Reduced mathematical model of blood coagulation taking into account thrombin activity switching as a basis for estimation of hemodynamic effects and its implementation in FlowVision package

Aksenov A.A., Zhluktov S.V., Kalugina M.D., Kashirin V.S., Lobanov A.I., Shaurman D.V.
 pdf (4272K)

The possibility of numerical 3D simulation of thrombi formation is considered.

The developed up to now detailed mathematical models describing formation of thrombi and clots include a great number of equations. Being implemented in a CFD code, the detailed mathematical models require essential computer resources for simulation of the thrombi growth in a blood flow. A reasonable alternative way is using reduced mathematical models. Two models based on the reduced mathematical model for the thrombin generation are described in the given paper.

The first model describes growth of a thrombus in a great vessel (artery). The artery flows are essentially unsteady. They are characterized by pulse waves. The blood velocity here is high compared to that in the vein tree. The reduced model for the thrombin generation and the thrombus growth in an artery is relatively simple. The processes accompanying the thrombin generation in arteries are well described by the zero-order approximation.

A vein flow is characterized lower velocity value, lower gradients, and lower shear stresses. In order to simulate the thrombin generation in veins, a more complex system of equations has to be solved. The model must allow for all the non-linear terms in the right-hand sides of the equations.

The simulation is carried out in the industrial software FlowVision.

The performed numerical investigations have shown the suitability of the reduced models for simulation of thrombin generation and thrombus growth. The calculations demonstrate formation of the recirculation zone behind a thrombus. The concentration of thrombin and the mass fraction of activated platelets are maximum here. Formation of such a zone causes slow growth of the thrombus downstream. At the upwind part of the thrombus, the concentration of activated platelets is low, and the upstream thrombus growth is negligible.

When the blood flow variation during a hart cycle is taken into account, the thrombus growth proceeds substantially slower compared to the results obtained under the assumption of constant (averaged over a hard cycle) conditions. Thrombin and activated platelets produced during diastole are quickly carried away by the blood flow during systole. Account of non-Newtonian rheology of blood noticeably affects the results.

Keywords: hemodynamics, thrombus, thrombin, platelet, fibrin, clot, artery, vein, numerical simulation, computational fluid dynamics (CFD), Navier – Stokes equations, equations “reaction – diffusion – convection”, non-Newtonian fluid, method of finite volumes
Citation in English: Aksenov A.A., Zhluktov S.V., Kalugina M.D., Kashirin V.S., Lobanov A.I., Shaurman D.V. Reduced mathematical model of blood coagulation taking into account thrombin activity switching as a basis for estimation of hemodynamic effects and its implementation in FlowVision package // Computer Research and Modeling, 2023, vol. 15, no. 4, pp. 1039-1067
Citation in English: Aksenov A.A., Zhluktov S.V., Kalugina M.D., Kashirin V.S., Lobanov A.I., Shaurman D.V. Reduced mathematical model of blood coagulation taking into account thrombin activity switching as a basis for estimation of hemodynamic effects and its implementation in FlowVision package // Computer Research and Modeling, 2023, vol. 15, no. 4, pp. 1039-1067
DOI: 10.20537/2076-7633-2023-15-4-1039-1067
URL: http://crm-en.ics.org.ru/journal/article/3373/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Indexed in Scopus

Full-text version of the journal is also available on the web site of the scientific electronic library eLIBRARY.RU

The journal is included in the Russian Science Citation Index

The journal is included in the RSCI

International Interdisciplinary Conference "Mathematics. Computing. Education"

Copyright © 2009–2024 Institute of Computer Science