Mathematical model of blood clotting in the portal vein

Andreeva A.A., Kazymov B.I., Lobanov A.I., Panyukov S.V., Yaremin B.I.
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Portal vein thrombosis (PVT) is a significant complication during both the pre-transplant and postoperative periods of liver transplantation. The multifactorial etiology of PVT, the paradoxical hemostatic state in liver cirrhosis and the limited usefulness of standard coagulation tests highlight the necessity of formalized models to assess thrombosis risk.

Objective: Using a mathematical model of the blood coagulation system, investigate the influence of hemodynamic conditions and coagulation factor levels on the likelihood of thrombus formation in the portal vein.

The portal vein is modelled as a flow-through reactor with rapid convective mixing. The mathematical model is based on Panteleev et al. (2010) detailed kinetic scheme, incorporating equations for the extrinsic pathway of coagulation activation, positive and negative feedback loops, and inhibition of active factors. The resulting system of ordinary differential equations was integrated using a one-stage Rosenbrock method with complex coefficients.

Thrombin generation was shown to exhibit threshold dependence on blood flow velocity. Above a critical velocity, the initiation phase does not transition to the amplification phase. This corresponds to physiological conditions that prevent thrombus formation. We demonstrated that, at reduced fibrinogen concentrations characteristic of hepatic dysfunction, the critical velocity threshold above which thrombus formation is suppressed increases. This indicates the system’s heightened susceptibility to stasis. Protein C deficiency had minimal effect on thrombogenesis dynamics under the modeled conditions. The modeling results qualitatively agree with clinical data on fibrinogen distribution in PVT patients ($n$ = 932, Sklifosovsky Research Institute).

Keywords: blood clotting system, thrombin generation, flow-through reactor, portal vein, vein thrombosis
Citation in English: Andreeva A.A., Kazymov B.I., Lobanov A.I., Panyukov S.V., Yaremin B.I. Mathematical model of blood clotting in the portal vein // Computer Research and Modeling, 2026, vol. 18, no. 3, pp. 561-587
Citation in English: Andreeva A.A., Kazymov B.I., Lobanov A.I., Panyukov S.V., Yaremin B.I. Mathematical model of blood clotting in the portal vein // Computer Research and Modeling, 2026, vol. 18, no. 3, pp. 561-587
DOI: 10.20537/2076-7633-2026-18-3-561-587
URL: http://crm-en.ics.org.ru/journal/article/3733/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Copyright © 2026 Andreeva A.A., Kazymov B.I., Lobanov A.I., Panyukov S.V., Yaremin B.I.

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