"Neural Fields with Multiple Timescales: applications to modeling Cortical Spreading Depression"

The objective of this project is to better understand certain kinds of migraines caused by the appearance of cortical spreading depression (CSD), corresponding to slowly-propagating waves causing depolarization of cells in the cerebral cortex and associated with several pathologies like migraines and strokes. To achieve this goal, mathematicians and biologists will collaborate in the hope that this will lead to future clinical research to test new procedures for treating these kinds of migraines.

Fighting migraines more effectively

The cellular depolarization waves are the source of many brain pathologies like migraines and strokes, but the initiation and propagation mechanisms of these waves are still not completely known nor understood. The goal of this project is therefore to better comprehend certain type of migraines with aura* by identifying the triggering elements in terms of both local neural dysfunction and propagation in entire regions of the brain. To accomplish this, this project combines mathematical modeling with biological investigations. The researchers want to develop and analyze a multiscale model connected to experimental data so as to study these conditions in detail. An innovative aspect is that they are especially interested in the joint role of inhibitory neurons (or interneurons) and glial cells. This model will have the potential to better explain experimental results as well as obtain accurate predictions of triggering elements and methods for their control.

Develop more realistic mathematical models

The mathematical component is central to this project and involves developing a theory of neural fields with several timescales, which currently does not exist. Existing models with continuous limits of neural networks allow the electrical activity of large populations of neurons and entire regions of the brain to be accounted for. Although such models are well-adapted for detailed, mathematical analyses, they are relatively simplified and lack many, relevant biological details. A first step to make these models more realistic is to add more equations to them to account for slowly-varying quantities. These slow variations are crucial in the emergence of pathological phenomena related to CSD and of certain ionic concentrations (e.g. extracellular potassium), which slowly increase until they exceed a threshold and put a whole region of the brain in a pathological state.


Leading to new, clinical protocols

This project unites mathematicians (J.A. Dieudonné Laboratory, Inria Sophia Antipolis, and the University of Nottingham in England) as well a biologist (Institute of Molecular and Cellular Pharmacology–IPMC). They will collaborate to link analytical and modeling results to experiments and vice versa, particularly for the identification of key parameters, which could be used to block the CSD waves. The project is part of an international initiative, which includes Prof. David Terman of the Ohio State University (USA), a world-renowned expert in neuronal modeling.

This initial stage of fundamental research could lead to future clinical research to test new procedures for improved treatment of these kinds of migraines. The project’s scope will sustainably anchor this topic at the UCA.

 The Complex Systems Academy of Excellence is supporting this project by funding the stay of one the team’s external members for several months in Nice.

Further information on this project by clicking here.


 * A type of migraine characterized by a series of symptoms (blurred vision, nausea, vertigo) followed by severe headaches.

Photo : © Shutterstock/Digital Storm- Caption : Figure representing a migraine with a simulation in white of the preliminary model of initiation developed by the researchers working on this project.

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