# Mathematics 146

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Using mathematics to help people with epilepsy

Most of us have no idea of the complex mathematical calculations that hide behind every medical image. Using brain activity data obtained by non-invasive electromagnetic measurements at the surface of the head, it is possible to localize the bioelectric activity associated with dysfunction in the brains of people with epilepsy. This what Jean-Marc Lina, researcher and member of the PhysNum team at the Centre de recherches mathématiques (CRM), is currently working on, in collaboration with the Montreal Neurological Institute.

Studying data relating to neurological dysfunction in people with epilepsy is no easy task. “It’s like trying to figure out who is talking to whom in a crowded room from the other side of a closed door”, explains Jean-Marc Lina. The problem is made even more complex by the need to take into account spatial dimensions (from which regions of the brain does the activity originate?), temporal dimensions (when?) and relational dimensions (what is the network of interactions between the different regions of the brain involved?) when analyzing the measured data. To answer these questions, the researcher uses numerical methods derived directly from information theory that make it possible to localize with great accuracy the neurological source of specific brain activity.

These measurements are of paramount importance in planning surgery for patients with severe and debilitating drug-resistant epilepsy.In the case of epilepsy, a neurologist identifies the areas of electroencephalographic (EEG) recordings that show abnormal brain activity linked to epilepsy. Using numerical tools, this information is then projected onto an anatomical image of the brain to identify the cortical regions involved. From a mathematical perspective, the data corresponding to each area come from hundreds of thousands of neurons interacting within a complex network. The single source of measurement obtained using a limited number of electrodes on the skin can be explained by an infinite number of solutions. The mathematical challenge facing the researcher is to associate the result of the clinical EEG examination with a single solution.
The research of Jean-Marc Lina is of particular importance to people whose only possible treatment option is surgical removal of the region or regions responsible for the epileptic seizures. The team of surgeons and neurologists must be able to localize these regions with the greatest possible precision, in order to avoid areas that are essential for other bodily functions. In the most difficult cases, such information may also guide the implantation of electrodes inside the patient’s skull to measure cerebral activity in vivo. These measurements are of paramount importance in planning surgery for patients with severe and debilitating drug-resistant epilepsy. Based on close collaboration with the clinical setting, this study is a shining example of the application of mathematics with the ultimate goal of improving health care.

Responsable : Francois Lalonde, Université de Montréal
Entité de recherche : Centre de recherches mathématiques (CRM)

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