Stochastic Models of the Slow/Fast Type of Atrioventricular Nodal Reentrant Tachycardia and Tachycardia with Conduction Aberration
References
- Brugada, J., Katritsis, D.G. and Arbelo, E. (2019). Guidelines of the European Society of Cardiology regarding diagnostics and treatment of patients with supraventricular tachycardia, Kardiologia Polska (Polish Heart Journal) 2(1): 1–74, (in Polish).
- Di Francesco, D. and Noble, D. (1985). A model of cardiac electrical activity incorporating ionic pumps and concentration changes, Philosophical Transactions of the Royal Society of London B 307(1): 353–398, DOI: 10.1098/rstb.1985.0001.
- Dieci, L., Li, W. and Zhou, H. (2016). A new model for realistic random perturbations of stochastic oscillators, Journal of Differential Equations 261(4): 2502–2527, DOI: 10.1016/j.jde.2016.05.005.
- Downing, K.F., Simeone, R.H., Oster, M.F. and Farr, S.L. (2022). Critical illness among patients hospitalized with acute COVID-19 with and without congenital heart defects, Circulation 145: 1182–1184.
- Gamilov, T.M., Liang, F.Y. and Simakov, S.S. (2019). Mathematical modeling of the coronary circulation during cardiac pacing and tachycardia, Lobachevskii Journal of Mathematics 40(1): 448–458, DOI: 10.1134/S1995080219040073.
- Ghorbanian, P., Ramakrishian, S.,Whitman, A. and Ashrafiuom, H. (2015). A phenomenological model of EEG based on the dynamics of a stochastic Duffing–van der Pol oscillator network, Biomedical Signal Processing and Control 15(1): 1–10, DOI: 10.1016/j.bspc.2014.08.013.
- Grudziński, K. (2007). Modeling of the Electrical Activity of the Heart’s Conduction System, PhD thesis, Warsaw University of Technology, Warsaw, (in Polish).
- Henggui, Z., Zhang, P., Aslanidi, O.V., Noble, D. and Boyett, M.R. (2009). Mathematical models of the electrical action potential of Purkinje fibre cells, Philosophical Transactions of the Royal Society A 367(1): 2225–2255, DOI:10.1098/rsta.2008.0283.
- Hodgkin, A. and Huxley, A. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve, Journal Physiology 117(4): 500–544, DOI: 10.1113/jphysiol.1952.sp004764.
- Jackowska-Zduniak, B. and Foryś, U. (2016). Mathematical model of the atrioventricular nodal double response tachycardia and double-fire pathology, Mathematical Biosciences and Engineering 13(6): 1143–1158, DOI: 10.3934/mbe.2016035.
- Jackowska-Zduniak, B. and Foryś, U. (2018). Mathematical model of two types of atrioventricular nodal reentrant tachycardia: Slow/fast and slow/slow, in J. Awrejcewicz (Ed.), Dynamical Systems in Theoretical Perspective. DSTA 2017, Springer, Cham, pp. 169–182.
- Kaneko, Y., Nakajima, T., Iizuka, T. and Tamura, S. (2020). Atypical slow-slow atrioventricular nodal reentrant tachycardia with use of a superior slow pathway, International Heart Journal 61(2): 380–383, DOI: 10.1536/ihj.19-082.
- Katrisis, D. and Josephson, M. (2016). Electrophysiological features and therapy of atrioventricular nodal reentrant tachycardia, Arrhythmia and Electrophysiology Review 5(2): 130–135, DOI: 10.15420/aer.2016.18.2.
- Konturek, S. (2001). The Human Physiology: The Cardiovascular System, Jagiellonian University Press, Cracow.
- Kussela, T. (2004). Stochastic heart-rate model can reveal pathologic cardiac dynamics, Physical Review E 69(3): 031916–031923, DOI: 10.1103/PhysRevE.69.031916.
- Leung, H. (1998). Stochastic Hopf bifurcation in a biased van der Pol model, Physica A: Statistical Mechanics and Its Applications 254(2): 146–155.
- Li, Y., Wu, Z. and Wang, F. (2019a). Stochastic p-bifurcation in a generalized van der Pol oscillator with fractional delayed feedback excited by combined Gaussian white noise excitations, Journal of Low Frequency Noise, Vibration and Active Control 40(1): 91–103.
- Li, Y., Wu, Z. and Zhang, G. (2019b). Stochastic p-bifurcation in a bistable van der Pol oscillator with fractional time-delay feedback under Gaussian white noise excitation, Advances in Difference Equations 2019: 448, DOI:10.1186/s13662-019-2356-1.
- Małaczyńska-Rajpold, K., Błaszczyk, K. and Koźluk, E. (2012). Atrioventricular nodal reentrant tachycardia, Polski Przegla˛d Kardiologiczny 14(3): 196–203, (in Polish).
- Mani, B.C. and Pavri, B. (2014). Dual atrioventricular nodal pathways physiology: A review of relevant anatomy, electrophysiology, and electrocardiographic manifestations, Indian Pacing Electrophysical Journal 14(1): 12–25, DOI: 10.1016/s0972-6292(16)30711-2.
- Mobitz, W. (1924). Uber die unvollständige störung der erregungs-überleitung zwischen vorhof und kammer des menschlichen herzens, Zeitschrift für die gesamte experimentelle Medizin 41(1): 380–383, DOI: 10.1536/ihj.19-082.
- Nagumo, J., Arimoto, S. and Yoshizawa, S. (1962). An active pulse transmission line simulating nerve axon, Proceedings of the IRE 50(1): 2061–2070.
- Postnov, D., Han, S.K. and Kook, H. (1999). Synchronization of diffusively coupled oscillators near the homoclinic bifurcation, Physical Review E 60(3): 2799–2807.
- Qu, Z., Hu, G., Garfinkel, A. and Weiss, J.N. (2014). Nonlinear and stochastic dynamics in the heart, Physics Reports 543(2): 61–162, DOI:10.1016/j.physrep.2014.05.002.
- Shenghong, L., Quanxin, Z. and Zudi, L. (2018). Probability density and stochastic stability for the coupled van der Pol oscillator system, Cogent Mathematics and Statistics 5(1): 1431092, DOI: 10.1080/23311835.2018.1431092.
- Tusscher, K.H.W.J. and Panfilov, A.V. (2006). Alternans and spiral breakup in a human ventricular tissue model, American Journal of Physiology-Heart and Circulatory Physiology 291(1): H1088–H1100.
- van der Pol, B. (1926). On “relaxation-oscillations”, Philosophical Magazine and Journal of Science 7(2): 978–992.
- van der Pol, B. and van der Mark, J. (1928). The heartbeat considered as a relaxation oscillation, and an electrical model of the heart, Philosophical Magazine and Journal of Science 6(38): 763–775, DOI: 10.1080/14786441108564652.
- Zduniak, B., Bodnar, M. and Foryś, U. (2014). A modified van der Pol equation with delay in a description of the heart action, International Journal of Applied Mathematics and Computer Science 24(4): 853–863, DOI: 10.2478/amcs-2014-0063.
- Zheng, J., Skufca, J.D. and Bollt, E.M. (2013). Heart rate variability as determinism with jump stochastic parameters, Mathematical Biosciences and Engineering 10(4): 1253–64, DOI: 10.3934/mbe.2013.10.1253.
Language: English
Page range: 429 - 440
Submitted on: Sep 29, 2021
Accepted on: May 30, 2022
Published on: Oct 8, 2022
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year
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© 2022 Beata Jackowska-Zduniak, published by University of Zielona Góra
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