Measurement of the current-distance relationship using a novel refractory interaction technique.

It is important to know the spatial extent of neural activation around the stimulating electrodes when using extracellular electrical stimulation for the determination of the structure and function of neural circuit connections or for the restoration of function. The current-distance relationship quantifies the relationship between the threshold current for excitation of a neuron, I(th), and the distance between the electrode and the neuron, r, with two parameters: the offset, I(0), and the current-distance constant, k, with a quadratic equation, I(th)(r) = I(0) + kr(2). We proposed a new method to determine the parameters of the current-distance relationship, and thereby estimate the spatial extent of activation, based on the refractory interaction technique. Refractory interaction is a method that exploits the interaction between the regions of activation produced by two electrodes, when the second stimulus is delivered while neurons activated by the first electrode are in their refractory period. Computer simulations of electrical stimulation of a population of nerve fibers were used to determine the accuracy of the method. The mean relative error in k was 19% and in I(0) was 17%, and the spatial extent of stimulation could be determined with an absolute error of 19 microm and a relative error less than 11%. Subsequently, the method was applied to measure the current-distance properties of peripheral motor nerve fibers and indicated that k = 27 microA mm(-2) and I(0) = 49 microA. This method provided robust estimates of the current-distance properties, and provides a means to determine the spatial extent of activation by extracellular stimulation.