Ilir Dema 1,2, Jeremie Lefebvre 1, 2, Tauk Valiante 2,3,4
1 Department of Mathematics, University of Toronto
2 Krembil Research Institute, University Health Network
3 Faculty of Medicine, University of Toronto
4 Institute of Medical Science, University of Toronto
Understanding the mechanism by which epileptic seizures appear and how they propagate in the epileptic brain is a dicult challenge with important clinical applications. But mathematics can help. Using a combination of modelling, machine learning, and human data, we developed a non-linear network model of seizure initiation and tted this model on human data. This model will allow us not only to understand the mechanism on seizure onset (and how to prevent it) but also to emulate epileptiform activity and study it’s spreading using patient-specific computer simulations. Using time series of the electric potentials measured right before, during and right after an epileptic seizures in patients, we have applied various machine learning techniques (such as hierarchical time series clustering) which enable classication of seizure dynamics. Specically, we have applied various time series distance measurement techniques on clinical measurements, producing data, which if fed to a number of algorithms, allow clustering and classication of epileptiform events, revealing links between dierent parameters and features of seizure activity.
In parallel, we aim to develop a framework that allows quick identication of various coefficients and parameters of our network model to patient-specic data, leading to personalized simulations. Using tted models, our goal is to understand the critical values of parameters that might lead to seizure events and what routes those into patients’ white matter pathways. Most importantly, such simulations could provide key insight about the location of seizure foci and hence provide support to clinicians. This project has the potential to revolutionize the way we understand and model the brain, catalyzing the development of personalized treatments to make surgery and other treatments strategies safer, more eective, and available to more epilepsy patients in Canada.
 T.Warren Liao. Clustering of time series data – a survey.
Pattern Recognition 38 (2005) 1857 – 1874