Model behavior on a two-node network.

<p><b>A</b>: The order parameter for unidirectional and bidirectional coupling between two nodes plotted against the global coupling parameter , accompanied by numerical results. The slow increase of the numerical result of with for unidirectional coupling is due to the finite size of the system with ocillators. <b>B</b>: The evolution of the signal of each node with random initial conditions and .</p

Illustration of the procedure to derive the functional network structure.

<p><b>A</b>: An artefact-free 20s resting-state segment of EEG from each subject is extracted. <b>B</b>: Applying the time-lagged cross-correlation to all combinations of channel pairs yields a bidirectional connectivity matrix. <b>C</b>: Connections are removed if they are not significantly different from surrogate data (% level of significance). <b>D</b>: Using the time-lags, a unidirectional connectivity matrix can be inferred. <b>E</b>: Setting to zero all connections that can be explained by stronger, indirect connections removes spurious connections.</p

Critical coupling constants in the functional networks obtained from the epilepsy cohort and the control cohort in different frequency bands.

<p><b>A</b>: A significantly lower in the theta and low alpha band indicates that the functional network in the interictal state of the epilepsy cohort is closer to synchronization than in the control cohort. Interestingly, ictal discharges occur in the theta band as well. Level of significance: . Error bars indicate the standard error of the mean. . <b>B</b>: Receiver operating characteristic for the detection of members of the epilepsy cohort through use of thresholded values of as the discriminating factor for networks inferred from either the theta or low-alpha band. The red dot indicates the point with best discrimination, which is the point closest to the point of perfect classification (,). Abbreviations: FPR - false positive rate, TPR - true positive rate, SNS - sensitivity, SPC - specificity, PPV - positive predictive value, AUC - area under the curve thr - threshold for discrimination.</p

The global (average) order parameter of the network when one node is self-synchronized.

<p><b>A</b>: We show here the result for self-synchronization in Fp1 and F7, and also the average over all electrodes, in the theta band and low alpha band. Other electrodes are omitted as they do not yield significant results when p-values are Bonferroni-corrected by a factor of (the number of electrodes). This finding confirms the result of previous studies (see text) that identified frontal and pre-frontal areas as seizure onset zones. Levels of significance: ; ; . Parameters: for all nodes except self-synchronized node with ; . Error bars indicate the standard error of the mean. <b>B</b>: Receiver operating characteristic for the detection of the epilepsy cohort by using the global (average) order parameter as discriminating factor in F7 in the theta-band, and Fp1 and F7 in the low-alpha band. Again, the red dot indicates the point with best discrimination. Abbreviations as per <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003947#pcbi-1003947-g008" target="_blank">Figure 8</a>.</p

The order parameter on a cycle.

<p><b>A</b>: Illustration of cycles with increasing number of nodes. <b>B</b>: A plot of analytical and numerical results of the order parameter on a cycle of nodes. The numerical example is obtained for oscillators per node.</p

Motivation of our modeling approach.

<p>The Electroencephalogram (EEG) records electrical signals from electrodes placed on the scalp. There exist various methods to derive functional network structure from the recorded time series. The primary challenge is to identify (statistically) significant differences between the functional networks of subjects with a particular neurological disorder, and healthy controls. The second challenge is to identify the underlying mechanisms that lead to these changes in network structure, and how they affect the behavior of the model constituents, i.e. the different brain regions. The EEG epochs used in this study are chosen from resting-state, eyes closed. For those subjects with epilepsy, epochs have been selected by a clinically trained expert and are far away from seizures.</p

Frequency bands.

<p>Frequency bands used in this study are motivated by the work of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003947#pcbi.1003947-Shackman1" target="_blank">[57]</a>.</p><p>Frequency bands.</p

The Kuramoto model with varying coupling strength to demonstrate the ictal (synchronized) and interictal (unsynchronized) behavior of the model.

<p><b>A</b>: For below a critical value (red, dotted line) the signal is irregular and the order parameter representing the degree of synchronicity is low. If is above the critical value, is sinusoidal with large amplitude, and the order parameter is large. <b>B</b>: At the onset of synchronization, the oscillators start forming a cluster resulting in an increase of the order parameter. Bars around the circles indicate the phase density of oscillators. The internal frequencies are drawn from a normal distribution with mean and standard deviation . Here we use oscillators.</p

Illustration of how subtle changes in the network structure affect the ability of the network to synchronize.

<p><b>A</b>: An arbitrarily chosen network shows partial synchronization due to a cycle () and two adjacent nodes (6,7). <b>B</b>: By removing one connection (red, dashed) the cycle is broken and the network loses its capability for synchronization. <b>C</b>: By reversing the connection between 1 and 2 (blue, bold), the network from <b>A</b> becomes globally synchronous for large enough . Numerical results are in agreement with analytical results, but omitted here. The intrinsic coupling constant of all nodes is set to .</p

Comparison of recorded seizure with model output.

<p>Here we present a comparison between the clinically recorded onset of a generalized seizure event and the output of the modular Kuramoto network, demonstrating that critical features of this transition are captured by the phenomenological model. <b>A</b>: Epileptic seizure as captured by EEG. <b>B</b>: The Kuramoto model displays behavior similar to epileptic seizures. In the model, we assume local networks (where a node represents a recording site) to be all-to-all connected, analogous to a collection of cortical columns. These nodes are then directionally connected, resulting in a modular network with two scales of coupling.</p