Numerical simulation of flow inversion in the portal vein

Kazymov B.I., Limareva M.J., Lobanov A.I., Fisher J.V., Yaremin B.I.
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A mathematical model of fluid movement in the portal vein is considered. The fundamental circumstance determining the whole variety of portal hemodynamic phenomena is the absence of a valve apparatus. The flow direction is solely a function of the pressure gradient, and, therefore, it is fundamentally reversible when the boundary conditions of the system change.

Calculations were performed in the area representing a CT image fragment of the portal vein of a particular patient, which does not contain vascular bifurcations. The interpolation of patient Dopplerography data published in the press was used as boundary conditions for the flow. The calculations were carried out using the FlowVision industrial hydrodynamics software package. A comparison of calculations using the ideal fluid model and the Kuemada model of viscoplastic flow is carried out.

Calculations were performed for different values of the resistance coefficient corresponding to the physiological norm and with an increased value of the resistance coefficient.

At a normal value of the resistance coefficient, the flow in the portal vein is characterized by strong convective mixing.

As a result of calculations, it was found that when using the Kuemada model, the flow in the portal vein is stratified. The nature of the stratification depends on the hematocrit. At a normal value of the resistance coefficient, a plastic core of the flow is formed as the velocity decreases. With an increased value of the resistance coefficient during flow inversion, the flow core is also formed. When the flow is inverted, the plastic core continues to move in the forward direction, while the wall layers of the liquid begin to move in the opposite direction.

It is noted that in order to obtain correct modeling results, it is necessary to refine the blood composition of the portal vein and, possibly, refine the rheological model. Such information can be obtained both from comparing simulation data with clinical data, and by laboratory examination of portal vein blood.

Keywords: portal vein, flow inversion, mathematical modeling, Quemada liquid model, FlowVision software package
Citation in English: Kazymov B.I., Limareva M.J., Lobanov A.I., Fisher J.V., Yaremin B.I. Numerical simulation of flow inversion in the portal vein // Computer Research and Modeling, 2026, vol. 18, no. 3, pp. 659-674
Citation in English: Kazymov B.I., Limareva M.J., Lobanov A.I., Fisher J.V., Yaremin B.I. Numerical simulation of flow inversion in the portal vein // Computer Research and Modeling, 2026, vol. 18, no. 3, pp. 659-674
DOI: 10.20537/2076-7633-2026-18-3-659-674
URL: http://crm-en.ics.org.ru/journal/article/3738/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Copyright © 2026 Kazymov B.I., Limareva M.J., Lobanov A.I., Fisher J.V., Yaremin B.I.

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