Modeling of cardiac electrophysiological mechanisms: from action potential genesis to its propagation in myocardium.

The aim of the present paper is to describe the different attempts at modeling cardiac electrophysiological mechanisms, mainly at the membrane and cellular level, from action potential genesis to its propagation in myocardium. The Hodgkin and Huxley model describing the nervous action potential's theoretical reconstruction is first recalled, for it represents the basic model for a large part of cardiac action potential models. These models (Beeler and Reuter, Van Capelle and Durrer, Luo and Rudy) are then successively studied as their main applications by diverse authors. Varied approaches, like the Fitzhugh-Nagumo model (derived from the Bonhoeffer-Van der Pol model of oscillatory systems) or cellular automata models applied to the study of ventricular activation wave propagation and diseases associated with its perturbation, are then presented and discussed. Other, different approaches, such as general studies of excitable media, are evoked. This paper concludes with a critical evaluation of these different methods of electrophysiological cardiac modeling and of the main domains in which they led to significant results and in which they appear able to generate future perspectives.

Role of the dispersion of refractoriness on cardiac reentries.

We used computer simulation to study the possible role of the dispersion of cellular coupling, refractoriness or both, in the mechanisms underlying cardiac arrhythmias. Local ischemia was first assumed to induce cell to cell dispersion of the coupling resistance (case 1), refractory period (case 2), or both (case 3). Our numerical experiments based on the van Capelle and Durrer model showed that vortices could not be induced. On the other hand, with cellular properties dispersed in a patchy way within the ischemic zone, a single activation wave could give rise to abnormal activities. This demonstrates the stability of the wave front under small inhomogeneities. Probabilities of reentry, estimated for the three cases cited above showed that a severe alteration of the coupling resistance may be an important factor in the genesis of reentry. Moreover, use of isochronal maps revealed that vortices were both stable and sustained with an alteration of the coupling alone or along with a reduction of the action potential duration. Conversely, simulations with reduction of the refractoriness alone, inducing only transient patterns, could exhibit functionally determined reentries.

Incidence of dispersion of refractoriness and cellular coupling resistance on cardiac reentries and ventricular fibrillation.

We used computer simulations to study the possible role of the dispersion of cellular coupling, refractoriness or both, in the mechanisms underlying cardiac arrhythmias. Local ischemia was first assumed to induce cell to cell dispersion of the coupling resistance (Case 1), refractory period (Case 2), or both of them (Case 3). Our numerical experiments based on the van Capelle and Durrer model showed that vortices could not be induced by cell to cell variations. With cellular properties dispersed in a patchy way within the ischemic zone, a single activation wave could give rise to abnormal activities. This demonstrates the stability of the wave front under small inhomogeneities. Probabilities of reentry, estimated for the three cases cited above showed that a severe alteration of the coupling resistance may be an important factor in the genesis of reentry. Moreover, use of isochronal maps revealed that vortices were both stable and sustained with an alteration of the coupling alone or combined with a reduction of the action potential duration. Conversely, simulations with reduction of the refractoriness alone, inducing only transient patterns, could exhibit functionally determined reentries.

Theoretical study of cardiac transient conduction blocks on reentries induction. Applications to antiarrhythmic drugs.

Limitations of antiarrhythmic drugs on cardiac sudden death prevention appeared since the early 80's. The "Cardiac Arrhythmia Suppression Trial" (CAST) showed more recently that mortality was significantly higher in patients treated with some particular antiarrhythmic drugs than in non-treated patients. In this field, our group recently demonstrated that a bolus of a Class 1 B antiarrhythmic drug was able to trigger a ventricular fibrillation due to transient blocks induction. The aim of the present work was to systematically study, by use of the van Capelle and Durrer (VCD) model which allows to simulate ventricular activation wave propagation, the link between arrhythmogenic effects and the ability of transient blocks to possibly degenerate in severe arrhythmias. A fragment of the ventricular wall is represented by an array of 16384 elements electrically coupled. Effects of induction of one or several transient blocks, as the effects of their size and duration on possible induction of reentries have been studied. Results obtained show that various combinations between these different parameters may trigger reentries, ventricular tachycardia and/or more complex patterns assimilable to ventricular fibrillation. These results clearly evidence the fact that possible induction of transient blocks may directly be related to risk factor associated to arrhythmogenic effects of antiarrhythmic drugs.

Effect of myocardial infarction and ischemia on induction of cardiac reentries and ventricular fibrillation.

The present work is aimed at investigating the effects of myocardial infarction and ischemia on induction of ventricular fibrillation. Electrophysiologic effects of global and local ischemia (variation of the dispersion of refractory periods as well as conduction velocity) on initiation of reentry mechanisms was studied by means of computer simulations based on a cellular automata model of propagation of activation wave through a ventricular surface element. A local area of ischemia where effects of the dispersion of refractory periods are investigated is then simulated. This is made using a Gaussian distribution characterized by its mean and standard deviation. These simulations show that ischemia is capable of initiating reentry phenomena which propagate through the whole ventricle; they are responsible for ventricular fibrillation which causes sudden cardiac death, even when ischemia only involves limited parts of the myocardium. Statistical study of the probability of reentries as a function of both of the size of ischemic zones and the rate of dispersion of refractory periods shows that the latter parameter is of primary importance in triggering cardiac reentries.

Directional variability of stimulation threshold measurements in isolated guinea pig cardiomyocytes: relationship with orthogonal sequential defibrillating pulses.

Reports on delivery of separated orthogonal pulses markedly improving cardiac defibrillation have suggested that the stimulation threshold of heart fibers varies in accordance with their orientation within the electric field. The present work was aimed at investigating the directional variability of stimulation thresholds in isolated guinea pig cardiomyocytes. This variability was measured in 48 single myocytes by rotating each one through a theta (theta) angle between two-fixed parallel electrodes 1.1 cm apart, thus making theta vary between the electric field and the myocyte axis. For theta = 0 degrees, the mean longitudinal current stimulation threshold was 16.92 +/- 4.20 mA (n = 48). When theta was increased by increments of 10 degrees up to 90 degrees, the stimulation threshold increased in an exponential way. For theta = 90 degrees, the mean transverse stimulation threshold was 63.13 +/- 13.30 mA. These results clearly demonstrate the dependence of isolated cardiomyocyte stimulation thresholds on their orientation within the electric field and may account for the improved efficacy of defibrillation previously observed after delivery of orthogonal pulses.