CENTER FOR APPLIED MATHEMATICS AND STATISTICS
NEW JERSEY INSTITUTE OF TECHNOLOGY 

MATHEMATICAL BIOLOGY SEMINAR

4:00 PM  Tuesday, December 9, 2003
611 Cullimore Hall, NJIT


Epilepsy in Small World Networks

Robert Clewley
 
Center for Biodynamics
Boston University

        In hippocampal slice models of epilepsy, two behaviors are seen: short bursts of electrical activity lasting 100 msec, and seizure-like electrical activity lasting seconds. The bursts originate from the CA3 region, where there is a high degree of recurrent excitatory connections. Seizures originate from the CA1 where there are fewer recurrent connections (if the connections between the CA3 and CA1 are cut). In attempting to explain this behavior we have made model networks of excitatory neurons, using several types of model neurons. The model neurons were connected in a small-world network, containing predominantly local connections and some long distance random connections. By changing parameters such as the synaptic strengths, number of synapses per neuron, proportion of local vs. long distance connections, we observed both epileptiform behaviors. Based on these simulations, we made a simple mathematical description of these networks, under some assumptions. This mathematical description explains why and when changes in the topology or synaptic strength in the model cause transitions from "normal" to "seizing" to "bursting". These behaviors appear to be general properties of excitatory networks.