Abstract
Based on the improved FitzHugh–Nagumo myocardial model driven by a constant external current, the effect of temperature fluctuation in a network of electrically coupled myocardial cells are investigated through analytical and numerical computations. Through the technique of multiple scale expansion, we successfully reduced the complex nonlinear system of equations to a more tractable and solvable nonlinear amplitude equation on which the analysis of linear stability is performed. Interestingly from this analysis, a plot of critical amplitude of action potential versus wave number revealed the growth rate of modulational instability (MI) is an increasing function of the thermoelectric couplings; T^{(1)} and T^{(2)}, under fixed conditions of nonlinear electrical couplings. In order to verify our analytical predictions through the study the long-time evolution of the modulated cardiac impulses, numerical computation is finally carried out. Numerical experiment revealed the existence of localized coherent structures with some recognized features of synchronization. Through the mechanism of MI, changes in thermoelectrical couplings promote wave localization and mode transition in electrical activities in the cell lattice. Results could provide new insights in understanding the underlying mechanism of the manifestation of sudden heart disorder subjected to heavily temperature fluctuation.
Highlights
Based on the improved FitzHugh–Nagumo myocardial model driven by a constant external current, the effect of temperature fluctuation in a network of electrically coupled myocardial cells are investigated through analytical and numerical computations
By setting the thermoelectric couplings at T(1) = 1.4 and T(2) = 2.4, we present the patterns of electrical activities of cardiac tissue in Figs. 3, 4 and 5 for an array of 400 cells
Modulational instability (MI) has been explored in the frame work of the improved myocardial cell model to investigate the effect of temperature fluctuation on electrical activity
Summary
Equation (4) obtained above is a system of nonlinear differential equations with no exact analytical solution. There exist several techniques of converting these equations into more integrable form[25,29,30]. We make use of the reductive perturbation method popularly known as the multiple scale expansion method. The discrete multiple scale expansion is an interesting technique developed by Leon and M anna[27,28]. It’s an asymptotic analysis of a perturbation series, based on the existence of different scales, with the amplitude and the carrier wave both kept discrete. This expansion enables the deduction of a more manipulable equation from the model. As a result of nonlinearity present in the media, which naturally exists and affects real systems, the natural frequency deviates, with actual frequency ωfgrreaoqnuudpewnvecalyvoecint0yu . maIfnbǫder=thqe,0b ,gertchoouempfriveneqgluoωecni=tcyyd ωis0pr+eerdǫsuiocanens2dtCoqgt=h=eq(n0∂∂a2+2tωqu)ǫr aV l.gWfr+ehqǫeur2eeCngciys[2]
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