NEUROSTOCHSIM

NEURAL FIELD EQUATIONS:

STOCHASTIC APPROACH

AND NUMERICAL SIMULATIONS

Marie Curie Intra European Fellowship

Call: FP7-PEOPLE-2013-IEF

Proposal Number: 629496

Host organization: Institute of Stochastics, University of Linz, Austria

Scientist in charge: Prof. Evelyn Buckwar

Researcher: Dr. Pedro Lima

Overview of the project

The applicant Prof. Dr. Pedro Lima will move from the Instituto Superior Técnico (IST) in Lisbon, Portugal, to the Institute for Stochastics at the Johannes Kepler University (JKU) in Linz, Austria, to undertake a program of scientific training and career development and carry out research in the combined fields of stochastic numerics and mathematical neuroscience. The aim of the present project is to advance the numerical modeling of neural processes, which for example can help to interpret the experimental data coming from EEG measurements. With this purpose we study Neural Field Equations (NFEs), a widely used class of equations to model connected areas of neurons in the brain, in one to three dimensions. Realistic models of neuronal activity must account for random perturbations resulting for example from noisy external sensory input, background firing of neighbouring neurons, or the random opening and closing of ion channels. This is often modelled by including a stochastic perturbation term into the deterministic equations describing the neuronal behaviour. We thus emphasise employing stochastic variants of NFEs to describe neural activity. We intend to develop new numerical methods for deterministic and stochastic NFEs targeted to their application in a neuroscience context. We will analyse the methods for their convergence and qualitative behaviour and also implement and test them. The project includes in its final phase a collaboration with a research team working with medical data.

Keywords: Neural field equations, mathematical neuroscience, stochastic processes, numerical methods.