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Conceived and designed the experiments: CM EB TG. Performed the experiments: CM. Analyzed the data: CM. Contributed reagents/materials/analysis tools: AS SHE. Wrote the paper: CM TG.

The authors have declared that no competing interests exist.

Critical dynamics are assumed to be an attractive mode for normal brain functioning as information processing and computational capabilities are found to be optimal in the critical state. Recent experimental observations of neuronal activity patterns following power-law distributions, a hallmark of systems at a critical state, have led to the hypothesis that human brain dynamics could be poised at a phase transition between ordered and disordered activity. A so far unresolved question concerns the medical significance of critical brain activity and how it relates to pathological conditions. Using data from invasive electroencephalogram recordings from humans we show that during epileptic seizure attacks neuronal activity patterns deviate from the normally observed power-law distribution characterizing critical dynamics. The comparison of these observations to results from a computational model exhibiting self-organized criticality (SOC) based on adaptive networks allows further insights into the underlying dynamics. Together these results suggest that brain dynamics deviates from criticality during seizures caused by the failure of adaptive SOC.

Over the recent years it has become apparent that the concept of phase transitions is not only applicable to the systems classically considered in physics. It applies to a much wider class of complex systems exhibiting phases, characterized by qualitatively different types of long-term behavior. In the critical states, which are located directly at the transition, small changes can have a large effect on the system. This and other properties of critical states prove to be advantageous for computation and memory. It is therefore suspected that also cerebral neural networks operate close to criticality. This is supported by the

In the terminology of physics, a system is said to be in a critical state if it is poised on a threshold where the emergent macroscopic behavior changes qualitatively. The hypothesis that the brain is operating in such a critical state is attractive because criticality is known to bring about optimal information processing and computational capabilities

Additional evidence for the existence of a critical state in human brain dynamics comes from a recent study by Kitzbichler et al.

Theory predicts local events to percolate through the system in the form of avalanches of activity at the critical state

A so far unresolved question concerns the medical relevance of critical brain activity. Diseases in the central nervous system are often associated with altered brain dynamics. It has been hypothesized that the dynamical properties characterizing a critical state may be seen as an important marker of brain well-being in both health and disease

Here, we confirm the previously observed power-law distribution of phase-lock intervals (PLI) with a complementary experimental methodology, providing additional evidence for the criticality hypothesis. Furthermore, we present evidence that human brain networks

We investigated data sets from ECoG acquired during presurgical monitoring of patients suffering from focal epilepsy. Data were continuously sampled at 200 Hz (patients 1–7) or 256 Hz (patient 8) with the number of channels ranging from 30 to 45 for different patients. The time series recorded from the anatomical site where the epileptic focus was assumed typically included one or more neurographically-identifiable seizure attacks.

To test brain dynamics for signatures of criticality we analyzed ECoG activity in different time windows. The data sets were split in intervals of 150 seconds length (30000 sample steps at 200 Hz sampling, 38400 in the case of 256 Hz) with consecutive intervals overlapping by 100 seconds (20000 sample steps at 200 Hz, 25600 at 256 Hz). Following the approach in

The distributions for all scales closely follow a power-law probability distribution with

While the PLI distribution followed a power-law in time intervals preceding the seizure onset, a deviation from power-law behavior was observed in intervals containing the seizure attack.

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.

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.

A more quantitative estimate of the deviation from the pre-ictal state can be obtained by calculating

During time intervals preceding the seizure

ECoG recordings from 8 patients showing a focal seizure attack are shown along with

For obtaining further insights into the underlying dynamics of the power-law probability distribution of PLI and its absence during epileptic seizure attacks, we compared experimental results to a simple computational model exhibiting self-organized criticality. Our numerical results build on a model proposed by Bornholdt and Rohlf

For a network with

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

Our goal was to compare the distribution of PLI at the self-organized connectivity and at connectivities below and above it. This would correspond to critical dynamics as well as dynamics in the ordered/frozen and disordered phase respectively. We therefore let the network evolve according to the adaptive self-organization (aSO) process described in

Next, we switched the aSO off at 8000 iterations, instead adding and deleting links with a certain probability independent of node activity after this point (iterations 8001–12000). We considered two cases: First, where links were added with probability

The close agreement between patient and model data suggests that the deviation from a power-law observed during epileptic seizure attacks indicates a shift of dynamics toward an ordered phase. In the model above this corresponds to the phase of frozen dynamics. It further hints that it is the mechanism of adaptive SOC, the ability to tune system parameters to values where network dynamics is at a phase transition and PLI are distributed according to a power-law, that could fail during epileptic seizure attacks in neuron networks in the brain.

The relevance of critical brain dynamics is currently a heavily debated topic. Indirect evidence for such a state comes from power-law distributed observables in neurophysiological data. Power-laws can arise through various mechanisms such as the combination of two exponential distributions or random extremal processes such as the Omori law for earthquake aftershocks for example

The power-laws observed in neural data are consistent with the hypothesis of neural criticality. The hypothesis is further supported by a) evolutionary arguments highlighting the advantages of operating in a critical state

Recently, the power-law distribution of phase-lock intervals between pairs of neurophysiological time series was shown to be a specific hallmark of dynamic criticality in human brain dynamics

Using this indicator on ECoG data, a complementary experimental methodology to

Our findings support the notion of a physiological default state of balanced brain dynamics between regimes of exuberant and frozen activity. Physiological neuronal activity is characterized by intermittent periods of synchronization between different anatomical regions. In terms of dynamical system's theory, such a state corresponds to a critical state at a phase transition between order and disorder. A deviation from this balanced state toward dynamics with pathologically increased times of synchronous activity as observed in epileptic patients leads to a deviation from the physiological critical state resulting in impaired functionality.

Optimal information processing capabilities of neuron networks have been related to a critical state before

A mechanism by which complex networks can self-organize toward a critical state is based on the adaptive interplay between the dynamics

Along this line of arguments the deviation from a power-law distribution of PLI reported here can be interpreted as a shift away from a balanced critical state and to our knowledge constitutes the first proof of impaired critical dynamics related to a pathology

In summary, experimental results from

Eight patients undergoing surgical treatment for intractable epilepsy participated in the study. Patients underwent a craniotomy for subdural placement of electrode grids and strips followed by continuous video and ECoG monitoring to localize epileptogenic zones. Solely clinical considerations determined the placement of electrodes and the duration of monitoring. Positions of the electrodes from patients 1–7 can be found in the supplementary material (

To derive a scale-dependent estimate of the phase difference between two time series, we follow the approach described in ref.

To quantify the deviation from a power-law we defined a measure

Positive values of

An influential model explaining how dynamical systems can self-organize towards a critical state was introduced in ref.

We first instantiated this model in a network of 1024 randomly interconnected binary elements with states

To organize the network away from

Cumulative distribution of phase-lock intervals for consecutive time windows and different scales (scale 2 green, scale 3 red, scale 4 blue) from patient 1.

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Schematic drawings of the positions of the electrodes from patients 1 to 7.

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C.M. thanks M. Kirsch and E. Noback for their support in preparing data sets for analysis. We further thank M. Ihle and A. Schulze-Bonhage for supplying the recordings of patient 8.