On the Heart Rhythm Analysis by an Intelligent Control Method Using Artificial Neural Networks: Analytical Study and Electronic Simulation
Main Article Content
Abstract
One of the fundamental characteristics of the Heart’s physiology is its heart rate. Heart rhythms are interpreted by Electrocardiogram (ECG) signals, which enable a better analysis of normal and pathological rhythms. For its normal functioning, the heart is modeled as an electrical system that generates its own electricity, and which enables to beat and play its role as a pump. This system is called the electrical conduction system of the heart. The electricity generated by the heart ensures contraction of the atria and ventricles. In this work, an intelligent control method is presented to establish a test for heart rhythm control, and the implementation of an electronic circuit for the heart model used is carried out. For a better analysis of the model used, an analysis of stability in its autonomous, unidirectionally coupled state is carried out. It reveals regions of stable and unstable periodicities describing very rich dynamic behaviours. The sinus node being the initiator of the electrical current that powers the heart, a control strategy for tracking sinus node signal trajectories in the event of a disturbance is developed. The observed dynamic is the Electrocardiogram (ECG) signal. To generate it, the heart is modeled on a network of three nonlinear oscillators linked by delayed Duffing-type connections: the sinus node, the atrioventricular node and the Purkinje His bundle. Other specificities of the cardiac rhythm are linked by external stimuli. The controlled variable is the sinus node signal. For better compensation of unknown or hidden heart dynamics, digitally, the feedback linearization method (FBL) by integrating an artificial neural network to compensate for the unknown dynamics is used. Based on synthetic ECGs, the results obtained show that FBL enables the heart to maintain its normal rhythm, avoiding pathological rhythms. For real-life implementation, an electronic simulation using analog components from OrCAD-Pspice software is carried out. The results obtained are in qualitative agreement.
Downloads
Article Details
Copyright (c) 2026 Fonkou RF, et al.

This work is licensed under a Creative Commons Attribution 4.0 International License.
Nazari S, Heydari A, Khaligh J. Modified modeling of the heart by applying nonlinear oscillators and designing proper control signal. Appl Math. 2013;4(7):972-978. Available from: https://doi.org/10.4236/am.2013.47134
La Sala L, Crestani M, Garavelli S, de Candia P, Pontiroli AE. Does microRNA perturbation control the mechanisms linking obesity and diabetes? Implications for cardiovascular risk. Int J Mol Sci. 2021;22(1):143. Available from: https://doi.org/10.3390/ijms22010143
Fonkou RF, Kengne R, Fotsing Kamgang HC, Talla PK. Dynamical behavior analysis of the heart system by the bifurcation structures. Heliyon. 2023;9:e12887. Available from: https://doi.org/10.1016/j.heliyon.2023.e12887
Kuate GCG, Fotsin HB. On the nonlinear dynamics of a cardiac electrical conduction system model: theoretical and experimental study. Phys Scr. 2022;97:045205. Available from: https://doi.org/10.1088/1402-4896/ac5855
Savi MA. Chaos and order in biomedical rhythms. J Braz Soc Mech Sci Eng. 2005;27(2):157-169. Available from: https://doi.org/10.1590/S1678-58782005000200008
Kuate GCG, Mabekou Takam JS, Ngagoum FX, Fotsin HB. Multiple time-scales dynamics of a cardiac pacemaker model with application to heart rhythm modeling: theoretical study and FPGA implementation. Int J Bifurcat Chaos. 2022;32(7):2250106. Available from: https://doi.org/10.1142/S021812742250106
Britin SN, Britina MA, Vlasenko RY. Cardiac conduction system: a generalized electrical model. Biomed Eng. 2021;55:41-45. Available from: https://doi.org/10.1007/s10527-021-10067-1
van der Schouw YT, van der Graaf Y, Steyerberg EW, Eijkemans MJC, Banga JD. Age at menopause as a risk factor for cardiovascular mortality. Lancet. 1996;347:714-718. Available from: https://doi.org/10.1016/S0140-6736(96)90075-6
Venkat Narayan KM, Thompson TJ, Boyle JP, Beckles GLA, Engelgau MM, Vinicor F, et al. The use of population attributable risk to estimate the impact of prevention and early detection of type 2 diabetes on population-wide mortality risk in US males. Health Care Manag Sci. 1999;2:223-237. Available from: https://doi.org/10.1023/A:1019048114376
Cheffer A, Savi MA, Pereira TL, de Paula AS. Heart rhythm analysis using a nonlinear dynamics perspective. Appl Math Model. 2021;96:152-176. Available from: https://doi.org/10.1016/j.apm.2021.03.014
Cheffer A, Savi MA. Biochaos in cardiac rhythms. Eur Phys J Spec Top. 2022;231:833-845. Available from: https://doi.org/10.1140/epjs/s11734-021-00314-7
Fonkou RF, Kengne R, Wamba MD, Fotsing Kamgang HC, Talla PK. On the heart rhythm analysis using a nonlinear dynamics perspective: analytical study and electronic simulation. Phys Scr. 2024;99:055270. Available from: https://doi.org/10.1088/1402-4896/ad3d9c
Park DS, Fishman GI. The cardiac conduction system. Circulation. 2011;123(8):904-915. Available from: https://doi.org/10.1161/CIRCULATIONAHA.110.942284
Cheffer A, Ritto TG, Savi MA. Uncertainty analysis of heart dynamics using random matrix theory. Int J Non Linear Mech. 2021;129:103653. Available from: https://doi.org/10.1016/j.ijnonlinmec.2020.103653
Ryzhii E, Ryzhii M. Modeling of heartbeat dynamics with a system of coupled nonlinear oscillators. In: Proceedings of the International Conference on Biomedical Informatics and Technology. Berlin (Germany): Springer; 2013. p. 67-75. Available from: https://doi.org/10.1007/978-3-642-54121-6_6
Tung R, Boyle NG, Shivkumar K. Catheter ablation of ventricular tachycardia. Circulation. 2010;122:e389-e391. Available from: https://doi.org/10.1161/CIRCULATIONAHA.110.963371
Clyburn C, Sepe JJ, Habecker BA. What gets on the nerves of cardiac patients? Pathophysiological changes in cardiac innervation. J Physiol. 2022;600(3):451-461. Available from: https://doi.org/10.1113/JP281118
Yokokawa M, Kim HM, Good E, Crawford T, Chugh A, Pelosi F Jr, et al. Impact of QRS duration of frequent premature ventricular complexes on the development of cardiomyopathy. Heart Rhythm. 2012;9:1460-1464. Available from: https://doi.org/:10.1016/j.hrthm.2012.04.036
Viskin S, Ish-Shalom M, Koifman E, Rozovski U, Zeltser D, Glick A, et al. Ventricular flutter induced during electrophysiologic studies in patients with old myocardial infarction: clinical and electrophysiologic predictors, and prognostic significance. J Cardiovasc Electrophysiol. 2003;14(9):913-919. Available from: https://doi.org/10.1046/j.1540-8167.2003.03082.x
Loen V, Vos AM, van der Heyden M. The canine chronic atrioventricular block model in cardiovascular preclinical drug research. Br J Pharmacol. 2022;179:859-881. Available from: https://doi.org/10.1111/bph.15436
Kashou HA, Adedinsewo AD, Peter A. Subclinical atrial fibrillation: a silent threat with uncertain implications. Annu Rev Med. 2022;73:355-362. Available from: https://doi.org/10.1146/annurev-med-042420-105906
Van der Pol B, Van der Mark J. The heartbeat as a negative resistance oscillator, and an electrical model of the heart. Philos Mag. 1928;6(38):763-775. Available from: https://doi.org/10.1080/1478644110856465 .
Fonkou RF, Louodop P, Talla PK, Woafo P. Van der Pol equation with sinusoidal nonlinearity: dynamic behaviour and real-time control of a target trajectory. Phys Scr. 2021;96:125203. Available from: https://doi.org/10.1088/1402-4896/ac19cd
Fonkou RF, Louodop P, Talla PK, Woafo P. Dynamic behaviour of pacemaker models subjected to a blood pressure excitation simulator: a theoretical and experimental study by microcontroller. Braz J Phys. 2021;51:1448-1458. Available from: https://doi.org/10.1007/s13538-021-00967-8
Fonkou RF, Louodop P, Talla PK. Nonlinear oscillators with variable state damping and elastic coefficients. Pramana J Phys. 2021;95:210. Available from: https://doi.org/10.1007/s12043-021-02230-w
Fonkou RF, Louodop P, Talla PK, Woafo P. Analysis of the dynamics of new models of nonlinear systems with state variable damping and elastic coefficients. Heliyon. 2022;8:e10112. Available from: https://doi.org/10.1016/j.heliyon.2022.e10112
Fonkou RF, Kengne R, Fotsing Kamgang HC, Talla PK. Dynamical behavior analysis of the Van der Pol oscillator with sine nonlinearity subjected to non-sinusoidal periodic excitations by the bifurcation structures. Phys Scr. 2023;98:085014. Available from: https://doi.org/10.1088/1402-4896/ace8cf
FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane. Biophys J. 1961;1:445-466. Available from: https://doi.org/10.1016/S0006-3495(61)86902-6
Hodgkin AL, Huxley AF. A quantitative description of membrane current and its applications to conduction and excitation in nerve. J Physiol. 1952;117:500-544. Available from: https://doi.org/10.1113/jphysiol.1952.sp004764
Gois RFSM, Savi MA. An analysis of heart rhythm dynamics using a three-coupled oscillator model. Chaos Solitons Fractals. 2009;41:2553-2565. Available from: https://doi.org/10.1016/j.chaos.2008.09.040
Fonkou RF, Louodop P, Talla PK. Dynamic behaviour of the cardiac conduction system under external disturbances: simulation based on microcontroller technology. Phys Scr. 2022;97:025001. Available from: https://doi.org/10.1088/1402-4896/ac47ba
De Paula AS, Savi MA, Wiercigroch M, Pavlovskaia E. Bifurcation control of a parametric pendulum. Int J Bifurcat Chaos. 2012;22(5):1250111. Available from: https://doi.org/10.1142/S0218127412501118
Elayan H, Aloqaily M, Guizani M. Digital twin for intelligent context-aware IoT healthcare systems. IEEE Internet Things J. 2021;8(23):16749-16757. Available from: https://doi.org/10.1109/JIOT.2021.3051158
Surucu M, Isler Y, Perc M, Kara R. Convolutional neural networks predict the onset of paroxysmal atrial fibrillation: theory and applications. Chaos. 2021;31(11):113119. Available from: https://doi.org/10.1063/5.0069272
Wang R, Fan J, Li Y. Deep multi-scale fusion neural network for multi-class arrhythmia detection. IEEE J Biomed Health Inform. 2020;24(9):2461-2472. Available from: https://doi.org/10.1109/JBHI.2020.2981526
Fonkou RF, Savi MA. Heart rhythm analysis using nonlinear oscillators with Duffing-type connections. Fractal Fract. 2023;7:592. Available from: https://doi.org/10.3390/fractalfract7080592
Krstacic G, Krstacic A, Smalcelj A, Milicic D, Jembrek-Gostovic M. The chaos theory and nonlinear dynamics in heart rate variability analysis: does it work in short-time series in patients with coronary heart disease? Ann Noninvasive Electrocardiol. 2007;12:130-136. Available from: https://doi.org/10.1111/j.1542-474X.2007.00151.x
Ernst J, Bar-Joseph Z. STEM: a tool for the analysis of short time series gene expression data. BMC Bioinformatics. 2006;7:191. Available from: https://doi.org/10.1186/1471-2105-7-191
Tobón DP, Jayaraman S, Falk TH. Spectro-temporal electrocardiogram analysis for noise-robust heart rate and heart rate variability measurement. IEEE J Transl Eng Health Med. 2017;5:1-11. Available from: https://doi.org/10.1109/JTEHM.2017.27676
Mulpuru SK, Madhavan M, McLeod CJ, Cha YM, Friedman PA. Cardiac pacemakers: function, troubleshooting, and management. J Am Coll Cardiol. 2017;69(2):189-210. Available from: https://doi.org/10.1016/j.jacc.2016.10.061
Lima GS, Savi MA, Bessa WM. Intelligent control of cardiac rhythms using artificial neural networks. Nonlinear Dyn. 2023;111:11543-11557. Available from: https://doi.org/10.1007/s11071-023-08447-1
Garfinkel A, Weiss JN, Ditto WL, Spano ML. Chaos control of cardiac arrhythmias. Trends Cardiovasc Med. 1995;5(2):76-80. Available from: https://doi.org/10.1016/1050-1738(94)00083-2
Karar ME. Robust RBF neural network-based backstepping controller for implantable cardiac pacemakers. Int J Adapt Control Signal Process. 2018;32(7):1040-1051. Available from: https://doi.org/10.1002/acs.2884
Lounis F, Boukabou A, Soukkou A. Implementing high-order chaos control scheme for cardiac conduction model with pathological rhythms. Chaos Solitons Fractals. 2020;132:109581. Available from: https://doi.org/10.1016/j.chaos.2019.109581
Garfinkel A, Spano ML, Ditto WL, Weiss JN. Controlling cardiac chaos. Science. 1992;257(5074):1230-1235. Available from: https://doi.org/10.1126/science.1519060
Ferreira BB, De Paula AS, Savi MA. Chaos control applied to heart rhythm dynamics. Chaos Solitons Fractals. 2011;44(8):587-599. Available from: https://doi.org/10.1016/j.chaos.2011.05.009
Ferreira BB, Savi MA, De Paula AS. Chaos control applied to cardiac rhythms represented by ECG signals. Phys Scr. 2014;89(10):105203. Available from: https://doi.org/10.1088/0031-8949/89/10/105203
Quiroz-Juárez M, Jiménez-Ramírez O, Vázquez-Medina R, Breña-Medina V, Aragón JL, Barrio RA. Generation of ECG signals from a reaction-diffusion model spatially discretized. Sci Rep. 2019;9(1):1-10. Available from: https://doi.org/10.1038/s41598-019-55448-5
Khan A, Nigar U. Combination projective synchronization in fractional-order chaotic system with disturbance and uncertainty. Int J Appl Comput Math. 2020;6(4):1-22. Available from: https://doi.org/10.1007/s40819-020-00852-z
Gharesi N, Arefi MM, Khayatian A, Bahrami Z. Extended state observer-based control of heartbeat described by heterogeneous coupled oscillator model. Commun Nonlinear Sci Numer Simul. 2021;101:105884. Available from: https://doi.org/10.1016/j.cnsns.2021.105884
Elayan H, Aloqaily M, Guizani M. Digital twin for intelligent context-aware IoT healthcare systems. IEEE Internet Things J. 2021;8(23):16749-16757. Available from: https://doi.org/10.1109/JIOT.2021.3051158
Surucu M, Isler Y, Perc M, Kara R. Convolutional neural networks predict the onset of paroxysmal atrial fibrillation: theory and applications. Chaos. 2021;31(11):113119. Available from: https://doi.org/10.1063/5.0069272
Wang R, Fan J, Li Y. Deep multi-scale fusion neural network for multi-class arrhythmia detection. IEEE J Biomed Health Inform. 2020;24(9):2461-2472. Available from: https://doi.org/10.1109/JBHI.2020.2981526
Bessa WM, Brinkmann G, Duecker DA, Kreuzer E, Solowjow E. A biologically inspired framework for the intelligent control of mechatronic systems and its application to a micro diving agent. Math Probl Eng. 2018;2018:9648126. Available from: https://doi.org/10.1155/2018/9648126
Dos Santos JDB, Bessa WM. Intelligent control for accurate position tracking of electrohydraulic actuators. Electron Lett. 2019;55(2):78-80. Available from: https://doi.org/10.1049/el.2018.7218
Lima GS, Porto DR, de Oliveira AJ, Bessa WM. Intelligent control of a single-link flexible manipulator using sliding modes and artificial neural networks. Electron Lett. 2021;57(23):869-872. Available from: https://doi.org/10.1049/ell2.12300
Karar ME. Robust RBF neural network-based backstepping controller for implantable cardiac pacemakers. Int J Adapt Control Signal Process. 2018;32(7):1040-1051. Available from: https://doi.org/10.1002/acs.2884
Irisawa H, Brown HF, Giles W. Cardiac pacemaking in the sinoatrial node. Physiol Rev. 1993;73(1):197-227. Available from: https://doi.org/10.1152/physrev.1993.73.1.197
Anderson RH, Yanni J, Boyett MR, Chandler NJ, Dobrzynski H. The anatomy of the cardiac conduction system. Clin Anat. 2009;22(1):99-113. Available from: https://doi.org/10.1002/ca.20681
Severs NJ, Bruce AF, Dupont E, Rothery S. Remodelling of gap junctions and connexin expression in diseased myocardium. Cardiovasc Res. 2008;80(1):9-19. Available from: https://doi.org/10.1093/cvr/cvn133
Kleber AG, Rudy Y. Basic mechanisms of cardiac impulse propagation and associated arrhythmias. Physiol Rev. 2004;84(2):431-488. Available from: https://doi.org/10.1152/physrev.00025.2003
Grudzinski K, Zebrowski JJ. Modeling cardiac pacemakers with relaxation oscillators. Physica A. 2004;336:153-162. Available from: https://doi.org/10.1016/j.physa.2004.01.020
Cunningham WJ. A nonlinear differential-difference equation of growth. Proc Natl Acad Sci U S A. 1954;40(8):708-713. Available from: https://doi.org/10.1073/pnas.40.8.708
Zheng Z, Lin J, Hu Y, Zhou Q, Yi C. Dynamic unbalance identification and quantitative diagnosis of cardan shaft in high-speed train based on improved TQWT-RBFNN-NSGA-II method. Eng Fail Anal. 2022;136:106226. Available from: https://doi.org/10.1016/j.engfailanal.2022.106226
World Health Organization. Cardiovascular diseases (CVDs) [Internet]. Geneva: World Health Organization; 2020 [cited 2020 Dec 13]. Available from: https://www.who.int/news-room/fact-sheets/detail/cardiovascular-diseases-(cvds)
Kim YG, Choi YY, Han KD, Min K, Choi HY, Shim J, et al. Atrial fibrillation is associated with increased risk of lethal ventricular arrhythmias. Sci Rep. 2021;11:18111. Available from: https://doi.org/10.1038/s41598-021-97335-y
PhysioNet. PhysioNet Databases [Internet]. Cambridge (MA): PhysioNet; 2020 [cited 2020 Dec 10]. Available from: https://physionet.org/about/database/
Davies MJ, Pomerance A. Pathology of atrial fibrillation in man. Br Heart J. 1972;34(5):520-525. Available from: https://doi.org/10.1136/hrt.34.5.520
Diamant MJ, Andrade JG, Virani SA, Jhund PS, Petrie MC, Hawkins NM. Heart failure and atrial flutter: a systematic review of current knowledge and practices. ESC Heart Fail. 2021;8:4484-4496. Available from: https://doi.org/10.1002/ehf2.13526
Wiggers CJ. The mechanism and nature of ventricular fibrillation. Am Heart J. 1940;20(4):399-412. Available from: https://doi.org/10.1016/S0002-8703(40)90874-2
Bessa WM, De Paula AS, Savi MA. Sliding mode control with adaptive fuzzy dead-zone compensation for uncertain chaotic systems. Nonlinear Dyn. 2012;70(3):1989-2001. Available from: https://doi.org/10.1007/s11071-012-0591-z
Bessa WM, De Paula AS, Savi MA. Adaptive fuzzy sliding mode control of a chaotic pendulum with noisy signals. Z Angew Math Mech. 2014;94(3):256-263. Available from: https://doi.org/10.1002/zamm.201200214
Bessa WM, Kreuzer E, Lange J, Pick MA, Solowjow E. Design and adaptive depth control of a micro diving agent. IEEE Robot Autom Lett. 2017;2(4):1871-1877. Available from: https://doi.org/10.1109/LRA.2017.2714142
Bessa WM, Otto S, Kreuzer E, Seifried R. An adaptive fuzzy sliding mode controller for uncertain underactuated mechanical systems. J Vib Control. 2019;25(9):1521-1535. Available from: https://doi.org/10.1177/1077546319827393
Bessa WM, De Paula AS, Savi MA. Adaptive fuzzy sliding mode control of smart structures. Eur Phys J Spec Top. 2013;222(7):1541-1551. Available from: https://doi.org/10.1140/epjst/e2013-01943-7
Park J, Sandberg IW. Universal approximation using radial-basis-function networks. Neural Comput. 1991;3(2):246-257. Available from: https://doi.org/10.1162/neco.1991.3.2.246
Ioannou P, Fidan B. Adaptive Control Tutorial. Philadelphia (PA): Society for Industrial and Applied Mathematics (SIAM); 2006. Available from: https://books.google.co.in/books/about/Adaptive_Control_Tutorial.html?id=o7d0R6Zj2pMC&redir_esc=yences