Parameters of the diffusion leaky integrate-and-fire
neuronal model for a slowly fluctuating signal
U. Picchini, S. Ditlevsen, A. De Gaetano and
P. Lansky
Published on Neural Computation (2008) 20(11), 2696-2714
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preprint (3.87 Mb, pdf)
The stochastic leaky integrate-and-fire (LIF) neuronal models are common theoretical
tools for studying properties of real neuronal systems. Experimental data of
frequently sampled membrane potential measurements between spikes show that the
assumption of constant parameter values is not realistic, and that some (random)
fluctuations are occurring. In this paper we extend the stochastic LIF model allowing
for a noise source determining slow fluctuations in the signal. This is achieved by
adding a random variable to one of the parameters characterizing the neuronal input,
considering each ISI as an independent experimental unit with a different realization
of this random variable. In this way, the variation of the neuronal input is split into
fast (within-interval) and slow (between intervals) components. A parameter estimation
method is proposed, allowing the parameters to be estimated simultaneously over
the entire data set. This increases the statistical power and the average estimate over
all ISIs will be improved in the sense of decreased variance of the estimator compared
to previous approaches, where the estimation has been conducted separately on each
individual ISI. The results obtained on real data show a good agreement with classical
regression methods.
Keywords: stochastic differential equations, mixed-effects, random parameters, maximum
likelihood estimation, interspike interval, spontaneous firing.
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