Sub-cellular modeling of platelet transport in blood flow through microchannels with constriction

Abstract

Platelet transport through arterial constrictions is one of the controlling processes influencing their adhesive functions and the formation of thrombi. We perform high-fidelity mesoscopic simulations of blood flow in microchannels with constriction, resembling arterial stenoses. The wall shear rates inside the constrictions reach levels as high as ≈8000 s(-1), similar to those encountered in moderate atherosclerotic plaques. Both red blood cells and platelets are resolved at sub-cellular resolution using the Dissipative Particle Dynamics (DPD) method. We perform a systematic study on the red blood cell and platelet transport by considering different levels of constriction, blood hematocrit and flow rates. We find that higher levels of constriction and wall shear rates lead to significantly enhanced margination of platelets, which may explain the experimental observations of enhanced post-stenosis platelet aggregation. We also observe similar margination effects for stiff particles of spherical shapes such as leukocytes. To our knowledge, such numerical simulations of dense blood through complex geometries have not been performed before, and our quantitative findings could shed new light on the associated physiological processes such as ATP release, plasma skimming, and thrombus formation.

Fig. 1

(a) Schematic of a microchannel with 75% degree constriction. Top: 3D presentation of the channel where the walls are triangulated. Bottom: 2D view of the same geometry in the x–y plane. Channel dimensions are 195 × 30 × 30 micron, and the constriction length is 40 μm. (b) Coarsegrained model of RBC membrane with 362 DPD particles forming a triangulated grid. (c) Coarse-grained model of platelet membrane with 42 DPD particles.

Fig. 2

(a) Snapshot of the blood simulation in a microchannel with 75% degree constriction. The channel height is 30 μm, and blood is at 25% hematocrit. Red cells represent the deformable red blood cells and black ellipsoidal cells are nondeformable platelets in their resting form. Following Yazdani et al., the driving body force is the non-uniform pressure gradient derived from numerical solution Navier–Stokes equation at Re = 0.35 for the same geometry (video for this simulation is provided in ESI†). (b) Left: Velocity contours and streamlines for the flow of blood in the 75%-constriction microchannel; right: profiles of streamwise velocity component at five different locations along the microchannel length specified by the same colors. A plug-like velocity profile is achieved for the blood except at the throat.

Fig. 3

Profiles of RBC concentration (hematocrit) at different locations along the 75% constriction (inlet, middle and outlet) as well as further downstream of the constriction (red dashed line considered at x = 160 μm). Here, the average hematocrit of blood is 25%.

Fig. 4

(a) Profiles of hematocrit and platelet concentration for blood flow through a straight microchannel. (b) Profile of effective diffusivity D_y scaled by the wall shear rate γ̇_w = 500 s⁻¹. Here, the average hematocrit of blood is 25%.

Fig. 5

Effect of constriction geometry on RBC and platelet distribution: (a) profiles of RBC concentration downstream of a constriction at 75 and 50% and plotted against the profile of H_ct for a straight channel. The mean hematocrit of the blood is 25%; (b) platelet volume concentration for the same simulations as in (a); (c) platelet concentrations at the inlet, center and outlet of a 75% constriction.

Fig. 6

Wall shear rate effect on RBC and platelet distribution downstream of a 50% constriction: (a) profiles of RBC concentration at the base, 1.5 and twice higher flow rates. Upstream wall shear rate at the base flow rate is γ̇_w = 500 s⁻¹, and the mean hematocrit of blood is 25% in all cases; (b) platelet volume concentration for the same simulations as in (a).

Fig. 7

Fractions of marginated platelets downstream of a constriction (after 0.72 s) vs. constriction levels (■; lower axis), and vs. wall shear rates (▲; upper axis).

Fig. 8

The effect of blood hematocrit on platelets concentration downstream of a constriction: (a) profiles of platelets concentration downstream of a 75% constriction; (b) profiles of platelets concentration downstream of a 50% constriction. The mean hematocrit of blood varies from 0 to 25%, and the upstream wall shear rate remains the same for all cases at γ̇_w = 500 s⁻¹.

Fig. 9

Trajectories of platelets inside a microchannel with 50% constriction (top row) and 75% constriction (bottom row), where X_p and Y_p are axial and vertical positions of the platelet’s center of mass, respectively, and t* is the DPD time unit; (a) and (c) axial positions vs. time for all platelets; (b) and (d) trajectories of three representative platelets: axial positions (dashed lines and left axis); vertical positions (solid lines and right axis).

Fig. 10

Contours of relative platelet concentration in channels with (a) 75% and (b) 50% constriction. The color map is the same for both figures.

Fig. 11

Snapshot of the platelet dynamics in a 50% constriction (video for this simulation is provided in ESI†). Red arrows show representative sliding and tumbling platelets passing through the constriction.

Fig. 12

Probability distribution for minimum distance of platelet’s surface from the wall inside the constrictions. Red bars are slightly shifted to the right for clarity.

Fig. 13

(a) Trajectories of four representative platelets inside a microchannel with 50% constriction (wall boundaries are shown with gray lines), where X_p and Y_p are axial and vertical positions of the platelet’s center of mass, respectively. (b) Minimum distance to the walls for platelets in (a) passing through the constriction (60 < X_p < 105 μm). The minimum distance is calculated based on the closest point on platelet’s surface from the wall.

Fig. 14

Concentration profiles of stiff spherical particles and platelets downstream of 75% constriction. The mean hematocrit of blood is 25%. Fraction of marginated particles is 83.6% for platelets and 79% for spherical particles.