Effects of Calcium-Channel Noise on Dynamics of Excitation-Contraction Coupling in Paced Cardiac Cells

Jiying Ma,Dongmei Xiao

doi:10.1155/2013/687472

Abstract

We study a simple discrete model with the impact of calcium-channel noise on the beat-to-beat dynamics of cardiac cells. The effects of the noise are assessed by bifurcation analysis and power spectrum analysis, respectively. It is shown that this model can undergo period-doubling bifurcation and Hopf bifurcation if there are not random perturbations. Under random perturbations, the period-doubling bifurcations of the model can be observed, and the invariant curve from Hopf bifurcation is perturbed to an annulus on the plane and then becomes a totally disordered and randomly scattered region. By the power spectrum analysis, we find that the existence of high-frequency peak in the power spectra links to the period-doubling orbits, while the existence of low-frequency peak corresponds to quasiperiodic orbit.

Highlights

The genesis of cardiac arrhythmias in the whole heart scale has been linked to dynamical instabilities at the cellular level [1,2,3,4,5,6]
It is well established that the contraction of cardiac cells is triggered by a considerable increase in intracellular calcium concentration and the interplay between membrane voltage and calcium cycling forms the basis of EC coupling [6,7,8]
We study the effects of calciumchannel noise on dynamical behavior of EC coupling in paced

Summary

Introduction

The genesis of cardiac arrhythmias in the whole heart scale has been linked to dynamical instabilities at the cellular level [1,2,3,4,5,6]. To study the mechanisms of the coupling, a range of experimental and theoretical studies has been conducted concerning the scale from cells to tissues (see [1, 3, 6] for a recent review) Most of these works focused on the dynamical instabilities in cardiac cells, such as the alternations and quasiperiodic oscillations in action potential duration (APD) and calcium transient [4, 5, 7,8,9,10,11,12,13,14,15,16]. To study the effects of random fluctuations, Sato et al [17] added Gaussian random variables to APD restitution in their iterated map analysis Such stochastic factors have been correlated with the beat-to-beat repolarization variability in cardiac cells [20]. As the noise intensity increases, the prominent peaks will gradually disappear, and power spectra tend to distribute more evenly in all frequencies

Model Formulation

Dynamics of the Model

Power Spectrum Analysis

Discussion