Modified Modeling of the Heart by Applying Nonlinear Oscillators and Designing Proper Control Signal

Siroos Nazari, Aghileh Heydari, Javad Khaligh

Department of Mathematics, Payame Noor University, Tehran, Iran.

DOI: 10.4236/am.2013.47134                

Abstract

Rhythmic phenomena are one of the most striking manifestations of dynamic behavior in biological systems. Understanding the mechanisms of biological rhythms, is crucial for understanding the dynamic of life. Each type of dynamic behaviors may be related to the performance of both normal physiology and pathological. Conductive system of the heart can be stimulated to action as a network of elements and these elements show the oscillatory behavior then can be modeled as nonlinear oscillators. This paper provides the mathematical model of the heart rhythm by considering different states of Vanderpol nonlinear oscillators. Proposed oscillator model is designed in order to reproduce time series of action potential of natural pacemakers cardiac, such as SA or AV nodes. So model of heart is presented by a system of differential equations and to be considered chaotic or nonchaotic for different parameters of the model by using of the 0-1 test. Finally, the model is synchronized by applying an appropriate control signal, if it is needed.

Keywords

Heart Oscillators; Vander Pol Equations; Biological Systems; Action Potential; Control; Synchronization

Conflicts of Interest

The authors declare no conflicts of interest.

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