A.V. Panfilov

Spiral breakup as a model of ventricular fibrillation.

The phenomenon of spiral breakup in a 2D and a 3D excitable medium is described. Differences between breakup in two dimensions and in three dimensions are discussed. Spiral breakup in an anatomical model of the ventricles of the heart is also studied. The patterns of excitation in the heart are presented at different wavelengths together with their electrocardiograms. Finally it is suggested that the phenomenon of spiral breakup is a possible mechanism of the ventricular fibrillation (VF). (c) 1998 American Institute of Physics.

Spiral breakup in a modified FitzHugh-Nagumo model

In a modified FitzHugh-Nagumo model for excitable tissue a spiral wave is found to break up into an irregular spatial pattern. The main difference between our equations and the standard FitzHugh-Nagumo model is that we use two different time constants: one for the relative refractory period and another for the absolute refractory period. Breakup occurs when the relative refractory period is short. The effect is numerically stable at least for a five-fold decrease in the space integration step.

Wave propagation in an excitable medium with a negatively sloped restitution curve

Recent experimental studies show that the restitution curve of cardiac tissue can have a negative slope. We study how the negative slope of the restitution curve can influence basic processes in excitable media, such as periodic forcing of an excitable cell, circulation of a pulse in a ring, and spiral wave rotation in two dimensions. We show that negatively sloped restitution curve can result in instabilities if the slope of the restitution curve is steeper than -1 and report different manifestations of this instability. (c) 2002 American Institute of Physics.

The drift of a vortex in an inhomogeneous system of two coupled fibers

Abstract We studied the behavior of a vortex in an excitable medium having a stepped inhomogeneity, which is represented by a system of two coupled fibers. Numerical experiments were performed and analytical expressions were obtained for the determination of vortex drift velocity as a function of the parameters in the FitzHugh-Nagumo model.

Models of Dictyostelium discoideum Aggregation

Since its discovery in the 1940’s, the life cycle of the cellular slime mould Dictyostelium discoideum has attracted the interest of developmental biologists. It involves a relatively simple transition from unicellular to multicellular organization. Briefly, amoebae feed on bacteria in the soil and divide. Exhaustion of the food supply triggers a developmental sequence which leads, via cell aggregation, to the formation of a migrating slug-like “organism”. The slug eventually culminates into a fruiting body, aiding the dispersal of spores from which, under favourable conditions, new amoebae develop. To date a variety of species in different taxonomic groups are known whose life cycles follow a similar pattern (Margulis & Schwartz 1988). Over the past fifty years, many of the molecular and cellular mechanisms which are involved in cell aggregation, collective movement and differentiation have been identified, and much work is devoted to the understanding of the interaction of these mechanisms in shaping Dictyostelium development. Mathematical modelling has proved a useful tool with which to study these interactions on a quantitative basis.

Large pulsating waves in a one-dimensional excitable medium

Abstract The term “pulsating wave” has been introduced by Kerner and Osipov for an unmoving wave whose shape changes periodically. Such waves are known to occur in reaction-diffusion systems where stationary waves become unstable. The present paper investigates numerically the properties of pulsating waves in a modified FitzHugh-Nagumo model. In the range of the model parameters the pulsating waves have been shown to appear in the intermediate region between the ones where stationary and propagating waves occur. The mechanisms of the “pulsations” are discussed in terms of the wave front and the wave back dynamics.

The role of Ca/sup 2+/-channel blockers in the transition from ventricular fibrillation to ventricular tachycardia in an anatomical model of the human ventricles: a simulation study

We have investigated the effect of blocking the Ca/sup 2+/-channel on the transition from fibrillation to tachycardia in simulations in an anatomical model of the human ventricles, using a previously developed model of human ventricular cells where ventricular fibrillation was obtained by the process of spiral wave breakup. We show that blocking the Ca/sup 2+/-current by 75% can convert fibrillation into a periodic regime with a single stable spiral waves, which anchored to an anatomical obstacle. We show that the observed effects were due to a flattening of the restitution curve, which prevented the generation of wave breaks and stabilized the activation patterns.