Synchronization of SA and AV Node Oscillators Using PSO Optimized RBF-based Controllers and Comparison with Adaptive Control

AUTHOR(S):

Abdolhossein Ayoubi, Mohammad Sadegh Sanie, Moharram Kazemi, Saman Sobh Heydar

TITLE

Synchronization of SA and AV Node Oscillators Using PSO Optimized RBF-based Controllers and Comparison with Adaptive Control

PDF

ABSTRACT

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., Doi S., and Nomura T., "Bonhoeffer-van der Pol Oscillator Model of the SinoAtrial Node: A Possible Mechanism of Heart Rate Regulation", Method of Information in Medicine, March 1994;Vol. 33, No. 1, pp. 116-119.

[23] El-sherif N., Denes P., Katz R., Capone R., Brent L., Carlson M., Reynolds R., "Definition of the Best Prediction Criteria of the Time Domain Signal- Averaged Electrocardiogram for Serious Arrhythmic Events in the Postinfarction Period", Journal of American College of Cardiology , March 1995;Vol. 25, No. 4, pp. 908-14.

[24] Kaplan B.Z., Gabay I., Sarafian G.and Sarafian D. "Biological application of filtered van der pol oscillator", Journal of the Franklin Institute, 2007.

[25] Zh. Hao, M. Xi-Kui and L. Wei-Zeng, “Synchronization of chaotic systems with parametric uncertainty using active sliding mode control”, Chaos, Solutions and Fractals , Vol. 21, No.5 , pp. 1249– 1257, September 2004.

[26] Thong T., McNames J., Aboy M. and Goldstein B., "Prediction of Paroxysmal Atrial Fibrillation by Analysis of Atrial Premature Complexes", IEEE Transaction on biomedical Engineering, April 2004;Vol. 51, No. 4, pp. 561-569.

[27] Govindan R. B., Narayanan K., and Gopinathan M. S., "On the evidence of deterministic chaos in ECG: Surrogate and predictability analysis", Journal of Chaos , June 1998;Vol. 8, No. 2, pp. 495-502.

[28] Jungi L., and Parlitz U., "synchronization using dynamic coupling", Physical review. E, Statistical, nonlinear, and soft matter physics, November 2001;Vol. 64, No.2, pp.055204-1-055204-4.

[29] Hoyer D., Hoyer O.and Zwiener U., "A new approach to uncover dynamic phase coordination and synchronization", IEEE Transaction on biomedical Engineering, January 2000;Vol.47, No. 1, pp. 68-73.

[30] Thong T., McNames J., Aboy M. and Goldstein B., "Paroxysmal Atrial Fibrillation Prediction Using Isolated Premature Atrial Events and Paroxysmal Atrial Tachycardia", proceedings of Annual International Conference of the IEEE Engineering in Medicine and Biology, September 2003;pp. 163-166.

[31] Jitao S., “Global synchronization criteria with channel time-delay for chaotic time-delay system”, Chaos, Solitons and Fractals, August 2004;Vol. 21, No.1, pp. 967–975.

[32] http://D. Noble; noble.physiol.ox.ac.uk/people/Dnoble

[33] Thong T. and Goldstein B., "Prediction of Tachyarrhythmia Episodes", Joint Meeting of the IEEE EMBS and the BMES, October 2002;Houston, Texas.

[34] Slotine J.J.E. and Li W., Applied nonlinear control. Prentice-Hall International Editions, Prentice-Hall International Edition, 1991.

[ 35] Wang Y., Guan Z.H. and Wen X.. "Adaptive synchronization for Chen chaotic system with fully unknown parameters", Chaos solution and fractals, March 2004;Vol. 19, No.4, pp. 899-903.

[36] C.Y. Su and Y. Stepanenko, “ of a class of nonlinear systems with fuzzy logic,” IEEE Trans. Fuzzy Syst., vol.2, pp.285-294, 1994.

[ 37] Sivan S. A. and Akselrod S., "Simulation of atrial activity by a phase response curve based model of two-dimensional pacemaker cells array: the transition from a normal activation to atrial fibrillation” ", Journal of Biological Cybernetics, February 1999;Vol. 80,No. 2, pp. 41-153.

[38] Sivan S. A. and Akselrod S., "A single pacemaker cell model based on the phase response curve", Journal of Biological Cybernetics, July 1998;Vol. 79, No. 1, pp. 67-76.

[39] Hartley T.T., “The duffing double scroll”, Proceedings of the American Control Conference, Pittsburgh, June 1989;pp. 419–423.

[40] Yoo B.and Ham W., “Adaptive fuzzy sliding mode control of nonlinear system,” IEEE Trans. Fuzzy Syst., 1998; vol.6, pp.315- 321.

[41] Lee H., Kim E., Kang H.J.and Park M., “A new sliding-mode control with fuzzy boundary layer,” Fuzzy Sets and Systems, May, 2001;vol. 120, no 1, pp. 135-143.

[42] Andrievskii B. R. and Fradkov A. L., “Control of Chaos: Methods and Applications. I. Methods”, Automation and Remote Control, May 2003;Vol. 64, No. 5, pp. 673-713.

[43] Wang J., Rad A.B., and Chan P.T., “Indirect adaptive fuzzy sliding mode control: Part I-Fuzzy Switching,” Fuzzy Sets and Systems, August, 2001; vol. 122, no 1, pp. 21-30.

[44] Kim S.W.and Lee J.J., “Design of a fuzzy controller with fuzzy sliding surface,” Fuzzy Sets and Systems, May, 1995;vol. 71, no 3, pp. 359-367. 45] Boccaletti S., Grebogi C., Lai Y. C., Mancini H., and Maza D., “The control of chaos: theory and applications”, Physics Reports, 2000;Vol.329, pp. 103- 197.

[46] Pecora L.and Caroll T., “Synchronization in Chaotic Systems”, Physics Review Letters, 1990;Vol. 64, No.8, pp. 821-824.

[47] Wang L.X., “Stable adaptive fuzzy control of nonlinear systems,” IEEE Trans. Fuzzy Syst., 1993; vol.1, pp.146-155.

[48] Abbas R., Aziz W.and Arif M., " Prediction of Ventricular Tachyarrhythmia in Electrocardiogram Signal using Neuro-Wavelet Approach", National Conference on Emerging Technologies, 2004; pp. 82- 87.

[49] Berstecher R.G., Palm R. and Unbehauen H.D., “An adaptive fuzzy sliding-mode controller,” IEEE Trans. Industrial Electron., 2001; vol. 48, pp. 18-31.

[50] Sivan S. A. and Akselrod S., "A pacemaker cell pair model based on the phase response curve", Journal of Biological Cybernetics, July 1998; Vol. 79,No. 1, pp. 77-86.

Cite this paper

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