Adiabatic solution of the Ohmic cable equation: a homogeneous cell. Possibilities for electrotonical measurements

Exact and adiabatic electrotonic solutions [1] were calculated for reconstr ucted motoneurone and hippocampal interneurone in case of linear and expone ntial ramp stimulation by the fixed current, potential or homogenous electr ic field. For the rising exponential ramp the solutions are identical. In c ase of the decaying exponent the adiabatic solution becomes an asymptote fo r the exact one if the stimulus decays slower than relaxation of the initia l conditions in the cell. If the stimulus decays faster, the asymptote is t he current or potential axis, depending on the stimulation mode. For electr otonically short cell, the exact solution approaches the asymptote faster. The solution for the exponentially rising field does not depend on the dend ritic tree configuration and depends only on the effective electrotonic len gth of the neurone. It could be useful to apply ramp stimulation, especiall y exponential ramp of the electric field, to estimate electrotonic paramete rs of cells.