Limitations of approximate solutions for computing the extracellular potential of single fibers and bundle equivalents

An examination and comparison are made of the rigorous and conventional approximate solutions of Laplace´s equation used to evaluate the extracellular potential of a single, cylindrical fiber. The single fiber is considered as both a prototypical element (such as a nerve or muscle fiber) and an elementary model of an entire multicellular preparation (e.g. nerve bundle or Purkinje strand). The effects of the fiber radius, the intracellular and extracellular conductiveness, and the shape and extent of the source function (either the transmembrane potential or the intracellular potential) on the solutions are discussed. The results show that, in general, the approximate solutions are unsatisfactory for computing the surface extracellular potential when the single fiber is used to represent a large bundle (>300 mu m).