Genesis of Ectopic Waves: Role of Coupling, Automaticity, and Heterogeneity

Abstract

Many arrhythmias are believed to be triggered by ectopic sources arising from the border of the ischemic tissue. However, the development of ectopic activity from individual sources to a larger mass of cardiac tissue remains poorly understood. To address this critical issue, we used monolayers of neonatal rat cardiomyocytes to create conditions that promoted progression of ectopic activity from single cells to the network that consisted of hundreds of cells. To explain complex spatiotemporal patterns observed in these experiments we introduced a new theoretical framework. The framework's main feature is a parameter space diagram, which uses cell automaticity and coupling as two coordinates. The diagram allows one to depict network behavior, quantitatively address the heterogeneity factor, and evaluate transitions between different regimes. The well-organized wave trains were observed at moderate and high cell coupling values and network heterogeneity was found to be qualitatively unimportant for these regimes. In contrast, at lower values of coupling, spontaneous ectopic activity led to the appearance of fragmented ectopic waves. For these regimes, network heterogeneity played an essential role. The ectopic waves occasionally gave rise to spiral activity in two different regions within the parameter space via two distinct mechanisms. Together, our results suggest that localized ectopic waves represent an essential step in the progression of ectopic activity. These studies add to the understanding of initiation and progression of arrhythmias and can be applied to other phenomena that deal with assemblies of coupled oscillators.

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

“…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.…”

Interaction between spiral and paced waves in cardiac tissue

“…This system has reduced structural complexity compared with the heart per se, which is an advantage when the goal is an understanding of the fundamental properties of wave propagation in cardiac tissue. It has provided a basis for many successful studies of wave propagation at the cellular level (19,30,35), generation of steadily rotating single and multiplearmed spiral waves (8,15), creation of controlled inhomogeneities and simulated defibrillation shocks (18), and propagation disturbances caused by local ischemia-reperfusion injury (6,33).…”

Genetically engineered cardiac pacemaker: Stem cells transfected with HCN2 gene and myocytes—A model

“…The period decreases and becomes normal when N,n continue increasing. It is the same homoclinic bifurcation [24] that describes the transition from oscillatory to excitable but quiescent behavior when expression level of I K1 is increased.…”

“…This indicates the change from oscillatory to excitable but quiescent behavior occurs through a homoclinic bifurcation [24], [14]). Cell pair model A "cell pair", consisting of a myocyte and a stem cell coupled together is described by the following set of equations : …”