# Using extended ODE systems to investigate the mathematical model of the blood coagulation

Andreeva, Anna Arkadievna and Mohan, Anand and Lobanov, Alexey I. and Nikolaev, Andrey Vladimirovich and Panteleev, Mikhail Aleksandrovich (2022) Using extended ODE systems to investigate the mathematical model of the blood coagulation. Computer Research and Modeling, 14 (4). pp. 1-21. ISSN 20767633

## 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. © 2022 Anna A. Andreeva, Mohan Anand, Aleksey I. Lobanov, Andrey V. Nicolaev, Mikhail A. Panteleev.

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IITH Creators:
IITH CreatorsORCiD
Mohan, Anandhttps://orcid.org/0000-0001-7191-4991
Item Type: Article
Additional Information: 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.
Uncontrolled Keywords: blood clotting; Broyden method; CROS method; equation in variations; mathematical models; ODE system; platelets; thrombin
Subjects: Chemical Engineering
Divisions: Department of Chemical Engineering
Depositing User: Ms Palak Jain
Date Deposited: 22 May 2023 09:26