)}$; capture rate using time-averaged wall shear stress $R(\overline{WSS})$ . (a) h = 0.1D; (b) h = 0.2D (same as figure 5b); (c) h = 0.3D, the scale in the inset is changed to emphasize the details of the mean capture rate distributions, $\overline{R(WSS)}$.

Figure 8:

Neutrophil rate of capture for the three dimensional stenosis: (a, b) h = 0.1D; (c, d) h = 0.2D. In (a) and (c), the capture rate is computed averaging the instantaneous capture over the cardiac cycle, $\overline{R(WSS)}$; in (b) and (d), capture is computed using the time-averaged shear stress, $R(\overline{WSS})$.

Figure 9:

Mean rate of neutrophil capture, $\overline{R(WSS)}$, for different artery geometry: straight pipe (no stenosis); h/D = 0.1; h/D = 0.2; h/D = 0.3.