چكيده به لاتين
Abstract:
Analysis of chaotic behaviors in heart cells as a dynamical system, can give us useful information about dynamical diseases and ultimately physiological diseases. By indicating the parameters’ ranges of the model which lead to abnormal behaviors in the normal system, one can find suitable health cares and medical actions to reduce or eliminate these kind of behaviors.
Abnormal oscillations of ventricular cell action potential can lead to cardiac arrhythmias. Early afterdepolarizations (EADs) is one kind of these oscillations that have been widely studied in the field of cardiac arrhythmias diagnosis and therapies.
Nowadays although ventricular cell models have been developed, yet dynamical mechanisms of EADs remain unknown that need more researches.
In this paper, using phase plane analysis of a minimal model of ventricular cell, we show that EADs areoccurredas a result of Hopf and homoclinicbifurcations in ventricular cell.
To analyze the ventricular cell model which has nonlinear dynamics, we studied the bifuecation diagram of the intended parameter and presented the intransitive conditions for occurance of hopf bifurcation via mathematical analysises. Then we study the probability of EAD occurance in the model which is one of the neccessary conditions of supercritical hopf bifurcation.
Wealsoshow that during a cardiac cycle, by injecting an external current in the case of EAD existence, there will be evidences of chaos which will be proved by calculating the lyapunov exponents and correlation dimension.
This result provides a distinct explanation for the EAD behavior of thecardiac cells and also explains EADs dynamics in accordance with experiment results.
Keywords: early afterdepolarizations, bifurcation, dynamical diseases, chaos.
