Auditory Nerve Model Research Articles

Predicting Dynamic Range and Intensity Discrimination for Electrical Pulse-Train Stimuli Using a Stochastic Auditory Nerve Model: The Effects of Stimulus Noise

This work investigates dynamic range and intensity discrimination for electrical pulse-train stimuli that are modulated by noise using a stochastic auditory nerve model. Based on a hypothesized monotonic relationship between loudness and the number of spikes elicited by a stimulus, theoretical prediction of the uncomfortable level has previously been determined by comparing spike counts to a fixed threshold, Nucl. However, no specific rule for determining Nucl has been suggested. Our work determines the uncomfortable level based on the excitation pattern of the neural response in a normal ear. The number of fibers corresponding to the portion of the basilar membrane driven by a stimulus at an uncomfortable level in a normal ear is related to Nucl at an uncomfortable level of the electrical stimulus. Intensity discrimination limens are predicted using signal detection theory via the probability mass function of the neural response and via experimental simulations. The results show that the uncomfortable level for pulse-train stimuli increases slightly as noise level increases. Combining this with our previous threshold predictions, we hypothesize that the dynamic range for noise-modulated pulse-train stimuli should increase with additive noise. However, since our predictions indicate that intensity discrimination under noise degrades, overall intensity coding performance may not improve significantly.

Erratum: “A phenomenological model for the responses of auditory-nerve fibers: II. Nonlinear tuning with a frequency glide” [J. Acoust. Soc. Am. 114, 2007–2020 (2003)

The schematic diagram and text erroneously omitted a component of the auditory-nerve model. A first-order low-pass filter with a cutoff frequency of 500 Hz was included in the feedback path within the model’s control-path, as shown here ~LP2, Fig. 1!; a scalar K with a value of 10 followed the low-pass filter in the feedback path. This low-pass filter was included in some but not all of the simulations shown in the original paper, as clarified below. The inclusion of LP2 did not significantly affect responses to pure tone stimuli ~Tan and Carney, 2003, Figs. 7–9,11,12! or to broadband noise ~Tan and Carney, 2003, Figs. 4,10!. The low-pass filter ~LP2! mainly affected responses to two-tone stimuli, and in particular was responsible for introducing the differences in growth of suppression for tones below or above CF. Figure 13 in Tan and Carney ~2003! did not include LP2; Fig. 2 here illustrates the effect of its inclusion. Figure 14 in Tan and Carney ~2003! did include LP2; the effects of its inclusion are illustrated here in Fig. 3.

Dynamic range and intensity discrimination with high-rate pulse-train carriers: predictions from a stochastic model and comparison with performance for noise-modulated pulse-train stimuli

This work investigates the properties of the neural response to a low frequency sinusoidal signal with a high-rate pulse-train carrier using a stochastic auditory nerve model. The agreement between the theoretical predictions, model simulations, and psychophysical data is demonstrated. Theoretical prediction of threshold (THL) and the most uncomfortable level (UCl), thus dynamic range, is considered as a function of various stimulus parameters, including carrier rate. Performance of dynamic range and intensity discrimination are compared for sinusoidal amplitude-modulated stimuli with high-rate pulse-train carriers and noise-modulated pulse-train stimuli.

A phenomenological model of peripheral and central neural responses to amplitude-modulated tones

A phenomenological model with time-varying excitation and inhibition was developed to study possible neural mechanisms underlying changes in the representation of temporal envelopes along the auditory pathway. A modified version of an existing auditory-nerve model [Zhang et al., J. Acoust. Soc. Am. 109, 648-670 (2001)] was used to provide inputs to higher hypothetical processing centers. Model responses were compared directly to published physiological data at three levels: the auditory nerve, ventral cochlear nucleus, and inferior colliculus. Trends and absolute values of both average firing rate and synchrony to the modulation period were accurately predicted at each level for a wide range of stimulus modulation depths and modulation frequencies. The diversity of central physiological responses was accounted for with realistic variations of model parameters. Specifically, enhanced synchrony in the cochlear nucleus and rate-tuning to modulation frequency in the inferior colliculus were predicted by choosing appropriate relative strengths and time courses of excitatory and inhibitory inputs to postsynaptic model cells. The proposed model is fundamentally different than others that have been used to explain the representation of envelopes in the mammalian midbrain, and it provides a computational tool for testing hypothesized relationships between physiology and psychophysics.

Predicting the threshold of single-pulse electrical stimuli using a stochastic auditory nerve model: the effects of noise

An important factor that may play a role in speech recognition by individuals with cochlear implants is that electrically stimulated nerves respond with a much higher level of synchrony than is normally observed in acoustically stimulated nerves. Recent work has indicated that the addition of noise to an electrical stimulus may result in neural responses whose statistical characteristics are more similar to those observed in acoustically driven neurons. Psychophysical data have indicated that performance on some tasks might also be enhanced by the addition of noise. However, little theoretical work has been done toward predicting the effect of noise on psychoacoustic measurements. In this paper, theoretical predictions of these effects are developed through the use of a stochastic computational model. The effect of additive noise on the input and output characteristics and aggregate threshold behavior of modeled auditory nerves (ANs) is specifically studied. This paper derives the stochastic properties of the model input and output when using adaptive threshold procedures. A closed form solution for the input, or amplitude, probability distribution is obtained via Markov models for both one-down one-up (1D1U) and two-down one-up (2D1U) experimental paradigms. The output statistics are derived by integrating over the noise-free probability mass function (PMF). All theoretical PMFs are verified by simulations with the model. Theoretical threshold is predicted as a function of noise level based on these PMFs and the predictions match simulated performance. The results indicate that threshold may be adversely affected by the presence of high levels of noise.

The importance of cochlear processing for the formation of auditory brainstem and frequency following responses.

A model for the generation of auditory brainstem responses (ABR) and frequency following responses (FFRs) is presented. The model is based on the concept introduced by Goldstein and Kiang [J. Acoust. Soc. Am. 30, 107-114 (1958)] that evoked potentials recorded at remote electrodes can theoretically be given by convolution of an elementary unit waveform (unitary response) with the instantaneous discharge rate function for the corresponding unit. In the present study, the nonlinear computational auditory-nerve model recently developed by Heinz et al. [ARLO 2(3), 91-96 (2001)] was used to calculate the instantaneous discharge rate ri(t) for fibers i in the frequency range from 0.1 and 10 kHz. The summed activity across frequency was convolved with a unitary response which is assumed to reflect contributions from different cell populations within the auditory brainstem, recorded at a given pair of electrodes on the scalp. Predicted potential patterns are compared with experimental data for a number of stimulus and level conditions. Clicks, chirps as defined in Dau et al. [J. Acoust. Soc. Am. 107, 1530-1540 (2000)], long-duration stimuli comprising the chirp, as well as tones and slowly varying tonal sweeps were considered. The results demonstrate the importance of considering the effects of the basilar-membrane traveling wave and auditory-nerve processing for the formation of ABR and FFR. Specifically, the results support the hypothesis that the FFR to low-frequency tones represents synchronized activity mainly stemming from mid- and high-frequency units at more basal sites, and not from units tuned to frequencies around the signal frequency.

Quantifying the implications of nonlinear cochlear tuning for auditory-filter estimates

The relation between auditory filters estimated from psychophysical methods and peripheral tuning was evaluated using a computational auditory-nerve (AN) model that included many of the response properties associated with nonlinear cochlear tuning. The phenomenological AN model included the effects of dynamic level-dependent tuning, compression, and suppression on the responses of high-, medium-, and low-spontaneous-rate AN fibers. Signal detection theory was used to evaluate psychophysical performance limits imposed by the random nature of AN discharges and by random-noise stimuli. The power-spectrum model of masking was used to estimate psychophysical auditory filters from predicted AN-model detection thresholds for a tone signal in fixed-level notched-noise maskers. Results demonstrate that the role of suppression in broadening peripheral tuning in response to the noise masker has implications for the interpretation of psychophysical auditory-filter estimates. Specifically, the estimated psychophysical auditory-filter equivalent-rectangular bandwidths (ERBs) that were derived from the nonlinear AN model with suppression always overestimated the ERBs of the low-level peripheral model filters. Further, this effect was larger for an 8-kHz signal than for a 2-kHz signal, suggesting a potential characteristic-frequency (CF) dependent bias in psychophysical estimates of auditory filters due to the increase in strength of cochlear nonlinearity with increases in CF.

Evaluating auditory performance limits: II. One-parameter discrimination with random-level variation.

Previous studies have combined analytical models of stochastic neural responses with signal detection theory (SDT) to predict psychophysical performance limits; however, these studies have typically been limited to simple models and simple psychophysical tasks. A companion article in this issue ("Evaluating Auditory Performance Limits: I") describes an extension of the SDT approach to allow the use of computational models that provide more accurate descriptions of neural responses. This article describes an extension to more complex psychophysical tasks. A general method is presented for evaluating psychophysical performance limits for discrimination tasks in which one stimulus parameter is randomly varied. Psychophysical experiments often randomly vary a single parameter in order to restrict the cues that are available to the subject. The method is demonstrated for the auditory task of random-level frequency discrimination using a computational auditory nerve (AN) model. Performance limits based on AN discharge times (all-information) are compared to performance limits based only on discharge counts (rate place). Both decision models are successful in predicting that random-level variation has no effect on performance in quiet, which is the typical result in psychophysical tasks with random-level variation. The distribution of information across the AN population provides insight into how different types of AN information can be used to avoid the influence of random-level variation. The rate-place model relies on comparisons between fibers above and below the tone frequency (i.e., the population response), while the all-information model does not require such across-fiber comparisons. Frequency discrimination with random-level variation in the presence of high-frequency noise is also simulated. No effect is predicted for all-information, consistent with the small effect in human performance; however, a large effect is predicted for rate-place in noise with random-level variation.

Response properties of the refractory auditory nerve fiber.

The refractory characteristics of auditory nerve fibers limit their ability to accurately encode temporal information. Therefore, they are relevant to the design of cochlear prostheses. It is also possible that the refractory property could be exploited by prosthetic devices to improve information transfer, as refractoriness may enhance the nerve's stochastic properties. Furthermore, refractory data are needed for the development of accurate computational models of auditory nerve fibers. We applied a two-pulse forward-masking paradigm to a feline model of the human auditory nerve to assess refractory properties of single fibers. Each fiber was driven to refractoriness by a single (masker) current pulse delivered intracochlearly. Properties of firing efficiency, latency, jitter, spike amplitude, and relative spread (a measure of dynamic range and stochasticity) were examined by exciting fibers with a second (probe) pulse and systematically varying the masker-probe interval (MPI). Responses to monophasic cathodic current pulses were analyzed. We estimated the mean absolute refractory period to be about 330 micros and the mean recovery time constant to be about 410 micros. A significant proportion of fibers (13 of 34) responded to the probe pulse with MPIs as short as 500 micros. Spike amplitude decreased with decreasing MPI, a finding relevant to the development of computational nerve-fiber models, interpretation of gross evoked potentials, and models of more central neural processing. A small mean decrement in spike jitter was noted at small MPI values. Some trends (such as spike latency-vs-MPI) varied across fibers, suggesting that sites of excitation varied across fibers. Relative spread was found to increase with decreasing MPI values, providing direct evidence that stochastic properties of fibers are altered under conditions of refractoriness.

Auditory nerve model for predicting performance limits of normal and impaired listeners

A computational auditory nerve (AN) model was developed for use in modeling psychophysical experiments with normal and impaired human listeners. In this phenomenological model, many physiologically vulnerable response properties associated with the cochlear amplifier are represented by a single nonlinear control mechanism, including the effects of level-dependent tuning, compression, level-dependent phase, suppression, and fast nonlinear dynamics on the responses of high, medium, and low spontaneous-rate (SR) AN fibers. Several model versions are described that can be used to evaluate the relative effects of these nonlinear properties.

A computational algorithm for computing nonlinear auditory frequency selectivity.

Computational algorithms that mimic the response of the basilar membrane must be capable of reproducing a range of complex features that are characteristic of the animal observations. These include complex input output functions that are nonlinear near the site's best frequency, but linear elsewhere. This nonlinearity is critical when using the output of the algorithm as the input to models of inner hair cell function and subsequent auditory-nerve models of low- and high-spontaneous rate fibers. We present an algorithm that uses two processing units operating in parallel: one linear and the other compressively nonlinear. The output from the algorithm is the sum of the outputs of the linear and nonlinear processing units. Input to the algorithm is stapes motion and output represents basilar membrane motion. The algorithm is evaluated against published chinchilla and guinea pig observations of basilar membrane and Reissner's membrane motion made using laser velocimetry. The algorithm simulates both quantitatively and qualitatively, differences in input/output functions among three different sites along the cochlear partition. It also simulates quantitatively and qualitatively a range of phenomena including isovelocity functions, phase response, two-tone suppression, impulse response, and distortion products. The algorithm is potentially suitable for development as a bank of filters, for use in more comprehensive models of the peripheral auditory system.

The representation of pure tones and noise in a model of cochlear nucleus neurons.

The limited dynamic range of the majority of auditory-nerve fibers represents a difficulty in accounting for normal hearing capabilities over the known psychoacoustic intensity range. The presence of noise is an additional complication because it will tend to saturate these fibers, thereby considerably reducing their dynamic range, i.e., the range of mean firing rates. In this study, simulations involving a model of auditory nerve and cochlear nucleus neurons were conducted using pure-tone stimuli in the presence of noise. The main focus is on the role of inhibition in regulating the activity of cells, improving their capability to represent signals in background noise. This concerns in particular those inhibitory neurons that receive input from a wide range of auditory-nerve fibers and respond with an onset chopper pattern. A detailed model of stellate cells is used. It allows several parameters such as the number, location, and strength of inputs to be manipulated. The fist part of this paper presents the model and its responses to pure-tone and noise stimuli presented separately. The model's capacity to generalize to tone/noise combinations is then tested. Responses to these stimuli are found to be qualitatively similar to neurophysiological findings. Model neurons exhibit appropriate shifts in their rate-level functions and their responses are inhibited or suppressed by tones outside their characteristic frequency. The model stellate cell is also found to display many of the temporal patterns reported in electrophysiological studies as a result of appropriate settings of certain parameters. Therefore, the model is sufficient to account for a larger number of findings and should serve as a basis for predicting responses to novel stimuli, or as a building block for modeling larger networks.

A stochastic model of the electrically stimulated auditory nerve: single-pulse response.

Most models of neural response to electrical stimulation, such as the Hodgkin-Huxley equations, are deterministic, despite significant physiological evidence for the existence of stochastic activity. For instance, the range of discharge probabilities measured in response to single electrical pulses cannot be explained at all by deterministic models. Furthermore, there is growing evidence that the stochastic component of auditory nerve response to electrical stimulation may be fundamental to functionally significant physiological and psychophysical phenomena. In this paper we present a simple and computationally efficient stochastic model of single-fiber response to single biphasic electrical pulses, based on a deterministic threshold model of action potential generation. Comparisons with physiological data from cat auditory nerve fibers are made, and it is shown that the stochastic model predicts discharge probabilities measured in response to single biphasic pulses more accurately than does the equivalent deterministic model. In addition, physiological data show an increase in stochastic activity with increasing pulse width of anodic/cathodic biphasic pulses, a phenomenon not present for monophasic stimuli. These and other data from the auditory nerve are then used to develop a population model of the total auditory nerve, where each fiber is described by the single-fiber model.

The effects of stochastic neural activity in a model predicting intensity perception with cochlear implants: low-rate stimulation.

Most models of auditory nerve response to electrical stimulation are deterministic, despite significant physiological evidence for stochastic activity. Furthermore, psychophysical models and analyses of physiological data using deterministic descriptions do not accurately predict many psychophysical phenomena. In this paper we investigate whether inclusion of stochastic activity in neural models improves such predictions. To avoid the complication of interpulse interactions and to enable the use of a simpler and faster auditory nerve model we restrict our investigation to single pulses and low-rate (< 200 pulses/s) pulse trains. We apply signal detection theory to produce direct predictions of behavioral threshold, dynamic range and intensity difference limen. Specifically, we investigate threshold versus pulse duration (the strength-duration characteristics), threshold and uncomfortable loudness (and the corresponding dynamic range) versus phase duration, the effects of electrode configuration on dynamic range and on strength-duration, threshold versus number of pulses (the temporal-integration characteristics), intensity difference limen as a function of loudness, and the effects of neural survival on these measures. For all psychophysical measures investigated, the inclusion of stochastic activity in the auditory nerve model was found to produce more accurate predictions.

Silicon auditory processors as computer peripherals

Several research groups are implementing analog integrated circuit models of biological auditory processing. The outputs of these circuit models have taken several forms, including video format for monitor display, simple scanned output for oscilloscope display, and parallel analog outputs suitable for data-acquisition systems. Here, an alternative output method for silicon auditory models, suitable for direct interface to digital computers, is described. As a prototype of this method, an integrated circuit model of temporal adaptation in the auditory nerve that functions as a peripheral to a workstation running Unix is described. Data from a working hybrid system that includes the auditory model, a digital interface, and asynchronous software are given. This system produces a real-time X-window display of the response of the auditory nerve model.

An auditory-nerve model for interaural time discrimination of high-frequency complex stimuli

Recent data on interaural time discrimination of high-frequency complex stimuli are described by a model based on auditory-nerve activity. This model is a simple extension of a model that was developed for detection and discrimination of low-frequency stimuli and that includes an explicit description of the activity in the auditory-nerve fibers. In the extension to high frequencies it is assumed, consistent with available physiological data, that the high-frequency neurons have instantaneous firing rates that follow the envelope of the tuning-curve filtered signal. Beyond the auditory nerve description, the model assumes a structure for processing timing information on high-frequency fibers that is the same as the structure for low frequencies. [Work supported by NIH.]