PMC

Distributions from seizure intervals tend to exhibit longer periods of phase-locking resulting in a deviation from a power-law of the distribution's tail. Plots are shown for scale 3 corresponding to the frequency band 25-12.5 Hz for patients 1–7 (P1–P7) and 32-16 Hz for patient 8 (P8), respectively.

Top: The electrocorticogram (ECoG) recording shows the onset of a focal epileptic seizure attack around 300 seconds time. Bottom: Cumulative distributions of phase-locking intervals (PLI) are obtained during three time intervals of 150 seconds: pre-ictal (left), ictal (middle) and post-ictal (right). Dashed lines indicate a power-law with exponent −3.1. While the distribution appears to follow a power-law during the pre-ictal period, intervals of increased phase-locking disturb this characteristic distribution with the onset of seizure activity. Data shown are from patient 1 at scale 3, corresponding to the frequency band 25–12.5 Hz.

ECoG recordings from 8 patients showing a focal seizure attack are shown along with values for consecutive time windows of 150 seconds duration overlapping by 100 seconds. The power-law fit of data in the first time window was taken as the reference to calculate . Although different in extent, an increase of quantifying the deviation from the initial pre-ictal distribution can be observed during seizures for all patients and different scales (scale 2 red, scale 3 blue, scale 4 green).

A Through an adaptive interplay of network dynamics and topology, the Bornholdt model self-organizes toward a characteristic connectivity independent of initial conditions. The plot shows the evolution to a characteristic connectivity of approximately in a network of 1024 nodes for three different initial connectivities, , and . B At this self-organized connectivity the network exhibits a phase transition between order and disorder. The plot shows the frozen component defined as the fraction of nodes that do not change their state along the attractor as a function of networks' average connectivities for a network of 1024 nodes. The data were measured along the dynamical attractor reached by the system, averaged over 100 random topologies for each value of . A transition around a value can be observed. C After a period of self-organization based on the adaptive interplay between topology and dynamics (aSO on, full black line), links were added and deleted solely with a certain probability independent of node activity (aSO off, dashed line: links were added with and deleted with , point-dashed line: links added with , deleted with ). Each iteration marks a topological update of the network, between iterations network activity was limited to 1000 time steps where topology was not changed. Phase-lock intervals between 20 randomly chosen nodes were calculated for scale 1 from 100 consecutive iterations at three time points: at the self-organized connectivity (bottom left), at a connectivity lower (bottom middle) and higher (bottom right) than the evolved connectivity. The distribution of PLI follows a power-law only at the self-organized connectivity (bottom left). All depicted distributions are cumulative distributions. The dashed line marks a power-law with exponent −1.5 to guide the eye.