A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. I. The model description. 1996

V I Zarnitsina, and A V Pokhilko, and F I Ataullakhanov
National Scientific Center for Hematology, Russian Academy of Medical Sciences, Moscow, Russia.

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.

UI MeSH Term Description Entries
D007700 Kinetics The rate dynamics in chemical or physical systems.
D008962 Models, Theoretical Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment. Experimental Model,Experimental Models,Mathematical Model,Model, Experimental,Models (Theoretical),Models, Experimental,Models, Theoretic,Theoretical Study,Mathematical Models,Model (Theoretical),Model, Mathematical,Model, Theoretical,Models, Mathematical,Studies, Theoretical,Study, Theoretical,Theoretical Model,Theoretical Models,Theoretical Studies
D011486 Protein C A vitamin-K dependent zymogen present in the blood, which, upon activation by thrombin and thrombomodulin exerts anticoagulant properties by inactivating factors Va and VIIIa at the rate-limiting steps of thrombin formation.
D001777 Blood Coagulation The process of the interaction of BLOOD COAGULATION FACTORS that results in an insoluble FIBRIN clot. Blood Clotting,Coagulation, Blood,Blood Clottings,Clotting, Blood
D002118 Calcium A basic element found in nearly all tissues. It is a member of the alkaline earth family of metals with the atomic symbol Ca, atomic number 20, and atomic weight 40. Calcium is the most abundant mineral in the body and combines with phosphorus to form calcium phosphate in the bones and teeth. It is essential for the normal functioning of nerves and muscles and plays a role in blood coagulation (as factor IV) and in many enzymatic processes. Coagulation Factor IV,Factor IV,Blood Coagulation Factor IV,Calcium-40,Calcium 40,Factor IV, Coagulation
D006801 Humans Members of the species Homo sapiens. Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D013917 Thrombin An enzyme formed from PROTHROMBIN that converts FIBRINOGEN to FIBRIN. Thrombase,Thrombin JMI,Thrombin-JMI,Thrombinar,Thrombostat,alpha-Thrombin,beta,gamma-Thrombin,beta-Thrombin,gamma-Thrombin,JMI, Thrombin
D015943 Factor Va Activated form of factor V. It is an essential cofactor for the activation of prothrombin catalyzed by factor Xa. Coagulation Factor Va,Factor V, Activated,Blood Coagulation Factor V, Activated,Factor 5A,Factor Five A,Activated Factor V,Factor Va, Coagulation
D015944 Factor VIIIa Activated form of factor VIII. The B-domain of factor VIII is proteolytically cleaved by thrombin to form factor VIIIa. Factor VIIIa exists as a non-covalent dimer in a metal-linked (probably calcium) complex and functions as a cofactor in the enzymatic activation of factor X by factor IXa. Factor VIIIa is similar in structure and generation to factor Va. Coagulation Factor VIIIa,Factor VIII, Activated,Factor VIII, Thrombin-Activated,Blood Coagulation Factor VIII, Activated,Factor 8A,Factor Eight A,Factor VIIIa Heavy Chain, 200 kDa Isoform,Factor VIIIa Heavy Chain, 92 kDa Isoform,Factor VIIIa Light Chain,Activated Factor VIII,Factor VIII, Thrombin Activated,Factor VIIIa, Coagulation,Thrombin-Activated Factor VIII
D015949 Factor IXa Activated form of factor IX. This activation can take place via the intrinsic pathway of blood coagulation by the action of factor XIa and calcium, or via the extrinsic pathway by the action of factor VIIa, thromboplastin, and calcium. Factor IXa serves to activate factor X to Xa by cleaving the arginyl-leucine peptide bond in factor X. Coagulation Factor IXa,Factor IX, Activated,Blood Coagulation Factor IX, Activated,Factor 9A,Factor Nine A,Activated Factor IX,Factor IXa, Coagulation

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