Dynamics of wave fronts and filaments in anisotropic cardiac tissue

The heartbeat is mediated between cardiac cells by waves of electrical depolarisation. During cardiac arrhythmias, electrical activity was found to be organised in scroll waves which rotate around a dynamical filament curve. In this thesis, a curved-space approach is used to mathematically capture anisotropy of wave propagation. We derive for the first time the covariant laws of motion for traveling wave fronts and scroll wave filaments in anisotropic excitable media such as cardiac tissue. We show that locally varying anisotropy yields non-zero Riemann tensor components, which may alter the stability of scroll wave filaments. The instability of scroll wave filaments has been linked to transition from ventricular tachycardia to fibrillation.