Endogenous driving and synchronization in cardiac and uterine virtual tissues: bifurcations and local coupling

Abstract

Cardiac and uterine muscle cells and tissue can be either autorhythmic or excitable. These behaviours exchange stability at bifurcations produced by changes in parameters, which if spatially localized can produce an ectopic pacemaking focus. The effects of these parameters on cell dynamics have been identified and quantified using continuation algorithms and by numerical solutions of virtual cells. The ability of a compact pacemaker to drive the surrounding excitable tissues depends on both the size of the pacemaker and the strength of electrotonic coupling between cells within, between, and outside the pacemaking region.We investigate an ectopic pacemaker surrounded by normal excitable tissue. Cell-cell coupling is simulated by the diffusion coefficient for voltage. For uniformly coupled tissues, the behaviour of the hybrid tissue can take one of the three forms: (i) the surrounding tissue electrotonically suppresses the pacemaker; (ii) depressed rate oscillatory activity in the pacemaker but no propagation; and (iii) pacemaker driving propagations into the excitable region.However, real tissues are heterogeneous with spatial changes in cell-cell coupling. In the gravid uterus during early pregnancy, cells are weakly coupled, with the cell-cell coupling increasing during late pregnancy, allowing synchronous contractions during labour. These effects are investigated for a caricature uterine tissue by allowing both excitability and diffusion coefficient to vary stochastically with space, and for cardiac tissues by spatial gradients in the diffusion coefficient.

The location of pacemakers in the uteri of pregnant guinea pigs and rats

“…Recently, several simulation studies have suggested that there need not be a site or a specific location for pacemaking in the pregnant uterus (1,32,36), in contrast to the presence of specific pacemakers in the heart (33,34) or in the stomach (23). In these simulations, mathematical models describe the interactions in heterogeneous populations of active and nonactive cells.…”

“…In these simulations, mathematical models describe the interactions in heterogeneous populations of active and nonactive cells. By varying the degree of coupling and the composition of the populations, various types of patterns of propagations could be mimicked, ranging from clusters, to local, and to global synchronization (1,32,36,37), including the appearance of ectopic and re-entrant or spiral activities (29). Such models could also explain the various types of local, circular, or major contractions described in this study in the guinea pig uterus and suggest that the structure of the tissue, in concert with the topographical expression of functional gap junctions, can determine the origin and pathway of excitation.…”

Spatial heterogeneity enhances and modulates excitability in a mathematical model of the myometrium

“…We use a mathematical model to investigate how the global excitation of the myometrium is affected by the spatial heterogeneity of the system. Benson et al [20] analysed a heterogeneously coupled model which is based on FitzHughNagumo dynamics, but this was a continuum-model in which the coupling between cells was not represented explicitly. Spatial heterogeneity was found to assist the transition between quiescence and excitability.…”

Alterations in gap junction connexin43/connexin45 ratio mediate a transition from quiescence to excitation in a mathematical model of the myometrium

“…Baigent et al [44,45] and Donnell et al [46] considered a two-cell model coupled by a dynamic gap junction which resides in one of three states, giving insights into cell connections on a local scale, emphasizing channel kinetics and ionic flows in great detail. By contrast, the present model focuses on overall excitability of the network as a function of spatial heterogeneity of the functional properties of the gap junctions, rather than on the propagation of activity wavefronts and the spatial patterning of such fronts; these aspects have been considered elsewhere [4,32,47,48]. Whereas we considered the global activation threshold in an electrotonically coupled smooth muscle syncytium, a general argument regarding the all-or-none character of synaptically coupled networks, such as the central nervous system, was advanced by Ashby et al [49].…”

“…However, parameters can be chosen such that cells are autorhythmic [13], that is, the cells continually oscillate through the excitation-relaxation cycle without any external stimulus. FitzHugh-Nagumo is a simplification of the Hodgkin-Huxley model for spiking neurons [28,29] and, as such, is often used in modelling excitable systems such as contractions of cardiac myocytes [30][31][32]. Each node in the network is considered to be an excitationrelaxation oscillator with a fast ('excitation') state variable v that corresponds to the transmembrane potential and a slow ('recovery') variable w that corresponds to gating kinetics which repolarize the excited cell.…”