Graeme Clark Collection
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ItemSynchronization of the neural response to noisy periodic synaptic input(M I T PRESS, 2001-12)The timing information contained in the response of a neuron to noisy periodic synaptic input is analyzed for the leaky integrate-and-fire neural model. We address the question of the relationship between the timing of the synaptic inputs and the output spikes. This requires an analysis of the interspike interval distribution of the output spikes, which is obtained in the gaussian approximation. The conditional output spike density in response to noisy periodic input is evaluated as a function of the initial phase of the inputs. This enables the phase transition matrix to be calculated, which relates the phase at which the output spike is generated to the initial phase of the inputs. The interspike interval histogram and the period histogram for the neural response to ongoing periodic input are then evaluated by using the leading eigenvector of this phase transition matrix. The synchronization index of the output spikes is found to increase sharply as the inputs become synchronized. This enhancement of synchronization is most pronounced for large numbers of inputs and lower frequencies of modulation and also for rates of input near the critical input rate. However, the mutual information between the input phase of the stimulus and the timing of output spikes is found to decrease at low input rates as the number of inputs increases. The results show close agreement with those obtained from numerical simulations for large numbers of inputs.
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ItemSynchronization of the neural response to noisy periodic synaptic input( 1999)The relationship between the timing of the synaptic inputs and the output spikes of leaky integrate and fire neurons with noisy periodic synaptic input is addressed using the recently developed integrated-input technique. The conditional output spike density in response to noisy periodic input is evaluated as a function of the initial phase of the inputs. This enables the phase transition matrix to be calculated, which relates the phase at which the output spike is generated to the initial phase of the inputs. The interspike interval histogram and the period histogram for the neural response to ongoing periodic input are then evaluated by using the leading eigenvector of this phase transition matrix. The dependence of the synchronization index of the neural response upon the number and amplitude of synaptic inputs, the membrane time constant, the average rate of inputs and their frequency of modulation is examined.
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ItemNew method for analyzing the synchronization of synaptic input and spike output in neural systems( 1998)We present a new technique for analyzing the probability distribution of output spikes for the integrate and fire model. Using this method we investigate models with arbitrary synaptic response functions and the results, which are compared with numerical simulations, are exact in the limit of a large number of small amplitude inputs. We apply this method to the synchronization problem, in which the relationship between the spread in arrival times of the inputs (the temporal jitter of the synaptic input) and the resultant spread in the times at which the output spikes are generated (output jitter) is analyzed. The results indicate that the ratio of the output jitter to the input jitter is consistently less than one and that it decreases for increasing numbers of inputs, in agreement with earlier studies. We identify the variation in the spike generating thresholds of the neurons and the variation in the number of active inputs as being important factors that determine the timing jitter in layered networks, in addition to those identified previously.
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ItemAnalysis of integrate and fire neurons: synchronization of synaptic input and spike output( 1999)A new technique for analysing the probability distribution of output spikes for the integrate-and-fire model is presented. This technique enables us to investigate models with arbitrary synaptic response functions that incorporate both leakage across the membrane and a rise time of the postsynaptic potential. The results, which are compared with numerical simulations, are exact in the limit of a large number of small-amplitude inputs. This method is applied to the synchronization problem, in which we examine the relationship between the spread in arrival times of the inputs (the temporal jitter of the synaptic input) and the resultant spread in the times at which the output spikes are generated (output jitter). The results of previous studies, which indicated that the ratio of the output jitter to the input jitter is consistently less than one and that it decreases for increasing numbers of inputs, are confirmed for three classes of the integrate-and-fire model. In addition to the previously identified factors of axonal propagation times and synaptic jitter, we identify the variation in the number of active inputs as being important factors that determine the timing jitter in layered networks. Previously observed phase differences between optimally and suboptimally stimulated neurons may be understood in terms of the relative time taken to reach threshold.
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ItemThe relationship between the output synchrony of cochlear nucleus neurons and the site of stimulation in the cochlea( 2001)A model has been developed to determine the relationship between the output synchrony of cochlear nucleus neurons and the site of stimulation in the cochlea. This is an Integrate and Fire Neuron Model in which noisy periodic synaptic inputs to the neuron are summed and a spike is generated when the membrane potential reaches threshold. The model describes the stochastic input that auditory nerve fibres provide to a cochlear nucleus neuron and the corresponding stochastic output. To investigate the relationship between the output synchrony of cochlear nucleus neurons (namely globular bushy cells) and the site of stimulation in the cochlea, phase differences between the periodic inputs of the model were incorporated, in order to mimic how the travelling wave consecutively activates auditory nerve fibres originating over a spatial spread of the basilar membrane. Analysis of the model found that output synchrony decreased with an increase in frequency and spatial spread. Furthermore, enhancement of the output synchrony relative to the input synchrony occurred for small spatial spreads of the basilar membrane over which input primary afferent fibres originate. Adding noise helped to make the model more realistic. As a result enhancement of synchrony occurred with a spatial spread of less than 1.25 mm and 0.75 mm for 0.5 kHz and I kHz respectively, while for the higher frequencies analysed (2 kHz and 5 kHz) enhancement of synchrony did not occur. This research has implications for the design of electrode arrays in cochlear implants. The number and geometry of the electrodes and the stimulus patterns to be used will depend on the degree of convergence of fibres and how phase information is processed by neurons in the brainstem.
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ItemEffects of sensorineural hearing loss on the refractory properties of auditory nerve fibers( 2000)We hypothesised that the loss of the peripheral processes and the partial demyelination of auditory nerve fibres (ANFs) following a sensorineural hearing loss would increase their refractory properties. Normal control, and long-term (2.5 months) systemically deafened rats were anaesthetised (urethane, 1.3 g/kg i.p.), a bipolar stimulating electrode was implanted into the scala tympani and glass microelectrodes (30-80 MΩ) used to record single ANF activity. Stimuli (pairs of 100 µs/phase charge balanced biphasic pulses with interpulse intervals (IPIs) of 0.34-10 ms) were presented at 6 dB above threshold using a repetition interval of 250 ms. Absolute refractory period (ARP) was defined as the IPI at which the probability of eliciting a spike to the second stimulus was 0.1. In the present results, based on recordings from 62 fibres, ANFs were distinguished from cochlear nucleus (CN) neurones by their significantly shorter median latencies (AN: 0.575ms vs CN: 1.137ms; Whitney-Mann Rank Sum, p<0.0001). There were no significant differences between minimum ANF latencies from normal and deafened animals. Although the median ARP was greater in deafened versus normal animals, this difference was not statistically significant (normals: median0.658ms, interquartile range 0.554-0.913ms; deafened: 0.772ms and 0.616-1.073ms; p=0.16). Finally, the spike latency associated with the second pulse of a pair systematically increased with decreasing IPI, contrasting with the stable latency of the response to the leading pulse. Although pathological changes to ANFs may increase their refractory properties, at this duration of deafness these changes were not significant.
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ItemThe effects of action potential propagation delay times and an absolute refractory period upon the synchronization index in the integrate and fire neuron model and a comparison with neurons in the auditory pathway( 2000)The effects of action potential (AP) propagation delay times and the absolute refractory period upon the synchronization index are analysed for the integrate and fire neuron model, and the results are compared with recordings from auditory ganglion neurons and cochlear nucleus neurons. In the model the noisy periodic synaptic input to the neuron is summed and an AP is generated when the membrane potential reaches threshold. The output phase distribution (phase histogram) is calculated at the site at which the APs are generated. The AP propagation delay times along an axon are modelled using a periodically wrapped Gaussian distribution, with the width fitted from experimental data. This distribution is convolved with the calculated phase distribution to obtain the phase distribution at the axon terminal.
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ItemModelling the response of neurons to auditory stimuli: differences between acoustical and electrical stimulation( 1999)There are significant differences in the responses of auditory nerves when they are stimulated acoustically (normal hearing situation) or electrically (with a cochlear implant). This paper addresses the underlying causes of these differences by studying the interspike interval histogram, the synchronization index, and the entrainment (degree of response to successive cycles of the stimulus). The new integrated-input technique is used to analyze the response to periodic synaptic input of integrate-and-fire neurons, in which the randomly arriving synaptic inputs are summed and an action potential is generated when the postsynaptic potential reaches threshold. The synaptic inputs in the model are a sinusoidally modulated inhomogeneous Poisson process, and each input generates a postsynaptic response that subsequently decays according to the membrane decay constant. The results provide a quantitative understanding of both the decrease of the synchronization index with increasing frequency of acoustical stimulation in the auditory pathway and the previously observed enhancement of synchronization in globular bushy cells of the cochlear nucleus. The differences in the responses of neurons in higher stages of the auditory pathway for acoustical and electrical stimulation may be accounted for by the differences in the degree of entrainment that they induce.
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ItemThe dependence of synchronization upon stimulus frequency for integrate and fire neurons [Abstract]( 1999)The response of a neural system to periodic synaptic input is analyzed using the new integrated input technique, in which the randomly arriving synaptic inputs are summed and an action potential is generated when the postsynaptic potential reaches threshold (i.e., integrate-and-fire neurons). The results provide a quantitative understanding of the decrease of the synchronization index with increasing frequency of acoustical stimulation in the auditory pathway. The conditions under which the observed enhancement of synchronization in globular bushy cells of the cochlear nucleus may occur are elucidated. The dependence of the synchronization index upon the frequency of stimulation is analyzed for a range of neurophysiological parameters, including the number of afferent fibres, the membrane time constant, the amplitude of the individual postsynaptic potentials, timing jitter in the axonal propagation of spikes, and the time course of the postsynaptic response. The inclusion of an absolute refractory period to the model is found to have little effect upon the period histogram. The interspike interval histogram and the period histogram for the neural response to ongoing periodic inputs are evaluated using the stationary solution to the phase transition matrix, which relates the phase at which the output spike is generated to the initial phase of the inputs. Spontaneous activity is included in the model, and the possible role of stochastic resonance in threshold detection is addressed.