The normal cardiac rhythm is the result of collective, synchronized action of a large number of cardiac oscillators which play a crucial role in the determination of the sinus rhythm. The physiological function of the cardiovascular system is under the control of the autonomic nervous system (ANS). The two limbs of the ANS, sympathetic and parasympathetic, are critical in determining the oscillations within the heart. The pumping effectiveness of the heart is controlled by the sympathetic and parasympathetic nerves, which abundantly supply the heart that act in opposing ways. However, the two divisions act together to regulate the activity of the internal organs as per the needs of the body at any particular time. The cardiac centers in the central nervous system exert an influence on the heart’s activity through sympathetic and parasympathetic nerves. This influence governs the rate of beat, the systolic contractile force and the velocity of atrioventricular conduction. The parasympathetic stimulation causes a decrease in heart rate whereas sympathetic stimulation increases it. The intrinsic cardiac nervous system is seen to play an active role in regulating cardiac function which consists of sympathetic and parasympathetic neurons and interconnecting local circuits. An appropriate mathematical model that describes the electrical activity and ion exchange in the sinoatrial node (SAN) is considered and the dynamical equations describing the behaviour of the chosen model are solved with the corresponding source code developed and implemented using Matlab.An Integrate and Fire Neuron (IFN) model is developed that mimics the role of ANS which acts as an external influence to the preferred SAN cell to in order to coax synchronization between the coupled cell pair. The influence of the suitable neuron model in effecting synchrony between the coupled SAN cell pair is demonstrated with the aid of simulation studies.
Mathematical models of nonlinear oscillators are used to describe a wide variety of physical and biological phenomena that exhibit self-sustained oscillatory behavior. When these oscillators are strongly driven by forces that are periodic in time, they often exhibit a remarkable ‘‘mode-locking’’ that synchronizes the nonlinear oscillations to the driving force. Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states and is characterized by their amplitude and their phase. Their interactions can result in a systematic process of synchronization which is the adjustment of rhythms of oscillating objects due to an interaction and is quite distinct from a simple stimulus response pattern. Oscillators respond to stimuli at some times in their cycle and may not respond at others. Many important physical, chemical and biological systems are composed of coupled nonlinear oscillators. The Van der Pol equation has been used to model a number of biological processes such as the heartbeat, circadian rhythms, biochemical oscillators, and pacemaker neurons. Two such resistively coupled Van der Pol oscillators are analyzed and the phenomenon of synchronization between the states of the coupled oscillators is explored. Several control techniques to achieve synchronization are designed, implemented and performance evaluation carried out by simulation using MATLAB Software.
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