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.

Injury-induced bleeding is stopped by a hemostatic plug formation that is controlled by a complex nonlinear and spatially heterogeneous biochemical network of proteolytic enzymes called blood coagulation. We studied spatial dynamics of thrombin, the central enzyme of this network, by developing a fluorogenic substrate-based method for time- and space-resolved imaging of thrombin enzymatic activity. Clotting stimulation by immobilized tissue factor induced localized thrombin activity impulse that propagated in space and possessed all characteristic traits of a traveling excitation wave: constant spatial velocity, constant amplitude, and insensitivity to the initial stimulation once it exceeded activation threshold. The parameters of this traveling wave were controlled by the availability of phospholipids or platelets, and the wave did not form in plasmas from hemophilia A or C patients who lack factors VIII and XI, which are mediators of the two principal positive feedbacks of coagulation. Stimulation of the negative feedback of the protein C pathway with thrombomodulin produced nonstationary patterns of wave formation followed by deceleration and annihilation. This indicates that blood can function as an excitable medium that conducts traveling waves of coagulation.

The paper is devoted to mathematical modelling of clot growth in blood flow. Great complexity of the hemostatic system dictates the need of usage of the mathematical models to understand its functioning in the normal and especially in pathological situations. In this work we investigate the interaction of blood flow, platelet aggregation and plasma coagulation. We develop a hybrid DPD-PDE model where dissipative particle dynamics (DPD) is used to model plasma flow and platelets, while the regulatory network of plasma coagulation is described by a system of partial differential equations. Modelling results confirm the potency of the scenario of clot growth where at the first stage of clot formation platelets form an aggregate due to weak inter-platelet connections and then due to their activation. This enables the formation of the fibrin net in the centre of the platelet aggregate where the flow velocity is significantly reduced. The fibrin net reinforces the clot and allows its further growth. When the clot becomes sufficiently large, it stops growing due to the narrowed vessel and the increase of flow shear rate at the surface of the clot. Its outer part is detached by the flow revealing the inner part covered by fibrin. This fibrin cap does not allow new platelets to attach at the high shear rate, and the clot stops growing. Dependence of the final clot size on wall shear rate and on other parameters is studied.

No abstract

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.