Extracellular stimulation by large (0.1-10 KV) and brief (0.01-5 ms) pulses applied by remote electrodes is widely used in clinical and experimental physiology to excite activity in nervous and muscular tissue: an important area of application is in pacing the heart [Zipes & Jalife, 1995]. Such field stimulation is also used to defibrillate heart muscle i.e. to eliminate all propagating activity when abnormal, re-entrant propagation is generating a life-threatening arrhythmia [Panfilov & Holden, 1996].
For a single cell in such a field, the current that flows in must equal the current that flows out of the cell, and so any effect must be generated by nonlinear summation of different behaviours of different parts of the cell. There must be potential gradients across the cell, and so each cell needs to be considered as a spatially extended object [Plonsey & Barr, 1986] and modelled by a partial differential system, as in [Cartee & Plonsey, 1992].
Here we present a simple ODE approach to the effects of extracellular field stimulation on excitable cells and tissues and apply it to estimate the defibrillation threshold for a model of mammalian ventricular tissue. We apply the singular perturbation approach of Krassowska and Neu [1994] to high-order biophysical excitation equations [Boyett et al., 1996] and extend the excitable medium models of cardiac tissue [Biktashev & Holden, 1996] to include the effects of external current inputs, and illustrate defibrillation via the theory of Pumir & Krinsky [1996]. Recent approaches to the theoretical basis of defibrillation [Keener, 1996, Pumir & Krinsky, 1996] lead to to coupled partial differential systems.