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Cardiac Cell as a Multystable System: Response to Stimulation by the Pulse Sequences with Constant and Stochastic Periods

Keywords:

O. L. Anosov, O. R. Nikitin


The response of cardiac cell to stimulation by the pulse sequences with constant and stochastic periods was investigated using the numerical simulation based on the ionic cardiac cell model. In numerical experiments we have stimulated the cardiac cell by the pulse sequences with different periods and noise levels and have studied the time series of action potential duration (APD) with which the cell responded to stimuli. The simulations have demonstrated that in both stimulation modes the cardiac cell could reside in several different states during the same stimulation period, i.e. the cardiac cell is a multystable system. During the stimulation with a constant period the cell possessed two contiguous but different regions of bistability close to the 1:1 → 2:1 bifurcation: one with the pair of (1:1; 2:1) states and other with the pair of (1:1; 2:2) states. We have shown that in this stimulation mode the cause of the cell multystability is the coupling of its final state with its initial state before stimulation: during pulse sequence stimulations with one and the same period the cardiac cell, that at the beginning resided in a 1:1 steady state, retained the 1:1 state or turned to 2:1 state or to 2:2 state, depending on the initial APD of the cell response. On the obtained results we have estimated the basins of final states attraction for cardiac cell during periodic pulse stimulation in the region of the 1:1 → 2:1 bifurcation point. The investigation of the cardiac cell response to stimulation by the pulse sequences with stochastic periods has shown that the cell demonstrates multystability even in case of small noise in the stimulation periods. The kind and range of multystability regions as well as the residing probability of the cell in one or another state depends on the noise level and is different from the case of pulse stimulation with constant period. We have estimated the positions of the cell state regions and the dependences of the cell residing probability in different states on the noise level in the stimulation periods. The obtained results shed light on the features of bifurcation properties of the cardiac cell and can be used to design new electronic devices and systems of telemedicine for cardiology, including apparatuses for the problem of heart arrhythmias control.
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