Blood coagulation in vivo is a spatially nonuniform, multistage process: coagulation factors from plasma bind to tissue factor (TF)-expressing cells, become activated, dissociate, and diffuse into plasma to form enzymatic complexes on the membranes of activated platelets. We studied spatial regulation of coagulation using two approaches: 1), an in vitro experimental model of clot formation in a thin layer of plasma activated by a monolayer of TF-expressing cells; and 2), a computer simulation model. Clotting in factor VIII- and factor XI-deficient plasmas was initiated normally, but further clot elongation was impaired in factor VIII- and, at later stages, in factor XI-deficient plasma. The data indicated that clot elongation was regulated by factor Xa formation by intrinsic tenase, whereas factor IXa was formed by extrinsic tenase on activating cells and diffused into plasma, thus sustaining clot growth. Far from the activating cells, additional factor IXa was produced by factor XIa. Exogenously added TF had no effect on the clot growth rate, suggesting that plasma TF does not contribute significantly to the clot propagation process in a reaction-diffusion system without flow. Addition of thrombomodulin at 3-100 nM caused dose-dependent termination of clot elongation with a final clot size of 2-0.2 mm. These results identify roles of specific coagulation pathways at different stages of spatial clot formation (initiation, elongation, and termination) and provide a possible basis for their therapeutic targeting.

The efficacy of platelet adhesion in shear flow is known to be substantially modulated by the physical presence of red blood cells (RBCs). The mechanisms of this regulation remain obscure due to the complicated character of platelet interactions with RBCs and vascular walls. To investigate this problem, we have created a mathematical model that takes into account shear-induced transport of platelets across the flow, platelet expulsion by the RBCs from the near-wall layer of the flow onto the wall, and reversible capture of platelets by the wall and their firm adhesion to it. This model analysis allowed us to obtain, for the first time to our knowledge, an analytical determination of the platelet adhesion rate constant as a function of the wall shear rate, hematocrit, and average sizes of platelets and RBCs. This formula provided a quantitative description of the results of previous in vitro adhesion experiments in perfusion chambers. The results of the simulations suggest that under a wide range of shear rates and hematocrit values, the rate of platelet adhesion from the blood flow is mainly limited by the frequency of their near-wall rebounding collisions with RBCs. This finding reveals the mechanism by which erythrocytes physically control platelet hemostasis.

Blood flows through vessels as a segregated suspension. Erythrocytes distribute closer to the vessel axis, whereas platelets accumulate near vessel walls. Directed platelet migration to the vessel walls promotes their hemostatic function. The mechanisms underlying this migration remain poorly understood, although various hypotheses have been proposed to explain this phenomenon (e.g., the available volume model and the drift-flux model). To study this issue, we constructed a mathematical model that predicts the platelet distribution profile across the flow in the presence of erythrocytes. This model considers platelet and erythrocyte dimensions and assumes an even platelet distribution between erythrocytes. The model predictions agree with available experimental data for near-wall layer margination using platelets and platelet-modeling particles and the lateral migration rate for these particles. Our analysis shows that the strong expulsion of the platelets from the core to the periphery of the blood vessel may mainly arise from the finite size of the platelets, which impedes their positioning in between the densely packed erythrocytes in the core. This result provides what we believe is a new insight into the rheological control of platelet hemostasis by erythrocytes.