Comment on "Auditory-nerve first-spike latency and auditory absolute threshold: a computer model" [J. Acoust. Soc. Am. 119, 406-417 (2006)]

Temporal summation of airborne tones in a California sea lion (Zalophus californianus)

The trade-off between sound level and duration on hearing sensitivity (temporal summation) was investigated in a California sea lion (Zalophus californianus) using airborne pure-tone stimuli. Thresholds were behaviorally measured using the method of constant stimuli at 2.5, 5, and 10 kHz for nine signal durations ranging from 25 to 500 ms. In general, thresholds decreased as duration increased up to 300 ms, beyond which thresholds did not significantly improve. When these data were fitted separately to two versions of an exponential model, the estimated time constants (92-167 ms) were generally consistent between the two fits. However, the model with more free parameters generated fits with consistently higher R(2) values, while avoiding potential arbitrary decisions about which data to include. The time constants derived for the California sea lion were generally consistent with those reported for other mammals, including other pinnipeds. The current study did not show a clear correlation between time constant and test frequency. The results should be considered when conducting audiometric work, assessing communications ranges, and evaluating potential noise impacts of airborne tonal signals on California sea lions.

Auditory signal detection appears to depend on temporal integration of subthreshold activity in auditory cortex

The threshold of hearing decreases with increasing sound duration up to a limit of a few hundred milliseconds, whereas other auditory time constants are orders of magnitude shorter. A possible solution to this resolution-integration paradox is that temporal integration occurs more centrally than computations depending on high temporal resolution. But this would require information about subthreshold events in the periphery to reach higher centers. Here we show that this prerequisite is fulfilled. The auditory evoked response to a just perceptible pulse series does basically not depend on whether single pulses are below or above behavioral threshold. The failure to find evidence of temporal integration up to response latencies of 30 ms suggests that the integrator is located more centrally than primary auditory cortex. By using noise to its advantage, the auditory system apparently has established a central integration mechanism that is about as efficient as the peripheral one in the visual system.

Level-dependent latency shifts quantified through binaural processing

The mammalian binaural system compares the timing of monaural inputs with microsecond precision. This temporal precision is required for localizing sounds in azimuth. However, temporal features of the monaural inputs, in particular their latencies, highly depend on the overall sound level. In a combined psychophysical, electrophysiological, and modeling approach, we investigate how level-dependent latency shifts of the monaural responses are reflected in the perception and neural representation of interaural time differences. We exploit the sensitivity of the binaural system to the timing of high-frequency stimuli with binaurally incongruent envelopes. Using these novel stimuli, both the perceptually adjusted interaural time differences and the time differences extracted from electrophysiological recordings systematically depend on overall sound pressure level. The perceptual and electrophysiological time differences of the envelopes can be explained in an existing model of temporal integration only if a level-dependent firing threshold is added. Such an adjustment of firing threshold provides a temporally accurate neural code of the temporal structure of a stimulus and its binaural disparities independent of overall sound level.

Auditory brainstem response at the detection limit

Specific predictions regarding the level dependence of auditory evoked responses near the detection limit were made in a companion modeling study (Lütkenhöner, J Assoc Res Otolaryngol 9:102-121, 2008). Here, these predictions are experimentally tested for auditory brainstem responses (ABR) to Gaussian-shaped 4-kHz tone pulses (full width at half maximum = 0.5 ms) that were presented at sound levels close to the subjective threshold. In the average of over about one million stimulus repetitions (repetition period = 16 ms), the amplitude of ABR wave V showed a smooth transition from a proportional to a logarithmic growth with increasing sound intensity. The latter type of growth corresponds to a linear increase with respect to sound level measured in decibels. Alternatively, the ABR amplitude near the detection limit may be considered a linear function of sound pressure, although-according to the model-this is only an approximation. Data and model are consistent with the view that a sensory threshold does not exist for the auditory modality, in accordance with signal detection theory. Even so, the model may be used to define a quasithreshold that is comparable to the subjective threshold.

Threshold and beyond: modeling the intensity dependence of auditory responses

In many studies of auditory-evoked responses to low-intensity sounds, the response amplitude appears to increase roughly linearly with the sound level in decibels (dB), corresponding to a logarithmic intensity dependence. But the auditory system is assumed to be linear in the low-intensity limit. The goal of this study was to resolve the seeming contradiction. Based on assumptions about the rate-intensity functions of single auditory-nerve fibers and the pattern of cochlear excitation caused by a tone, a model for the gross response of the population of auditory nerve fibers was developed. In accordance with signal detection theory, the model denies the existence of a threshold. This implies that regarding the detection of a significant stimulus-related effect, a reduction in sound intensity can always be compensated for by increasing the measurement time, at least in theory. The model suggests that the gross response is proportional to intensity when the latter is low (range I), and a linear function of sound level at higher intensities (range III). For intensities in between, it is concluded that noisy experimental data may provide seemingly irrefutable evidence of a linear dependence on sound pressure (range II). In view of the small response amplitudes that are to be expected for intensity range I, direct observation of the predicted proportionality with intensity will generally be a challenging task for an experimenter. Although the model was developed for the auditory nerve, the basic conclusions are probably valid for higher levels of the auditory system, too, and might help to improve models for loudness at threshold.

Auditory evoked field at threshold

Auditory evoked responses are widely used for estimating electrophysiological thresholds, but the relationships to psychophysical thresholds are not necessarily straightforward. Among the aspects that are not well understood is the near-threshold intensity dependence of the evoked response. Here, we investigated wave N100m of the auditory evoked field. The stimulus was a 1-kHz tone with an effective duration of about 110 ms. Up to 10 dB above the psychophysical threshold, the level was varied in steps of 2dB; further measurements were done at 15, 20, 30, and 40 dB SL. Lower levels were presented with higher probability, to partially compensate for the expected signal-to-noise ratio reduction with decreasing level. The latency of the N100m could be characterized as a transmission delay and an integration time. The level dependence of the latter was consistent with the assumption of an almost perfectly operating sound-pressure integrator. The N100m amplitude increased roughly linearly with the level in dB (thus, as a logarithmic function of intensity), showing signs of saturation at higher levels.

Reply to comment on "Auditory-nerve first-spike latency and auditory absolute threshold: a computer model"

Krisha [J. Acoust. Soc. Am., in press (2006)] has commented that an explanation based on presynaptic calcium accumulation at the inner hair cell is an incorrect explanation for the success of a model of the auditory periphery [Meddis, R., J. Acoustic. Soc. Am. 119, 406-417 (2006)] in explaining data on first-spike auditory nerve latency. This reply accepts the criticism and accepts the strength of an alternative explanation based on expected latencies in random sequences of low-probability events. This reply also goes on briefly to explore the application of this argument to other phenomena, including the dependence of absolute auditory threshold on the duration of the stimulus. This has wide-ranging implications for the concept of "temporal integration" in psychophysics.