(226f) Platelet-Platelet Collisions and Brownian Motion of Platelets near a Surface

Platelets are the key participant in the thrombotic events that take place following vascular injury. These tiny blood cells, 1-2 μm in size, are recruited to the exposed subendothelial region at the vascular lesion and aggregate to form a hemostatic plug that blocks further blood loss and seals the wound. Platelets are far from spherical in shape and appear as flattened ellipsoids. Such a vast difference in shape is expected to play a large influencing factor on the cell's flow behavior near a solid boundary, specifically the manner, frequency, and duration of cell-surface contact, the manner in which the cells collide, their frequency of collision, the duration of contact, the collision contact area, and the magnitude of shear and normal forces acting on the platelet(s) and on inter-platelet bonds formed between two or more cells.

Initial platelet adhesion with the exposed subendothelial components at physiological shear rates in arterioles (500 ? 2,000 s^-1) is mediated by the platelet glycoprotein GPIbα surface receptor. The GPIbα receptor binds the A1 domain of collagen-bound von Willebrand factor (vWF), a large multimeric plasma glycoprotein. GPIbα-vWF-A1 tether bond formation is critically important for enabling platelets to initiate binding to the injured exposed subendothelial surface. This tether bond exhibits selectin-like binding kinetics. Abnormally high shear rates in the range of 5,000 ? 20,000 s^-1 typical of stenosed regions of the arteries have been found to induce platelet activation and aggregation both in vivo and in vitro even in the absence of any chemical agonists or vascular lesions, resulting in platelet thrombi formation that may occlude blood flow through the stenosed region. Very high levels of shear stress >80 dyn/cm² have been shown to promote initial GPIbα-vWF binding with no involvement of a surface, which leads to shear-induced activation of platelets and the formation of stable platelet aggregates via α_IIbβ₃-vWF binding.

Because theoretical solutions of motion of spheres in a variety of bounding conditions and flow patterns are abundant, much computational modeling of cellular flows and adhesion has focused on single spherical cell tethering to the endothelium, cell-cell hydrodynamic effects on leukocyte tethering to the vascular wall, and spherical blood cell collisions and subsequent aggregation in shear flow. Erythrocyte and platelet-platelet aggregation have also been modeled by approximating these cells as perfect spheres. Solutions for non-spherical particulate flows are much more difficult to obtain compared to that for suspended spheres however, because of the difficulties in determining the hydrodynamic interactions between non-spherical particles or between a non-spherical particle and a bounding surface. Computational models of platelet adhesion to a surface under flow have been lacking due to limited availability of theoretical studies on non-spherical particle-wall interactions under flow [1]. The majority of the hydrodynamic solutions that are available are not adaptable to multiparticle flows. While a few studies have looked at collisions between oblate spheroids, they do not include the presence of a bounding wall of any sort.

We developed a new multiscale simulation that fuses a boundary elements calculation of cellular-scale fluid mechanics, with a stochastic Monte Carlo simulation of the formation and breakage of receptor-ligand molecular bonds [2]. The computational method employed in our study for calculating the rigid body motion of one or more oblate spheroid-shaped particles (platelets) is based on the Completed Double Layer ? Boundary Integral Equation Method (CDL-BIEM), a boundary element method developed by Kim and Karilla (1991) [3] to solve the integral representation of the Stokes equation. Our fully 3-D computational model incorporates the influence of the proximity of the wall and determines the cells' translational and rotational trajectories prior to, during and after surface contact or cell collisions [4].

We have studied the collision behavior of two platelet-shaped particles both in close proximity of and far from a bounding wall, and found that the contact area, contact time and flow trajectories are significantly different from that observed in the case of sphere-sphere or sphere-spheroid collisions. Importantly we have quantified the effects of the presence of a wall on the physics of platelet-platelet collision and contact. Platelets that collide close to a wall are found to remain in contact significantly longer than those colliding far from a bounding surface, i.e., in unbounded fluid. The resulting trajectories during and after a collision event were compared to that of a single platelet that begins flow at the same height but does not experience any collision, to explicitly determine the effects of a collision and of the presence of the bounding wall on the cells' subsequent flow patterns. We will also discuss the hydrodynamic influence of particle shape on the flow of neighboring particle(s) in the viscous fluid.

We have also studied the dynamics of platelet aggregation via GPIbα-vWF-A1 binding by including multiple intercellular stochastic bond formation/breakage in the multi-platelet flow simulations. When the platelet nears a second platelet and is within binding range, bond formation between GPIbα and surface-bound vWF is tested. Bonds that form are represented as linear springs with fixed end-points on either surface. The bond forces and torques acting on the cell are a function of the length and orientation of each of the bond springs that bind the cells, as well as on the physical state of compression and extension. The Fortran 95 random number generator is used to test both bond formation and breakage against their respective probabilities calculated from the instantaneous bond association and dissociation rate. The Bell model parameters for single GPIbα-vWF bond dissociation kinetics as obtained by Doggett et al. (2002) [5] are incorporated into the adhesive dynamics calculations.

Finally, we have looked at the Brownian motion of a platelet-shaped particle near a bounding wall, and quantified the ?time to contact? of the platelet with the surface as a function of distance from the wall under zero flow conditions. In the presence of shear flow, we show how the relevance of Brownian motion of a platelet-shaped particle, with aspect ratio 0.2 and diameter 2.5 µm, diminishes with increase in shear rate. Brownian motion is observed to have negligible influence on platelet motion at physiological arterial and arteriolar flow conditions where shear rates are greater than 100 s^-1.

References:

1. Mody, N. A., O. Lomakin, T. A. Doggett, T. G. Diacovo, and M. R. King, 2005. Mechanics of transient platelet adhesion to von Willebrand factor under flow. Biophys. J. 88:1432-1443.

2. Mody, N. A. and M. R. King. 2005. Dynamics of Platelet Aggregation and Adhesion to Reactive Surfaces Under Flow, in Principles of Cellular Engineering: Understanding the Biomolecular Interface, M.R. King (Ed.), Academic Press, San Diego, pp. 267-295.

3. Kim, S., and S. Karrila. 1991. Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann, Stoneham, MA.

4. Mody, N. A. and M. R. King. 2005. Three-dimensional simulations of a platelet-shaped spheroid near a wall in shear flow. Phys. Fluids. 17: 113302-113312.

5. Doggett, T. A., G. Girdhar, A. Lawshé, D. W. Schmidtke, I. J. Laurenzi, S. L. Diamond, and T. G. Diacovo. 2002. Selectin-like kinetics and biomechanics promote rapid platelet adhesion in flow: The GPIbα - vWF tether bond. Biophys. J. 83:94-205.