Primary: 37N25, 92C30; Secondary: 70K20, 70K50.

Export file:

Format

• RIS(for EndNote,Reference Manager,ProCite)
• BibTex
• Text

Content

• Citation Only
• Citation and Abstract

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
2. Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw

## Abstract    Related pages

A proposed model consisting of two coupled models (Hodgkin-Huxley and Yanagihara-Noma-Irisawa model) is considered as a description of the heart's action potential. System of ordinary differential equations is used to recreate pathological behaviour in the conducting heart's system such as double fire and the most common tachycardia: atrioventricular nodal reentrant tachycardia (AVNRT). Part of the population has an abnormal accessory pathways: fast and slow (Fujiki, 2008). These pathways in the atrioventricular node (AV node) are anatomical and functional contributions of supraventricular tachycardia. However, the appearance of two pathways in the AV node may be a contribution of arrhythmia, which is caused by coexistent conduction by two pathways (called double fire). The difference in the conduction time between these pathways is the most important factor. This is the reason to introduce three types of couplings and delay to our system in order to reproduce various types of the AVNRT. In our research, introducing the feedback loops and couplings entails the creation of waves which can correspond to the re-entry waves occurring in the AVNRT. Our main aim is to study solutions of the given equations and take into consideration the influence of feedback and delays which occur in these pathological modes. We also present stability analysis for both components, that is Hodgkin-Huxley and Yanagihara-Noma-Irisawa models, as well as for the final double-fire model.
Figure/Table
Supplementary
Article Metrics

Citation: Beata Jackowska-Zduniak, Urszula Foryś. Mathematical model of the atrioventricular nodal double response tachycardia and double-fire pathology. Mathematical Biosciences and Engineering, 2016, 13(6): 1143-1158. doi: 10.3934/mbe.2016035

References

• 1. U.o. Dayton, Editor, 2009.
• 2. Journal of Arrhythmia, 31 (2015), 328-330.
• 3. Models and Methods in Neurophysics, Proc Les Houches Summer School, 80 (2005), 17-19, 21-72.
• 4. Medycyna Praktyczna, 6 (2004) (in Polish).
• 5. Springer, Tokyo, 2010.
• 6. Rev Esp Cardiol., 66 (2013), 145-156.
• 7. J. Biological Systems, 12 (2004), 45-60.
• 8. Cardiac pacing and electrophysiology, 1991.
• 9. Europace, 10 (2008), 928-987.
• 10. The Journal of Physiology, 117 (1952).
• 11. Kardiologia Polska, 67 (2009), 77-84.
• 12. Indian Pacing Electrophysiol. J., 14 (2014), 44-48.
• 13. Europace, 15 (2013), 1231-1240.
• 14. $2^{nd}$ edition, Springer, New York, 2009.
• 15. Wydawnictwo Uniwersytetu Jagielońskiego, 2001, (in Polish).
• 16. Polski Przegląd Kardiologiczny, 14 (2012), 196-203.
• 17. Front. Cell. Neurosci., 9 (2015), 1-21.
• 18. J Clin Monit Comput., 27 (2013), 481-498.
• 19. J. Am. Coll. Cardiol., 29 (1997).
• 20. Chaos, Solitons and Fractals, 31 (2007), 247-256.
• 21. Eur J Cardiol., 2 (1975), 459-466.
• 22. Japanese Journal of Physiology, 30 (1980), 841-857.
• 23. Int. J. Appl. Math. Comput. Sci., 24 (2014), 853-863.
• 24. Computational and Mathematical Methods in Medicine, (2014), Art. ID 761907, 9 pp.