11/12/2013, 14:00 — 16:00 — Sala V1.08, Pavilhão de Eng. Civil, IST
Marco Leite, UCL Institute of Neurology and Instituto de Sistemas e Robótica, IST
Modelling populations of integrate and fire neurons: a
Fokker-Planck approach to population density dynamics
Much of the phenomenology of interest in the field of
neuroscience arises from the interaction of large populations of
densely interconnected neurons (~\(10^5\) neurons per
mm3 of mammal cortex, averaging \(10^4\) connections per
neuron). Different levels of abstraction may be adopted when
modelling such systems, and these need to be well suited with
regards to the phenomena one is interested in studying. Here we aim
at the study of the (sparse) synchronization of neurons observed
during electrophysiologically recorded fast oscillatory behavior of
networks of large populations. For that we use a ubiquitous
simplified neuronal model - the conductance based leaky integrate
and fire neuron. This model may be described by a one dimensional
stochastic differential equation. Under mean field assumptions we
may describe, using a linear Fokker-Planck equation, the behavior
of a single population of uncoupled neurons with a PDE. The
coupling of different populations will render this Fokker-Planck
equation strongly non-linear. In this presentation I will also
explore some details of such modelling approaches, namely: the
non-natural boundary conditions generated by the neuronal firing
mechanism and the numerical scheme used to deal with the
brittleness from there ensued. I will also present results on the
types of behavior, data, and statistics that such modelling
approach is able to predict, e.g. neuronal (a)synchrony, neuronal
input currents, firing rates, inter spike intervals, etc... This
type of approach allows for a computationally tractable and
scalable study of networks of populations of neurons. In the future
we plan to implement parameter estimation algorithms to this family
of models.
