PDFAbstract: This paper studies the synchronization of SA and AV Node Oscillators using PSO optimized RBF-based controllers systems. High levels of control activities may excite unmodeled dynamics of a system. The objective is to reach a trade-off between tracking performance and parametric uncertainty. Two methods are proposed to synchronize general forms of Van Der Pol (VDP) Model and their performance. These methods use the radial basis function (RBF)- based neural controllers for this purpose. The first method uses a standard RBF neural controller. Particle swarm optimization (PSO) algorithm is used to derive and optimize RBF controller parameters. In the second method, an error integral term is added to the equations of RBF neural network. The coefficients of error integral component and parameters of RBF neural network are also derived and optimized via PSO algorithm. Simulation results show the effectiveness and superiority of proposed methods in both performances in comparison with adaptive controller
Keywords: Synchronization, Van der Pol Model, SA and AV Node Oscillators, RBF, PSO Algorithm, Adaptive Conrol, Optimization Algorithm, system Dynamics, Simulation Results, Controller Parameters, impulses. REFERENCES [1] Grudzinski K. and Zebrowski J., Modeling cardiac pacemakers with relaxation oscillators, Journal of Physica A: Statistical and Theoretical Physics, May 2004; Vol.336, No.1, pp. 153-162. [2] Tsagalou E. P., Anastasiou-Nana M. I., Karagounis L. A., Alexopoulos G. P., Batziou C., Toumanidis S., Papadaki E., Nanas J. N. and Stamatelopoulos S. F., Dispersion of QT and QRS in Patients with Severe Congestive Heart Failure: Relation to Cardiac and Sudden Death Mortality, The Hellenic Journal of Cardiology, Vol. 43, 2002; pp. 209-215. [3] Sivan S. A. and Akselrod S., A Phase Response Curve Based Model: Effect of Vagal and Sympathetic Stimulation and Interaction on Pacemaker cell, Journal of Theoretical Biology, June 1998;Vol. 192, No.4, pp. 567-579. [4] Vibe K., Vesin J. M. and Pruvot E., Chaos and Heart Rate Variability, International Conference of IEEE-EMBS and CMBEC, Physiological Systems/Modeling and Identification, 1997 pp.1481- 1482. [5] Gebber G. L., Zhong S., and Barman S. M., Synchronization of cardiac-related discharges of sympathetic nerves with inputs from widely separated spinal segments, American Journal of Physiology, June 1995; Vol. 268, No.6, pp. 1472-1483. [6] Gebber G. L., Zhong S., Barman S. M., and Orer H. S., "Coordination of cardiac-related discharges of sympathetic nerves with different targets", American Journal of Physiology, August 1994; Vol. 167, No.2, pp. 400-407. [7] Demir S., Clark J. and Giles W., "Effects of Hyperpolarizing Pulses on a Cardiac Pacemaker Cell", IEEE Transaction on Computer in Cardiology, 1997; Vol. 24, pp. 713-716. [8] Sundes J., Lines G.and Tveito A., “Efficient solution of ordinary differential equation modeling electrical activity in cardiac cells” Mathematical Biosciences, August 2002;Vol. 72, pp. 55-72. [9] Luo C. H. and Rudy Y., “A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction”, Circulation Research, Vol. 68, No. 6, pp.1501-1562, June 1991. [10] Timo H. Ma¨kikallio, MD, Heikki V. Huikuri, MD, FACC, Anne Ma¨kikallio, MD,Leif B. Sourander, MD, Raul D. Mitrani, MD, FACC, Agustin Castellanos, MD, FACC,Robert J. Myerburg, MD, FACC," Prediction of Sudden Cardiac Death by Fractal Analysis of Heart Rate Variability in Elderly Subjects", Journal of the American College of Cardiology , 2001;Vol. 37, No. 5. [11] Schafer K., Rosenblum M. G., Kurths J., and Abel H. H., "Heartbeat synchronized with ventilation", Nature, March 1998;Vol. 392, pp. 239-240. [12] Bernardo D. D., "A Model of two Nonlinear Coupled Oscillators for the Study of Heart Beat Dynamics", International Journal of Bifurcation and Chaos, 1998; Vol. 8, No. 10, pp. 1975-1985. 13] Dragoi V., and Grosu I., "Synchronization of locally coupled neural oscillators", Neural Processing Letters, June 1998;Vol. 7, No.3, pp. 199-210. [14] Volkov E. I., "Limit cycles arising in a chain of inhibitory coupled identical relaxation oscillators near the self-oscillation threshold", Radiophysics and Quantum Electronics, June 2005;Vol. 48, No. 3, pp. 212-221. [15] Verheijck E., Wilders R., Joyner R., Golod D., Kumar R., Jomgsma H., Bouman L. and Ginneken A., Pacemaker Synchronization of Electrically Coupled Rabbit Sinoatrial Node Cell, Journal of General physiology, January 1998;Vol. 111, No.1, pp. 95-112. [16] Y. Yu and S. Zhang, “The synchronization of linearly bidirectional coupled chaotic systems”, Chaos, Solitons and Fractals, October 2004;Vol. 22, No. 1, pp. 189–197. [17] Zhang Y.and Sun J., “Some simple global synchronization criterions for coupled time-varying chaotic systems”, Chaos, Solitons and Fractals, January 2004; Vol. 19, No.1, pp. 93–98. [18] Buric N., and Todorovic D, "Dynamic of Fitzhugh-Nagumo excitable systems with delayed coupling", Physical review. E, Statistical, nonlinear, and soft matter physics, June 2003;Vol. 67, No.2, pp. 066222-1-066222-13 . [19] Gebber G. L., Zhong S., Zhou S. Y., and Barman S. M., "Nonlinear dynamics of the frequency locking of baroreceptor and sympathetic rhythms", American Journal of Physiology., December 1997;Vol. 273, No.6, pp. 1932-1945 . [20] Van der pol & Van der mark, "The heartbeat considered as a relaxation oscillation and an electrical model of the heart", Philosophical Magazine 6, 1928; pp 763-775. [21] Humg J.Y., Gao W.and Hung J.C., “Variable structure control: A survey,” IEEE Trans. Industrial Electron., 1993; vol. 40,pp. 2-22. [22] Sato S.,
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Abdolhossein Ayoubi, Mohammad Sadegh Sanie, Moharram Kazemi, Saman Sobh Heydar. (2017) Synchronization of SA and AV Node Oscillators Using PSO Optimized RBF-based Controllers and Comparison with Adaptive Control. International Journal of Biology and Biomedicine, 2 , 98-108
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