Mathematical model of the atrioventricular nodal double response tachycardia and double-fire pathology
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...
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| Language: | English |
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AIMS Press
2016-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016035 |
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| author | Beata Jackowska-Zduniak Urszula Foryś |
| author_facet | Beata Jackowska-Zduniak Urszula Foryś |
| author_sort | Beata Jackowska-Zduniak |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-90d3032f2f934326a465ceddb8221e8c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-90d3032f2f934326a465ceddb8221e8c2025-01-24T02:37:49ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-07-011361143115810.3934/mbe.2016035Mathematical model of the atrioventricular nodal double response tachycardia and double-fire pathologyBeata Jackowska-Zduniak0Urszula Foryś1Faculty of Applied Informatics and Mathematics, Warsaw University of Life Sciences, Nowoursynowska 159, 02-776 WarsawInstitute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 WarsawA 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.https://www.aimspress.com/article/doi/10.3934/mbe.2016035couplingsordinary differential equations with delayfeedbackavnrt.action potentialhodgkin-huxley modeldouble-fire pathology |
| spellingShingle | Beata Jackowska-Zduniak Urszula Foryś Mathematical model of the atrioventricular nodal double response tachycardia and double-fire pathology Mathematical Biosciences and Engineering couplings ordinary differential equations with delay feedback avnrt. action potential hodgkin-huxley model double-fire pathology |
| title | Mathematical model of the atrioventricular nodal double response tachycardia and double-fire pathology |
| title_full | Mathematical model of the atrioventricular nodal double response tachycardia and double-fire pathology |
| title_fullStr | Mathematical model of the atrioventricular nodal double response tachycardia and double-fire pathology |
| title_full_unstemmed | Mathematical model of the atrioventricular nodal double response tachycardia and double-fire pathology |
| title_short | Mathematical model of the atrioventricular nodal double response tachycardia and double-fire pathology |
| title_sort | mathematical model of the atrioventricular nodal double response tachycardia and double fire pathology |
| topic | couplings ordinary differential equations with delay feedback avnrt. action potential hodgkin-huxley model double-fire pathology |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016035 |
| work_keys_str_mv | AT beatajackowskazduniak mathematicalmodeloftheatrioventricularnodaldoubleresponsetachycardiaanddoublefirepathology AT urszulaforys mathematicalmodeloftheatrioventricularnodaldoubleresponsetachycardiaanddoublefirepathology |