A diffusion-equation model for neuron firing with exponential decay of potential

by Brian Gluss


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A neuron is assumed to receive synaptic input of both excitatory and inhibitory natures from a large number of neighboring neurons; it is also assumed that a large number of such impulses are required to raise the neuron's transmembrane potential to its threshold potential, at which it "fires" or "spikes". The model is similar to one of Gerstein and Mandelbrot, except tht, in the absence of input, an exponential decay of potential toward a resting level is introduced. Computational methods of determining the spike time-interal distribution are discussed, along with the inverse problem of estimating the parameters of the system from observed spike time-interval data.

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