Figure 5

Characterising the Focal or Generalised Nature of a Brain Network. (A) Onset index (OI) and participation index (PI) for a “focal” network. (a) Network structure with 6 nodes (A, B, C, D, E, F) and edges describing directed connectivity between the nodes. (b) Activation Matrix for the given network. Each node is set into the locally synchronised state once, and its response of the remaining nodes calculated (which constitute the entries of the activation matrix). The OI (PI) for a node j corresponds to the averaged column (row) sum of column j. The variability in the OI (PI) is found by dividing the standard deviation over all the OIs (PIs) and dividing this by its mean. The normalised standard deviation for the OI and PI are shown in the bottom right of the activation matrix (light grey). (c) The dynamics of each node corresponds to the collective activity of a subpopulation of Kuramoto oscillators and can be thought of as a single channel of simulated EEG, where low amplitude activity represents the non-synchronised state (interictal), and high amplitude oscillatory activity represents the synchronised state (ictal). In each subpanel, a node is set into the synchronised state (blue), and the network response simulated. Note that the response of the network is variable and depends on the location of seizure initiation, indicating a high degree of heterogeneity in the network’s behaviour. (B) OI and PI for a “generalised” network. (a) Network structure with 6 nodes (A, B, C, D, E, F) and edges describing directed connectivity between the nodes. (b) Activation Matrix for the given network. Normalised standard deviations for the OI and the PI are shown in the bottom right of the activation matrix (light grey). (c) In each subpanel, a node is set into the synchronised state (blue), and the network response simulated. Note that the response of the network is homogeneous throughout, indicating a high degree of similarity across the network’s behaviour. All simulations were carried out with 4000 oscillators per population, oscillators initialised randomly across the unit circle, natural frequencies drawn from a Gaussian distribution with mean frequency 0.5 and standard deviation 1.0, coupling strength of the “non-activated” nodes set to 0.4 and the “activated” node at 5.0, using a standard Euler method with time-step 0.1.