Epilepsy in Small-World Networks
The Journal of Neuroscience, (2004)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.