A mathematical model to quantify the effects of platelet count, shear rate, and injury size on the initiation of blood coagulation under venous flow conditions.

Anass Bouchnita,Patrice Nony,Vitaly Volpert,Vitaly Volpert,Vitaly Volpert,Vitaly Volpert,Vitaly Volpert,Vitaly Volpert,Yuri Vassilevski,Yuri Vassilevski,Yuri Vassilevski,Yuri Vassilevski,Kirill Terekhov,Kirill Terekhov,Fang-Bao Tian

doi:10.1371/journal.pone.0235392

Abstract

Platelets upregulate the generation of thrombin and reinforce the fibrin clot which increases the incidence risk of venous thromboembolism (VTE). However, the role of platelets in the pathogenesis of venous cardiovascular diseases remains hard to quantify. An experimentally validated model of thrombin generation dynamics is formulated. The model predicts that a high platelet count increases the peak value of generated thrombin as well as the endogenous thrombin potential (ETP) as reported in experimental data. To investigate the effects of platelets density, shear rate, and wound size on the initiation of blood coagulation, we calibrate a previously developed model of venous thrombus formation and implement it in 3D using a novel cell-centered finite-volume solver. We conduct numerical simulations to reproduce in vitro experiments of blood coagulation in microfluidic capillaries. Then, we derive a reduced one-equation model of thrombin distribution from the previous model under simplifying hypotheses and we use it to determine the conditions of clotting initiation on the platelet count, the shear rate, and the plasma composition. The initiation of clotting also exhibits a threshold response to the size of the wounded region in good agreement with the reported experimental findings.

Highlights

Blood coagulation can be initiated when the tissue factor (TF) is exposed to the bloodstream [1]
We extend the previously developed model of clot growth dynamics [26, 27] to include the aggregation of platelets
We suggest a new model for thrombin generation in the presence of platelets in the motionless plasma

Summary

Introduction

Blood coagulation can be initiated when the tissue factor (TF) is exposed to the bloodstream [1]. In order to describe the interaction between thrombus growth and hemodynamics, some studies consider clot as a permeable medium whose hydraulic resistance depends on the concentration of fibrin polymer [21], or the density of platelets [22] Another approach consists in the modelling of the effects of the clot on the viscoelastic properties of blood flow [23]. The models describing the formation of venous thrombi focus on the distribution of clotting factors in plasma while those studying the development of arterial white thrombi are primarily interested by the dynamics of platelets activation and aggregation [24]. We estimate the thresholds of the shear rate that prevent clotting for different platelet count values as well as the critical size of the injured area leading to the initiation of clot growth

Spatiotemporal modelling of thrombus development

Thrombin generation model

A simplified model of thrombin distribution

Identification of the parameters

Discussion