Narrow Results

We propose a fairly general model of active media by considering of the interaction between pacemakers via their phase response curves. This model describes a network of pulse oscillators coupled by their response to the internal depolarization of mutual stimulations.

First, a macroscopic level corresponding to an arbitrary large number of oscillatory elements coupled globally is considered. As a specific and important case of the proposed model, the bidirectional interaction of two cardiac nodes is described. This case is generalized by means of an additional pacemaker, which can be expounded as an external stimulator. The behavior of such a system is analyzed. Second, the microscopic level corresponding to the representation of cardiac nodes by two-dimensional lattices of pulse oscillators coupled via the nearest neighbors is described. The model is a universal one in the sense that on its basis one can easily construct discrete distributed media of active elements, which interact via phase response curves.

Connexins are specialized ionic channels that control the action potential propagation between cardiac myocytes. In this paper, we study the connexin dynamics in a one-dimensional model of cardiac tissue. We show that the connexin dynamics may lead to a spatial organization of the gap junction conductance. In the numerical simulations presented in this paper we have found two different regimes for the spatial organization of the conductances: (a) a spatially uniform conductance; (b) a spatially complex pattern of local values of high and low conductances. In addition, we have observed that, locally, the two final states are limit cycles with a period equal to the period associated with the external excitation of the tissue strand. The conductance dispersion usually takes place on a very large time scale, i.e. thousands of heart beats, and on a very short spatial scale. Due to its simplicity, the one-dimensional setting allows a detailed study of the emerging structure and in particular very long simulations. We have studied the transition between the two aforementioned states as a function of the gap junction conductance characteristics. Furthermore, we have studied the effect of initially added noises on the outcome of the system. Finally, using spatial autocorrelation functions we have characterized the spatial dispersion in conductance values.

The nonlinear dynamical properties of the recently proposed $T\pm 𝜖$ feedback control for suppressing cardiac alternans is investigated in detail for the discrete cardiac restitution map model and the continuous Luo–Rudy I ionic model. It is shown that cardiac alternans, induced by fast pacing, can be dramatically reduced by small changes of fixed magnitude ($𝜖$) under feedback control when $𝜖$ exceeds a critical threshold. Remarkably, the suppression is achieved by utilizing the induced chaotic dynamics. Detailed information on the nature and mechanism of the control, and properties of the attractors are analyzed and discussed in the light of nonlinear dynamics.

Current models of cardiac dynamics include a time-varying spring generating the pumping power. They ignore therefore the chemo-mechanical process of transduction. We present a new model, based on the bond graph notion of a two-port capacity which represents this transduction and is compatible with the dynamic spring idea. In addition to showing the power of bond graphs, our model suggests that the transduction is reversible and length-dependent.

The Allan (ADEV) and Hadamard (HDEV) deviations are mathematical tools developed in the field of time and frequency metrology to define quantitatively the frequency instabilities of an oscillator; which consist of any unwanted departure from its nominal frequency value over a specified time interval. We use both deviations to analyze the stability of the heart interbeat rate for healthy subjects and patients with congestive heart failure (CHF) during wake and sleep periods. We find that the ADEV and HDEV profiles for the subjects in the CHF group exhibit remarkably different trends between wake and sleep periods, namely, larger dispersion between the results for each member of the group while the results for the healthy subjects show some uniformity across the members of the group. Moreover, we observe that the stability for both groups degrades for low scales during the sleep phase, being more significant for the CHF group. Both ADEV and HDEV statistics reveal that healthy data can be described by more uniform deviation values along several scales, particularly for the wake period, whereas CHF data shows important variations.