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Parameters of the Diffusion Leaky Integrate-and-Fire Neuronal Model for a Slowly Fluctuating Signal

umberto{at}math.ku.dk Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark; and Biomathematics Laboratory, IASI–CNR, Università Cattolica Del Sacro Cuore, Largo A. Gemelli 8, 00168 Rome, Italy

Susanne Ditlevsen

susanne{at}math.ku.dk Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark

Andrea De Gaetano

andrea.degaetano{at}gmx.net Biomathematics Laboratory, IASI-CNR, Università Cattolica Del Sacro Cuore, Largo A. Gemelli 8, 00168 Rome, Italy

Petr Lansky

lansky{at}biomed.cas.cz Institute of Physiology, Academy of Sciences of the Czech Republic, Videnska 1083, 142 20 Prague 4, Czech Republic

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 letter, we extend the stochastic LIF model, allowing 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 interspike interval (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 good agreement with classical regression methods.