Anchoring of vortex filaments in 3D excitable media

We investigate the drift and anchoring of scroll waves in three-dimensional excitable media in the presence of a parameter gradient and a localized inhomogeneity (defect), using a modified FitzHugh-Nagumo model. Computer simulations show that there are two separate stages in the anchoring process, with two distinct time scales; first, rapid acceleration and attachment when the phase singularity (filament) of a drifting scroll approaches the defect. Second, the slow equilibrium of the free part of the filament. During the second stage, the filament may detach from the defect, and subsequently evolve with a complex, “spring-like” motion. The dynamics of these effects are explained on the basis of intrinsic filament motion (determined by local geometry of the filament) and motion due to a parameter gradient. These phenomena may have important applications in the study of cardiac arrhythmias caused by vortex-like activity.