Study of Reversible Platelet Aggregation Model by Nonlinear Dynamics
Blood cell platelets form aggregates upon vessel wall injury. Under certain conditions, a disintegration of the platelet aggregates, called “reversible aggregation”, is observed in vitro. Previously, we have proposed an extremely simple (two equations, five parameters) ordinary differential equation...
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MDPI AG
2021-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/7/759 |
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| author | Grigorii A. Vasilev Aleksandra A. Filkova Anastasia N. Sveshnikova |
| author_facet | Grigorii A. Vasilev Aleksandra A. Filkova Anastasia N. Sveshnikova |
| author_sort | Grigorii A. Vasilev |
| collection | DOAJ |
| description | Blood cell platelets form aggregates upon vessel wall injury. Under certain conditions, a disintegration of the platelet aggregates, called “reversible aggregation”, is observed in vitro. Previously, we have proposed an extremely simple (two equations, five parameters) ordinary differential equation-based mathematical model of the reversible platelet aggregation. That model was based on mass-action law, and the parameters represented probabilities of platelet aggregate formations. Here, we aimed to perform a nonlinear dynamics analysis of this mathematical model to derive the biomedical meaning of the model’s parameters. The model’s parameters were estimated automatically from experimental data in COPASI software. Further analysis was performed in Python 2.7. Contrary to our expectations, for a broad range of parameter values, the model had only one steady state of the stable type node, thus eliminating the initial assumption that the reversibility of the aggregation curve could be explained by the system’s being near a stable focus. Therefore, we conclude that during platelet aggregation, the system is outside of the influence area of the steady state. Further analysis of the model’s parameters demonstrated that the rate constants for the reaction of aggregate formation from existing aggregates determine the reversibility of the aggregation curve. The other parameters of the model influenced either the initial aggregation rate or the quasi-steady state aggregation values. |
| first_indexed | 2024-03-10T12:43:01Z |
| format | Article |
| id | doaj.art-e6f8d7654a4d4b42bf2368fd38e98998 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T12:43:01Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e6f8d7654a4d4b42bf2368fd38e989982023-11-21T13:47:27ZengMDPI AGMathematics2227-73902021-04-019775910.3390/math9070759Study of Reversible Platelet Aggregation Model by Nonlinear DynamicsGrigorii A. Vasilev0Aleksandra A. Filkova1Anastasia N. Sveshnikova2Faculty of Physics, Lomonosov Moscow State University, 1/2 Leninskie Gory, 119991 Moscow, RussiaCenter for Theoretical Problems of Physico-Chemical Pharmacology, Russian Academy of Sciences, 30 Srednyaya Kalitnikovskaya Str., 109029 Moscow, RussiaFaculty of Physics, Lomonosov Moscow State University, 1/2 Leninskie Gory, 119991 Moscow, RussiaBlood cell platelets form aggregates upon vessel wall injury. Under certain conditions, a disintegration of the platelet aggregates, called “reversible aggregation”, is observed in vitro. Previously, we have proposed an extremely simple (two equations, five parameters) ordinary differential equation-based mathematical model of the reversible platelet aggregation. That model was based on mass-action law, and the parameters represented probabilities of platelet aggregate formations. Here, we aimed to perform a nonlinear dynamics analysis of this mathematical model to derive the biomedical meaning of the model’s parameters. The model’s parameters were estimated automatically from experimental data in COPASI software. Further analysis was performed in Python 2.7. Contrary to our expectations, for a broad range of parameter values, the model had only one steady state of the stable type node, thus eliminating the initial assumption that the reversibility of the aggregation curve could be explained by the system’s being near a stable focus. Therefore, we conclude that during platelet aggregation, the system is outside of the influence area of the steady state. Further analysis of the model’s parameters demonstrated that the rate constants for the reaction of aggregate formation from existing aggregates determine the reversibility of the aggregation curve. The other parameters of the model influenced either the initial aggregation rate or the quasi-steady state aggregation values.https://www.mdpi.com/2227-7390/9/7/759platelet aggregationphase planebifurcation analysisparameter estimationordinary differential equations |
| spellingShingle | Grigorii A. Vasilev Aleksandra A. Filkova Anastasia N. Sveshnikova Study of Reversible Platelet Aggregation Model by Nonlinear Dynamics Mathematics platelet aggregation phase plane bifurcation analysis parameter estimation ordinary differential equations |
| title | Study of Reversible Platelet Aggregation Model by Nonlinear Dynamics |
| title_full | Study of Reversible Platelet Aggregation Model by Nonlinear Dynamics |
| title_fullStr | Study of Reversible Platelet Aggregation Model by Nonlinear Dynamics |
| title_full_unstemmed | Study of Reversible Platelet Aggregation Model by Nonlinear Dynamics |
| title_short | Study of Reversible Platelet Aggregation Model by Nonlinear Dynamics |
| title_sort | study of reversible platelet aggregation model by nonlinear dynamics |
| topic | platelet aggregation phase plane bifurcation analysis parameter estimation ordinary differential equations |
| url | https://www.mdpi.com/2227-7390/9/7/759 |
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