A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. I. The model description.

We developed and analyzed the mathematical model of the intrinsic pathway based on the current biochemical data on the kinetics of blood coagulation individual stages. The model includes eight differential equations describing the spatio-temporal dynamics of activation of factors XI, IX, X, II, I, VIII, V, and protein C. The assembly of tenase and prothrombinase complexes is considered as a function of calcium concentration. The spatial dynamics of coagulation was analyzed for the one-dimensional case. We examined the formation of active factors, their spreading, and growth of the clot from the site of injury in the direction perpendicular to the vessel wall, into the blood thickness. We assumed that the site of injury (in the model one boundary of the space segment under examination) becomes a source of the continuous influx of factor XIa. In the first part, we described the model, selected the parameters, etc. In the second part, we compared the model with experimental data obtained in the homogeneous system and analyzed the spatial dynamics of the clot growth.

[1]  R. Colman,et al.  Inactivation of factor XIa by plasma protease inhibitors: predominant role of alpha 1-protease inhibitor and protective effect of high molecular weight kininogen. , 1982, The Journal of clinical investigation.

[2]  B. Dahlbäck.  Physiological anticoagulation. Resistance to activated protein C and venous thromboembolism. , 1994, The Journal of clinical investigation.

[3]  F Keller,et al.  The quick machine--a mathematical model for the extrinsic activation of coagulation. , 1994, Haemostasis.

[4]  A. Muller,et al.  Chapter 1 Blood coagulation as a part of the haemostatic system , 1986 .

[5]  R. Rosenberg,et al.  Inhibition of human factor IXa by human antithrombin. , 1975, The Journal of biological chemistry.

[6]  K. Mann,et al.  The contribution of bovine Factor V and Factor Va to the activity of prothrombinase. , 1979, The Journal of biological chemistry.

[7]  K. Mann,et al.  Surface-dependent reactions of the vitamin K-dependent enzyme complexes. , 1990, Blood.

[8]  J. Jesty,et al.  Thrombin-activated and factor Xa-activated human factor VIII: differences in cofactor activity and decay rate. , 1992, Archives of biochemistry and biophysics.

[9]  F. Ataullakhanov,et al.  Calcium threshold in human plasma clotting kinetics. , 1994, Thrombosis research.

[10]  J. Jesty.  Analysis of the generation and inhibition of activated coagulation factor X in pure systems and in human plasma. , 1986, The Journal of biological chemistry.

[11]  M. Tucker,et al.  Kinetics of inactivation of membrane-bound factor Va by activated protein C. Protein S modulates factor Xa protection. , 1988, The Journal of biological chemistry.

[12]  J. Griffin,et al.  Inhibition and complexation of activated protein C by two major inhibitors in plasma , 1989 .

[13]  B. Dahlback.  Resistance to Activated Protein C and Venous Thromboembolism , 1994 .

[14]  P. Lollar,et al.  Activation of porcine factor VIII:C by thrombin and factor Xa. , 1985, Biochemistry.

[15]  J. Griffin,et al.  Inhibition and complexation of activated protein C by two major inhibitors in plasma. , 1989, Blood.

[16]  H C Hemker,et al.  Simulation model for thrombin generation in plasma. , 1991, Haemostasis.

[17]  J. Griffin,et al.  Human blood coagulation factor IX. Purification, properties, and mechanism of activation by activated factor XI. , 1978, The Journal of biological chemistry.

[18]  K. Mann,et al.  Prothrombinase complex assembly. Kinetic mechanism of enzyme assembly on phospholipid vesicles. , 1988, The Journal of biological chemistry.

[19]  J Jesty,et al.  A comparison of phospholipid and platelets in the activation of human factor VIII by thrombin and factor Xa, and in the activation of factor X. , 1988, Blood.

[20]  D. Bergel.  Geigy Scientific Tables , 1991 .

[21]  H. Hemker,et al.  The role of phospholipid and factor VIIIa in the activation of bovine factor X. , 1981, The Journal of biological chemistry.

[22]  R. Colman,et al.  Fibrinogen blocks the autoactivation and thrombin-mediated activation of factor XI on dextran sulfate. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[23]  C. L. La Porta,et al.  Activation of factor XI in plasma is dependent on factor XII. , 1993, Blood.

[24]  F. Krogh,et al.  Solving Ordinary Differential Equations , 2019, Programming for Computations - Python.

[25]  M A Khanin,et al.  A mathematical model of the kinetics of blood coagulation. , 1989, Journal of theoretical biology.

[26]  G. Broze,et al.  Factor XI activation in a revised model of blood coagulation , 1991, Science.

[27]  J. Miletich,et al.  The light chain of factor Va contains the activity of factor Va that accelerates protein C activation by thrombin. , 1983, The Journal of biological chemistry.

[28]  K. Mann,et al.  A model for the tissue factor pathway to thrombin. II. A mathematical simulation. , 1994, Journal of Biological Chemistry.

[29]  H C Hemker,et al.  The role of phospholipids and factor Va in the prothrombinase complex. , 1980, The Journal of biological chemistry.

[30]  J. Griffin,et al.  Human blood coagulation factor XI. Purification, properties, and mechanism of activation by activated factor XII. , 1977, The Journal of biological chemistry.