Analytic treatment of the compound action potential: estimating the summed post-stimulus time histogram and unit response.

The convolution of an equation representing a summed post-stimulus time histogram computed across auditory nerve fibers [P(t)] with an equation representing a single-unit wave form [U(t)], resulted in an analytic expression for the compound action potential (CAP). The solution was fit to CAPs recorded to low and high frequency stimuli at various signal levels. The correlation between the CAP and the analytic expression was generally greater than 0.90. At high levels the width of P(t) was broader for low frequency stimuli than for high frequency signals, but delays were comparable. This indicates that at high signal levels there is an overlap in the population of auditory nerve fibers contributing to the CAP for both low and high frequency stimuli but low frequencies include contributions from more apical regions. At low signal levels the width of P(t) decreased for most frequencies and delays increased. The frequency of oscillation of U(t) was largest for high frequency stimuli and decreased for low frequency stimuli. The decay of U(t) was largest at 8 kHz and smallest at 1 kHz. These results indicate that the hair cell or neural mechanisms involved in the generation of action potentials may differ along the cochlear partition.