Chaos analysis and synchronization control of coronary artery systems. (English) Zbl 1341.93008

Wang, Cheng-Chi; Yau, Her-Terng

Abstr. Appl. Anal. 2013, Article ID 209718, 11 p. (2013).

Summary: The present study uses the differential transformation method to solve the governing equations of the coronary artery system and then analyzes the dynamic behavior of the system by means of phase portraits, power spectra, bifurcation diagrams, and Poincaré maps. Also, a master-slave control system is proposed to suppress the nonlinear chaotic behavior of the coronary artery system. The results show that the dynamic behavior of the coronary artery system is significantly dependent on the magnitude of the vibrational amplitude. Specifically, the motion changes from \(T\)-periodic to \(2T\)-periodic, then from \(4T\)-periodic to \(8T\)-periodic, and finally to chaotic motion with windows of periodic motion as the vibrational amplitude is increased from 0.3 to 0.6 and from 4.5 to 5.9. In addition, it is shown that the proposed control scheme enables the coronary artery system to be synchronized to any state asymptotically such that the risk of cardiopathy is reduced.

MSC:

93A30	Mathematical modelling of systems (MSC2010)
92C50	Medical applications (general)
34H10	Chaos control for problems involving ordinary differential equations
93A14	Decentralized systems
93C10	Nonlinear systems in control theory

Keywords:

coronary artery systems; nonlinear chaotic behaviot; synchronization control

References:

[1]	Jadhav, S. M.; Nalbalwar, S. L.; Ghatol, A. A., ECG arrhythmia classification using modular neural network model, Proceedings of the IEEE EMBS Conference on Biomedical Engineering and Sciences (IECBES ’10) · doi:10.1109/IECBES.2010.5742200
[2]	Coast, D. A.; Stern, R. M.; Cano, G. G.; Briller, S. A., An approach to cardiac arrhythmia analysis using hidden Markov models, IEEE Transactions on Biomedical Engineering, 37, 9, 826-836 (1990) · doi:10.1109/10.58593
[3]	Blondel, C.; Malandain, G.; Vaillant, R.; Ayache, N., Reconstruction of coronary arteries from a single rotational X-ray projection sequence, IEEE Transactions on Medical Imaging, 25, 5, 653-663 (2006) · doi:10.1109/TMI.2006.873224
[4]	Gao, D.; Madden, M.; Chambers, D.; Lyons, G., Bayesian ANN classifier for ECG arrhythmia diagnostic system: A Comparison Study, Proceedings of the International Joint Conference on Neural Networks (IJCNN ’05) · doi:10.1109/IJCNN.2005.1556275
[5]	Khalil, I.; Sufi, F., CardioGrid: ECG analysis on demand to detect cardiovascular abnormalities, Proceedings of the 9th International Conference on Information Technology and Applications in Biomedicine (ITAB ’09) · doi:10.1109/ITAB.2009.5394436
[6]	Sun, Z.; Ding, W., Analysis of coronary arterial dynamics from X-ray angiographic sequences, Proceedings of the International Symposium on Computational Intelligence and Design (ISCID ’09) · doi:10.1109/ISCID.2009.57
[7]	Puentes, J.; Roux, C.; Garreau, M.; Coatrieux, J. L., Dynamic feature extraction of coronary artery motion using DSA image sequences, IEEE Transactions on Medical Imaging, 17, 6, 857-871 (1998) · doi:10.1109/42.746619
[8]	Guan, X. P.; Fan, Z. P.; Chen, C. L., Chaotic Control and Its Application in Secret Communication (2002), Beijing, China: National Defense Industry Press, Beijing, China
[9]	Gong, C. Y.; Li, Y. M.; Sun, X. H., Backstepping control of synchronization for biomathematical model of muscular blood vessel, Journal of Applied Sciences, 24, 604-607 (2006)
[10]	Wang, C.-C.; Jang, M.-J.; Yeh, Y.-L., Bifurcation and nonlinear dynamic analysis of a flexible rotor supported by relative short gas journal bearings, Chaos, Solitons and Fractals, 32, 2, 566-582 (2007) · doi:10.1016/j.chaos.2005.10.098
[11]	Wang, C.-C., Theoretical and nonlinear behavior analysis of a flexible rotor supported by a relative short herringbone-grooved gas journal-bearing system, Physica D, 237, 18, 2282-2295 (2008) · Zbl 1142.70328 · doi:10.1016/j.physd.2008.02.004
[12]	Wang, C.-C., Application of a hybrid method to the nonlinear dynamic analysis of a flexible rotor supported by a spherical gas-lubricated bearing system, Nonlinear Analysis: Theory, Methods & Applications, 70, 5, 2035-2053 (2009) · Zbl 1180.76017 · doi:10.1016/j.na.2008.02.108
[13]	Bianca, C.; Rondoni, L., The nonequilibrium Ehrenfest gas: a chaotic model with flat obstacles?, Chaos, 19, 1 (2009) · Zbl 1311.76118 · doi:10.1063/1.3085954
[14]	Jepps, O. G.; Bianca, C.; Rondoni, L., Onset of diffusive behavior in confined transport systems, Chaos, 18, 1 (2008) · doi:10.1063/1.2888759
[15]	Yau, H.-T.; Shieh, C.-S., Chaos synchronization using fuzzy logic controller, Nonlinear Analysis: Real World Applications, 9, 4, 1800-1810 (2008) · Zbl 1154.34334 · doi:10.1016/j.nonrwa.2007.05.009