Thresholds for transverse stimulation: fiber bundles in a uniform field.

Cable theory is used to model fibers (neural or muscular) subjected to an extracellular stimulus or activating function along the fiber (longitudinal stimulation). There are cases however, in which activation from fields across a fiber (transverse stimulation) is dominant and the activating function is insufficient to predict the relative stimulus thresholds for cells in a bundle. This work proposes a general method of quantifying transverse extracellular stimulation using ideal cases of long fibers oriented perpendicular to a uniform field (circular cells in a 2-D extracellular domain). Several methods are compared against a fully coupled model to compute electrical potentials around each cell of a bundle and predict the magnitude of applied plate potential (Phi(p)) needed to activate a given cell (Phi(pact)). The results show that with transverse stimulation, the effect of cell presence on the external field must be considered to accurately compute Phi(pact). They also show that approximating cells as holes can accurately predict firing order and Phi(pact) of cells in bundles. Potential profiles from this hole model can also be applied to single cell models to account for time-dependent transmembrane voltage responses and more accurately predict Phi(pact). The approaches used herein apply to other examples of transverse cell stimulation where cable theory is inapplicable and coupled model simulation is too costly to compute.