Back to Ian's Home Page Many theories of hearing hypothesize that spatiotemporal combination of single-fiber activity forms an important feature of the auditory system. One mechanism which has been proposed to explain perceptual performance is spatiotemporal summation of Auditory Nerve (AN) firings. Anatomical and physiological studies have found a number of different cell types in the Cochlear Nucleus (CN) which appear to perform such summations. The purpose of this paper is to determine theoretically how various degrees of AN fiber convergence onto summing neurons in the CN would affect estimation and discrimination of stimulus features from the summing neurons' outputs. To achieve this, we utilize an analytical model, based on a point process representation of AN activity, which includes parameterized measures of stimulus properties. The summing neuron model allows for an arbitrary degree of AN fiber convergence, thus facilitating an investigation of the feasibility of theories of neural coding of sound for different summing neuron types. Results obtained from the model indicate that for coding of the stimulus frequency in the periodicity of firings, the optimal spread of input fibers is very narrow and temporal integration is very short. This suggests that AN fibers which converge onto CN cells exhibiting enhanced synchronization originate from sites on the basilar membrane very close together. In contrast, CN cell types which exhibit reduced synchronization could be useful in performing estimation and discrimination tasks based on the average discharge rate. The model indicates that this could be achieved by a very wide spread of inputs and/or long-term temporal integration. We postulate that a wide spread of inputs would be preferential to long-term temporal integration, because this would enable the neuron's output to follow rapid changes in the average discharge rate of a population of fibers. Consequently, transients in the stimulus intensity which produce rapid changes in the average discharge rate of a population of fibers could be detected by a rapid change in the output of such a summing neuron.
Historically computational models of electrical stimulation of the cochlea have been unable to explain or predict a number of basic perceptual phenomena found in cochlear implant users. This could be due to either (i) an imperfect understanding of auditory nerve activity resulting from electrical stimulation of the cochlea, and/or (ii) an incomplete understanding of the relationship between auditory nerve activity and perception. In this study we investigate the former of these two possibilities. In particular, we hypothesize that stochastic (random) auditory nerve activity, which is present in responses to electrical stimulation but has been ignored in most previous models of cochlear implant physiology and perception, may largely account for many of these discrepancies. We have developed two different computationally efficient models of electrical stimulation, one incorporating stochastic activity in single auditory nerve fibers (stochastic model) and the other ignoring it (deterministic model). Using a standard model for relating auditory nerve activity to loudness perception, predictions were made of threshold, intensity difference limen and dynamic range. The results indicate that the stochastic model consistently gives better predictions of perceptual data than the deterministic model. In conclusion, understanding of the functional significance of auditory nerve responses to electrical stimulation of the cochlea is improved by consideration of stochastic activity.
In this thesis spatiotemporal patterns of auditory nerve activity are modelled, in order to determine how they may code features of acoustical and electrical stimuli. In particular, questions and applications of interest to cochlear implant development are investigated, including temporal coding of stimulus features in populations of nerve fibres and stochastic activity in responses to electrical stimulation.
A model of acoustical stimulation of the auditory nerve is developed to investigate how inter-spike intervals across a pair of auditory nerve fibres may code acoustical stimulus frequency. The results indicate that such frequency coding may take place across fibres for frequencies below 1–3 kHz, if the fibres originate from nearby sites in the cochlea. This investigation is then extended to spatiotemporal combination, specifically spatiotemporal summation, of activity in more than two fibres. A model is developed to determine theoretically how various degrees of auditory nerve fibre convergence onto summing neurons in the cochlear nucleus would affect estimation and discrimination of stimulus features from the summing neurons’ outputs. Results obtained from the model indicate that for coding of the stimulus frequency in the periodicity of firings, the optimal spread of input fibres is very narrow and temporal integration is very short. In contrast, cochlear nucleus cell types which have a wide spread of inputs and a very short temporal integration window may be useful in performing estimation and discrimination tasks based on the average discharge rate. The first two investigations are of responses to pure-tone stimuli in identical auditory nerve fibres—the possibility of coding different complex-stimulus features in fibres with different response properties is therefore investigated next. A model of acoustical stimulation is developed to determine an expression for the Cramer–Rao bound for frequency estimation of the envelope and fine structure of complex sounds by groups of fibres with different response properties. The estimation variances are calculated for some typical estimation tasks and demonstrate how, in the examples studied, a combination of low and high threshold fibres may improve the estimation performance of an ‘efficient’ observer.
A stochastic model of auditory response to single electrical pulses is also derived, and direct comparisons are made between this model and the same model without the stochastic component. In contrast to the deterministic model, the stochastic model accurately predicts probabilities of discharge measured in response to single biphasic pulses. A model of loudness in cochlear implant users is developed, which includes spatiotemporal summation of auditory nerve activity and can incorporate either the deterministic or the stochastic description of auditory nerve response. For all parameters investigated, the inclusion of stochastic activity in the model is found to produce more accurate predictions of behavioural performance than it is not included. The stochastic model of auditory nerve response to electrical stimulation is then extended to describe responses to pulse-train stimuli. The stochastic model, unlike the deterministic model, accurately predicts means and variances of discharge rates measured in response to pulse trains. The pulse-train stochastic model provides a means for extending the loudness model to predict psychophysical data for higher pulse rates.
Mathematical models are a useful means of formally describing and investigating pertinent features of complex systems such as the human auditory system. These features may be deduced from physiological and psychophysical experiments utilising animal models or humans, and from engineering studies. Historically, models of the auditory nerve’s (AN) response to electrical stimulation have ignored randomness in single-fiber activity which has been recorded in physiological studies. These models, however, have been unable to accurately predict a number of important psychophysical phenomena. In this study, a model that incorporates random activity of the AN is presented, and is shown to predict psychophysical performance. These results indicate that random activity is indeed an important part of the response of the AN to electrical stimulation.
Human perception of sound arises from the transmission of action-potentials (APs) through a neural network consisting of the auditory nerve and elements of the brain. Analysis of the response properties of individual neurons provides information regarding how features of sounds are coded in their firing patterns, and hints as to how higher brain centres may decode these neural response patterns to produce a perception of sound. Auditory neurons differ in the frequency of sound to which they respond most actively (their characteristic frequency), in their spontaneous (zero input) response, and also in their onset and saturation thresholds. Experiments have shown that neurons with low spontaneous rates show enhanced responses to the envelopes of complex sounds, while fibres with higher spontaneous rates respond to the temporal fine structure. In this paper, we determine an expression for the Cramer-Rao bound for frequency estimation of the envelope and fine structure of complex sounds by groups of neurons with parameterised response properties. The estimation variances are calculated for some typical estimation tasks, and demonstrate how, in the examples studied, a combination of low and high threshold fibres may improve the estimation performance of a fictitious `efficient' observer. Also, threshold comination may improve the estimation performance of neural systems, such as biological neural networks, which are based on the detection of dominant interspike times.
An understanding of mechanisms by which the human auditory system codes acoustical information has application to automated speech recognition and cochlear implants. In this paper, we formulate and analyze a mathematical model of the auditory system. The results are used to evaluate certain key theories of intensity and frequency coding.
The peripheral auditory system codes sound properties in the firing patterns of the auditory nerve (AN). The 30,000 AN fibers are each tuned to a particular frequency of sound, and the response of each fiber is a sudden jump in its electrical potential known as a spike or action potential (AP). Since these spikes are largely identical, sound properties must be encoded by the place and timing of the spikes.
Many theories of intensity and frequency coding reflect the convergence of groups of AN fibers on individual neurons of the brain stem by assuming spatial summation of nerve fiber activity. This motivates the analysis of population, or summed responses. However, due to the large number of fibers in the AN, physiological investigations of such responses are quite difficult.
Mathematical models can easily deal with summed stochastic systems, and can also be used to determine the information content of various aspects of neural firing patterns. In order to best achieve this, the model developed here is general enough to encompass a wide range of coding theories, analytical to facilitate investigation of information content and parametric to permit such an investigation under various scenarios. Previous models such as that of Carney, 1994 show the validity of summing mechanisms, but do not combine all the desired features. In Section 2, the neural response models are developed. Section 3 details the properties of a summing mechanism. Section 4 applies the model to explore the feasibility of various theories of hearing. Conclusions are drawn in Section 5.
Electrical stimulation strategies for cochlear implants may be improved by studying temporal frequency coding in single auditory fibres and across fibres in acoustic stimulation. In single nerve fibres, phase locking between action potentials and the acoustic stimulus can only be maintained at frequencies below 600 Hz. At these frequencies, the time interval between successive action potentials, called Interspike Interval (ISI), is the same as the period of the stimulus, and it can therefore be used to code frequency within single fibres. At higher frequencies, the phase locking of individual nerve fibres diminishes but it may still be possible to retain phase locking properties by combining the action potentials in an ensemble of nerve fibres. In an ensemble of fibres innervating different regions in the cochlea, the ISI in each nerve is affected by factors such as the spectral shape of the stimulus, the characteristic frequency, and the maximum firing rate of the nerve. The ISI between the fibres, however, is further affected by the propagation or phase delay of the travelling wave. It is therefore uncertain how these factors would affect frequency coding across fibres. It is possible that the propagation delay between the fibres may lower the phase locking in an ensemble of nerves—because the probability that the majority of nerves in an ensemble will fire simultaneously may be low. It is also possible that the combined firing statistics of the fibres in an ensemble may result in a higher degree of synchrony such that the predominant intervals in an ensemble is preserved over a wider frequency range than in a single fibre. Are these accurate postulations of the physical system? In a future electrical stimulation strategy that incorporates temporal frequency coding, is it necessary to mimic the spatial-temporal delay in the firing patterns caused by the travelling wave? These are important questions that need to be studied and answered.
To try to shed some light on these questions, this paper investigates the statistical relationship of spike events between pairs of nerve fibres with different spatial separations and propagation delays by using a mathematical model of the cochlea, a hair cell/auditory neuron transduction model and an integral expression for the Cross-Fibre Interspike Interval Probability Distribution (CFISI). Given a time-varying acoustic stimulus, the cochlear model simulates the propagating waves in the cochlear fluid resulting in the vibrations on the basilar membrane and the shearing movements on the hair cells. The auditory neuron model then takes the hair cell shearing displacements and converts them into the fluctuating firing probabilities of the neurons. The CFISI probability distribution is then calculated from the firing probabilities using the integral expression. The effect of the propagation delay on the CFISI is studied and its implications for cross-fibre temporal frequency coding are discussed.
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 single-pulse model of the companion paper [this issue, pp. 617–629] is extended to describe responses to pulse trains by introducing a phenomenological refractory mechanism. Comparisons with physiological data from cat auditory nerve fibers are made for pulse rates between 100 and 800 pulses/s. First, it is shown that both the shape and slope of mean discharge rate curves are better predicted by the stochastic model than by the deterministic model. Second, while inter-pulse effects such as refractory effects do indeed increase the dynamic range at higher pulse rates, both the physiological data and the model indicate that much of the dynamic range for pulse-train stimuli is due to stochastic activity. Thirdly, it is shown that the stochastic model is able to predict the general magnitude and behavior of variance in discharge rate as a function of pulse rate, while the deterministic model predicts no variance at all.
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 inter-pulse 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.
Models of auditory perception from both acoustic stimuli and from cochlear implants predict that the stochastic nature of auditory spike activity affects psychophysical performance. A fundamental aspect of neural stochastic behaviour is the variance of the spike discharge rate. It can be shown that this variance is a key aspect in determining the quantity of information which can be transmitted via an auditory neuron. This feature has been investigated in models of cochlear implant perception (Bruce et al, IEEE Trans. Biomed. Eng., accepted for publication). Further understanding of this feature may provide further direction for future cochlear implant development.
In this paper, we investigate the variance of the spike rate - showing a good fit between experimental results, and theoretical predictions. A range of stimulus conditions (bipolar, biphasic charge balanced pulses, 100-400 us/phase, current: threshold to response saturation, pulse rate: 50-600 pulses/s) were presented via a feline model of cochlear implantation. Variance was zero at a spike probability (p(spike)) of 0, rose to a maximum and fell to zero at a p(spike) of 1. The maximum occurred at a p(spike) of 0.5 for pulse rates <200 pulses/s and at 200 pulses/s for ANF with latencies of =0.5 ms. A leftward shift was apparent at 200 pulses/s in ANF with latencies 0.5 ms, or all units at 200 pulses/s. Variance was unaffected by pulse width between 50-400 us/phase. Estimates of discriminability, cumulative d' and weber fractions, were derived from the mean-variance data. Cumulative d' increased with pulse rate, but not pulse width. Weber fractions were approx. = 10-15 dB and the their relationship to dynamic range was affected by latency. At latencies <0.5 ms weber fractions were constant across dynamic range. For latencies 0.5 ms weber fractions increased in magnitude across the dynamic range. A stochastic point process of the auditory nerve response to electrical pulse-train stimulation (Irlicht and Clark, JASA, 100:3237-3247, 1996) was used to predict the general shape of the mean-variance plots. The modelling shows that the main factors affecting mean-variance data and the estimates of discriminability are an intrinsic source of stochasticity (probably neural membrane noise) and the duration of the neural refractoriness relative to the stimulus inter-pulse-interval. The effect of latency upon mean-variance data could be explained if the duration of refractoriness is proportional to latency.
In a recent set of modeling studies we have developed a stochastic threshold model of auditory nerve response to single biphasic electrical pulses (Bruce et al., 1999b) and moderate rate (less than 800 pulse per second) pulse trains (Bruce et al., 1999a). In this paper we derive an analytical approximation for the single-pulse model, which is then extended to describe the pulse-train model in the case of evenly timed, uniform pulses. This renewal-process description provides an accurate and computationally efficient model of electrical stimulation of single auditory nerve fibers by a cochlear implant that may be extended to other forms of electrical neural stimulation.
In [Bruce et al., IEEE Trans. Biomed. Eng. 46, 1393–1404 (1999b)], a composite physiological/psychophysical model of cochlear implant stimulation was developed to investigate whether inclusion of physiologically-observed stochastic activity in the auditory nerve (AN) section of the model improves predictions of psychophysical data from human cochlear implant users. It was shown that the stochastic version of the model better predicts how psychophysical threshold and uncomfortable loudness vary with two stimulus parameters that directly affect single-fiber responses, stimulus phase duration and electrode configuration. In this paper, the hypothesis is investigated that the major properties of such psychophysical data are consistent across mammalian species and can be well understood from the basic physiological properties of the mammalian AN if stochastic activity is considered. In addition to the psychophysical measures of the previous study, the investigation is extended to intensity discrimination as function of stimulus intensity. Also examined are the effects of one feature of the AN population response, the number of surviving AN fibers, and of one feature of the psychophysical section of the model, temporal integration. Predictions of data from humans, monkeys, guinea pigs and cats provide substantial evidence for the perceptual importance of neural stochastic activity.
Created by Ian Bruce <ibruce@ieee.org> - last modified Monday 21 January 2002