Untitled - Laboratory of Neurophysics and Physiology

Tutorials
T1
Neural-mass and neural-field models
Space Curie, (9.00-12.20; 13.30-16.50)
Axel Hutt, INRIA Nancy, France
Viktor Jirsa, Institut de Neuroscience de Systemes, France
John Terry, University Exeter, UK
Wolfram Erlhagen, University Minho, Portugal
The brain exhibits dynamical processes on different spatial and temporal scales. Single neurons have a
size of tens of micrometers and fire during few milliseconds, whereas macroscopic brain activity, such
as encephalographic data or the BOLD response in functional Magnetic Resonance Imaging, evolve
on a millimeter or centimeter scale during tens of milliseconds. To understand the relation between
the two dynamical scales, the mesoscopic scale of neural populations between these scales is helpful.
Moreover, it has been found experimentally that neural populations encode and decode cognitive
functions. The tutorial presents a specific type of rate-coding models which is both mathematically
tractable and verifiable experimentally. It starts with a physiological motivation of the model, followed
by mathematical analysis techniques applied to explain experimental data and applications to epilepsy
and robotics. In detail:
Fundamentals of neural-mass and neural-field models: Physiological motivation and
mathematical descriptions (Axel Hutt)
The talk will motivate physiologically the mathematical description of neural populations based on
microscopic neural properties. Several different mathematical models will be discussed, explained and
compared. The major aim of this presentation is to explain the standard models found in the literature
in terms of mathematical elements and physiological assumptions.
Pattern formation in neural network systems and applications to movement dynamics
(Viktor Jirsa)
We will introduce and systematically evaluate the mechanisms underlying pattern formation in neuronal
networks. A particular focus will be given to the contribution of network connectivity. The conditions
will be derived aiding in the emergence of low-dimensional sub-spaces, in which nonlinear dynamic
flows are constrained to manifolds. Applications of these concepts and experimental examples will be
provided from the field of human movement sciences.
Brain networks in epilepsy: Fusing models and clinical data (John Terry)
We will explore how both physiological and phenomenological mathematical models can be developed
to understand the mechanisms that underpin transitions in clinically recorded EEG between
activity corresponding to normal function and the pathological activity associated with epilepsy. We
present evidence that the bifurcation sequences of physiologically inspired models give rise to dynamical
sequences that precisely map those observed in both focal and generalised seizures. We further
demonstrate that seizure frequency can be understood through the relationship between the dynamics
of brain regions and the network structures that connect them. Our mathematical models help to explain
previously counterintuitive experimental studies demonstrating loss of connectivity paradoxically
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