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Mathematical model of the atrioventricular nodal double response tachycardia and double-fire pathology
1. | Faculty of Applied Informatics and Mathematics, Warsaw University of Life Sciences, Nowoursynowska 159, 02-776 Warsaw, Poland |
2. | Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw |
References:
[1] |
D. A. Aabby, Comparatitative Study of Numerical Methods for the Hodgkin-Huxley model of Nerve Cell Action Potentials, U.o. Dayton, Editor, 2009. |
[2] |
M. A. Akbarzadeh, A. F. Fazelifar and N. B. Bafruee, A case of dual atrioventricular nodal nonreentrant tachycardia: An unusual cause of tachycardia-induced cardiomyopathy, Journal of Arrhythmia, 31 (2015), 328-330.
doi: 10.1016/j.joa.2015.04.008. |
[3] |
A. Borisyuk and J. Rinzel, Understanding neuronal dynamics by geometrical dissection of minimal models, Models and Methods in Neurophysics, Proc Les Houches Summer School, 80 (2005), 17-19, 21-72.
doi: 10.1016/S0924-8099(05)80008-3. |
[4] |
B. Dąbrowska and P. Gajewski, Postępowanie u chorych z nadkomorowymi zaburzeniami rytmu Wytyczne American College of Cardiology, American Heart Association European Society of Cardiology, Medycyna Praktyczna, 6 (2004) (in Polish). |
[5] |
S. Doi, J. Inoue, Z. Pan and K. Tsumoto, Computational Electrophysiology, Springer, Tokyo, 2010.
doi: 10.1007/978-4-431-53862-2. |
[6] |
R. Evertz, F. Merschon, A. Berruezo and L. Mont, Dual ventricular response: Another road to supraventricular tachycardia in dual atrioventricular nodal physiology, Rev Esp Cardiol., 66 (2013), 145-156.
doi: 10.1016/j.rec.2012.05.016. |
[7] |
U. Foryś, Biological delay systems and the Mikhailov Criterion of stability, J. Biological Systems, 12 (2004), 45-60. |
[8] |
R. A. Freedman and J. W. Mason, Sustained ventricular tachycardia, clinical aspects, Cardiac pacing and electrophysiology, 1991. |
[9] |
A. Fujiki et al., Junctional rhythm associated with ventriculoatrial block during slow pathway ablation in atypical atrioventricular nodal re-entrant tachycardia, Europace, 10 (2008), 928-987. |
[10] |
A. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology, 117 (1952). |
[11] |
M. Jastrzębski and P. Kukla, Tachycardia caused by a double fire- simultaneous double atrioventricular nodal conduction: a rare or underdiagnosed arrhythmia. Spectrum of electrocardiographic pictures in three patients, Kardiologia Polska, 67 (2009), 77-84. |
[12] |
A. Karnik, K. Hematpour, A. Bhatt and M. Mazzini, Dual AV nodal nonreentrant tachycardia resulting in inappropriate icd therapy in a patient with cardiac sarcoidosis, Indian Pacing Electrophysiol. J., 14 (2014), 44-48.
doi: 10.1016/S0972-6292(16)30715-X. |
[13] |
D. G. Katritsis and M. E. Josephson, Classification of electrophysiological types of atrioventricular nodal re-entrant tachycardia: A reappraisal, Europace, 15 (2013), 1231-1240.
doi: 10.1093/europace/eut100. |
[14] |
J. Keener and J. Sneyd, Mathematical Physiology. Systems Physiology, $2^{nd}$ edition, Springer, New York, 2009.
doi: 10.1007/978-0-387-75847-3. |
[15] |
S. Konturek, Fizjologia człowieka. Układ krążenia, Wydawnictwo Uniwersytetu Jagielońskiego, 2001, (in Polish). |
[16] |
K. Małaczyńska and K. Błaszczyk, Atrioventricular nodal reentrant tachycardia, Polski Przegląd Kardiologiczny, 14 (2012), 196-203. |
[17] |
S. Masoli, S. Solinas and E. D'Angelo, Action potential processing in a detailed Purkinje cell model reveals a critical role for axonal compartmentalization, Front. Cell. Neurosci., 9 (2015), 1-21.
doi: 10.3389/fncel.2015.00047. |
[18] |
P. Podziemski and J. J. .Zebrowski, A simple model of the right atrium of the human heart with the sinoatrial and atrioventricular nodes included, J Clin Monit Comput., 27 (2013), 481-498.
doi: 10.1007/s10877-013-9429-6. |
[19] |
W. G. Stevenson, Exploring postinforction reentrant ventrivular tachycardia with entertainment mapping, J. Am. Coll. Cardiol., 29 (1997). |
[20] |
J. Wang, L. Chen and X. Fei, Analysis and control of the bifurcation Hodgkin-Huxley model, Chaos, Solitons and Fractals, 31 (2007), 247-256.
doi: 10.1016/j.chaos.2005.09.060. |
[21] |
D. Wu, P. Denes, R. Dhingra and R. Pietras, New manifestation of dual AV nodal pathways, Eur J Cardiol., 2 (1975), 459-466. |
[22] |
K. Yanagihara, A. Noma and H. Irisawa, Reconstruction of sino-atrial node pacemaker potential based on the voltage clamp experiments, Japanese Journal of Physiology, 30 (1980), 841-857.
doi: 10.2170/jjphysiol.30.841. |
[23] |
B. Zduniak, M. Bodnar and U. Foryś, A modified van der Pol equation with delay in a description of the heart action, Int. J. Appl. Math. Comput. Sci., 24 (2014), 853-863.
doi: 10.2478/amcs-2014-0063. |
[24] |
Y. Zhang, K. Wang, Y. Yuan, D. Sui and H. Zhang, Effects of Maximal Sodium and Potassium Conductance on the Stability of Hodgkin-Huxley model, Computational and Mathematical Methods in Medicine, (2014), Art. ID 761907, 9 pp.
doi: 10.1155/2014/761907. |
show all references
References:
[1] |
D. A. Aabby, Comparatitative Study of Numerical Methods for the Hodgkin-Huxley model of Nerve Cell Action Potentials, U.o. Dayton, Editor, 2009. |
[2] |
M. A. Akbarzadeh, A. F. Fazelifar and N. B. Bafruee, A case of dual atrioventricular nodal nonreentrant tachycardia: An unusual cause of tachycardia-induced cardiomyopathy, Journal of Arrhythmia, 31 (2015), 328-330.
doi: 10.1016/j.joa.2015.04.008. |
[3] |
A. Borisyuk and J. Rinzel, Understanding neuronal dynamics by geometrical dissection of minimal models, Models and Methods in Neurophysics, Proc Les Houches Summer School, 80 (2005), 17-19, 21-72.
doi: 10.1016/S0924-8099(05)80008-3. |
[4] |
B. Dąbrowska and P. Gajewski, Postępowanie u chorych z nadkomorowymi zaburzeniami rytmu Wytyczne American College of Cardiology, American Heart Association European Society of Cardiology, Medycyna Praktyczna, 6 (2004) (in Polish). |
[5] |
S. Doi, J. Inoue, Z. Pan and K. Tsumoto, Computational Electrophysiology, Springer, Tokyo, 2010.
doi: 10.1007/978-4-431-53862-2. |
[6] |
R. Evertz, F. Merschon, A. Berruezo and L. Mont, Dual ventricular response: Another road to supraventricular tachycardia in dual atrioventricular nodal physiology, Rev Esp Cardiol., 66 (2013), 145-156.
doi: 10.1016/j.rec.2012.05.016. |
[7] |
U. Foryś, Biological delay systems and the Mikhailov Criterion of stability, J. Biological Systems, 12 (2004), 45-60. |
[8] |
R. A. Freedman and J. W. Mason, Sustained ventricular tachycardia, clinical aspects, Cardiac pacing and electrophysiology, 1991. |
[9] |
A. Fujiki et al., Junctional rhythm associated with ventriculoatrial block during slow pathway ablation in atypical atrioventricular nodal re-entrant tachycardia, Europace, 10 (2008), 928-987. |
[10] |
A. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology, 117 (1952). |
[11] |
M. Jastrzębski and P. Kukla, Tachycardia caused by a double fire- simultaneous double atrioventricular nodal conduction: a rare or underdiagnosed arrhythmia. Spectrum of electrocardiographic pictures in three patients, Kardiologia Polska, 67 (2009), 77-84. |
[12] |
A. Karnik, K. Hematpour, A. Bhatt and M. Mazzini, Dual AV nodal nonreentrant tachycardia resulting in inappropriate icd therapy in a patient with cardiac sarcoidosis, Indian Pacing Electrophysiol. J., 14 (2014), 44-48.
doi: 10.1016/S0972-6292(16)30715-X. |
[13] |
D. G. Katritsis and M. E. Josephson, Classification of electrophysiological types of atrioventricular nodal re-entrant tachycardia: A reappraisal, Europace, 15 (2013), 1231-1240.
doi: 10.1093/europace/eut100. |
[14] |
J. Keener and J. Sneyd, Mathematical Physiology. Systems Physiology, $2^{nd}$ edition, Springer, New York, 2009.
doi: 10.1007/978-0-387-75847-3. |
[15] |
S. Konturek, Fizjologia człowieka. Układ krążenia, Wydawnictwo Uniwersytetu Jagielońskiego, 2001, (in Polish). |
[16] |
K. Małaczyńska and K. Błaszczyk, Atrioventricular nodal reentrant tachycardia, Polski Przegląd Kardiologiczny, 14 (2012), 196-203. |
[17] |
S. Masoli, S. Solinas and E. D'Angelo, Action potential processing in a detailed Purkinje cell model reveals a critical role for axonal compartmentalization, Front. Cell. Neurosci., 9 (2015), 1-21.
doi: 10.3389/fncel.2015.00047. |
[18] |
P. Podziemski and J. J. .Zebrowski, A simple model of the right atrium of the human heart with the sinoatrial and atrioventricular nodes included, J Clin Monit Comput., 27 (2013), 481-498.
doi: 10.1007/s10877-013-9429-6. |
[19] |
W. G. Stevenson, Exploring postinforction reentrant ventrivular tachycardia with entertainment mapping, J. Am. Coll. Cardiol., 29 (1997). |
[20] |
J. Wang, L. Chen and X. Fei, Analysis and control of the bifurcation Hodgkin-Huxley model, Chaos, Solitons and Fractals, 31 (2007), 247-256.
doi: 10.1016/j.chaos.2005.09.060. |
[21] |
D. Wu, P. Denes, R. Dhingra and R. Pietras, New manifestation of dual AV nodal pathways, Eur J Cardiol., 2 (1975), 459-466. |
[22] |
K. Yanagihara, A. Noma and H. Irisawa, Reconstruction of sino-atrial node pacemaker potential based on the voltage clamp experiments, Japanese Journal of Physiology, 30 (1980), 841-857.
doi: 10.2170/jjphysiol.30.841. |
[23] |
B. Zduniak, M. Bodnar and U. Foryś, A modified van der Pol equation with delay in a description of the heart action, Int. J. Appl. Math. Comput. Sci., 24 (2014), 853-863.
doi: 10.2478/amcs-2014-0063. |
[24] |
Y. Zhang, K. Wang, Y. Yuan, D. Sui and H. Zhang, Effects of Maximal Sodium and Potassium Conductance on the Stability of Hodgkin-Huxley model, Computational and Mathematical Methods in Medicine, (2014), Art. ID 761907, 9 pp.
doi: 10.1155/2014/761907. |
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