Theoretical study of transmembrane and extracellular potentials under propagation block due to geometrical inhomogeneity

A mathematical model was used to study transmembrane and extracellular potentials produced by active geometrically inhomogeneous excitable structures under conditions of propagation block. The structures were electrical analogues of intact or damaged unmyelinated nerve fibres, of the soma to axon transition, or of branching axons or dendrites. It was shown that: (1) damage to a cell is equivalent to the presence of a geometrical inhomogeneity, namely of a region of increased diameter; (2) propagation block caused by a geometrical inhomogeneity, results in; (a) a sharp decrease in the calculated transmembrane potential amplitude not only for the blocked region but also before it; (b) a considerable increase in the amplitude of both the negative phase of extracellular potentials at the points of the volume conductor preceding the blocked region and the first positive phase at points in the proximity of the region; (c) a more pronounced increase in the first positive phase amplitude at small radial distances, if the geometrical inhomogeneity is short compared with the length constant (gamma); (3) the membrane damage results in recording of potentials resembling "giant" ones.