- Graeme Clark Collection
Graeme Clark Collection
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ItemAnalysis of integrate and fire neurons: synchronization of synaptic input and spike outputBurkitt, A. N. ; Clark, Graeme M. ( 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 cochleaKuhlmann, L. ; Burkitt, A. N. ; Paolini, A. G. ; Clark, Graeme M. ( 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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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 pathwayKuhlmann, L. ; Burkitt, A. N. ; Clark, Graeme M. ( 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.