METHODS OF IDENTIFICATION OF THE DYNAMIC MODEL OF THE CARDIOVASCULAR SYSTEM REACTION TO PHYSICAL ACTIVITY IN PATIENTS WITH MYOCARDIAL INFARCTION IN THE PROCESS OF REHABILITATION
DOI:
https://doi.org/10.11603/mie.1996-1960.2019.1.10111Keywords:
dynamic model of the reaction of the cardiovascular system on exercise, myocardial infarction, cardio-rehabilitationAbstract
Background. Predicting the dynamics of pulse and blood pressure under physical activity is a key task in planning the patient's rehabilitation process after cardiovascular events and, firstly, myocardial infarction. Nowadays, it is empirically solved, however, the development of an adequate mathematical model for predicting major hemodynamic indicators would avoid the subjectivity of assessments and increase the reliability of the prognosis, safety and effectiveness of rehabilitation technology.
The aim of the study: to develop and identify a dynamic model of the cardiovascular system response to physical activity in patients with myocardial infarction during the rehabilitation process.
Materials and methods. Results. In order to formulate the judgment about changing the patient's condition under the action of physical activity in the process of rehabilitation, a system for modeling the levels of pulse and blood pressure using a package of applied programs for mathematical modeling was implemented. Its main subsystems are processing and data identification, forecasting data generation. To verify the adequacy of the constructed model, a mode to check the tolerance to physical activity was used. Observations were conducted on a group of patients with myocardial infarction of the functional class I-II in the sub acute phase of rehabilitation. The dynamics of the body's response to patients with identical physical activity was recorded at an interval of 3 minutes in the course of a defined phase of the rehabilitation program.
The obtained results testify to the adequacy of the constructed mathematical model for the analyzed stage of the rehabilitation process. The maximum error rate for the entire observation period was 9.5 % for pulse, and 5.2 % for blood pressure.
Conclusions. 1. The mathematical model of the dynamics of pulse and blood pressure under the action of physical activity in the sub-stage of the rehabilitation phase allows predicting the body's response to the graduated exercise.
2. The method of identification of a set of differential equations that simulates the dynamics of pulse and blood pressure under the action of exercise on the basis of the modified gradient Levenberg-Marquardt method, supplemented by the procedure for choosing the initial values of the coefficients, confirms the adequacy of the developed mathematical model.
References
De Pater, L., & Van den Berg, J.W. (1964). An electrical analogue of the entire human circulatory system. Med. Electron. Biol. Engineering. DOI: https://doi.org/10.1007/BF02484215
Mirzaee, M.R., Ghasemalizadeh, O., & Firoozabadi, B. (2008). Simulating of Human Cardiovascular System and Blood Vessel Obstruction Using Lumped Method. World Academy of Science, Engineering and Technology, 41, 367-374.
Perktold, K., & Rappitsch, G. (1995). Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model. J. Biomech., 28, 845-856. DOI: https://doi.org/10.1016/0021-9290(95)95273-8
Kordas, M. (1968). Analysis of a simplified electrical analog of circulation. Med Biol Eng, 6, 109-114. DOI: https://doi.org/10.1007/BF02478809
Quarteroni, A. Modeling the Cardiovascular System -A Mathematical Adventure: Part I. from SIAM News, 34, 5, 2-3.
Van de Vosse, F.N. (2003). Mathematical modeling of the cardiovascular system. Journal of Engineering Mathematics, 47, 175-183. DOI: https://doi.org/10.1023/B:ENGI.0000007986.69547.5a
Ottesen, J.T., Olufsen, M.S., & Larsen, J.K. (2004). Applied mathematical models in human physiology. SIAM, Philadelphia, PA. DOI: https://doi.org/10.1137/1.9780898718287
Kappel, F., & Peer, R.O. (1993). A mathematical model for fundamental regulation processes in the cardiovascular system. Journal of Mathematical Biology, 31, 6, 611-631. DOI: https://doi.org/10.1007/BF00161201
Timischl, S. (1998). A global model of the cardiovascular and respiratory system. Candidate's thesis. University of Graz, Institute for Mathematics and Scientic Computing.
Magosso, E., Felicani, A., & Ursino, M. (2001). A mathematical model of cardiovascular response to dynamic exercise. 23rd Annual Conference - IEEE/ EMBS, (Oct. 25-28), Istanbul, Turkey.
Magosso, E., & Ursino, M. (2002). Cardiovascular response to dynamic aero bicexercise: amathematical model. Med Biol Eng Comput., 40 (6), 660-674. Retrieved from: https://www.ncbi.nlm.nih.gov/ pubmed/12507317.
Magosso, E., Felicani, A., & Ursino, M. (2001). A mathematical model of cardiovascular response to dynamic exercise. 23rd Annual Conference - IEEE/ EMBS, (Oct. 25-28), Istanbul, Turkey. DOI: https://doi.org/10.1109/IEMBS.2001.1018953
Kyugeryan, S.G., & Petrosyan, T.G. (2005). Matematicheskaya model serdechno-sosudistoy sistemy organizma pri fizicheskoy nagruzke [Mathematical model of the cardiovascular system of the body during exercise]. Avtomatizatsiya i sistemy upravleniya -Automation and control systems, LVIII, 3 [in Russian].
Amosov, N.M., & Bendet, Ya.A. (1984). Fizicheskaya aktivnost i serdtse [Physical activity and heart]. The 2nd edn, revised and enlarged. Kyiv: Zdorovia, p. 230 [in Russian].
Shved, M.I., Levytska, L.V. (2018). Suchasni tekhnolohii vidnovnoho likuvannia khvorykh iz hostiym koronarnym syndromom [Modern technologies of restorative treatment of patients with acute coronary syndrome]. Kyiv: Vydavnychyi dim Medknyha, p. 176 [in Ukrainian].
Shved, M.I., & Levytska, L.V. 2018. Pidkhody do otsinky ryzykiv ta funktsionalnykh rezerviv sertsevo-sudynnoi systemy u khvorykh na infarkt miokarda z komorbidnoyu patolohiieiu, yaki perebuvaiut u hostromu periodi kardioreabilitatsii [Approaches to the assessment of the risks and functional reserves of the cardiovascular system in patients with myocardial infarction with comorbid pathology, which are in the acute period of cardio-rehabilitation]. Svit medytsyny ta biolohii - The world of medicine and biology, 4 (66), 124-130 [in Ukrainian]. DOI: https://doi.org/10.26724/2079-8334-2018-4-66-124-130
Vovkodav, O.V. (2015). Matematychni modeli dynamiky reabilitatsii patsiientiv v kardiolohichnykh systemakh : matematychne modelyuvannia ta obchysliuvalni metody. Candidate's thesis. Lviv, p. 154. Retrieved from: http://dspace.tneu.edu.ua/jspui/handle/316497/780 [in Ukrainian].
Shved, M.I., Vovkodav, O.V., Levytska, L.V., & Pasichnyk, R.M. (2017). Sposib prohnozuvannia dynamiky pulsu ta arterialnoho tysku v protsesi reabilitatsii khvorykh na infarkt miokarda [A method of forecasting the dynamics of pulse and blood pressure in the process of rehabilitation of patients with myocardial infarction]. Patent number: 117742. Published: 07.10.2017.
Downloads
Published
How to Cite
Issue
Section
License
Journal Medical Informatics and Engineering allows the author(s) to hold the copyright without registration
The majority of Medical Informatics and Engineering Open Access journals publish open access articles under the terms of the Creative Commons Attribution (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited. The remaining journals offer a choice of licenses.
This journal is available through Creative Commons (CC) License CC-BY 4.0
