An index for evaluating distance of a healthy heart from Sino-Atrial blocking arrhythmia
ABSTRACT
In this paper, an index for evaluating Distance of a healthy heart from Sino-Atrial Blocking Arrhythmia (SABA) is presented. After definition of the main pacemakers' model of heart, Sino-Atrial (SA) and Atrio-Ventricular nodes (AV), the boundary of synchronization, which demonstrates the boundary of blocking arrhythmia, is obtained using perturbation method. In order to estimate of healthy heart characteristics, a parameter estimator is introduced. The distance from SABA is calculated using Lagrange method and Kohn-Tucker conditions. In addition, the maximum admissible decrease in the coupling intensity and the maximum admissible increase in the discrepancy between the natural frequencies of two pacemakers are determined in order to maintain the synchronization between the two pacemakers.
In this paper, an index for evaluating Distance of a healthy heart from Sino-Atrial Blocking Arrhythmia (SABA) is presented. After definition of the main pacemakers' model of heart, Sino-Atrial (SA) and Atrio-Ventricular nodes (AV), the boundary of synchronization, which demonstrates the boundary of blocking arrhythmia, is obtained using perturbation method. In order to estimate of healthy heart characteristics, a parameter estimator is introduced. The distance from SABA is calculated using Lagrange method and Kohn-Tucker conditions. In addition, the maximum admissible decrease in the coupling intensity and the maximum admissible increase in the discrepancy between the natural frequencies of two pacemakers are determined in order to maintain the synchronization between the two pacemakers.
Cite this paper
nullGholizade-Narm, H. , Khademi, M. , Azemi, A. and Karimi-Ghartemani, M. (2010) An index for evaluating distance of a healthy heart from Sino-Atrial blocking arrhythmia. Journal of Biomedical Science and Engineering, 3, 308-316. doi: 10.4236/jbise.2010.33042.
nullGholizade-Narm, H. , Khademi, M. , Azemi, A. and Karimi-Ghartemani, M. (2010) An index for evaluating distance of a healthy heart from Sino-Atrial blocking arrhythmia. Journal of Biomedical Science and Engineering, 3, 308-316. doi: 10.4236/jbise.2010.33042.
References
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[1] World Helth Organization (WHO), Internet Available: www.who.int. [2] El-Sherif, N., Denes, P., Katz, R., Capone, R., Brent , L., Carlson, M. and Reynolds, R. (1995) Definition of the best prediction criteria of the time domain signal-averaged electrocardiogram for serious arrhythmic events in the post infraction period. Journal of American Collection Cardiology, 25(4), 908-914. [3] Tsagalou, E. P., Anastasiou-Nava, M. I., Karagounis, L. A., Alexopoulos, G. P., Batziou, C., Toumanidis, S., Papadaki, E. and Nanas, J. N. (2002) Dispersion of QT and QRS in patients with severe congestive heart failure: Relation to cardiac and sudden death mortality, Hellenic Jornal of Cardiology, 43, 209-215. [4] Thong, T., McNames, J., Aboy, M. and Goldstein, B. (2003) Paroxysmal atrial fibrillation prediction using isolated premature atrial events and paroxysmal atrial tachycardia. Proceedings of IEEE International Conference on Biomedical Engineering, EMBC, 163-166. [5] Thong, T., McNames, J., Aboy, M. and Goldstein, B. (2004) Prediction of paroxysmal atrial fibrillation by analysis of atrial premature complexes. IEEE Transactions On Biomedical Engineering, 51(4), 561-569. [6] Owis, I., Abou-Zied, H. and Youssef, M. (2002) Study of Features Based on Nonlinear Dynamical Modeling in ECG Arrhythmia Detection and Classification. IEEE Transactions On Biomedical Engineering, 49(7), 733-736. [7] Abbas, R., Aziz, W. and Arif, M. (2004) Prediction of ventricular Tachyarrhythmia in Electrocardiograph Signal Using Neuro-wavelet Approach. National Conference on Emerging Technologies, 82-87. [8] Van der Pol, B. and Van der mark, J. (1927) Frequency demultiplication. Nature, 120, 363-364. [9] Van der Pol, B. and Van der mark, J. (1928) The Heartbeat considered as a relaxation oscillation and electrical model of heart. Phil. Mag. Supll., 6, 763-775. [10] Grudzinsky, K. and Zebrowski, J. (2004) Modeling cardiac pacemakers with relaxation oscillators. Physica A: Statistical Mechanics and its Applications, 153-162. [11] Sato, S., Doi, S. and Nomura, T. (1994) Bonhoffer-van der pol oscillator model of the Sino-Atrial node: A possible mechanism of heart rate regulation. Method of Information in Medicin, 116-119. [12] Fitzhugh, R. (1961) Impulses and physiological in theoretical models of nerve membranes. Biophysical Journal, 1, 445-466. [13] FitzHugh, R. (1969) Mathematical models of excitation and propagation in nerve. In: Schwan H.P. Ed., Biological Engineering, McGraw Hill, New York. [14] Nagumo, J., Arimoto, S. and Yoshizawa, S. (1962) An active pulse transmission line simulating nerve axon. Proceedings of the IRE, 50, 2061-2070. [15] Hodgkin, A. L., Huxley, A. F. and Katz, B. (1952) Measurement of current-voltage relations in the membrane of the giant axon of Loligo, The Journal of physiology, 116, 424. [16] Beeler, G.W. and Reuter, H. (1977) Reconstruction of the action potential of ventricular myocardial fibres. The Journal of physiology, 268, 177-210. [17] Lou, C.H. and Rudy, Y. (1994) A dynamic model of the cardiac ventricular action potential I. Circulation Research, 74, 1071-1096. [18] Pikovsky, A., Rosenblum, M. and Kurths, J. (2002) Synchronization: A universal concept nonlinear science, Cambridge University Press. [19] Santos, A. M., Lopes, S. R. and Viana, R. L. (2004) Rhythm synchronization and chaotic modulation of couplead van der pol oscillatiors in a model for the heartbeat. Physica A, 338, 335-355. [20] Rand R. H. (2004) Lecture notes in nonlinear vibrations. 45 version, The Internet-First University Press, Ithaca. http://dspace.library.cornell.edu/handle/1813/79. [21] Rompala, K., Rand, R. and Howland, H. (2007) Dynamics of three coupled van der Pol oscillators with application to circadian rhythms. Communications in Nonlinear Science and Numerical Simulation, 12, 794-803. [22] Nayfeh, A. H. (1973) Perturbation Methods, John Wiley & Sons Ltd., Chichester. [23] Grudzinski, K., Zebrowski, J.J. and Baranowski, R. (2006) Model of the sino-atrial and atrio-ventricular nodes of the conduction system of the human heart. Biomedical Technology, 51, 210-214. [24] Gauthier, J. P., Hammouri, H. and Othman, S. (1992) A simple observer for nonlinear systems – applications to bioreactors. IEEE Transactions on Automatic Control. 37(6), 875-880. [25] Besancon, G., Zhang, Q. and Hammouri, H., (2002) High-Gain observer based state and parameter estimation in nonlinear systems. International Federation of Automatic Control.