Dynamics of thrombin formation using a mathematical model including both intrinsic and extrinsic pathways of blood coagulation
by
Liliana Braescu
Department of Computer Science, West University of Timisoara, Romania
Coauthors: Thomas F. George (University of Missouri–St. Louis, USA) Carmen Orbulescu (West University of Timisoara, Romania) Marius Leretter (University of Medicine and Pharmacy Victor Babes, Romania)

Blood coagulation is a basic physiological defense mechanism that occurs in all vertebrates to prevent blood loss following vascular injury. The coagulation is composed of a set of pro- and anticoagulant systems that maintain the balance of blood fluidity. Defects in this balance can result in either thrombosis or bleeding tendencies. Qualitative or quantitative alterations in this haemostatic balance can have devastating effects, producing hemorrhagic diseases or thrombosis diseases. An understanding of the working mechanism of coagulation is based on the well-known scheme of the reactions cascade. This has two pathways – intrinsic and extrinsic – representing a series of reactions of coagulation factors (indicated by roman numerals according to the standard system of designations) in which a stable form of a protein is activated to become an enzyme which then catalyzes the next reaction in the cascade. Both the intrinsic and extrinsic pathways join in a common pathway starting with an activation of factor X to factor Xa; after that factor Xa activates prothrombin (factor II) to thrombin (factor IIa) which is the essential enzyme product of the blood coagulation cascade leading fibrin formation.

A mathematical modeling approach of the extrinsic pathway was proposed by Jones et al. [1]. Extensive revisions were subsequently made by Hockin et al. [2], incorporating additional steps to the pro-coagulant system and including the stoichiometric anticoagulants. The resulting mathematical model has 34 nonlinear differential equations which describe the fates of 34 species, with 42 rate constants, that join together in 27 independent chemical reactions of the first order, second order and of the Michaelis-Menten type. A time-dependent mathematical model of an intrinsic pathway of blood coagulation was reported by Zarnitsina et al. [3], including 8 differential equations describing the dynamics of activation of factors XI, IX, X, II, I, VIII, V, and protein C. Because the intrinsic and extrinsic pathways meet at a common point – factor X – and the production of factor X by an intrinsic pathway is 100 times more than what is produced in an extrinsic pathway only, here a more realistic mathematical model is proposed, based on the scheme of the biochemical reactions of both intrinsic and extrinsic pathways. Numerical results are presented for the considered IVP problem. The computed thrombin formation from the proposed combined mathematical model is compared with the thrombin profiles computed using the above mathematical models for the intrinsic, and extrinsic pathways.

[1] K. C. Jones and K. G. Mann, J. Biol. Chem. 269 (1994) 23367.

[2] M. F. Hockin, K. C. Jones, S. J. Everse, and K.G. Mann, J. Biol. Chem. 277 (2002) 18322.

[3] V. I. Zarnitsina, A. V. Pokhilko, and F. I. Ataullakhanov, Thrombosis Res. 84 (1996) 225.

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Date received: January 28, 2008