Comparison between the role of discontinuities in cardiac conduction and in a one-dimensional hardware model

Abstract

In real electrophysiological experiments, irregularities in the extracellular excitation spread are believed to depend on cardiac tissue microstructure. An electronic hardware model was developed to analyze this dependence by placing some inhomogeneities (slow propagation areas) in the medium. The position of such inhomogeneities is correlated with abnormal delays and irregularities measured in signal propagation.

Continuous description of lattice discreteness effects in front propagation

“…The discreteness effects may modify severely the dynamics of the front propagation even in the framework of the simplest models (see the pioneering works of Ishimori & Munakata [14] and Peyrard & Kruskal [15]). The relevant physical contexts can be quite diverse, including hydrogen-bonded chains [16], calcium release waves in living cells [17][18][19], reaction fronts in chains of coupled chemical reactors [20][21][22], arrays of coupled diode resonators [23], semiconductor superlattices [24], discontinuous propagation of action potential in cardiac tissue [25][26][27], arrays of autocrine cells [28], superconductivity in Josephson junctions [29], nonlinear optics and waveguide arrays [30] and the dynamics of neuron chains [31] to mention a few. The dynamics of all these systems is mainly driven by their inherently discrete nature.…”

Nucleation from the Boundaries in Excitable Media

“…Chua's circuit is a nonlinear circuit [Madan, 1993;Chua, 1992] which works in an excitable state with the set of parameters shown in Table 1 [ Gómez-Gesteira et al, 1999;deCastro et al, 1998;deCastro et al, 1999]. Initially, all these circuits were adjusted to have the same initial stable state within the tolerances commercially allowed.…”

Propagation failure in discrete bistable reaction-diffusion systems: Theory and experiments

“…The flame of a candle, the nerve impulse, spiral waves in excitable chemical reagents as well as cell or animal populations dynamic, to cite but a few, are examples of nonlinear diffusion. Furthermore, as many reaction-diffusion systems of biological origin, for example in neuro [3,4] and cardio physiology [5,6], are intrinsically discrete, it has become clear that continuous reaction diffusion equations provide an inadequate description of the behavior of these systems, where the interplay between nonlinearity and spatial discreteness can lead to novel effects not present in the continuum models. Among these effects is the important phenomenon of wave propagation failure, shared by most diffusively coupled systems of excitable cells (there exist also particular cases of nonlinear diffusive lattices which do not exhibit this phenomenon [7,8]).…”

“…Among these effects is the important phenomenon of wave propagation failure, shared by most diffusively coupled systems of excitable cells (there exist also particular cases of nonlinear diffusive lattices which do not exhibit this phenomenon [7,8]). As propagation failure may lead, in the context of neuro and cardio physiology, to the breakdown of the systems with potentially fatal consequences, it has been the subject of numerous studies [5,6,[9][10][11][12][13][14]. In particular, it has been observed that there exists a nonzero critical value of the intercellular coupling strength under which wave fronts fail to propagate.…”