First-order Markov property of the auditory spiking neuron model response (original) (raw)
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A stochastic model of the electrically stimulated auditory nerve: single-pulse response
IEEE Transactions on Biomedical Engineering, 1999
Most models of neural response to electrical stimulation, such as the Hodgkin-Huxley equations, are deterministic, despite significant physiological evidence for the existence of stochastic activity. For instance, the range of discharge probabilities measured in response to single electrical pulses cannot be explained at all by deterministic models. Furthermore, there is growing evidence that the stochastic component of auditory nerve response to electrical stimulation may be fundamental to functionally significant physiological and psychophysical phenomena. In this paper we present a simple and computationally efficient stochastic model of single-fiber response to single biphasic electrical pulses, based on a deterministic threshold model of action potential generation. Comparisons with physiological data from cat auditory nerve fibers are made, and it is shown that the stochastic model predicts discharge probabilities measured in response to single biphasic pulses more accurately than does the equivalent deterministic model. In addition, physiological data show an increase in stochastic activity with increasing pulse width of anodic/cathodic biphasic pulses, a phenomenon not present for monophasic stimuli. These and other data from the auditory nerve are then used to develop a population model of the total auditory nerve, where each fiber is described by the single-fiber model.
Journal of Computational Neuroscience, 2003
The cochlear nucleus (CN) presents a unique opportunity for quantitatively studying input-output transformations by neurons because it gives rise to a variety of different response types from a relatively homogeneous input source, the auditory nerve (AN). Particularly interesting among CN neurons are Onset (On) neurons, which have a prominent response to the onset of sustained sounds followed by little or no response in the steady-state. On neurons contrast sharply with their AN inputs, which respond vigorously throughout stimuli. On neurons can entrain to stimuli (firing once per cycle of a periodic stimulus) at up to 1000 Hz, unlike their AN inputs. To understand the mechanisms underlying these response patterns, we tested whether an integrate-to-threshold point-neuron model with a fixed refractory period can account for On discharge patterns for tones, systematically examining the effect of membrane time constant and the number and strength of the exclusively excitatory AN synaptic inputs. To produce both onset responses to high-frequency tone bursts and entrainment to a broad range of low-frequency tones, the model must have a short time constant (≈0.125 ms) and a large number (>100) of weak synaptic inputs, properties that are consistent with the electrical properties and anatomy of On-responding cells. With these parameters, the model acts like a coincidence detector with a threshold-like relationship between the instantaneous discharge rates of the output and the inputs. Onset responses to high-frequency tone bursts result because the threshold effect enhances the initial response of the AN inputs and suppresses their relatively lower sustained response. However, when the model entrains across a broad range of frequencies, it also produces short interspike intervals at the onset of high-frequency tone bursts, a response pattern not found in all types of On neurons. These results show a tradeoff, that may be a general property of many neurons, between following rapid stimulus fluctuations and responding without short interspike intervals at the onset of sustained stimuli.
An Improved Model for the Rate-Level Functions of Auditory-Nerve Fibers
Journal of Neuroscience, 2011
Acoustic information is conveyed to the brain by the spike patterns in auditory-nerve fibers (ANFs). In mammals, each ANF is excited via a single ribbon synapse in a single inner hair cell (IHC), and the spike patterns therefore also provide valuable information about those intriguing synapses. Here we reexamine and model a key property of ANFs, the dependence of their spike rates on the sound pressure level of acoustic stimuli (rate-level functions). We build upon the seminal model of Sachs and Abbas (1974), which provides good fits to experimental data but has limited utility for defining physiological mechanisms. We present an improved, physiologically plausible model according to which the spike rate follows a Hill equation and spontaneous activity and its experimentally observed tight correlation with ANF sensitivity are emergent properties. We apply it to 156 cat ANF rate-level functions using frequencies where the mechanics are linear and find that a single Hill coefficient of 3 can account for the population of functions. We also demonstrate a tight correspondence between ANF rate-level functions and the Ca 2ϩ dependence of exocytosis from IHCs, and derive estimates of the effective intracellular Ca 2ϩ concentrations at the individual active zones of IHCs. We argue that the Hill coefficient might reflect the intrinsic, biochemical Ca 2ϩ cooperativity of the Ca 2ϩ sensor involved in exocytosis from the IHC. The model also links ANF properties with properties of psychophysical absolute thresholds.
SpontaneousActivityofAuditory-NerveFibers:Insightsinto StochasticProcessesatRibbonSynapses
2007
In several sensory systems, the conversion of the representation of stimuli from graded membrane potentials into stochastic spike trains is performed by ribbon synapses. In the mammalian auditory system, the spiking characteristics of the vast majority of primary afferent auditory-nerve (AN) fibers are determined primarily by a single ribbon synapse in a single inner hair cell (IHC), and thus provide a unique window into the operation of the synapse. Here, we examine the distributions of interspike intervals (ISIs) of cat AN fibers under conditions when the IHC membrane potential can be considered constant and the processes generating AN fiber activity can be considered stationary, namely in the absence of auditory stimulation. Such spontaneous activity is commonly thought to result from an excitatory Poisson point process modified by the refractory properties of the fiber, but here we show that this cannot be the case. Rather, the ISI distributions are one to two orders of magnitude better and very accurately described as a result of a homogeneous stochastic process of excitation (transmitter release events) in which the distribution of interevent times is a mixture of an exponential and a gamma distribution with shape factor 2, both with the same scale parameter. Whereas the scale parameter varies across fibers, the proportions of exponentially and gamma distributed intervals in the mixture, and the refractory properties, can be considered constant. This suggests that all of the ribbon synapses operate in a similar manner, possibly just at different rates. Our findings also constitute an essential step toward a better understanding of the spike-train representation of time-varying stimuli initiated at this synapse, and thus of the fundamentals of temporal coding in the auditory pathway.
IEEE Transactions on Biomedical Engineering, 2003
An important factor that may play a role in speech recognition by individuals with cochlear implants is that electrically stimulated nerves respond with a much higher level of synchrony than is normally observed in acoustically stimulated nerves. Recent work has indicated that the addition of noise to an electrical stimulus may result in neural responses whose statistical characteristics are more similar to those observed in acoustically driven neurons. Psychophysical data have indicated that performance on some tasks might also be enhanced by the addition of noise. However, little theoretical work has been done toward predicting the effect of noise on psychoacoustic measurements. In this paper, theoretical predictions of these effects are developed through the use of a stochastic computational model. The effect of additive noise on the input and output characteristics and aggregate threshold behavior of modeled auditory nerves (ANs) is specifically studied. This paper derives the stochastic properties of the model input and output when using adaptive threshold procedures. A closed form solution for the input, or amplitude, probability distribution is obtained via Markov models for both one-down one-up (1D1U) and two-down one-up (2D1U) experimental paradigms. The output statistics are derived by integrating over the noise-free probability mass function (PMF). All theoretical PMFs are verified by simulations with the model. Theoretical threshold is predicted as a function of noise level based on these PMFs and the predictions match simulated performance. The results indicate that threshold may be adversely affected by the presence of high levels of noise.
Hearing Research, 2008
For signal detection and identification, the auditory system needs to integrate sound over time. It is frequently assumed that the quantity ultimately integrated is sound intensity and that the integrator is located centrally. However, we have recently shown that absolute thresholds are much better specified as the temporal integral of the pressure envelope than of intensity, and we proposed that the integrator resides in the auditory pathway's first synapse. We also suggested a physiologically plausible mechanism for its operation, which was ultimately derived from the specific rate of temporal integration, i.e., the decrease of threshold sound pressure levels with increasing duration. In listeners with sensorineural hearing losses, that rate seems reduced, but it is not fully understood why. Here we propose that in such listeners there may be an elevation in the baseline above which sound pressure is effective in driving the system, in addition to a reduction in sensitivity. We test this simple model using thresholds of cats to stimuli of differently shaped temporal envelopes and durations obtained before and after hearing loss. We show that thresholds, specified as the temporal integral of the effective pressure envelope, i.e., the envelope of the pressure exceeding the elevated baseline, behave almost exactly as the lower thresholds, specified as the temporal integral of the total pressure envelope before hearing loss. Thus, the mechanism of temporal integration is likely un-changed after hearing loss, but the effective portion of the stimulus is. Our model constitutes a successful alternative to the model currently favored to account for altered temporal integration in listeners with sensorineural hearing losses, viz., reduced peripheral compression. Our model does not seem to be at variance with physiological observations and it also qualitatively accounts for a number of phenomena observed in such listeners with suprathreshold stimuli.
Modelling the auditory system: preprocessing and associative memories using spiking neurons
Neurocomputing, 2004
We implemented a model of the auditory system incorporating the cochlea, the cochlear nucleus, the inferior colliculus and the primary auditory cortex. For the simulation of the cochlea gammaton ÿlters are used. The other areas are simulated by neural networks consisting of leaky integrate and ÿre neurons. The peripheral processing in the cochlear nucleus and the inferior colliculus is modelled by special neural networks for pitch processing and the primary auditory cortex is implemented as an associative memory. Binaural interactions are not considered in the model.
A Markovian event-based framework for stochastic spiking neural networks
Journal of Computational Neuroscience, 2011
In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks.
Processing of sounds by population spikes in a model of primary auditory cortex
Frontiers in Neuroscience, 2007
We propose a model of the primary auditory cortex (A1), in which each iso-frequency column is represented by a recurrent neural network with short-term synaptic depression. Such networks can emit Population Spikes, in which most of the neurons fire synchronously for a short time period. Different columns are interconnected in a way that reflects the tonotopic map in A1, and population spikes can propagate along the map from one column to the next, in a temporally precise manner that depends on the specific input presented to the network. The network, therefore, processes incoming sounds by precise sequences of population spikes that are embedded in a continuous asynchronous activity, with both of these response components carrying information about the inputs and interacting with each other. With these basic characteristics, the model can account for a wide range of experimental findings. We reproduce neuronal frequency tuning curves, whose width depends on the strength of the intracortical inhibitory and excitatory connections. Non-simultaneous twotone stimuli show forward masking depending on their temporal separation, as well as on the duration of the first stimulus. The model also exhibits non-linear suppressive interactions between sub-threshold tones and broad-band noise inputs, similar to the hypersensitive locking suppression recently demonstrated in auditory cortex. We derive several predictions from the model. In particular, we predict that spontaneous activity in primary auditory cortex gates the temporally locked responses of A1 neurons to auditory stimuli. Spontaneous activity could, therefore, be a mechanism for rapid and reversible modulation of cortical processing.