(623e) Multiscale Model Of Receptor-Mediated Platelet-Platelet Aggregation Under High Shear Flow

At the time of vascular injury, platelets are recruited from the bloodstream to the exposed subendothelial region at the vascular lesion where they aggregate to form a hemostatic plug that blocks further blood loss and seals the wound. Initial adhesion of these microscopic ellipsoidal blood cells (2-4 μm in size) to the exposed subendothelial components at physiological shear rates (500 ? 2,000 s^-1) is mediated by the platelet glycoprotein GPIbα surface receptor. The GPIbα receptor binds the A1 domain of subendothelial collagen-bound von Willebrand factor (vWF), a large multimeric plasma glycoprotein. Von Willebrand factor exists in plasma in a range of sizes, each multimer containing a varying number of repeating identical subunits. High molecular weight multimers are found to have greater binding affinity to platelet surface receptors GPIbα and α_IIbβ₃ than vWF molecules of lower molecular weight. 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, which is characterized by fast association and dissociation rates and high tensile strength.

Flowing platelets do not bind circulating vWF at physiological shear rates encountered in the blood. Abnormally high shear rates in the range of 5,000 ? 20,000 s^-1 typical of stenosed arterial regions are found to induce initial platelet(GPIbα)-vWF binding without the involvement of a surface, leading to platelet activation and formation of stable platelet aggregates. Such platelet thrombi can critically block blood flow through a stenosed region resulting in ischemic organ damage such as a heart attack or stroke. Pathological presence of ultra-large forms of vWF in blood is responsible for enhanced platelet-vWF binding affinity, causing shear-induced platelet aggregation at normal arteriolar shear rates and resulting in the fatal disorder, TTP (thrombotic thrombocytopenic purpura).

Few attempts have been made to date to develop computational models to elucidate the influence of hydrodynamic shear flow, platelet shape, presence of bounding walls, and experimentally-determined receptor-ligand molecular binding kinetics, on physiological and pathological thrombus formation. Theoretical fluid mechanical studies of three-dimensional multi-particle non-spherical particulate (ellipsoidal) flows (1-3), especially for bounded flows, are much less commonly available than those for spheres, since determining the hydrodynamic interactions between two or more non-spherical shapes in an unbounded or bounded region is a more challenging task as compared to that for spherical particles. Hence, fluid mechanical solutions in the literature for flow of spheres with a variety of boundaries and flow conditions are relatively abundant, and have been adapted by biomedical researchers for studying blood cell adhesive phenomena (4-9). Sphere-sphere collisions have been well characterized in an unbounded medium and well-defined collision efficiency parameters have been computed taking into consideration the influence of hydrodynamic interactions between particles (4). Erythrocyte and platelet-platelet aggregation have been modeled by approximating these cells as perfect spheres. Activated platelets are somewhat spherical in shape, although they have a rough surface with many filopodia extending in different directions. However, unactivated platelets are far from spherical in shape, instead appearing as flattened ellipsoids. Such a vast difference in shape is expected to influence the manner in which the cells collide, their frequency of collision, collision contact time, contact area, and the magnitude of shear and normal forces acting on the platelet(s) and on inter-platelet bonds formed between two cells (10). Few studies have simulated hydrodynamic collisions between oblate spheroids, and they do not include the presence of a bounding wall of any sort (1).

For the first time, a 3-D multi-scale numerical model (Platelet Adhesive Dynamics) is developed to study platelet collisions and formation of aggregates in shear flow near a bounding wall. This new multi-scale simulation 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 (10). The computational method employed in our study for calculating the rigid body motion of 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 (11) 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 cell collisions (12).

Oblate-spheroid (platelet) collisions have not been characterized to date. We studied the influence of a bounding wall on the physics of platelet-platelet collisions, and quantified with respect to proximity of the wall, duration of collisions and collision contact areas to gauge the probability of adhesion between two platelet cells. We characterized the unique collision mechanisms associated with platelets and quantified the effects of particle shape (sphere versus oblate spheroid) and proximity of a bounding wall on the physics of two-particle collisions. Wall presence is found to have a profound effect on the collision outcome of two particles encountering one another near a wall in the Stokes regime of flow and significantly influences the adhesion probability between two colliding cells. Frequency of platelet-platelet collisions is quantified close to and far from the wall and compared to that obtained for sphere-sphere collisions to determine a relative measure of platelet collision frequencies.

We studied the dynamics of transient platelet aggregation via GPIbα-vWF-GPIbα bridging by including multiple intercellular stochastic bond formation/breakage in the multi-platelet flow simulations, in order to study the biophysical aspects of the onset of shear-induced platelet aggregation. Binding and unbinding of platelet GPIbα receptors with vWF in solution is simulated as a dynamic process allowing continuous redecoration of the platelet surfaces with these molecules that is dependent on the GPIbα-vWF-A1 binding kinetics and on the equilibrium characteristics of platelet-vWF binding. When the platelet nears a second platelet and is within binding range, bond formation between GPIbα receptors on one platelet and vWF bound by another platelet is tested. Bonds that form are represented as linear springs, and the bond forces and torques acting on the bridged cells are a function of the length and orientation of each of the bond springs that bind the cells. The Bell model parameters for single GPIbα-vWF-A1 bond dissociation kinetics as obtained by Arya and coworkers (13) are incorporated into the adhesive dynamics calculations. The binding kinetics of healthy GPIbα-vWF-A1 binding and that typical of type-2B/platelet-type VWD are applied. Also platelet aggregation is studied as a function of the vWF size; two sizes were chosen corresponding to the average vWF size found in plasma (14) and the largest size found in healthy plasma (15). Our experimentally-matched simulations qualitatively demonstrate how vWF size and binding kinetics critically govern the capture probability for two colliding platelets. Insightful metrics characterizing transient aggregate formation are obtained for a range of high shear rates (4000 ? 12000 s^-1).

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