The time constants for the electric stimulation of nerve an muscle fibers by point electrodes

For the same nerve or muscle fiber the chronaxy measured using a small electrode located inside the fiber, is different from the chronaxies measured using the same electrode located in the volume conductor outside the fiber. Furthermore, measured chronaxies increase with the distance between the electrode and the fiber. A mathematical formula that relates the time constant of the strength duration curve with the parameters of the system composed by the electrode, the volume conductor and the fiber is used to explain the aforementioned differences for unmyelinated nerve and skeletal muscle fibers. For both extracellular and intracellular electrodes, the time constant is an increasing function of a characteristic length. This length is obtained from a relation between the unstable stationary solutions of Nagumo´s nonlinear cable equation and the polarizing effect of the electrodes on the fiber. In the case of extracellular electrodes, the characteristic length is defined as the measure of an interval of influence constructed from the activating function. In the case of point intracellular electrodes,the characteristic length is defined by a construction done with the help of the only bounded but not constant stationary solution of Nagumo´s equation