**Numerical Simulations of Dynamics Behaviour of the Action Potential of the Human Heart's Conduction System**

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http://dx.doi.org/10.5772/63017

#### **Abstract**

A proposed model consisting of two coupled van der Pol models is considered as a description of the heart action potential. A system of ordinary differential equations is used to recreate pathological behaviour in the conducting system of the heart such as Wolff-Parkinson-White (WPW) syndrome and the most common tachycardia: atrioventricular nodal reentrant tachycardia (AVNRT). Part of the population has abnormal accessory pathways: fast and slow. These pathways in the atrioventricu‐ lar node (AV node) are anatomical and functional excipients of supraventricular tachycardia. However, the appearance of two pathways in the AV node may be an excipient of arrhythmia—the WPW syndrome. The difference in the conduction time between these pathways is the most important factor. This is the reason to intro‐ duce three types of couplings and delay to our system in order to reproduce different types of the AVNRT. In our research, the result of introducing the feedback loops and couplings entails the creation of waves which can correspond to the re-entry waves which occur in the AVNRT. Our main aim is to study solutions of the equations of the system and to take into consideration the influence of feedback and delays which occur in the pathological modes. The proposed models made it possible to reproduce the most important physiological properties of the discussed patholo‐ gies. Since the model is phenomenological, the results are accurate as far as a simple model can describe the potential found in one of the more complex oscillators found in biology.

**Keywords:** van der Pol model, ordinary differential equations, delay, feedback, couplings, action potential, WPW syndrome, AVNRT, numerical analysis

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