Figure 2: Neural fragility in a 2-node network.

To build quantitative intuition on what neural fragility means in the context of a dynamical iEEG system, we construct a 2-node EEG network example with an excitatory (E) and inhibitory (I) population of neurons. For a qualitative description, see Figure 1. x_I(t) and x_E(t) are the EEG activity of the I and E neuronal population respectively. ‘A’ is a linear network model quantifying how each population affects the rest over time. Δ (i.e. the fragility), is the amount of change added to a node’s connections. The fragility of the node is quantified as the minimal amount of change necessary to cause seizure-like phenomena. (a) shows a stable network without a perturbation added, such that the network responses due to an impulse at I result in a transient that reverts to baseline. (b) shows a perturbation added, but the network is still stable with a slightly larger transient when an impulse is applied to node I. Then (c) shows enough of a perturbation is added, such that the network becomes unstable; an impulse applied at node I results in oscillatory activity that does not quickly return to baseline. The magnitude of the Δ added in (c) is the fragility of node I (i.e. $\sqrt{8}$).