A Probabilistic Model of Absolute Auditory Thresholds and Its Possible Physiological Basis

Abstract

Detection thresholds for auditory stimuli, specified in terms of their -amplitude or level, depend on the stimulus temporal envelope and decrease with increasing stimulus duration. The neural mechanisms underlying these fundamental across-species observations are not fully understood. Here, we present a "continuous look" model, according to which the stimulus gives rise to stochastic neural detection events whose probability of occurrence is proportional to the 3rd power of the low-pass filtered, time-varying stimulus amplitude. Threshold is reached when a criterion number of events have occurred (probability summation). No long-term integration is required. We apply the model to an extensive set of thresholds measured in humans for tones of different envelopes and durations and find it to fit well. Subtle differences at long durations may be due to limited attention resources. We confirm the probabilistic nature of the detection events by analyses of simple reaction times and verify the exponent of 3 by validating model predictions for binaural thresholds from monaural thresholds. The exponent originates in the auditory periphery, possibly in the intrinsic Ca(2+) cooperativity of the Ca(2+) sensor involved in exocytosis from inner hair cells. It results in growth of the spike rate of auditory-nerve fibers (ANFs) with the 3rd power of the stimulus amplitude before saturating (Heil et al., J Neurosci 31:15424-15437, 2011), rather than with its square (i.e., with stimulus intensity), as is commonly assumed. Our work therefore suggests a link between detection thresholds and a key biochemical reaction in the receptor cells.

Towards a Unifying Basis of Auditory Thresholds: Binaural Summation

“…The thresholds are lowest for stimulus 1, followed by stimuli 4, 2, and 3. The difference in thresholds for stimuli 2 and 3 is consistent with the observations of Carlyon et al (1990) and Heil et al (2013a). The error bars show the 95 % CI after compensating for individual differences in sensitivity.…”

“…The derivation is based on a model developed earlier to explain monaural absolute thresholds as well as the dependence of the timing of the first (stimulusdriven) spike of auditory-nerve fibers (i.e., a neural threshold) on stimulus onset envelope and amplitude (see Heil and Neubauer 2003;Heil 2004, 2008;Heil et al 2008Heil et al , 2013a. In brief, the model assumes that the stimulus is low-pass or bandpass filtered and its temporal envelope extracted.…”

“…All stimuli had a carrier frequency of 3.125 kHz, as in some previous studies from this lab (e.g., Heil et al 2006;Tiefenau et al 2006;Heil et al 2013a;Zoefel and Heil 2013). The stimuli, however, differed substantially in temporal envelope (Fig.…”

“…The data are compatible only with exponents close to 3. A preliminary account of this work has been presented as part of a more detailed account of the monaural model (Heil et al 2013a).…”

Sensorimotor integration on a rapid time scale

“…Our model shows that the short response latency of the Lombard effect is probably due to the very few audio-vocal processes involved: Envelope extraction, leaky integration, and scaling. Because both envelope extraction and leaky integration can be accomplished by the peripheral auditory system (20,21), it is likely that the initiation of the Lombard effect does not require higher auditory centers. The output from the peripheral auditory system can be directly sent to the vocal-motor system of the brainstem to guide the vocal amplitude adjustments, as indicated by the finding that decerebrate cats show the Lombard effect (22).…”