Adiabatic solution of Ohmic cable equation: General theory and applicationfor a homogeneous cylindrical cable

An adiabatic solution of the Ohmic cable equation is suggested, which reduc es the non-stationary equation to a stationary form.-The adiabatic length c onstant of the stationary equation is time-dependent. The adiabatic solutio ns for the boundary conditions that change in time linearly and exponential ly were studied. In the latter case, the adiabatic length constant does not depend on time though it differs from the usual length constant.:The cable input characteristics of exact and adiabatic solutions were compared in th e cases of the voltage- and current-clamp, and electric field stimulation. The adiabatic and exact solutions are identical for the rising exponential stimuli. For the falling exponential stimuli, the adiabatic solution determ ines the exact asymptotic solution if the stimulus decays slower than the r elaxation of initial conditions. It is propose to use linear and exponentia l ramp stimulation in electrotonic measurements.