Heinrich Neubauer

A unifying basis of auditory thresholds based on temporal summation

Thresholds of auditory-nerve (AN) fibers and auditory neurons are commonly specified in terms of sound pressure only, implying that they are independent of time. At the perceptual level, however, the sound pressure required for detection decreases with increasing stimulus duration, suggesting that the auditory system integrates sound over time. The quantity commonly believed to be integrated is sound intensity, implying that the auditory system would have an energy threshold. However, leaky integrators of intensity with time constants of hundreds of milliseconds are required to fit the data. Such time constants are unknown in physiology and are also incompatible with the high temporal resolution of the auditory system, creating the resolution–integration paradox. Here we demonstrate that cortical and perceptual responses are based on integration of the pressure envelope of the sound, as we have previously shown for AN fibers, rather than on intensity. The functions relating the pressure envelope integration thresholds and time for AN fibers, cortical neurons, and perception in the same species (cat), as well as for perception in many different vertebrate species, are remarkably similar. They are well described by a power law that resolves the resolution–integration paradox. The data argue for the integrator to be located in the first synapse in the auditory pathway and we discuss its mode of operation.

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.

Spontaneous Activity of Auditory-Nerve Fibers: Insights into Stochastic Processes at Ribbon Synapses

In several sensory systems, the conversion of the representation of stimuli from graded membrane potentials into stochastic spike trains is performed by ribbon synapses. In the mammalian auditory system, the spiking characteristics of the vast majority of primary afferent auditory-nerve (AN) fibers are determined primarily by a single ribbon synapse in a single inner hair cell (IHC), and thus provide a unique window into the operation of the synapse. Here, we examine the distributions of interspike intervals (ISIs) of cat AN fibers under conditions when the IHC membrane potential can be considered constant and the processes generating AN fiber activity can be considered stationary, namely in the absence of auditory stimulation. Such spontaneous activity is commonly thought to result from an excitatory Poisson point process modified by the refractory properties of the fiber, but here we show that this cannot be the case. Rather, the ISI distributions are one to two orders of magnitude better and very accurately described as a result of a homogeneous stochastic process of excitation (transmitter release events) in which the distribution of interevent times is a mixture of an exponential and a gamma distribution with shape factor 2, both with the same scale parameter. Whereas the scale parameter varies across fibers, the proportions of exponentially and gamma distributed intervals in the mixture, and the refractory properties, can be considered constant. This suggests that all of the ribbon synapses operate in a similar manner, possibly just at different rates. Our findings also constitute an essential step toward a better understanding of the spike-train representation of time-varying stimuli initiated at this synapse, and thus of the fundamentals of temporal coding in the auditory pathway.

Towards a unifying basis of auditory thresholds: Distributions of the first-spike latencies of auditory-nerve fibers

Detecting sounds in quiet is the simplest task performed by the auditory system, but the neural mechanisms underlying perceptual detection thresholds for sounds in quiet are still not understood. Heil and Neubauer [Heil, P., Neubauer, H., 2003. A unifying basis of auditory thresholds based on temporal summation. Proc. Natl. Acad. Sci. USA 100, 6151-6156] have provided evidence for a simple probabilistic model according to which the stimulus, at any point in time, has a certain probability of exceeding threshold and being detected. Consequently, as stimulus duration increases, the cumulative probability of detection events increases, performance improves, and threshold amplitude decreases. The origin of these processes was traced to the first synapse in the auditory system, between the inner hair cell and the afferent auditory-nerve fiber (ANF). Here we provide further support for this probabilistic continuous-look model. It is derived from analyses of the distributions of the latencies of the first spikes of cat ANFs with very low spontaneous discharge rates to tones of different amplitudes. The first spikes in these fibers can be considered detection events. We show that, as predicted, the distributions can be explained by the joint probability of the occurrence of three independent sub-events, where the probability of each of those occurring is proportional to the low-pass filtered stimulus amplitude. The temporal integration functions of individual ANFs, derived from their first-spike latencies, are remarkably similar in shape to temporal integration functions, which relate threshold sound pressure level at the perceptual level to stimulus duration. This further supports a close link between the mechanisms determining the timing of the first (and other) evoked spikes at the level of the auditory nerve and detection thresholds at the perceptual level. The possible origin and some functional consequences of the expansive power-law non-linearity are discussed.

Towards a Unifying Basis of Auditory Thresholds: The Effects of Hearing Loss on Temporal Integration Reconsidered

For signal detection and identification, the auditory system needs to integrate sound over time. It is frequently assumed that the quantity ultimately integrated is sound intensity and that the integrator is located centrally. However, we have recently shown that absolute thresholds are much better specified as the temporal integral of the pressure envelope than of intensity, and we proposed that the integrator resides in the auditory pathway’s first synapse. We also suggested a physiologically plausible mechanism for its operation, which was ultimately derived from the specific rate of temporal integration, i.e., the decrease of threshold sound pressure levels with increasing duration. In listeners with sensorineural hearing losses, that rate seems reduced, but it is not fully understood why. Here we propose that in such listeners there may be an elevation in the baseline above which sound pressure is effective in driving the system, in addition to a reduction in sensitivity. We test this simple model using thresholds of cats to stimuli of differently shaped temporal envelopes and durations obtained before and after hearing loss. We show that thresholds, specified as the temporal integral of the effective pressure envelope, i.e., the envelope of the pressure exceeding the elevated baseline, behave almost exactly as the lower thresholds, specified as the temporal integral of the total pressure envelope before hearing loss. Thus, the mechanism of temporal integration is likely unchanged after hearing loss, but the effective portion of the stimulus is. Our model constitutes a successful alternative to the model currently favored to account for altered temporal integration in listeners with sensorineural hearing losses, viz., reduced peripheral compression. Our model does not seem to be at variance with physiological observations and it also qualitatively accounts for a number of phenomena observed in such listeners with suprathreshold stimuli.

A physiological model for the stimulus dependence of first-spike latency of auditory-nerve fibers

Recent studies have shown a close correspondence between perceptual detection thresholds for sounds in quiet and a measure of neuronal thresholds derived from the stimulus-dependent timing of the first spike of auditory-nerve fibers. In addition, stimulus properties might be encoded by differences in first-spike timing of neurons in the central auditory system. Therefore, the physiological mechanisms underlying first-spike timing are of considerable interest, but are not thoroughly understood. Here, we present a physiological model which accurately explains the observed stimulus dependence of the first-spike latency of auditory-nerve fibers with a minimum number of physiologically plausible parameters. Two of the 5 parameters can be considered constant (at least for the vast majority of fibers), while the other 3 vary in meaningful ways with the fibers spontaneous discharge rates. The elements of the model and some implications are discussed.

Summing Across Different Active Zones can Explain the Quasi-Linear Ca2+-Dependencies of Exocytosis by Receptor Cells

Several recent studies of mature auditory and vestibular hair cells (HCs), and of visual and olfactory receptor cells, have observed nearly linear dependencies of the rate of neurotransmitter release events, or related measures, on the magnitude of Ca2+-entry into the cell. These relationships contrast with the highly supralinear, third to fourth power, Ca2+-dependencies observed in most preparations, from neuromuscular junctions to central synapses, and also in HCs from immature and various mutant animals. They also contrast with the intrinsic, biochemical, Ca2+-cooperativity of the ubiquitous Ca2+-sensors involved in fast exocytosis (synaptotagmins I and II). Here, we propose that the quasi-linear dependencies result from measuring the sum of several supralinear, but saturating, dependencies with different sensitivities at individual active zones of the same cell. We show that published experimental data can be accurately accounted for by this summation model, without the need to assume altered Ca2+-cooperativity or nanodomain control of release. We provide support for the proposal that the best power is 3, and we discuss the large body of evidence for our summation model. Overall, our idea provides a parsimonious and attractive reconciliation of the seemingly discrepant experimental findings in different preparations.

An Improved Model for the Rate–Level Functions of Auditory-Nerve Fibers

Acoustic information is conveyed to the brain by the spike patterns in auditory-nerve fibers (ANFs). In mammals, each ANF is excited via a single ribbon synapse in a single inner hair cell (IHC), and the spike patterns therefore also provide valuable information about those intriguing synapses. Here we reexamine and model a key property of ANFs, the dependence of their spike rates on the sound pressure level of acoustic stimuli (rate–level functions). We build upon the seminal model of Sachs and Abbas (1974), which provides good fits to experimental data but has limited utility for defining physiological mechanisms. We present an improved, physiologically plausible model according to which the spike rate follows a Hill equation and spontaneous activity and its experimentally observed tight correlation with ANF sensitivity are emergent properties. We apply it to 156 cat ANF rate–level functions using frequencies where the mechanics are linear and find that a single Hill coefficient of 3 can account for the population of functions. We also demonstrate a tight correspondence between ANF rate–level functions and the Ca2+ dependence of exocytosis from IHCs, and derive estimates of the effective intracellular Ca2+ concentrations at the individual active zones of IHCs. We argue that the Hill coefficient might reflect the intrinsic, biochemical Ca2+ cooperativity of the Ca2+ sensor involved in exocytosis from the IHC. The model also links ANF properties with properties of psychophysical absolute thresholds.

Comparison of Absolute Thresholds Derived from an Adaptive Forced-Choice Procedure and from Reaction Probabilities and Reaction Times in a Simple Reaction Time Paradigm

An understanding of the auditory systems operation requires knowledge of the mechanisms underlying thresholds. In this work we compare detection thresholds obtained with a three-interval-three-alternative forced-choice paradigm with reaction thresholds extracted from both reaction probabilities (RP) and reaction times (RT) in a simple RT paradigm from the same listeners under otherwise nearly identical experimental conditions. Detection thresholds, RP, and RT to auditory stimuli exhibited substantial variation from session to session. Most of the intersession variation in RP and RT could be accounted for by intersession variation in a listeners absolute sensitivity. The reaction thresholds extracted from RP were very similar, if not identical, to those extracted from RT. On the other hand, reaction thresholds were always higher than detection thresholds. The difference between the two thresholds can be considered as the additional amount of evidence required by each listener to react to a stimulus in an unforced design on top of that necessary for detection in the forced-choice design. This difference is inversely related to the listeners probability of producing false alarms. We found that RT, once corrected for some irreducible minimum RT, reflects the time at which a given stimulus reaches the listeners reaction threshold. This suggests that the relationships between simple RT and loudness (reported in the literature) are probably caused by a tight relationship between temporal summation at threshold and temporal summation of loudness.

Why longer song elements are easier to detect: threshold level-duration functions in the Great Tit and comparison with human data

Our study estimates detection thresholds for tones of different durations and frequencies in Great Tits (Parus major) with operant procedures. We employ signals covering the duration and frequency range of communication signals of this species (40–1,010xa0ms; 2, 4, 6.3xa0kHz), and we measure threshold level-duration (TLD) function (relating threshold level to signal duration) in silence as well as under behaviorally relevant environmental noise conditions (urban noise, woodland noise). Detection thresholds decreased with increasing signal duration. Thresholds at any given duration were a function of signal frequency and were elevated in background noise, but the shape of Great Tit TLD functions was independent of signal frequency and background condition. To enable comparisons of our Great Tit data to those from other species, TLD functions were first fitted with a traditional leaky-integrator model. We then applied a probabilistic model to interpret the trade-off between signal amplitude and duration at threshold. Great Tit TLD functions exhibit features that are similar across species. The current results, however, cannot explain why Great Tits in noisy urban environments produce shorter song elements or faster songs than those in quieter woodland environments, as detection thresholds are lower for longer elements also under noisy conditions.