Keywords: congenital heart disease, approximation, exponential law, mathematical modeling, quasi-stationary system, cardiovascular system
Building dependencies of changes in the parameters of the child's body on age
UDC 651.471
DOI: 10.26102/2310-6018/2024.46.3.004
The relevance of the research conducted in the article is due to the need to predict the risks that threaten the life of a child with congenital heart disease in order to plan surgical interventions. The prognosis of the state of the cardiovascular system is based on a zero-dimensional model of blood circulation. To do this, it is proposed to create a quasi-stationary model in which the parameters of the cardiovascular system vary depending on the age of the child. Based on the analysis of data from regional monitoring of children's health, the article formulates a hypothesis that the parameters of a child's body change exponentially depending on age. Experimental studies based on monitoring data have confirmed the hypothesis put forward. A method for constructing changes in the parameters of a child's cardiovascular system depending on age is proposed and investigated. To establish this dependence, it is sufficient to have the parameter value for the child at the current time and at another time for the average child of a given gender. An algorithm for obtaining an experimental exponential dependence based on the use of Newton's iterative method for solving a nonlinear equation is proposed. The implementation of the proposed technique makes it possible to predict the state of the child's cardiovascular system for planning such interventions as surgical removal of congenital heart defects.
1. Bokareva A.A. Sbor i analiz dannykh po serdechno-sosudistym zabolevaniyam na fone Covid-19 dlya vyyavleniya zakonomernostei i veroyatnykh prognozov na osnove sushchestvuyushchei statistiki. In: Pyatidesyataya nauchnaya i uchebno-metodicheskaya konferentsiya Universiteta ITMO: Al'manakh nauchnykh rabot molodykh uchenykh Universiteta ITMO: Volume 3, 01-04 February 2021, Saint Petersburg, Russia. Saint Petersburg: ITMO University; 2021. pp. 26–30. (In Russ.).
2. Hall J.E. Guyton and Hall Textbook of Medical Physiology. Moscow: Logosfera; 2018. 1328 p. (In Russ.).
3. Bokeriya L.A., Gudkova R.G., Milievskaya E.B., Kudzoeva Z.F., Pryanishnikov V.V. Serdechno-sosudistaya khirurgiya-2016. Bolezni i vrozhdennye anomalii sistemy krovoobrashcheniya. Moscow: A.N. Bakulev National Medical Research Center for Cardiovascular Surgery; 2017. 228 p. (In Russ.).
4. Lishchuk V.A. Matematicheskaya teoriya krovoobrashcheniya. Moscow: Meditsina; 1991. 256 p. (In Russ.).
5. Frolov S.V., Sindeev S.V., Lischouk V.A., Gazizova D.S., Liepsch D., Balasso A. A lumped parameter model of cardiovascular system with pulsating heart for diagnostic studies. Journal of Mechanics in Medicine and Biology. 2017;17(3). https://doi.org/10.1142/S0219519417500567
6. Al-Mayah A. Biomechanics of Soft Tissues: Principles and Applications. Boca Raton: CRC Press; 2018. 188 p. https://doi.org/10.1201/9781351135825
7. Babakov N.A., Voronov A.A., Voronova A.A. et al. Teoriya avtomaticheskogo upravleniya. V 2-kh ch. Ch. I. Teoriya lineinykh sistem avtomaticheskogo upravleniya. Moscow: Vysshaya shkola; 1986. 367 p. (In Russ.).
8. Frolov S.V., Lyadov M.A., Ostapenko O.A. Expert system for the physical development of children based on apparatus of the relational algebra. Biotekhnosfera. 2013;(6):28–39. (In Russ.).
9. Yablonskii A.I., Kuznetsov A.V., Shilkina E.I. et al. Vysshaya matematika. Obshchii kurs. Minsk: Vysheishaya shkola; 2000. 352 p. (In Russ.).
10. Petukhov D.S., Telyshev D.V. A Mathematical Model of the Cardiovascular System of Pediatric Patients with Congenital Heart Defect. Biomedical Engineering. 2016;50(4):229–232. https://doi.org/10.1007/s10527-016-9626-y
11. Szabó G., Soans D., Graf A., Beller C.J., Waite L., Hagl S. A new computer model of mitral valve hemodynamics during ventricular filling. European Journal of Cardio-Thoracic Surgery. 2004;26(2):239–247. https://doi.org/10.1016/j.ejcts.2004.03.018
Keywords: congenital heart disease, approximation, exponential law, mathematical modeling, quasi-stationary system, cardiovascular system
For citation: Frolov S.V. Sudakov D.E. Starykh D.G. Building dependencies of changes in the parameters of the child's body on age. Modeling, Optimization and Information Technology. 2024;12(3). Available from: https://moitvivt.ru/ru/journal/pdf?id=1622 DOI: 10.26102/2310-6018/2024.46.3.004 (In Russ).
Received 03.07.2024
Revised 11.07.2024
Accepted 15.07.2024