On a Stochastic Leaky Integrate-and-Fire Neuronal Model

• Published in: Neural computation Vol. 22; no. 10; pp. 2558 - 2585
• Main Authors: Buonocore, A., Caputo, L., Pirozzi, E., Ricciardi, L.M.
• Format: Journal Article
• Language: English
• Published: One Rogers Street, Cambridge, MA 02142-1209, USA MIT Press 01.10.2010; MIT Press Journals, The
• Subjects: Action Potentials - physiology; Algorithms; Animals; Applied sciences; Artificial intelligence; Biological and medical sciences; Computer science; control theory; systems; Computer Simulation - standards; Exact sciences and technology; Fundamental and applied biological sciences. Psychology; General aspects; Humans; Integral equations; Learning and adaptive systems; Letters; Mathematical analysis; Mathematics; Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects); Membrane Potentials - physiology; Membranes; Miscellaneous; Models, Statistical; Neurons - physiology; Probability; Sciences and techniques of general use; Stochastic models; Stochastic Processes; Synaptic Transmission - physiology; Time Factors; Neural computation; Prior distribution; Median; Neural network; Mean estimation; Time variation; Tuning; Implementation; Coefficient of skewness; Probability density; Statistical computation; Diffusion process; First passage time; Behavior; Membrane potential; Ornstein Uhlenbeck process; Volterra integral equations
• ISSN: 0899-7667; 1530-888X
• DOI: 10.1162/NECO_a_00023

The leaky integrate-and-fire neuronal model proposed in Stevens and Zador ( ), in which time constant and resting potential are postulated to be time dependent, is revisited within a stochastic framework in which the membrane potential is mathematically described as a gauss-diffusion process. The first-passage-time probability density, miming in such a context the firing probability density, is evaluated by either the Volterra integral equation of Buonocore, Nobile, and Ricciardi ( ) or, when possible, by the asymptotics of Giorno, Nobile, and Ricciardi ( ). The model examined here represents an extension of the classic leaky integrate-and-fire one based on the Ornstein-Uhlenbeck process in that it is in principle compatible with the inclusion of some other physiological characteristics such as relative refractoriness. It also allows finer tuning possibilities in view of its accounting for certain qualitative as well as quantitative features, such as the behavior of the time course of the membrane potential prior to firings and the computation of experimentally measurable statistical descriptors of the firing time: mean, median, coefficient of variation, and skewness. Finally, implementations of this model are provided in connection with certain experimental evidence discussed in the literature.