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

A computational modelling framework for assessing information transmission with cochlear implants

Computational models are useful tools to investigate scientific questions that would be complicated to address using an experimental approach. In the context of cochlear-implants (CIs), being able to simulate the neural activity evoked by these devices could help in understanding their limitations to provide natural hearing. Here, we present a computational modelling framework to quantify the transmission of information from sound to spikes in the auditory nerve of a CI user. The framework includes a model to simulate the electrical current waveform sensed by each auditory nerve fiber (electrode-neuron interface), followed by a model to simulate the timing at which a nerve fiber spikes in response to a current waveform (auditory nerve fiber model). Information theory is then applied to determine the amount of information transmitted from a suitable reference signal (e.g., the acoustic stimulus) to a simulated population of auditory nerve fibers. As a use case example, the framework is applied to simulate published data on modulation detection by CI users obtained using direct stimulation via a single electrode. Current spread as well as the number of fibers were varied independently to illustrate the framework capabilities. Simulations reasonably matched experimental data and suggested that the encoded modulation information is proportional to the total neural response. They also suggested that amplitude modulation is well encoded in the auditory nerve for modulation rates up to 1000 Hz and that the variability in modulation sensitivity across CI users is partly because different CI users use different references for detecting modulation.

Resolving molecular contributions of ion channel noise to interspike interval variability through stochastic shielding

Molecular fluctuations can lead to macroscopically observable effects. The random gating of ion channels in the membrane of a nerve cell provides an important example. The contributions of independent noise sources to the variability of action potential timing have not previously been studied at the level of molecular transitions within a conductance-based model ion-state graph. Here we study a stochastic Langevin model for the Hodgkin-Huxley (HH) system based on a detailed representation of the underlying channel state Markov process, the "[Formula: see text]D model" introduced in (Pu and Thomas in Neural Computation 32(10):1775-1835, 2020). We show how to resolve the individual contributions that each transition in the ion channel graph makes to the variance of the interspike interval (ISI). We extend the mean return time (MRT) phase reduction developed in (Cao et al. in SIAM J Appl Math 80(1):422-447, 2020) to the second moment of the return time from an MRT isochron to itself. Because fixed-voltage spike detection triggers do not correspond to MRT isochrons, the inter-phase interval (IPI) variance only approximates the ISI variance. We find the IPI variance and ISI variance agree to within a few percent when both can be computed. Moreover, we prove rigorously, and show numerically, that our expression for the IPI variance is accurate in the small noise (large system size) regime; our theory is exact in the limit of small noise. By selectively including the noise associated with only those few transitions responsible for most of the ISI variance, our analysis extends the stochastic shielding (SS) paradigm (Schmandt and Galán in Phys Rev Lett 109(11):118101, 2012) from the stationary voltage clamp case to the current clamp case. We show numerically that the SS approximation has a high degree of accuracy even for larger, physiologically relevant noise levels. Finally, we demonstrate that the ISI variance is not an unambiguously defined quantity, but depends on the choice of voltage level set as the spike detection threshold. We find a small but significant increase in ISI variance, the higher the spike detection voltage, both for simulated stochastic HH data and for voltage traces recorded in in vitro experiments. In contrast, the IPI variance is invariant with respect to the choice of isochron used as a trigger for counting "spikes."

Fast and Accurate Langevin Simulations of Stochastic Hodgkin-Huxley Dynamics

Fox and Lu introduced a Langevin framework for discrete-time stochastic models of randomly gated ion channels such as the Hodgkin-Huxley (HH) system. They derived a Fokker-Planck equation with state-dependent diffusion tensor D and suggested a Langevin formulation with noise coefficient matrix S such that SS⊤=D. Subsequently, several authors introduced a variety of Langevin equations for the HH system. In this article, we present a natural 14-dimensional dynamics for the HH system in which each directed edge in the ion channel state transition graph acts as an independent noise source, leading to a 14 × 28 noise coefficient matrix S. We show that (1) the corresponding 14D system of ordinary differential equations is consistent with the classical 4D representation of the HH system; (2) the 14D representation leads to a noise coefficient matrix S that can be obtained cheaply on each time step, without requiring a matrix decomposition; (3) sample trajectories of the 14D representation are pathwise equivalent to trajectories of Fox and Lu's system, as well as trajectories of several existing Langevin models; (4) our 14D representation (and those equivalent to it) gives the most accurate interspike interval distribution, not only with respect to moments but under both the L1 and L∞ metric-space norms; and (5) the 14D representation gives an approximation to exact Markov chain simulations that are as fast and as efficient as all equivalent models. Our approach goes beyond existing models, in that it supports a stochastic shielding decomposition that dramatically simplifies S with minimal loss of accuracy under both voltage- and current-clamp conditions.

Neural coding and perception of auditory motion direction based on interaural time differences

While motion is important for parsing a complex auditory scene into perceptual objects, how it is encoded in the auditory system is unclear. Perceptual studies suggest that the ability to identify the direction of motion is limited by the duration of the moving sound, yet we can detect changes in interaural differences at even shorter durations. To understand the source of these distinct temporal limits, we recorded from single units in the inferior colliculus (IC) of unanesthetized rabbits in response to noise stimuli containing a brief segment with linearly time-varying interaural time difference ("ITD sweep") temporally embedded in interaurally uncorrelated noise. We also tested the ability of human listeners to either detect the ITD sweeps or identify the motion direction. Using a point-process model to separate the contributions of stimulus dependence and spiking history to single-neuron responses, we found that the neurons respond primarily by following the instantaneous ITD rather than exhibiting true direction selectivity. Furthermore, using an optimal classifier to decode the single-neuron responses, we found that neural threshold durations of ITD sweeps for both direction identification and detection overlapped with human threshold durations even though the average response of the neurons could track the instantaneous ITD beyond psychophysical limits. Our results suggest that the IC does not explicitly encode motion direction, but internal neural noise may limit the speed at which we can identify the direction of motion.NEW & NOTEWORTHY Recognizing motion and identifying an object's trajectory are important for parsing a complex auditory scene, but how we do so is unclear. We show that neurons in the auditory midbrain do not exhibit direction selectivity as found in the visual system but instead follow the trajectory of the motion in their temporal firing patterns. Our results suggest that the inherent variability in neural firings may limit our ability to identify motion direction at short durations.

Modeling of spike trains in auditory nerves with self-exciting point processes of the von Mises type

This article presents the modeling of spike trains in auditory nerve fiber (ANF) models with a one-memory self-exciting point process (SEPP) of the von Mises type. The ANF models were acoustically stimulated by a synaptic current of inner hair cells, or electrically stimulated by sinusoidally amplitude-modulated pulsatile waveforms. It has been shown that the parameters of one-memory SEPP of the von Mises type could be estimated by numerically maximizing the likelihood function from sample realizations of the spike trains in response to acoustic or electric stimulus. Furthermore, it was found that period histograms of the one-memory SEPP generated artificially on the basis of the estimated von Mises parameters agreed well with those of acoustic or electric stimulus, by performing the uniform-scores test. It implies that the waveforms of pulsatile electric stimuli should be selected such that the spike trains can be represented by one-memory SEPP of the von Mises type with appropriate parameters, efficiently carrying information to the cochlear implant user's brain, like that in acoustic stimulation of the healthy ear. The findings presented in this paper may play an important role in determining optimal parameters of pulsatile electric stimuli by using one-memory SEPP of the von Mises type, and further in the design of better cochlear prostheses.

Development and validation of a spectro-temporal processing test for cochlear-implant listeners

Psychophysical tests of spectro-temporal resolution may aid the evaluation of methods for improving hearing by cochlear implant (CI) listeners. Here the STRIPES (Spectro-Temporal Ripple for Investigating Processor EffectivenesS) test is described and validated. Like speech, the test requires both spectral and temporal processing to perform well. Listeners discriminate between complexes of sine sweeps which increase or decrease in frequency; difficulty is controlled by changing the stimulus spectro-temporal density. Care was taken to minimize extraneous cues, forcing listeners to perform the task only on the direction of the sweeps. Vocoder simulations with normal hearing listeners showed that the STRIPES test was sensitive to the number of channels and temporal information fidelity. An evaluation with CI listeners compared a standard processing strategy with one having very wide filters, thereby spectrally blurring the stimulus. Psychometric functions were monotonic for both strategies and five of six participants performed better with the standard strategy. An adaptive procedure revealed significant differences, all in favour of the standard strategy, at the individual listener level for six of eight CI listeners. Subsequent measures validated a faster version of the test, and showed that STRIPES could be performed by recently implanted listeners having no experience of psychophysical testing.

Simulated auditory nerve axon demyelination alters sensitivity and response timing to extracellular stimulation

Since cochlear implant function involves direct depolarization of spiral ganglion neurons (SGNs) by applied current, SGN physiological health must be an important factor in cochlear implant (CI) outcomes. This expected relationship has, however, been difficult to confirm in implant recipients. Suggestively, animal studies have demonstrated both acute and progressive SGN ultrastructural changes (notably axon demyelination), even in the absence of soma death, and corresponding altered physiology following sensorineural deafening. Whether such demyelination occurs in humans and how such changes might impact CI function remains unknown. To approach this problem, we incorporated SGN demyelination into a biophysical model of extracellular stimulation of SGN fibers. Our approach enabled exploration of the entire parameter space corresponding to simulated myelin diameter and extent of fiber affected. All simulated fibers were stimulated distally with anodic monophasic, cathodic monophasic, anode-phase-first (AF) biphasic, and cathode-phase-first (CF) biphasic pulses from an extracellular disc electrode and monitored for spikes centrally. Not surprisingly, axon sensitivity generally decreased with demyelination, resulting in elevated thresholds, however, this effect was strongly non-uniform. Fibers with severe demyelination affecting only the most peripheral nodes responded nearly identically to normally myelinated fibers. Additionally, partial demyelination (<50%) yielded only minimal increases in threshold even when the entire fiber was impacted. The temporal effects of demyelination were more unexpected. Both latency and jitter of responses demonstrated resilience to modest changes but exhibited strongly non-monotonic and stimulus-dependent relationships to more profound demyelination. Normal, and modestly demyelinated fibers, were more sensitive to cathodic than anodic monophasic pulses and to CF than AF biphasic pulses, however, when demyelination was more severe these relative sensitivities were reversed. Comparison of threshold crossing between nodal segments demonstrated stimulus-dependent shifts in action potential initiation with different fiber demyelination states. For some demyelination scenarios, both phases of biphasic pulses could initiate action potentials at threshold resulting in bimodal latency and initiation site distributions and dramatically increased jitter. In summary, simulated demyelination leads to complex changes in fiber sensitivity and spike timing, mediated by alterations in action potential initiation site and slowed action potential conduction due to non-uniformities in the electrical properties of axons. Such demyelination-induced changes, if present in implantees, would have profound implications for the detection of fine temporal cues but not disrupt cues on the time scale of speech envelopes. These simulation results highlight the importance of exploring the SGN ultrastructural changes caused by a given etiology of hearing loss to more accurately predict cochlear implantation outcomes.

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.

Effect of stimulus level on the temporal response properties of the auditory nerve in cochlear implants

Electrically evoked compound action potentials (ECAPs) have been used to examine temporal response patterns of the auditory nerve in cochlear implant (CI) recipients. ECAP responses to individual pulses in a pulse train vary across stimulation rates for individual CI users. For very slow rates, auditory neurons have ample time to discharge, recover, and respond to each pulse in the train. As the pulse rate increases, an alternating ECAP-amplitude pattern occurs. As the stimulation rate increases further, the alternating pattern eventually ceases and the overall ECAP amplitudes are diminished, yielding a relatively stochastic state that presumably reflects a combination of adaptation, desynchronization, and facilitation across fibers. Because CIs operate over a range of current levels in everyday use, it is important to understand auditory-nerve responses to pulse trains over a range of levels. The effect of stimulus level on ECAP temporal response patterns in human CI users has not been well studied. The first goal of this study was to examine the effect of stimulus level on various aspects of ECAP temporal responses to pulse-train stimuli. Because higher stimulus levels yield more synchronous responses and faster recovery, it was hypothesized that: (1) the maximum alternation would occur at slower rates for lower levels and faster rates at higher levels, (2) the alternation depth at its maximum would be smaller for lower levels, (3) the rate that produces a stochastic state ('stochastic rate') would decrease with level, (4) adaptation would be greater for lower levels as a result of slower recovery, and (5) refractory-recovery time constants would be longer (slower) for lower levels, consistent with earlier studies. The second goal of this study was to examine how refractory-recovery time constants relate specifically to maximum alternation and stochastic rate. Data were collected for 12 ears in 10 CI recipients. ECAPs were recorded in response to each of 13 pulses in an equal-amplitude pulse train ranging in rate from 900-3500 pps for three levels (low, medium, high). The results generally supported hypotheses 1-4; there were no significant effects of level on the refractory-recovery time constants (hypothesis 5). When data were pooled across level, there was a significant negative correlation between alternation depth and refractory recovery time. Understanding the effects of stimulus level on auditory-nerve responses may provide further insight into improving the use of objective measures for potentially optimizing speech-processing 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.

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.

Simulating electrical modulation detection thresholds using a biophysical model of the auditory nerve

Modulation detection thresholds (MDTs) assess listeners' sensitivity to changes in the temporal envelope of a signal and have been shown to strongly correlate with speech perception in cochlear implant users. MDTs are simulated with a stochastic model of a population of auditory nerve fibers that has been verified to accurately simulate a number of physiologically important temporal response properties. The procedure to estimate detection thresholds has previously been applied to stimulus discrimination tasks. The population model simulates the MDT-stimulus intensity relationship measured in cochlear implant users. The model also recreates the shape of the modulation transfer function and the relationship between MDTs and carrier rate. Discrimination based on fluctuations in synchronous firing activity predicts better performance at low carrier rates, but quantitative measures of modulation coding predict better neural representation of high carrier rate stimuli. Manipulating the number of fibers and a temporal integration parameter, the width of a sliding temporal integration window, varies properties of the MDTs, such as cutoff frequency and peak threshold. These results demonstrate the importance of using a multi-diameter fiber population in modeling the MDTs and demonstrate a wider applicability of this model to simulating behavioral performance in cochlear implant listeners.

The development of biophysical models of the electrically stimulated auditory nerve: Single-node and cable models

In the last few decades, biophysical models have emerged as a prominent tool in the study and improvement of cochlear implants, a neural prosthetic that restores a degree of sound perception to the profoundly deaf. Owing to the spatial phenomena associated with extracellular stimulation, these models have evolved to a relatively high degree of morphological and physiological detail: single-node models in the tradition of Hodgkin-Huxley are paired with cable descriptions of the auditory nerve fiber. No singular model has emerged as a frontrunner to the field; rather, parameter sets deriving from the channel kinetics and morphologies of numerous organisms (mammalian and otherwise) are combined and tuned to foster strong agreement with response properties observed in vivo, such as refractoriness, summation, and strength-duration relationships. Recently, biophysical models of the electrically stimulated auditory nerve have begun to incorporate adaptation and stochastic mechanisms, in order to better realize the goal of predicting realistic neural responses to a wide array of stimuli.

The history and future of neural modeling for cochlear implants

This special issue of Network: Computation in Neural Systems on the topic of "Computational models of the electrically stimulated auditory system" incorporates review articles spanning a wide range of approaches to modeling cochlear implant stimulation of the auditory system. The purpose of this overview paper is to provide a historical context for the different modeling endeavors and to point toward how computational modeling could play a key role in the understanding, evaluation, and improvement of cochlear implants in the future.

Computing loss of efficiency in optimal Bayesian decoders given noisy or incomplete spike trains

We investigate Bayesian methods for optimal decoding of noisy or incompletely-observed spike trains. Information about neural identity or temporal resolution may be lost during spike detection and sorting, or spike times measured near the soma may be corrupted with noise due to stochastic membrane channel effects in the axon. We focus on neural encoding models in which the (discrete) neural state evolves according to stimulus-dependent Markovian dynamics. Such models are sufficiently flexible that we may incorporate realistic stimulus encoding and spiking dynamics, but nonetheless permit exact computation via efficient hidden Markov model forward-backward methods. We analyze two types of signal degradation. First, we quantify the information lost due to jitter or downsampling in the spike-times. Second, we quantify the information lost when knowledge of the identities of different spiking neurons is corrupted. In each case the methods introduced here make it possible to quantify the dependence of the information loss on biophysical parameters such as firing rate, spike jitter amplitude, spike observation noise, etc. In particular, decoders that model the probability distribution of spike-neuron assignments significantly outperform decoders that use only the most likely spike assignments, and are ignorant of the posterior spike assignment uncertainty.

Psychophysically based site selection coupled with dichotic stimulation improves speech recognition in noise with bilateral cochlear implants

The ability to perceive important features of electrical stimulation varies across stimulation sites within a multichannel implant. The aim of this study was to optimize speech processor MAPs for bilateral implant users by identifying and removing sites with poor psychophysical performance. The psychophysical assessment involved amplitude-modulation detection with and without a masker, and a channel interaction measure quantified as the elevation in modulation detection thresholds in the presence of the masker. Three experimental MAPs were created on an individual-subject basis using data from one of the three psychophysical measures. These experimental MAPs improved the mean psychophysical acuity across the electrode array and provided additional advantages such as increasing spatial separations between electrodes and/or preserving frequency resolution. All 8 subjects showed improved speech recognition in noise with one or more experimental MAPs over their everyday-use clinical MAP. For most subjects, phoneme and sentence recognition in noise were significantly improved by a dichotic experimental MAP that provided better mean psychophysical acuity, a balanced distribution of selected stimulation sites, and preserved frequency resolution. The site-selection strategies serve as useful tools for evaluating the importance of psychophysical acuities needed for good speech recognition in implant users.

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.

Ability of primary auditory cortical neurons to detect amplitude modulation with rate and temporal codes: neurometric analysis

Amplitude modulation (AM) is a common feature of natural sounds, and its detection is biologically important. Even though most sounds are not fully modulated, the majority of physiological studies have focused on fully modulated (100% modulation depth) sounds. We presented AM noise at a range of modulation depths to awake macaque monkeys while recording from neurons in primary auditory cortex (A1). The ability of neurons to detect partial AM with rate and temporal codes was assessed with signal detection methods. On average, single-cell synchrony was as or more sensitive than spike count in modulation detection. Cells are less sensitive to modulation depth if tested away from their best modulation frequency, particularly for temporal measures. Mean neural modulation detection thresholds in A1 are not as sensitive as behavioral thresholds, but with phase locking the most sensitive neurons are more sensitive, suggesting that for temporal measures the lower-envelope principle cannot account for thresholds. Three methods of preanalysis pooling of spike trains (multiunit, similar to convergence from a cortical column; within cell, similar to convergence of cells with matched response properties; across cell, similar to indiscriminate convergence of cells) all result in an increase in neural sensitivity to modulation depth for both temporal and rate codes. For the across-cell method, pooling of a few dozen cells can result in detection thresholds that approximate those of the behaving animal. With synchrony measures, indiscriminate pooling results in sensitive detection of modulation frequencies between 20 and 60 Hz, suggesting that differences in AM response phase are minor in A1.