Fragility in networks: Application to the epileptic brain

Networks consist of interacting components that often function together to achieve a particular goal. For example, in the human cortex, populations of neurons in different layers continuously communicate and encode information about the subject's environment and cognitive state to govern behavior. In cortical networks, neurons (network nodes) can be structurally connected (through synapses) in addition to being functionally connected; and in epilepsy, structural connections in just a few nodes change to destabilize the network and cause seizures. We define these nodes as fragile and set out to quantify fragility in networks. We first consider arbitrary linear networks whose state-evolution matrices characterize functional connectivity. Nodal fragility is then computed as the minimum energy perturbation required on the node's functional connectivity to destabilize the network. We then apply our perturbation theory to a stable probabilistic nonlinear neural network model. We show how the destabilizing perturbation in functional connectivity translates to a perturbation on the structural connections between neurons, i.e., the synaptic weights. Our results suggest that the most fragile nodes in the network are excitatory neurons that become more active or inhibitory neurons that become less active. This is consistent with abnormal axonal sprouting of excitatory neurons and loss of inhibitory chandelier cells observed in epileptic cortical tissue. The simulated activity before and after seizure also highlight the heterogeneity observed in actual recordings from epilepsy patients, where parts of the network either increase or decrease baseline firing while the rest of the neurons become silenced.