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

Vestibular implant stimulation: pulse amplitude modulation versus combined pulse rate and amplitude modulation

Objective. The vestibular implant is a potential treatment approach for bilateral vestibulopathy patients. To restore gaze stabilization, the implant should elicit vestibulo-ocular reflexes (VORs) over a wide range of eye velocities. Different stimulation strategies to achieve this goal were previously described. Vestibular information can be encoded by modulating stimulation amplitude, rate, or a combination of both. In this study, combined rate and amplitude modulation was compared with amplitude modulation, to evaluate their potential for vestibular implant stimulation.Approach. Nine subjects with a vestibulo-cochlear implant participated in this study. Three stimulation strategies were tested. The combined rate and amplitude modulation setting (baseline rate 50%) was compared with amplitude modulation (baseline rate 50%, and baseline rate equal to the maximum rate). The resulting VOR was evaluated.Main results. Combining rate and amplitude modulation, or using amplitude modulation with a baseline equal to the maximum rate, both significantly increased peak eye velocities (PEVs). Misalignment increased with higher PEVs and higher pulse rate. No significant differences were found in PEVs and misalignment, between both stimulation strategies. Amplitude modulation with a baseline rate at 50%, demonstrated the lowest PEVs.Significance. Combining rate and amplitude modulation, or amplitude modulation with a baseline equal to the maximum rate, can both be considered for future vestibular implant fitting.ClinicalTrials.gov Identifier: NCT04918745.

Peripheral Neural Synchrony in Postlingually Deafened Adult Cochlear Implant Users

OBJECTIVES

This paper reports a noninvasive method for quantifying neural synchrony in the cochlear nerve (i.e., peripheral neural synchrony) in cochlear implant (CI) users, which allows for evaluating this physiological phenomenon in human CI users for the first time in the literature. In addition, this study assessed how peripheral neural synchrony was correlated with temporal resolution acuity and speech perception outcomes measured in quiet and in noise in postlingually deafened adult CI users. It tested the hypothesis that peripheral neural synchrony was an important factor for temporal resolution acuity and speech perception outcomes in noise in postlingually deafened adult CI users.

DESIGN

Study participants included 24 postlingually deafened adult CI users with a Cochlear™ Nucleus® device. Three study participants were implanted bilaterally, and each ear was tested separately. For each of the 27 implanted ears tested in this study, 400 sweeps of the electrically evoked compound action potential (eCAP) were measured at four electrode locations across the electrode array. Peripheral neural synchrony was quantified at each electrode location using the phase-locking value (PLV), which is a measure of trial-by-trial phase coherence among eCAP sweeps/trials. Temporal resolution acuity was evaluated by measuring the within-channel gap detection threshold (GDT) using a three-alternative, forced-choice procedure in a subgroup of 20 participants (23 implanted ears). For each ear tested in these participants, GDTs were measured at two electrode locations with a large difference in PLVs. For 26 implanted ears tested in 23 participants, speech perception performance was evaluated using consonant-nucleus-consonant (CNC) word lists presented in quiet and in noise at signal to noise ratios (SNRs) of +10 and +5 dB. Linear Mixed effect Models were used to evaluate the effect of electrode location on the PLV and the effect of the PLV on GDT after controlling for the stimulation level effects. Pearson product-moment correlation tests were used to assess the correlations between PLVs, CNC word scores measured in different conditions, and the degree of noise effect on CNC word scores.

RESULTS

There was a significant effect of electrode location on the PLV after controlling for the effect of stimulation level. There was a significant effect of the PLV on GDT after controlling for the effects of stimulation level, where higher PLVs (greater synchrony) led to lower GDTs (better temporal resolution acuity). PLVs were not significantly correlated with CNC word scores measured in any listening condition or the effect of competing background noise presented at an SNR of +10 dB on CNC word scores. In contrast, there was a significant negative correlation between the PLV and the degree of noise effect on CNC word scores for a competing background noise presented at an SNR of +5 dB, where higher PLVs (greater synchrony) correlated with smaller noise effects on CNC word scores.

CONCLUSIONS

This newly developed method can be used to assess peripheral neural synchrony in CI users, a physiological phenomenon that has not been systematically evaluated in electrical hearing. Poorer peripheral neural synchrony leads to lower temporal resolution acuity and is correlated with a larger detrimental effect of competing background noise presented at an SNR of 5 dB on speech perception performance in postlingually deafened adult CI users.

Estimating User-Specific Current Spread and Neural Health Parameters in a Model of Hearing with Cochlear Implants

The hearing performance of cochlear implant users can be potentially improved by adjusting the coding strategies according to the patterns of current spread and neural health in the cochlea. These patterns are important for the development of better sound coding strategies, but they are user-specific and it can be overly time consuming to obtain in the clinical setting. In this research, we developed a method to estimate current spread and neural health in the implanted cochlea using a user-specific computational model. The results demonstrated the possibility of estimating the user-specific parameters in a model of hearing with cochlear implants using the basic psychophysical measurements.

Towards biologically plausible phosphene simulation for the differentiable optimization of visual cortical prostheses

Blindness affects millions of people around the world. A promising solution to restoring a form of vision for some individuals are cortical visual prostheses, which bypass part of the impaired visual pathway by converting camera input to electrical stimulation of the visual system. The artificially induced visual percept (a pattern of localized light flashes, or 'phosphenes') has limited resolution, and a great portion of the field's research is devoted to optimizing the efficacy, efficiency, and practical usefulness of the encoding of visual information. A commonly exploited method is non-invasive functional evaluation in sighted subjects or with computational models by using simulated prosthetic vision (SPV) pipelines. An important challenge in this approach is to balance enhanced perceptual realism, biologically plausibility, and real-time performance in the simulation of cortical prosthetic vision. We present a biologically plausible, PyTorch-based phosphene simulator that can run in real-time and uses differentiable operations to allow for gradient-based computational optimization of phosphene encoding models. The simulator integrates a wide range of clinical results with neurophysiological evidence in humans and non-human primates. The pipeline includes a model of the retinotopic organization and cortical magnification of the visual cortex. Moreover, the quantitative effects of stimulation parameters and temporal dynamics on phosphene characteristics are incorporated. Our results demonstrate the simulator's suitability for both computational applications such as end-to-end deep learning-based prosthetic vision optimization as well as behavioral experiments. The modular and open-source software provides a flexible simulation framework for computational, clinical, and behavioral neuroscientists working on visual neuroprosthetics.

A computational model to simulate spectral modulation and speech perception experiments of cochlear implant users

Speech understanding in cochlear implant (CI) users presents large intersubject variability that may be related to different aspects of the peripheral auditory system, such as the electrode-nerve interface and neural health conditions. This variability makes it more challenging to proof differences in performance between different CI sound coding strategies in regular clinical studies, nevertheless, computational models can be helpful to assess the speech performance of CI users in an environment where all these physiological aspects can be controlled. In this study, differences in performance between three variants of the HiRes Fidelity 120 (F120) sound coding strategy are studied with a computational model. The computational model consists of (i) a processing stage with the sound coding strategy, (ii) a three-dimensional electrode-nerve interface that accounts for auditory nerve fiber (ANF) degeneration, (iii) a population of phenomenological ANF models, and (iv) a feature extractor algorithm to obtain the internal representation (IR) of the neural activity. As the back-end, the simulation framework for auditory discrimination experiments (FADE) was chosen. Two experiments relevant to speech understanding were performed: one related to spectral modulation threshold (SMT), and the other one related to speech reception threshold (SRT). These experiments included three different neural health conditions (healthy ANFs, and moderate and severe ANF degeneration). The F120 was configured to use sequential stimulation (F120-S), and simultaneous stimulation with two (F120-P) and three (F120-T) simultaneously active channels. Simultaneous stimulation causes electric interaction that smears the spectrotemporal information transmitted to the ANFs, and it has been hypothesized to lead to even worse information transmission in poor neural health conditions. In general, worse neural health conditions led to worse predicted performance; nevertheless, the detriment was small compared to clinical data. Results in SRT experiments indicated that performance with simultaneous stimulation, especially F120-T, were more affected by neural degeneration than with sequential stimulation. Results in SMT experiments showed no significant difference in performance. Although the proposed model in its current state is able to perform SMT and SRT experiments, it is not reliable to predict real CI users' performance yet. Nevertheless, improvements related to the ANF model, feature extraction, and predictor algorithm are discussed.

A Computational Model of a Single Auditory Nerve Fiber for Electric-Acoustic Stimulation

Cochlear implant (CI) recipients with preserved acoustic low-frequency hearing in the implanted ear are a growing group among traditional CI users who benefit from hybrid electric-acoustic stimulation (EAS). However, combined ipsilateral electric and acoustic stimulation also introduces interactions between the two modalities that can affect the performance of EAS users. A computational model of a single auditory nerve fiber that is excited by EAS was developed to study the interaction between electric and acoustic stimulation. Two existing models of sole electric or acoustic stimulation were coupled to simulate responses to combined EAS. Different methods of combining both models were implemented. In the coupled model variant, the refractoriness of the simulated fiber leads to suppressive interaction between electrically evoked and acoustically evoked spikes as well as spontaneous activity. The second model variant is an uncoupled EAS model without electric-acoustic interaction. By comparing predictions between the coupled and the noninteracting EAS model, it was possible to infer electric-acoustic interaction at the level of the auditory nerve. The EAS model was used to simulate fiber populations with realistic inter-unit variability, where each unit was represented by the single-fiber model. Predicted thresholds and dynamic ranges, spike rates, latencies, jitter, and vector strengths were compared to empirical data. The presented EAS model provides a framework for future studies of peripheral electric-acoustic interaction.

Comparison of response properties of the electrically stimulated auditory nerve reported in human listeners and in animal models

Cochlear implants (CIs) provide acoustic information to implanted patients by electrically stimulating nearby auditory nerve fibers (ANFs) which then transmit the information to higher-level neural structures for further processing and interpretation. Computational models that simulate ANF responses to CI stimuli enable the exploration of the mechanisms underlying CI performance beyond the capacity of in vivo experimentation alone. However, all ANF models developed to date utilize to some extent anatomical/morphometric data, biophysical properties and/or physiological data measured in non-human animal models. This review compares response properties of the electrically stimulated auditory nerve (AN) in human listeners and different mammalian models. Properties of AN responses to single pulse stimulation, paired-pulse stimulation, and pulse-train stimulation are presented. While some AN response properties are similar between human listeners and animal models (e.g., increased AN sensitivity to single pulse stimuli with long interphase gaps), there are some significant differences. For example, the AN of most animal models is typically more sensitive to cathodic stimulation while the AN of human listeners is generally more sensitive to anodic stimulation. Additionally, there are substantial differences in the speed of recovery from neural adaptation between animal models and human listeners. Therefore, results from animal models cannot be simply translated to human listeners. Recognizing the differences in responses of the AN to electrical stimulation between humans and other mammals is an important step for creating ANF models that are more applicable to various human CI patient populations.

Unifying information theory and machine learning in a model of electrode discrimination in cochlear implants

Despite the development and success of cochlear implants over several decades, wide inter-subject variability in speech perception is reported. This suggests that cochlear implant user-dependent factors limit speech perception at the individual level. Clinical studies have demonstrated the importance of the number, placement, and insertion depths of electrodes on speech recognition abilities. However, these do not account for all inter-subject variability and to what extent these factors affect speech recognition abilities has not been studied. In this paper, an information theoretic method and machine learning technique are unified in a model to investigate the extent to which key factors limit cochlear implant electrode discrimination. The framework uses a neural network classifier to predict which electrode is stimulated for a given simulated activation pattern of the auditory nerve, and mutual information is then estimated between the actual stimulated electrode and predicted ones. We also investigate how and to what extent the choices of parameters affect the performance of the model. The advantages of this framework include i) electrode discrimination ability is quantified using information theory, ii) it provides a flexible framework that may be used to investigate the key factors that limit the performance of cochlear implant users, and iii) it provides insights for future modeling studies of other types of neural prostheses.

Phenomenological model of auditory nerve population responses to cochlear implant stimulation

BACKGROUND

Models of auditory nerve fiber (ANF) responses to electrical stimulation are helpful to develop advanced coding for cochlear implants (CIs). A phenomenological model of ANF population responses to CI electrical stimulation with a lower computational complexity compared to a biophysical model would be beneficial to evaluate new CI coding strategies.

NEW METHOD

This study presents a phenomenological model which combines four temporal characteristics of ANFs (refractoriness, facilitation, accommodation and spike rate adaptation) in addition to a spatial spread of the electric field.

RESULTS

The model predicts the performances of CI subjects in the melodic contour identification (MCI) experiment. The simulations for the MCI experiment were consistent with CI recipients' experimental outcomes that were not predictable from the electrical stimulation patterns themselves.

COMPARISON WITH EXISTING METHODS

Previously, no phenomenological population model of ANFs has combined all four aforementioned temporal phenomena.

CONCLUSIONS

The proposed model would help the further investigations of ANFs responses to different electrical stimulation patterns and comparison of different sound coding strategies in CIs.

Short and long-term adaptation in the auditory nerve stimulated with high-rate electrical pulse trains are better described by a power law

Despite the introduction of many new sound-coding strategies speech perception outcomes in cochlear implant listeners have leveled off. Computer models may help speed up the evaluation of new sound-coding strategies, but most existing models of auditory nerve responses to electrical stimulation include limited temporal detail, as the effects of longer stimulation, such as adaptation, are not well-studied. Measured neural responses to stimulation with both short (400 ms) and long (10 min) duration high-rate (5kpps) pulse trains were compared in terms of spike rate and vector strength (VS) with model outcomes obtained with different forms of adaptation. A previously published model combining biophysical and phenomenological approaches was adjusted with adaptation modeled as a single decaying exponent, multiple exponents and a power law. For long duration data, power law adaptation by far outperforms the single exponent model, especially when it is optimized per fiber. For short duration data, all tested models performed comparably well, with slightly better performance of the single exponent model for VS and of the power law model for the spike rates. The power law parameter sets obtained when fitted to the long duration data also yielded adequate predictions for short duration stimulation, and vice versa. The power law function can be approximated with multiple exponents, which is physiologically more viable. The number of required exponents depends on the duration of simulation; the 400 ms data was well-replicated by two exponents (23 and 212 ms), whereas the 10-minute data required at least seven exponents (ranging from 4 ms to 600 s). Adaptation of the auditory nerve to high-rate electrical stimulation can best be described by a power-law or a sum of exponents. This gives an adequate fit for both short and long duration stimuli, such as CI speech segments.

Effect of neural adaptation and degeneration on pulse-train ECAPs: A model study

Electrically evoked compound action potentials (eCAPs) are measurements of the auditory nerve's response to electrical stimulation. ECAP amplitudes during pulse trains can exhibit temporal alternations. The magnitude of this alternation tends to diminish over time during the stimulus. How this pattern relates to the temporal behavior of nerve fibers is not known. We hypothesized that the stochasticity, refractoriness, adaptation of the threshold and spike-times influence pulse-train eCAP responses. Thirty thousand auditory nerve fibers were modeled in a three-dimensional cochlear model incorporating pulse-shape effects, pulse-history effects, and stochasticity in the individual neural responses. ECAPs in response to pulse trains of different rates and amplitudes were modeled for fibers with different stochastic properties (by variation of the relative spread) and different temporal properties (by variation of the refractory periods, adaptation and latency). The model predicts alternation of peak amplitudes similar to available human data. In addition, the peak alternation was affected by changing the refractoriness, adaptation, and relative spread of auditory nerve fibers. As these parameters are related to factors such as the duration of deafness and neural survival, this study suggests that the eCAP pattern in response to pulse trains could be used to assess the underlying temporal and stochastic behavior of the auditory nerve. As these properties affect the nerve's response to pulse trains, they are of uttermost importance to sound perception with cochlear implants.

Analysis of a purely conductance-based stochastic nerve fibre model as applied to compound models of populations of human auditory nerve fibres used in cochlear implant simulations

The study presents the application of a purely conductance-based stochastic nerve fibre model to human auditory nerve fibres within finite element volume conduction models of a semi-generic head and user-specific cochleae. The stochastic, threshold and temporal characteristics of the human model are compared and successfully validated against physiological feline results with the application of a mono-polar, bi-phasic, cathodic first stimulus. Stochastic characteristics validated include: (i) the log(Relative Spread) versus log(fibre diameter) distribution for the discharge probability versus stimulus intensity plots and (ii) the required exponential membrane noise versus transmembrane voltage distribution. Intra-user, and to a lesser degree inter-user, comparisons are made with respect to threshold and dynamic range at short and long pulse widths for full versus degenerate single fibres as well as for populations of degenerate fibres of a single user having distributed and aligned somas with varying and equal diameters. Temporal characteristics validated through application of different stimulus pulse rates and different stimulus intensities include: (i) discharge rate, latency and latency standard deviation versus stimulus intensity, (ii) period histograms and (iii) interspike interval histograms. Although the stochastic population model does not reduce the modelled single deterministic fibre threshold, the simulated stochastic and temporal characteristics show that it could be used in future studies to model user-specific temporally encoded information, which influences the speech perception of CI users.

Modeled auditory nerve responses to amplitude modulated cochlear implant stimulation

Cochlear implants encode speech information by stimulating the auditory nerve with amplitude-modulated pulse trains. A computer model of the auditory nerve's response to electrical stimulation can be used to evaluate different approaches to improving CI patients' perception. In this paper a computationally efficient stochastic and adaptive auditory nerve model was used to investigate full nerve responses to amplitude-modulated electrical pulse trains. The model was validated for nerve responses to AM pulse trains via comparison with animal data. The influence of different parameters, such as adaptation and stochasticity, on long-term adaptation and modulation-following behavior was investigated. Responses to pulse trains with different pulse amplitudes, amplitude modulation frequencies, and modulation depths were modeled. Rate responses as well as period histograms, Vector Strength and the fundamental frequency were characterized in different time bins. The response alterations, including frequency following behavior, observed over the stimulus duration were similar to those seen in animal experiments. The tested model can be used to predict complete nerve responses to arbitrary input, and thus to different sound coding strategies.

A Model of Electrically Stimulated Auditory Nerve Fiber Responses with Peripheral and Central Sites of Spike Generation

A computational model of cat auditory nerve fiber (ANF) responses to electrical stimulation is presented. The model assumes that (1) there exist at least two sites of spike generation along the ANF and (2) both an anodic (positive) and a cathodic (negative) charge in isolation can evoke a spike. A single ANF is modeled as a network of two exponential integrate-and-fire point-neuron models, referred to as peripheral and central axons of the ANF. The peripheral axon is excited by the cathodic charge, inhibited by the anodic charge, and exhibits longer spike latencies than the central axon; the central axon is excited by the anodic charge, inhibited by the cathodic charge, and exhibits shorter spike latencies than the peripheral axon. The model also includes subthreshold and suprathreshold adaptive feedback loops which continuously modify the membrane potential and can account for effects of facilitation, accommodation, refractoriness, and spike-rate adaptation in ANF. Although the model is parameterized using data for either single or paired pulse stimulation with monophasic rectangular pulses, it correctly predicts effects of various stimulus pulse shapes, stimulation pulse rates, and level on the neural response statistics. The model may serve as a framework to explore the effects of different stimulus parameters on psychophysical performance measured in cochlear implant listeners.

A computational model that predicts behavioral sensitivity to intracortical microstimulation

OBJECTIVE

Intracortical microstimulation (ICMS) is a powerful tool to investigate the neural mechanisms of perception and can be used to restore sensation for patients who have lost it. While sensitivity to ICMS has previously been characterized, no systematic framework has been developed to summarize the detectability of individual ICMS pulse trains or the discriminability of pairs of pulse trains.

APPROACH

We develop a simple simulation that describes the responses of a population of neurons to a train of electrical pulses delivered through a microelectrode. We then perform an ideal observer analysis on the simulated population responses to predict the behavioral performance of non-human primates in ICMS detection and discrimination tasks.

MAIN RESULTS

Our computational model can predict behavioral performance across a wide range of stimulation conditions with high accuracy (R ² = 0.97) and generalizes to novel ICMS pulse trains that were not used to fit its parameters. Furthermore, the model provides a theoretical basis for the finding that amplitude discrimination based on ICMS violates Weber's law.

SIGNIFICANCE

The model can be used to characterize the sensitivity to ICMS across the range of perceptible and safe stimulation regimes. As such, it will be a useful tool for both neuroscience and neuroprosthetics.

Predictions of the Contribution of HCN Half-Maximal Activation Potential Heterogeneity to Variability in Intrinsic Adaptation of Spiral Ganglion Neurons

Spiral ganglion neurons (SGNs) exhibit a wide range in their strength of intrinsic adaptation on a timescale of 10s to 100s of milliseconds in response to electrical stimulation from a cochlear implant (CI). The purpose of this study was to determine how much of that variability could be caused by the heterogeneity in half-maximal activation potentials of hyperpolarization-activated cyclic nucleotide-gated cation (HCN) channels, which are known to produce intrinsic adaptation. In this study, a computational membrane model of cat type I SGN was developed based on the Hodgkin-Huxley model plus HCN and low-threshold potassium (KLT) conductances in which the half-maximal activation potential of the HCN channel was varied and the response of the SGN to pulse train and paired-pulse stimulation was simulated. Physiologically plausible variation of HCN half-maximal activation potentials could indeed determine the range of adaptation on the timescale of 10s to 100s of milliseconds and recovery from adaptation seen in the physiological data while maintaining refractoriness within physiological bounds. This computational model demonstrates that HCN channels may play an important role in regulating the degree of adaptation in response to pulse train stimulation and therefore contribute to variable constraints on acoustic information coding by CIs. This finding has broad implications for CI stimulation paradigms in that cell-to-cell variation of HCN channel properties are likely to significantly alter SGN excitability and therefore auditory perception.

Loudness and pitch perception using Dynamically Compensated Virtual Channels

Reducing power consumption is important for the development of smaller cochlear implant (CI) speech processors. Simultaneous electrode stimulation may improve power efficiency by minimizing the required current applied to a given electrode. Simultaneous in-phase stimulation on adjacent electrodes (i.e. virtual channels) can be used to elicit pitch percepts intermediate to the ones provided by each of the physical electrodes in isolation. Virtual channels are typically implemented in monopolar stimulation mode, producing broad excitation patterns. Focused stimulation may reduce the excitation patterns, but is inefficient in terms of power consumption. To create a more power efficient virtual channel, we developed the Dynamically Compensated Virtual Channel (DC-VC) using four adjacent electrodes. The two central electrodes are current steered using the coefficient α (0<α<1 ) whereas the two flanking electrodes are used to focus/unfocus the stimulation with the coefficient σ (-1<σ<1). With increasing values of σ, power can be saved at the potential expense of generating broader electric fields. Additionally, reshaping the electric fields might also alter place pitch coding. The goal of the present study is to investigate the tradeoff between place pitch encoding and power savings using simultaneous electrode stimulation in the DC-VC configuration. A computational model and psychophysical experiments in CI users have been used for that purpose. Results from 10 adult Advanced Bionics CI users have been collected. Results show that the required current to produce comfortable levels is significantly reduced with increasing σ as predicted by the computational model. Moreover, no significant differences in the estimated number of discriminable steps were detected for the different values of σ. From these results, we conclude that DC-VCs can reduce power consumption without decreasing the number of discriminable place pitch steps.

Development of a voltage-dependent current noise algorithm for conductance-based stochastic modelling of auditory nerve fibres

This study presents the development of an alternative noise current term and novel voltage-dependent current noise algorithm for conductance-based stochastic auditory nerve fibre (ANF) models. ANFs are known to have significant variance in threshold stimulus which affects temporal characteristics such as latency. This variance is primarily caused by the stochastic behaviour or microscopic fluctuations of the node of Ranvier's voltage-dependent sodium channels of which the intensity is a function of membrane voltage. Though easy to implement and low in computational cost, existing current noise models have two deficiencies: it is independent of membrane voltage, and it is unable to inherently determine the noise intensity required to produce in vivo measured discharge probability functions. The proposed algorithm overcomes these deficiencies while maintaining its low computational cost and ease of implementation compared to other conductance and Markovian-based stochastic models. The algorithm is applied to a Hodgkin-Huxley-based compartmental cat ANF model and validated via comparison of the threshold probability and latency distributions to measured cat ANF data. Simulation results show the algorithm's adherence to in vivo stochastic fibre characteristics such as an exponential relationship between the membrane noise and transmembrane voltage, a negative linear relationship between the log of the relative spread of the discharge probability and the log of the fibre diameter and a decrease in latency with an increase in stimulus intensity.

Temporal Considerations for Stimulating Spiral Ganglion Neurons with Cochlear Implants

A wealth of knowledge about different types of neural responses to electrical stimulation has been developed over the past 100 years. However, the exact forms of neural response properties can vary across different types of neurons. In this review, we survey four stimulus-response phenomena that in recent years are thought to be relevant for cochlear implant stimulation of spiral ganglion neurons (SGNs): refractoriness, facilitation, accommodation, and spike rate adaptation. Of these four, refractoriness is the most widely known, and many perceptual and physiological studies interpret their data in terms of refractoriness without incorporating facilitation, accommodation, or spike rate adaptation. In reality, several or all of these behaviors are likely involved in shaping neural responses, particularly at higher stimulation rates. A better understanding of the individual and combined effects of these phenomena could assist in developing improved cochlear implant stimulation strategies. We review the published physiological data for electrical stimulation of SGNs that explores these four different phenomena, as well as some of the recent studies that might reveal the biophysical bases of these stimulus-response phenomena.

Optogenetic stimulation of the cochlea-A review of mechanisms, measurements, and first models

This review evaluates the potential of optogenetic methods for the stimulation of the auditory nerve and assesses the feasability of optogenetic cochlear implants (CIs). It provides an overview of all critical steps like opsin targeting strategies, how opsins work, how their function can be modeled and included in neuronal models and the properties of light sources available for optical stimulation. From these foundations, quantitative estimates for the number of independent stimulation channels and the temporal precision of optogenetic stimulation of the auditory nerve are derived and compared with state-of-the-art electrical CIs. We conclude that optogenetic CIs have the potential to increase the number of independent stimulation channels by up to one order of magnitude to about 100, but only if light sources are able to deliver confined illumination patterns independently and parallelly. Already now, opsin variants like ChETA and Chronos enable driving of the auditory nerve up to rates of 200 spikes/s, close to the physiological value of their maximum sustained firing rate. Apart from requiring 10 times more energy than electrical stimulation, optical CIs still face major hurdles concerning the safety of gene transfection and optrode array implantation, for example, before becoming an option to replace electrical CIs.

Models of the electrically stimulated binaural system: A review

In an increasing number of countries, the standard treatment for deaf individuals is moving toward the implantation of two cochlear implants. Today's device technology and fitting procedure, however, appears as if the two implants would serve two independent ears and brains. Many experimental studies have demonstrated that after careful matching and balancing of left and right stimulation in controlled laboratory studies most patients have almost normal sensitivity to interaural level differences and some sensitivity to interaural time differences (ITDs). Mechanisms underlying the limited ITD sensitivity are still poorly understood and many different aspects may contribute. Recent pioneering computational approaches identified some of the functional implications the electric input imposes on the neural brainstem circuits. Simultaneously these studies have raised new questions and certainly demonstrated that further refinement of the model stages is necessary. They join the experimental study's conclusions that binaural device technology, binaural fitting, specific speech coding strategies, and binaural signal processing algorithms are obviously missing components to maximize the benefit of bilateral implantation. Within this review, the existing models of the electrically stimulated binaural system are explained, compared, and discussed from a viewpoint of a "CI device with auditory system" and from that of neurophysiological research.

Phenomenological modelling of electrically stimulated auditory nerve fibers: A review

Auditory nerve fibers (ANFs) play a crucial role in hearing by encoding and transporting the synaptic input from inner hair cells into afferent spiking information for higher stages of the auditory system. If the inner hair cells are degenerated, cochlear implants may restore hearing by directly stimulating the ANFs. The response of an ANF is affected by several characteristics of the electrical stimulus and of the ANF, and neurophysiological measurements are needed to know how the ANF responds to a particular stimulus. However, recording from individual nerve fibers in humans is not feasible and obtaining compound neural or psychophysical responses is often time-consuming. This motivates the design and use of models to estimate the ANF response to the electrical stimulation. Phenomenological models reproduce the ANF response based on a simplified description of ANF functionality and on a limited parameter space by not directly describing detailed biophysical mechanisms. Here, we give an overview of phenomenological models published to date and demonstrate how different modeling approaches can account for the diverse phenomena affecting the ANF response. To highlight the success achieved in designing such models, we also describe a number of applications of phenomenological models to predict percepts of cochlear implant listeners.

Stimulation strategies and electrode design in computational models of the electrically stimulated cochlea: An overview of existing literature

Since the 1970s, computational modeling has been used to investigate the fundamental mechanisms of cochlear implant stimulation. Lumped parameter models and analytical models have been used to simulate cochlear potentials, as well as three-dimensional volume conduction models based on the Finite Difference, Finite Element, and Boundary Element methods. Additionally, in order to simulate neural responses, several of these cochlear models have been combined with nerve models, which were either simple activation functions or active nerve fiber models of the cochlear auditory neurons. This review paper will present an overview of the ways in which these computational models have been employed to study different stimulation strategies and electrode designs. Research into stimulation strategies has concentrated mainly on multipolar stimulation as a means of achieving current focussing and current steering, while modeling work on electrode design has been chiefly concerned with finding the optimal position and insertion depth of the electrode array. Finally, the present and future of computational modeling of the electrically stimulated cochlea is discussed.

A Phenomenological Model of the Electrically Stimulated Auditory Nerve Fiber: Temporal and Biphasic Response Properties

We present a phenomenological model of electrically stimulated auditory nerve fibers (ANFs). The model reproduces the probabilistic and temporal properties of the ANF response to both monophasic and biphasic stimuli, in isolation. The main contribution of the model lies in its ability to reproduce statistics of the ANF response (mean latency, jitter, and firing probability) under both monophasic and cathodic-anodic biphasic stimulation, without changing the model's parameters. The response statistics of the model depend on stimulus level and duration of the stimulating pulse, reproducing trends observed in the ANF. In the case of biphasic stimulation, the model reproduces the effects of pseudomonophasic pulse shapes and also the dependence on the interphase gap (IPG) of the stimulus pulse, an effect that is quantitatively reproduced. The model is fitted to ANF data using a procedure that uniquely determines each model parameter. It is thus possible to rapidly parameterize a large population of neurons to reproduce a given set of response statistic distributions. Our work extends the stochastic leaky integrate and fire (SLIF) neuron, a well-studied phenomenological model of the electrically stimulated neuron. We extend the SLIF neuron so as to produce a realistic latency distribution by delaying the moment of spiking. During this delay, spiking may be abolished by anodic current. By this means, the probability of the model neuron responding to a stimulus is reduced when a trailing phase of opposite polarity is introduced. By introducing a minimum wait period that must elapse before a spike may be emitted, the model is able to reproduce the differences in the threshold level observed in the ANF for monophasic and biphasic stimuli. Thus, the ANF response to a large variety of pulse shapes are reproduced correctly by this model.

A neural-based vocoder implementation for evaluating cochlear implant coding strategies

Most simulations of cochlear implant (CI) coding strategies rely on standard vocoders that are based on purely signal processing techniques. However, these models neither account for various biophysical phenomena, such as neural stochasticity and refractoriness, nor for effects of electrical stimulation, such as spectral smearing as a function of stimulus intensity. In this paper, a neural model that accounts for stochastic firing, parasitic spread of excitation across neuron populations, and neuronal refractoriness, was developed and augmented as a preprocessing stage for a standard 22-channel noise-band vocoder. This model was used to subjectively and objectively assess consonant discrimination in commercial and experimental coding strategies. Stimuli consisting of consonant-vowel (CV) and vowel-consonant-vowel (VCV) tokens were processed by either the Advanced Combination Encoder (ACE) or the Excitability Controlled Coding (ECC) strategies, and later resynthesized to audio using the aforementioned vocoder model. Baseline performance was measured using unprocessed versions of the speech tokens. Behavioural responses were collected from seven normal hearing (NH) volunteers, while EEG data were recorded from five NH participants. Psychophysical results indicate that while there may be a difference in consonant perception between the two tested coding strategies, mismatch negativity (MMN) waveforms do not show any marked trends in CV or VCV contrast discrimination.

Three-dimensional models of cochlear implants: A review of their development and how they could support management and maintenance of cochlear implant performance

Three-dimensional (3D) computational modeling of the auditory periphery forms an integral part of modern-day research in cochlear implants (CIs). These models consist of a volume conduction description of implanted stimulation electrodes and the current distribution around these, coupled with auditory nerve fiber models. Cochlear neural activation patterns can then be predicted for a given input stimulus. The objective of this article is to present the context of 3D modeling within the field of CIs, the different models, and approaches to models that have been developed over the years, as well as the applications and potential applications of these models. The process of development of 3D models is discussed, and the article places specific emphasis on the complementary roles of generic models and user-specific models, as the latter is important for translation of these models into clinical application.

Stimulus-dependent refractoriness in the Frankenhaeuser-Huxley model

Phenomenological neural models, such as the leaky integrate-and-fire model, normally have a fixed refractory time-course that is independent of the stimulus. The recovery of threshold following an action potential is typically based on physiological experiments that use a two-pulse paradigm in which the first pulse is suprathreshold and causes excitation and the second pulse is used to determine the threshold at various intervals following the first. In such experiments, the nerve is completely unstimulated between the two pulses. This contrasts the receptor stimuli in normal physiological systems and the electrical stimuli used by cochlear implants and other neural prostheses. A numerical study of the Frankenhaeuser-Huxley conductance-based model of nerve fibre was therefore undertaken to investigate the effect of stimulation on refractoriness. We found that the application of a depolarizing stimulus during the later part of what is classically regarded as the absolute refractory period could effectively prolong the absolute refractory period, while leaving the refractory time-constants and other refractory parameters largely unaffected. Indeed, long depolarizing pulses, which would have been suprathreshold if presented to a resting nerve fibre, appeared to block excitation indefinitely. Stimulation during what is classically regarded as the absolute refractory period can therefore greatly affect the temporal response of a nerve. We conclude that the classical definition of absolute refractory period should be refined to include only the initial period following an action potential when an ongoing stimulus would not affect threshold; this period was found to be about half as long as the classical absolute refractory period. We further conclude that the stimulus-dependent nature of the relative refractory period must be considered when developing a phenomenological nerve model for complex stimuli.

A phenomenological model of myelinated nerve with a dynamic threshold

To evaluate coding strategies for cochlear implants a model of the human cochlear nerve is required. Nerve models based on voltage-clamp experiments, such as the Frankenhaeuser-Huxley model of myelinated nerve, can have over forty parameters and are not amenable for fitting to physiological data from a different animal or type of nerve. Phenomenological nerve models, such as leaky integrate-and-fire (LIF) models, have fewer parameters but have not been validated with a wide range of stimuli. In the absence of substantial cochlear nerve data, we have used data from a toad sciatic nerve for validation (50 Hz to 2 kHz with levels up to 20 dB above threshold). We show that the standard LIF model with fixed refractory properties and a single set of parameters cannot adequately predict the toad rate-level functions. Given the deficiency of this standard model, we have abstracted the dynamics of the sodium inactivation variable in the Frankenhaeuser-Huxley model to develop a phenomenological LIF model with a dynamic threshold. This nine-parameter model predicts the physiological rate-level functions much more accurately than the standard LIF model. Because of the low number of parameters, we expect to be able to optimize the model parameters so that the model is more appropriate for cochlear implant simulations.

Modeling binaural responses in the auditory brainstem to electric stimulation of the auditory nerve

Bilateral cochlear implants (CIs) provide improvements in sound localization and speech perception in noise over unilateral CIs. However, the benefits arise mainly from the perception of interaural level differences, while bilateral CI listeners' sensitivity to interaural time difference (ITD) is poorer than normal. To help understand this limitation, a set of ITD-sensitive neural models was developed to study binaural responses to electric stimulation. Our working hypothesis was that central auditory processing is normal with bilateral CIs so that the abnormality in the response to electric stimulation at the level of the auditory nerve fibers (ANFs) is the source of the limited ITD sensitivity. A descriptive model of ANF response to both acoustic and electric stimulation was implemented and used to drive a simplified biophysical model of neurons in the medial superior olive (MSO). The model's ITD sensitivity was found to depend strongly on the specific configurations of membrane and synaptic parameters for different stimulation rates. Specifically, stronger excitatory synaptic inputs and faster membrane responses were required for the model neurons to be ITD-sensitive at high stimulation rates, whereas weaker excitatory synaptic input and slower membrane responses were necessary at low stimulation rates, for both electric and acoustic stimulation. This finding raises the possibility of frequency-dependent differences in neural mechanisms of binaural processing; limitations in ITD sensitivity with bilateral CIs may be due to a mismatch between stimulation rate and cell parameters in ITD-sensitive neurons.

Information theoretic optimization of cochlear implant electrode usage probabilities

Cochlear implants are neural prostheses that can restore hearing. Contemporary cochlear implant devices consist of up to 22 electrodes. An open question for future cochlear implants is whether new electrode designs that enable less current spread may provide improved hearing performance through more precise control of neural activation, more electrodes, or more precise positioning. Here we use a recently proposed information theoretic model for the electro-neural interface that enables estimates to be made of the optimal number of electrodes for different amounts of current spread. We apply information theoretic approaches for finding the channel capacity in the model to enable estimates of optimal electrode usage probabilities and positions. We also compare the performance in the model when auditory nerve fibers are assumed to be heterogenous, with a random distribution of firing thresholds and relative spreads, versus an assumption that they are all identical.

A point process framework for modeling electrical stimulation of the auditory nerve

Model-based studies of responses of auditory nerve fibers to electrical stimulation can provide insight into the functioning of cochlear implants. Ideally, these studies can identify limitations in sound processing strategies and lead to improved methods for providing sound information to cochlear implant users. To accomplish this, models must accurately describe spiking activity while avoiding excessive complexity that would preclude large-scale simulations of populations of auditory nerve fibers and obscure insight into the mechanisms that influence neural encoding of sound information. In this spirit, we develop a point process model of individual auditory nerve fibers that provides a compact and accurate description of neural responses to electric stimulation. Inspired by the framework of generalized linear models, the proposed model consists of a cascade of linear and nonlinear stages. We show how each of these stages can be associated with biophysical mechanisms and related to models of neuronal dynamics. Moreover, we derive a semianalytical procedure that uniquely determines each parameter in the model on the basis of fundamental statistics from recordings of single fiber responses to electric stimulation, including threshold, relative spread, jitter, and chronaxie. The model also accounts for refractory and summation effects that influence the responses of auditory nerve fibers to high pulse rate stimulation. Throughout, we compare model predictions to published physiological data of response to high and low pulse rate stimulation. We find that the model, although constructed to fit data from single and paired pulse experiments, can accurately predict responses to unmodulated and modulated pulse train stimuli. We close by performing an ideal observer analysis of simulated spike trains in response to sinusoidally amplitude modulated stimuli and find that carrier pulse rate does not affect modulation detection thresholds.

Prediction and control of neural responses to pulsatile electrical stimulation

This paper aims to predict and control the probability of firing of a neuron in response to pulsatile electrical stimulation of the type delivered by neural prostheses such as the cochlear implant, bionic eye or in deep brain stimulation. Using the cochlear implant as a model, we developed an efficient computational model that predicts the responses of auditory nerve fibers to electrical stimulation and evaluated the model's accuracy by comparing the model output with pooled responses from a group of guinea pig auditory nerve fibers. It was found that the model accurately predicted the changes in neural firing probability over time to constant and variable amplitude electrical pulse trains, including speech-derived signals, delivered at rates up to 889 pulses s(-1). A simplified version of the model that did not incorporate adaptation was used to adaptively predict, within its limitations, the pulsatile electrical stimulus required to cause a desired response from neurons up to 250 pulses s(-1). Future stimulation strategies for cochlear implants and other neural prostheses may be enhanced using similar models that account for the way that neural responses are altered by previous stimulation.

Modeling the electrode-neuron interface of cochlear implants: effects of neural survival, electrode placement, and the partial tripolar configuration

The partial tripolar electrode configuration is a relatively novel stimulation strategy that can generate more spatially focused electric fields than the commonly used monopolar configuration. Focused stimulation strategies should improve spectral resolution in cochlear implant users, but may also be more sensitive to local irregularities in the electrode-neuron interface. In this study, we develop a practical computer model of cochlear implant stimulation that can simulate neural activation in a simplified cochlear geometry and we relate the resulting patterns of neural activity to basic psychophysical measures. We examine how two types of local irregularities in the electrode-neuron interface, variations in spiral ganglion nerve density and electrode position within the scala tympani, affect the simulated neural activation patterns and how these patterns change with electrode configuration. The model shows that higher partial tripolar fractions activate more spatially restricted populations of neurons at all current levels and require higher current levels to excite a given number of neurons. We find that threshold levels are more sensitive at high partial tripolar fractions to both types of irregularities, but these effects are not independent. In particular, at close electrode-neuron distances, activation is typically more spatially localized which leads to a greater influence of neural dead regions.

Neural response telemetry reconsidered: II. The influence of neural population on the ECAP recovery function and refractoriness

OBJECTIVE

The Neural Response Telemetry (NRT) recovery function measures the electrically evoked compound action potential (ECAP) in response to a second biphasic pulse (the probe) after masking by a first pulse (the masker). The masker-probe interval is varied and the ECAP amplitude is measured at each masker-probe interval, giving an inverse exponential recovery. The prevailing understanding of the recovery function has been that faster recovery indicates a more efficient response to the individual pulses within a pulse sequence. Psychophysical data in the past have not supported this view, and in fact, the opposite result has been observed. This study explores this phenomenon from theoretical and experimental viewpoints. Fundamentally, a distinction is made between the refractoriness of a single fiber and the refractoriness of the whole nerve. The hypothesis is that the size of the neural population heavily influences whole nerve refractoriness: large neural populations operate near threshold and are more susceptible to masking, leading to slower ECAP recovery; however, they maintain temporal responsiveness through greater numbers of nonrefractory neurons.

DESIGN

In phase I, the hearing loss durations (indicators of neural survival) of 21 adult Nucleus Freedom implantees were compared with the corresponding median recovery function time-constants (calculated per implant array). The data were separated by implant (nine Contour, 12 Straight) and the means of these two groups were compared. The Straight array, delivering broader excitation, is expected to engage a larger neural population. In phase II, a computational model of the ECAP recovery function was constructed based on data from the cat auditory nerve. The model allows the neural population size to be manipulated; accordingly, recovery functions from different neural populations were compared. In phase III, ECAP thresholds (via AutoNRT), ECAP recovery functions, and T- and C-levels were obtained from a subset of 12 subjects. Psychophysical levels were measured using pulse train stimuli at six different stimulation rates, spanning 250 to 3500 Hz. At each electrode, the recovery function time-constant tau was compared with two measures of temporal responsiveness: (i) the gradient of the linear trend in psychophysical levels with stimulation rate; and (ii) the difference between ECAP threshold (a single pulse measure) and 900 Hz T-level (a pulse train measure).

RESULTS

In phase I, a trend toward shorter recovery function time-constants with increasing hearing loss durations was observed. The mean recovery function time-constant of the Contour implant group (0.51 msec) was significantly shorter than that of the Straight implant group (0.90 msec). When, in phase II, the recovery functions from the computational model were compared at equal ECAP amplitude, the larger neural population was associated with slower ECAP recovery. In phase III, the recovery function time-constant was significantly correlated with both temporal responsiveness measures, with slower ECAP, recovery associated with greater temporal responsiveness, thus confirming the results of previous studies.

CONCLUSIONS

: Slower ECAP recovery, at equal loudness, is associated with larger neural populations. The collective results suggest that this neural population view of the recovery function explains the observed association between slower ECAP recovery and greater temporal responsiveness.

Encoding and decoding amplitude-modulated cochlear implant stimuli--a point process analysis

Cochlear implant speech processors stimulate the auditory nerve by delivering amplitude-modulated electrical pulse trains to intracochlear electrodes. Studying how auditory nerve cells encode modulation information is of fundamental importance, therefore, to understanding cochlear implant function and improving speech perception in cochlear implant users. In this paper, we analyze simulated responses of the auditory nerve to amplitude-modulated cochlear implant stimuli using a point process model. First, we quantify the information encoded in the spike trains by testing an ideal observer's ability to detect amplitude modulation in a two-alternative forced-choice task. We vary the amount of information available to the observer to probe how spike timing and averaged firing rate encode modulation. Second, we construct a neural decoding method that predicts several qualitative trends observed in psychophysical tests of amplitude modulation detection in cochlear implant listeners. We find that modulation information is primarily available in the sequence of spike times. The performance of an ideal observer, however, is inconsistent with observed trends in psychophysical data. Using a neural decoding method that jitters spike times to degrade its temporal resolution and then computes a common measure of phase locking from spike trains of a heterogeneous population of model nerve cells, we predict the correct qualitative dependence of modulation detection thresholds on modulation frequency and stimulus level. The decoder does not predict the observed loss of modulation sensitivity at high carrier pulse rates, but this framework can be applied to future models that better represent auditory nerve responses to high carrier pulse rate stimuli. The supplemental material of this article contains the article's data in an active, re-usable format.

The dependence of auditory nerve rate adaptation on electric stimulus parameters, electrode position, and fiber diameter: a computer model study

This paper describes results from a stochastic computational neuron model that simulates the effects of rate adaptation on the responses to electrical stimulation in the form of pulse trains. We recently reported results from a single-node computational model that included a novel element that tracks external potassium ion concentration so as to modify membrane voltage and cause adaptation-like responses. Here, we report on an improved version of the model that incorporates the anatomical components of a complete feline auditory nerve fiber (ANF) so that conduction velocity and effects of manipulating the site of excitation can be evaluated. Model results demonstrate rate adaptation and changes in spike amplitude similar to those reported for feline ANFs. Changing the site of excitation from a central to a peripheral axonal site resulted in plausible changes in latency and relative spread (i.e., dynamic range). Also, increasing the distance between a modeled ANF and a stimulus electrode tended to decrease the degree of rate adaptation observed in pulse-train responses. This effect was clearly observed for high-rate (5,000 pulse/s) trains but not low-rate (250 pulse/s) trains. Finally, for relatively short electrode-to-ANF distances, increases in modeled ANF diameter increased the degree of rate adaptation. These results are compared against available feline ANF data, and possible effects of individual parameters are discussed.

Spatial spread of neural excitation: comparison of compound action potential and forward-masking data in cochlear implant recipients

The feasibility of using the electrically evoked compound action potential (ECAP), measured with the NRT system (Neural Response Telemetry) and the NRT software (version 2.04), to quantify the longitudinal spread of neural excitation was examined in four subjects fitted with the Nucleus C124M cochlear implant. The ECAP and psychophysical forward-masking profiles were measured using stimulation on each of three electrodes, in basal, middle and apical positions. Spatial spread profiles derived from the ECAP measure produced broader functions than those derived from the psychophysical measure. These results, together with investigation of the change of ECAP spread pattern with stimulation current, suggest that functions derived from this 'simple' method were more influenced by the spread of electric field from excited neuron to electrode array than by breadth of the neural excitation pattern. The recently released NRT version 3.0 permits the masker and probe pulses to be delivered to separate electrodes, thus removing a fundamental limitation of version 2.04. Results from a pilot study, in which this capability was exploited, suggest that the spatial functions from this 'advanced' method may provide a better correlation with results from psychophysical forward masking.

Effects of I(h) and I(KLT) on the response of the auditory nerve to electrical stimulation in a stochastic Hodgkin-Huxley model

An accurate model of auditory nerve fibers (ANFs) would help in improving cochlear implant (CI) functionality. Previous studies have shown that the original Hodgkin-Huxley (1952) model (with kinetics adjusted for mammalian body temperature) may be better at describing nodes of Ranvier in ANFs than models for other mammalian axon types. However, the HH model is still unable to explain a number of phenomena observed in auditory nerve responses to CI stimulation such as long-term accommodation, adaptation and the time-course of relative refractoriness. Recent physiological investigations of spiral ganglion cells have shown the presence of a number of ion channel types not considered in the previous modeling studies, including low-threshold potassium (I(KLT)) channels and hyperpolarization-activated cation (I(h)) channels. In this paper we investigate inclusion of these ion channel types in a stochastic HH model. For single biphasic charge-balanced pulse, an increase in spike threshold was typically produced by inclusion of one or both of these channel types. The addition of I(KLT) increases random threshold fluctuations in the stochastic model, particularly for longer pulse widths. Pulse-train responses were investigated for pulse rates of 200, 800, and 2000 pulse/s. Initial results suggests that both the I(KLT) channels and I(h) channels can produce adaptation in the spike rate. However, the adaptation due to I(KLT) is restricted to higher stimulation rates, whereas the adaptation due to I(h) is observed across all stimulation rates.

Spontaneous activity of auditory nerve fibers in the barn owl (Tyto alba): analyses of interspike interval distributions

In vertebrate auditory systems, the conversion from graded receptor potentials across the hair-cell membrane into stochastic spike trains of the auditory nerve (AN) fibers is performed by ribbon synapses. The statistics underlying this process constrain auditory coding but are not precisely known. Here, we examine the distributions of interspike intervals (ISIs) from spontaneous activity of AN fibers of the barn owl (Tyto alba), a nocturnal avian predator whose auditory system is specialized for precise temporal coding. The spontaneous activity of AN fibers, with the exception of those showing preferred intervals, is commonly thought to result from excitatory events generated by a homogeneous Poisson point process, which lead to spikes unless the fiber is refractory. We show that the ISI distributions in the owl are better explained as resulting from the action of a brief refractory period ( approximately 0.5 ms) on excitatory events generated by a homogeneous stochastic process where the distribution of interevent intervals is a mixture of an exponential and a gamma distribution with shape factor 2, both with the same scaling parameter. The same model was previously shown to apply to AN fibers in the cat. However, the mean proportions of exponentially versus gamma-distributed intervals in the mixture were different for cat and owl. Furthermore, those proportions were constant across fibers in the cat, whereas they covaried with mean spontaneous rate and with characteristic frequency in the owl. We hypothesize that in birds, unlike in mammals, more than one ribbon may provide excitation to most fibers, accounting for the different proportions, and that variation in the number of ribbons may underlie the variation in the proportions.

Estimation of stimulus attenuation in cochlear implants

Neural excitation profile widths at the neural level, for monopolar stimulation with Nucleus straight and contour arrays respectively, were simulated using a combined volume-conduction-neural model. The electrically evoked compound action potential profile widths at the electrode array level were calculated with a simple approximation method employing stimulus attenuation inside the cochlear duct, and the results compared to profile width data from literature. The objective of the article is to develop a simple method to estimate stimulus attenuation values by calculating the values that best fit the modelled excitation profile widths to the measured evoked compound action potential profile widths. Results indicate that the modelled excitation profile widths decrease with increasing stimulus attenuation. However, fitting of modelled excitation profile widths to measured evoked compound action potential profile widths show that different stimulus attenuation values are needed for different stimulation levels. It is suggested that the proposed simple model can provide an estimate of stimulus attenuation by calculating the value of the parameter that produces the best fit to experimental data in specific human subjects.

Evaluation of stochastic differential equation approximation of ion channel gating models

Fox and Lu derived an algorithm based on stochastic differential equations for approximating the kinetics of ion channel gating that is simpler and faster than "exact" algorithms for simulating Markov process models of channel gating. However, the approximation may not be sufficiently accurate to predict statistics of action potential generation in some cases. The objective of this study was to develop a framework for analyzing the inaccuracies and determining their origin. Simulations of a patch of membrane with voltage-gated sodium and potassium channels were performed using an exact algorithm for the kinetics of channel gating and the approximate algorithm of Fox & Lu. The Fox & Lu algorithm assumes that channel gating particle dynamics have a stochastic term that is uncorrelated, zero-mean Gaussian noise, whereas the results of this study demonstrate that in many cases the stochastic term in the Fox & Lu algorithm should be correlated and non-Gaussian noise with a non-zero mean. The results indicate that: (i) the source of the inaccuracy is that the Fox & Lu algorithm does not adequately describe the combined behavior of the multiple activation particles in each sodium and potassium channel, and (ii) the accuracy does not improve with increasing numbers of channels.