# Modelling of platelet–fibrin clot formation in flow with a DPD–PDE method

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## Abstract

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.

### Keywords

Blood coagulation Clot growth Hybrid models Dissipative particle dynamics### Mathematics Subject Classification

92C35 92C50 74F10## Notes

### Acknowledgments

The study was supported by the Russian Foundation for Basic Research Grants 14-04-00670, 15-04-99595, 15-51-15008, by Dynasty Foundation Fellowship and by the Russian Academy of Sciences Presidium Basic Research Programs “Molecular and Cellular Biology” and “Basic Research for Development of Biomedical Technologies”, by the Russian Federation President Grant for Young Doctors of Science MD-6347.2015.4, and by “Russian Federation Presidential Scholarship for Young Scientists and Graduate Students”. The work was also supported by the research Grant ANR “Bimod”.

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