Joshua H. Goldwyn

Stochastic differential equation models for ion channel noise in Hodgkin-Huxley neurons.

The random transitions of ion channels between conducting and nonconducting states generate a source of internal fluctuations in a neuron, known as channel noise. The standard method for modeling the states of ion channels nonlinearly couples continuous-time Markov chains to a differential equation for voltage. Beginning with the work of R. F. Fox and Y.-N. Lu [Phys. Rev. E 49, 3421 (1994)], there have been attempts to generate simpler models that use stochastic differential equation (SDEs) to approximate the stochastic spiking activity produced by Markov chain models. Recent numerical investigations, however, have raised doubts that SDE models can capture the stochastic dynamics of Markov chain models.We analyze three SDE models that have been proposed as approximations to the Markov chain model: one that describes the states of the ion channels and two that describe the states of the ion channel subunits. We show that the former channel-based approach can capture the distribution of channel noise and its effects on spiking in a Hodgkin-Huxley neuron model to a degree not previously demonstrated, but the latter two subunit-based approaches cannot. Our analysis provides intuitive and mathematical explanations for why this is the case. The temporal correlation in the channel noise is determined by the combinatorics of bundling subunits into channels, but the subunit-based approaches do not correctly account for this structure. Our study confirms and elucidates the findings of previous numerical investigations of subunit-based SDE models. Moreover, it presents evidence that Markov chain models of the nonlinear, stochastic dynamics of neural membranes can be accurately approximated by SDEs. This finding opens a door to future modeling work using SDE techniques to further illuminate the effects of ion channel fluctuations on electrically active cells.

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.

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.

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.

Adaptation in electric hearing: analysis of level and amplitude modulation encoding.

Neural adaptation in sensory systems can potentially improve the efficiency and fidelity of neural encoding (e.g. [1]). In the auditory system, for instance, the firing rates of peripheral and midbrain neurons can shift to better represent the range of most likely stimulus levels [2,3]. Adaptation has long been known to exist throughout the auditory system in response to acoustic stimulation, and now studies have revealed that the auditory nerve exhibits firing rate adaptation in response to electric stimulation [4]. Adaptation may, therefore, have important implications for the function and design of cochlear implants, but there have been few attempts to investigate the relationship between neural adaptation, cochlear implant design, and listening outcomes for cochlear implant users. We hypothesize that it will be possible to identify time scales of adaptation that optimally encode a stimulus, depending on the time scales of the stimulus. The time course of adaptation appears to depend on stimulus parameters [5], so if our hypothesis is true, then it may be possible to design stimulation strategies that induce adaptation in a way that improves encoding of cochlear implant stimuli. To address this hypothesis, we use a point process model to simulate the response of an auditory nerve cell to electric stimulation. The model replicates known features of the auditory nerve’s response to electric stimulation including spike threshold, input/output function, and refractory effects. For this study, we implement firing rate adaptation in the model via a spike-history feedback mechanism. The adaptation component has two parameters that control the time scale and degree of adaptation. We simulate the effect of adaptation on encoding of stimulus level and sinusoidal amplitude modulation. We use the likelihood function associated with the point process model to quantify spike timing information, as well as common measures of spike count information, strength of phase-locking to the amplitude-modulated signal, and signal-to-noise ratio of firing rates. We find that at high stimulus levels, firing rate adaptation prevents saturation and therefore improves sensitivity to level increments and modulation. In response to weaker stimuli, adaptation typically degrades the encoding of level and amplitude modulation. In general, we find that the degree, not time scale, of adaptation is the more important factor in determining the effect of adaptation on encoding. In order to further probe the effects of the time scale of adaptation, we analyze neural encoding of dynamic stimuli that feature multiple time scales and non-stationary levels.

Amplitude modulation discrimination in a model of the electrically stimulated auditory nerve

Cochlear implants (CI) are neural prostheses that can restore hearing for individuals with severe to profound hearing loss through electrical stimulation of the auditory nerve (AN). Despite continuing advances in CI function, complicated listening tasks such as speech perception in noise, sound localization, and music perception remain difficult for CI users. It is believed that a key to enhancing performance on these tasks is improving fine-structure temporal processing. A valuable test of such temporal processing is amplitude modulation discrimination, wherein subjects are asked to distinguish between stimuli of constant intensity and weakly amplitude-modulated waveforms. Amplitude modulation discrimination has been tested in CI listeners and the key finding is that performance is typically good for low modulation frequencies, but degrades rapidly for modulation frequencies above ~100 Hz [1].