Temporal integration of sound pressure determines thresholds of auditory-nerve fibers

Current propositions of the quantity of sound driving the central auditory system, specifically around threshold, are diverse and at variance with one another. They include sound pressure, sound power, or intensity, which are proportional to the square of pressure, and energy, i.e., the integral of sound power over time. Here we show that the relevant sound quantity and the nature of the threshold can be obtained from the timing of the first spike of auditory-nerve (AN) fibers after the onset of a stimulus. We reason that the first spike is triggered when the stimulus reaches threshold and occurs with fixed delay thereafter. By probing cat AN fibers with characteristic frequency tones of different sound pressure levels and rise times, we show that the differences in relative timing of the first spike (including latencies >100 msec of fibers with low spontaneous rates) can be well accounted for by essentially linear integration of pressure over time. The inclusion of a constant pressure loss or gain to the integrator improves the fit of the model and also accounts for most of the variation of spontaneous rates across fibers. In addition, there are tight correlations among delay, threshold, and spontaneous rate. First-spike timing cannot be explained by models based on a fixed pressure threshold, a fixed power or intensity threshold, or an energy threshold. This suggests that AN fiber thresholds are best measured in units of pressure by time. Possible mechanisms of pressure integration by the inner hair cell-AN fiber complex are discussed.