TENSION OF ORGANIZING FILAMENTS OF SCROLL WAVES

We consider the asymptotic theory for the dynamics of organizing filam ents of three-dimensional scroll waves. For a generic autowave medium where two-dimensional vortices do not meander, we show that some of th e coefficients of the evolution equation are always zero. This simpler evolution equation predicts a monotonic change of the total filament length with time, independently of initial conditions. Whether the fil ament will shrink or expand is determined by a single coefficient, the filament tension, that depends on the medium parameters. We illustrat e the behaviour of scroll wave filaments with positive and negative te nsion by numerical experiments. In particular, we show that in the cas e of negative filament tension, the straight filament is unstable, and its evolution may lead to a multiplication of vortices.