Description:

Epilepsy is a neuronal disorder, characterized by an increased probability of recurring seizures, that affects 1% of world population. Studying epilepsy is a complex task because most clinical data is obtained with electroencephalography with a very low spacial resolution: every electrode records the electrical activity of millions of neurons. These data are therefore hard to relate to activity of individual neurons recorded during patch clamp experiments.

My research focuses on using mathematical models to bridge the gap from spiking neurons to 'brain waves'. In collaboration with Radboud University Nijmegen, University of Chicago and Academisch Medisch Centrum Utrecht, different approaches are investigated, i.e. large-scale numerical simulations of detailed neuronal models and bifurcation analysis of simpler population models, to gain new insights in abnormal processes in an epileptic brain.

A detailed model is implemented in a custom C++ program, of which both a serial and a parallel (using openMP) version are available. Due to the complexity of this large system, only numerical analysis of the generated time series is feasible. For analysis of the population model we use both analytical methods and numerical bifurcation packages (e.g. MATCONT and PDDE-CONT).

fig 1:Simulation results of the detailed model of neocortex. The layered structured is clearly visible in the left diagram, as is the complex   connection architecture. The right part shows the relation of a single neuron with respect to a larger group of neurons.