Spiral waves and target waves in single cells

Abstract

The theoretical study of spatio-temporal phenomena such as target waves or spiral waves in reaction-diffusion systems is several decades old. However the investigations generally have been limited to systems where the reaction vessel is considered as infmitly large and uniform in all dimensions. Few years ago A. Babloyantz and J.A. Sepulchre (1) investigated the dynamics of spiral and target wave activity in finite media where typically the system size does not exceed a few wavelength of spiral or target activity. They also considered the influence of internal obstacles in the system which prevent wave propagation localy. They could show that the behaviour of target waves and spiral waves in an oscillatory system of small size can be very different from what is expected in a infinite medium. They have considered reacting media governed by Ginzburg-Landau type equation. All their published results were limited to oscillatory media. As the formalism of normal form was used, the results are valid for any oscillatory media stemming from a supercritical Hopf bifurcation. They have seen similar phenomena in excitatory systems. (unpublished work)