Abstract:
Many properties of ordinary differential equations systems solutions are determined by the properties of the equations in variations. An ODE system, which includes both the original nonlinear system and the equations in variations, will be called an extended system further. When studying the properties of the Cauchy problem for the systems of ordinary differential equations, the transition to extended systems allows one to study many subtle properties of solutions. For example, the transition to the extended system allows one to increase the order of approximation for numerical methods, gives the approaches to constructing a sensitivity function without using numerical differentiation procedures, allows to use methods of increased convergence order for the inverse problem solution. Authors used the Broyden method belonging to the class of quasi-Newtonian methods. The Rosenbroke method with complex coefficients was used to solve the stiff systems of the ordinary differential equations. In our case, it is equivalent to the second order approximation method for the extended system.
As an example of the proposed approach, several related mathematical models of the blood coagulation process were considered. Based on the analysis of the numerical calculations results, the conclusion was drawn that it is necessary to include a description of the factor XI positive feedback loop in the model equations system. Estimates of some reaction constants based on the numerical inverse problem solution were given.
Effect of factor V release on platelet activation was considered. The modification of the mathematical model allowed to achieve quantitative correspondence in the dynamics of the thrombin production with experimental data for an artificial system. Based on the sensitivity analysis, the hypothesis tested that there is no influence of the lipid membrane composition (the number of sites for various factors of the clotting system, except for thrombin sites) on the dynamics of the process.
The reported study was funded by RFBR, project number 20-31-90046, and in process of State assignment for FRC ChPh RAS (No. State registration index 122040400089-6), also supported by the Russian Science Foundation grant 20-45-01014.
Received: 14.01.2022 Accepted: 10.02.2022
Document Type:
Article
UDC:519.6
Language: Russian
Citation:
A. A. Andreeva, M. Anand, A. I. Lobanov, A. V. Nikolaev, M. A. Panteleev, “Using extended ODE systems to investigate the mathematical model of the blood coagulation”, Computer Research and Modeling, 14:4 (2022), 931–951
\Bibitem{AndAnaLob22}
\by A.~A.~Andreeva, M.~Anand, A.~I.~Lobanov, A.~V.~Nikolaev, M.~A.~Panteleev
\paper Using extended ODE systems to investigate the mathematical model of the blood coagulation
\jour Computer Research and Modeling
\yr 2022
\vol 14
\issue 4
\pages 931--951
\mathnet{http://mi.mathnet.ru/crm1008}
\crossref{https://doi.org/10.20537/2076-7633-2022-14-4-931-951}
Linking options:
https://www.mathnet.ru/eng/crm1008
https://www.mathnet.ru/eng/crm/v14/i4/p931
This publication is cited in the following 3 articles:
Anastasia N. Sveshnikova, Alexey M. Shibeko, Tatiana A. Kovalenko, Mikhail A. Panteleev, “Kinetics and regulation of coagulation factor X activation by intrinsic tenase on phospholipid membranes”, Journal of Theoretical Biology, 582 (2024), 111757
A.R. Gantseva, E.R. Gantseva, A.N. Sveshnikova, M.A. Panteleev, T.A. Kovalenko, “Kinetic analysis of prothrombinase assembly and substrate delivery mechanisms”, Journal of Theoretical Biology, 594 (2024), 111925
A.A. Bozhko, M.A. Panteleev, Proceedings of the International Conference “Mathematical Biology and Bioinformatics”, 10, Proceedings of the International Conference “Mathematical Biology and Bioinformatics”, 2024
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