Influence of Brownian motion on blood platelet flow behavior and adhesive dynamics near a planar wall

Abstract

We used the platelet adhesive dynamics computational method to study the influence of Brownian motion of a platelet on its flow characteristics near a surface in the creeping flow regime. Two important characterizations were done in this regard: (1) quantification of the platelet's ability to contact the surface by virtue of the Brownian forces and torques acting on it, and (2) determination of the relative importance of Brownian motion in promoting surface encounters in the presence of shear flow. We determined the Peclet number for a platelet undergoing Brownian motion in shear flow, which could be expressed as a simple linear function of height of the platelet centroid, H from the surface Pe (platelet) = . (1.56H + 0.66) for H > 0.3 microm. Our results demonstrate that at timescales relevant to shear flow in blood Brownian motion plays an insignificant role in influencing platelet motion or creating further opportunities for platelet-surface contact. The platelet Peclet number at shear rates >100 s-1 is large enough (>200) to neglect platelet Brownian motion in computational modeling of flow in arteries and arterioles for most practical purposes even at very close distances from the surface. We also conducted adhesive dynamics simulations to determine the effects of platelet Brownian motion on GPIbalpha-vWF-A1 single-bond dissociation dynamics. Brownian motion was found to have little effect on bond lifetime and caused minimal bond stressing as bond rupture forces were calculated to be less than 0.005 pN. We conclude from our results that, for the case of platelet-shaped cells, Brownian motion is not expected to play an important role in influencing flow characteristics, platelet-surface contact frequency, and dissociative binding phenomena under flow at physiological shear rates (>50 s(-1)).

Figure 1

Schematic diagram of the flow geometry in which a single platelet (oblate spheroid of aspect ratio = 0.25) is translating and rotating in linear shear flow near an infinite planar surface. At the instant shown in the figure, the platelet is oriented with its major axis parallel to the surface and its centroid is located at a distance H from the surface.

Figure 2

Plot of the distances translated in the x-, y- and z-direction in each timestep of 0.1 s by a platelet undergoing Brownian motion near a surface in a quiescent fluid of viscosity 1 cP in the Stokes regime of flow. Fluctuations in platelet position with respect to its previous position are shown for a period of 5 seconds for (a) an initial platelet centroid height of 3.0 μm and (b) an initial platelet centroid height of 1.5 μm. The average velocities in each direction over the 5 second interval are listed in each plot.

Figure 3

Plot of the average time taken T_c for a platelet at an initial height H to contact the surface when undergoing translational and rotational Brownian motion in a quiescent fluid in the Stokes regime of flow. The dashed trendline does not include data points at initial H = 0.5 μm and 0.625 μm.

Figure 4

Histograms of the log of time taken T_c for a platelet to contact the surface when undergoing translational and rotational Brownian motion in a quiescent fluid for three different initial heights H: (a) H_initial = 0.625 μm, (b) H_initial = 1.5 μm, and (c) H_initial = 2.0 μm, representing approximately 200 cell-surface contact events for each H_initial.

Figure 5

Plots of the time until surface contact T_c as a function of shear rate for a Brownian platelet at an initial centroid height of 0.8 μm in linear shear flow. The dashed line indicates ‘time until surface contact’ for platelets undergoing linear shear flow only, i.e. Brownian force and torque were not included in the mobility calculations. In (a) ‘Time to contact’ the surface for a platelet is non-dimensionalized with shear rate, and in (b) ‘Time to contact’ is kept in dimensional form. Plot (c) is a magnified version of 5(a) with a trendline plotted to demonstrate the simple linear dependency of non-dimensionalized ‘time to surface contact’ on shear rate when Brownian motion (diffusion) is the dominant mode of cell transport to the surface.

Figure 6

Schematic diagram of a horizontally-oriented platelet bound to the surface via a single GPIbα-vWF bond. Both the surface and platelet are coated with a surface roughness layer of 25 nm.

Figure 7

Plots of GPIbα-vWF-A1 bond lifetimes and bond rupture forces for a platelet undergoing Brownian motion in a quiescent fluid. (a) Bond lifetimes when the fluid medium has constant viscosity = 1.0 cP. (b) Bond rupture forces when the fluid medium has constant viscosity = 1.0 cP. For both figures 7(a) and 7(b), 41 observations were collected for each temperature. (c) Bond lifetimes for a fluid medium with temperature-dependent viscosity. (d) Bond rupture forces for a fluid medium with temperature-dependent viscosity. For both figures 7(c) and 7(d), 37 observations were collected for each temperature. Quadratic trendlines drawn in figures 7(c) and 7(d) are within 10% and 7.8% average error respectively.