A Mathematical Model of Venous Thrombosis Initiation

Abstract

We present a mathematical model for the initiation of venous thrombosis (VT) due to slow flow and the consequent activation of the endothelial cells (ECs) lining the vein, in the absence of overt mechanical disruption of the EC layer. It includes all reactions of the tissue factor (TF) pathway of coagulation through fibrin formation, incorporates the accumulation of blood cells on activated ECs, accounts for the flow-mediated delivery and removal of coagulation proteins and blood cells from the locus of the reactions, and accounts for the activity of major inhibitors including heparan-sulfate-accelerated antithrombin and activated protein C. The model reveals that the occurrence of robust thrombin generation (a thrombin burst) depends in a threshold manner on the density of TF on the activated ECs and on the concentration of thrombomodulin and the degree of heparan-sulfate accelerated antithrombin activity on those cells. Small changes in any of these in appropriate narrow ranges switches the response between ''no burst'' and ''burst.'' The model predicts synergies among the inhibitors, both in terms of each inhibitor's multiple targets, and in terms of interactions between the different inhibitors. The model strongly suggests that the rate and extent of accumulation of activated monocytes, platelets, and MPs that can support the coagulation reactions has a powerful influence on whether a thrombin burst occurs and the thrombin response when it does. The slow rate of accumulation of cells supporting coagulation is one reason that the progress of VT is so much slower than that of arterial thrombosis initiated by subendothelial exposure.

Establishing the Transient Mass Balance of Thrombosis

“…Using the D-dimer assay, the first measurement of intrathrombus fibrin concentration revealed that fresh fibrinogen substrate can also continually enter the clot and be converted to fibrin monomer and incorporated into fibrin. While the binding of thrombin into fibrin has been studied in the literature, 30 the conditions of a thrombus formed under flow are unique relative to those found in a tube of clotting blood or plasma. Clearly, γ′-fibrin can bind endogeneously produced thrombin to a significant extent (Figures 2 and 3 ).…”

A local and global sensitivity analysis of a mathematical model of coagulation and platelet deposition under flow

“…The first model to track limited numbers of cell binding sites [ 12 ] is the original version of the model considered in this paper. That model was further developed in [ 14 , 16 , 20 , 21 ] and inspired similar models [ 4 , 6 ]. These models account for reversible binding of proteins to these sites with rates k on and rates k off for binding and unbinding, respectively.…”

Untitled

“…Although these concentrations are below the threshold values of 500 and 800 pM that are required to activate platelets and factors V and XIII, 3 one can expect that these plasma levels induce a hypercoagulable state when reaching low flow areas or areas of circulating flow such as in the valve pockets. 14,15 To estimate the relation between the total amount of thrombin formed and the amount of thrombin that is released into the circulating blood, plasma levels of F1.2 were compared with plasma levels of thrombin and TAT. Plasma levels of F1.2 significantly increased during surgery, whereas plasma levels of TAT were measured within the same molar ranges as F1.2.…”