Epilepsy in Small-World Networks

TLDR

Hippocampal slice models of epilepsy exhibit short bursts from CA3 and longer seizure‑like activity from CA1, reflecting differing recurrent excitatory connectivity. The study seeks to explain these dynamics by simulating networks of excitatory neurons. Simulations used small‑world ring networks with predominantly local connections and some long‑distance links, varying synaptic strength, synapse count, and connection proportions to generate normal, seizing, and bursting behaviors. A simple mathematical description derived from the simulations shows that changes in network topology or synaptic strength trigger transitions from normal to seizing to bursting, a property general to excitatory networks.

Abstract

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. In attempting to explain this behavior, we simulated model networks of excitatory neurons using several types of model neurons. The model neurons were connected in a ring containing predominantly local connections and some long-distance random connections, resulting in a small-world network connectivity pattern. By changing parameters such as the synaptic strengths, number of synapses per neuron, proportion of local versus long-distance connections, we induced “normal,” “seizing,” and “bursting” behaviors. Based on these simulations, we made a simple mathematical description of these networks under well-defined assumptions. This mathematical description explains how specific changes in the topology or synaptic strength in the model cause transitions from normal to seizing and then to bursting. These behaviors appear to be general properties of excitatory networks.