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Failure of adaptive self-organized criticality during epileptic seizure attacks
Christian Meisel, Alexander Storch, Susanne Hallmeyer-Elgner, Ed Bullmore, Thilo Gross
TL;DR
The paper examines whether critical brain dynamics have medical relevance in epilepsy. Using invasive ECoG recordings and an adaptive-network SOC model, it finds that seizures disrupt power-law phase-locking patterns, suggesting failure of adaptive SOC.
Problem
The medical relevance of critical brain activity and its relation to pathological conditions remained unresolved.
Method
The study analyzes ECoG-derived phase-lock intervals and compares human observations with a computational model exhibiting adaptive self-organized criticality.
Results
During epileptic seizures, the phase-lock-interval distribution deviates from the power law observed during normal critical dynamics.
Takeaways & Limitations
The findings suggest that seizure-related pathological synchronization involves deviation from criticality associated with failure of adaptive SOC.
Takeaways & Limitations
Assessing the usefulness and performance of the proposed measure requires statistical validation of sensitivity and specificity, which was beyond the article’s scope.
Abstract
from arXiv · showhide
Critical dynamics are assumed to be an attractive mode for normal brain functioning as information processing and computational capabilities are found to be optimized there. 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.
I. INTRODUCTION
Criticality is proposed as a normal operating state of brain networks because it supports information processing and computational capabilities. The paper asks whether this critical state has medical relevance and reports that seizures disturb it, consistent with adaptive SOC failure.
- Critical states occur at thresholds where emergent macroscopic behavior changes qualitatively.
- Power-law neuronal activity distributions, including neuronal avalanches, support the hypothesis that cortical networks operate near criticality.Such avalanches have been observed in reduced rat preparations and invasive recordings from monkeys and cats.
- Human MEG and fMRI studies found power-law distributions of phase-synchronization measures, supporting endogenous dynamical criticality.
- Adaptive networks can exhibit robust self-organized criticality by combining network-topology evolution with node dynamics and simple local rules.
- The paper addresses the unresolved medical relevance of critical brain activity by examining whether epilepsy involves deviation from critical dynamics.Epileptic seizures involve abnormal synchronized neuronal firing, and prior animal studies linked altered activity distributions to departures from normal dynamics.
- Using ECoG-derived phase-lock intervals and an SOC model, the study finds that seizure activity disrupts scale invariance and suggests failure of adaptive SOC.The PLI-based measure may support future seizure-prediction algorithms.
Data
The study analyzed invasive ECoG recordings from eight patients undergoing surgery for intractable epilepsy. Electrode placement and monitoring duration were determined by clinical needs.
- Eight patients undergoing surgical treatment for intractable epilepsy participated in the study.
- Subdural electrode grids and strips were implanted during craniotomy, followed by continuous video and ECoG monitoring.The recordings were used to localize epileptogenic zones.
- ECoG signals were recorded with a clinical EEG system and bandpass filtered between 0.53 Hz and 70 Hz.
- Electrode placement and monitoring duration were determined solely by clinical considerations, and all patients provided informed consent.
Estimation Of Phase Synchronization
The method estimates scale-dependent phase differences from Hilbert-wavelet coefficients and identifies phase-locking intervals when the local phase difference remains below a threshold.
- Scale-dependent phase differences are estimated from Hilbert-transform-derived pairs of wavelet coefficients.
- The instantaneous complex phase vector is formed from wavelet coefficients at a chosen scale for two signals.
- The local mean phase difference is calculated within the frequency interval defined by the selected wavelet scale.
- Phase-locking intervals are periods when the absolute local phase difference is smaller than π/4.The estimate is averaged over a brief interval to reduce noise.
Distribution
The deviation measure Δp compares empirical phase-lock-interval distributions with a fitted reference power law. Its sign indicates whether phase-locking intervals are increased or decreased relative to that reference.
- Δp measures the difference between the empirical cumulative distribution of phase-lock intervals and a fitted theoretical power-law distribution.
- The reference power law is fitted from the first 0-150 seconds of each data set and compared with successive 150-second intervals.
- Positive Δp indicates increased phase-locking intervals relative to the reference power law, whereas negative Δp indicates decreased phase-locking.
Computational Model
The computational model couples node-state dynamics with adaptive rewiring so network topology evolves toward critical connectivity. Phase-locking intervals are then measured across networks with subcritical, critical, and supercritical average connectivities.
- Adaptive network model: The model changes network topology according to node activity, coupling dynamics on the network with dynamics of the network.Active nodes lose links while frozen nodes gain links.
- Adaptive network model: A network of 200 randomly interconnected binary elements with states σ_i = ±1 is updated in parallel while connections are locally rewired.Under the adaptive algorithm, topology evolves toward a critical connectivity of K_c ∼3.1.
- Measurement procedure: Phase-locking intervals between pairs of nodes are estimated to compare model dynamics with neurophysiological time series.The analysis uses cumulative PLI distributions as the reference observable.
- Measurement procedure: The model compares cumulative PLI distributions from 20 randomly chosen nodes in networks with average connectivities K = 2.75, K = 3.1, and K = 5.0.Each run lasts 40000 time steps without further topological rewiring.
III. RESULTS
ECoG recordings from eight patients show that PLI distributions follow power-law behavior before seizures but deviate during seizure activity, with longer phase-locking intervals. Comparison with the adaptive-network model suggests a shift toward ordered dynamics and failure of adaptive SOC during seizures.
- III. RESULTS: Eight patients with focal epilepsy provided presurgical ECoG recordings sampled at 200 or 256 Hz across 30–45 channels.Recordings were obtained during continuous monitoring of sites including the presumed epileptic focus.
- III. RESULTS: PLI distributions followed a power-law before seizure onset but deviated during seizure-containing intervals in all 8 patients and across scales.Longer phase-locking intervals increased during attacks, destroying the original scale-free property.
- III. RESULTS: During seizure activity, Δp increased from low pre-ictal values to positive values, indicating divergence from the initial power-law distribution.After seizures, Δp slowly decreased, suggesting relaxation back toward a power-law distribution.
- III. RESULTS: Pre-ictal power-law behavior remained conserved while the amount of phase-locking tended to decrease toward seizure onset.The decline was most prominent at scale 4, corresponding to 12–6 Hz for patients 1–7 and 16–8 Hz for patient 8.
- III. RESULTS: At self-organized critical connectivity, PLI power-law hypotheses were accepted, whereas they were rejected below and above K_c.The ordered-phase distribution shifted toward larger PLI, resembling seizure-attack distributions.
- III. RESULTS: The agreement between patient and model data suggests seizures shift dynamics toward an ordered phase through failure of adaptive SOC.Adaptive SOC normally tunes network parameters to a phase transition where PLI follows a power-law.
IV. DISCUSSION
The study links seizure-related loss of PLI power-law scaling to impaired critical dynamics, while adaptive-network modeling suggests a failure of the mechanisms maintaining criticality. Pre-ictal phase-locking can change substantially before the power-law signature is lost at seizure onset.
- Human observations: During seizures, PLI distributions deviate from power-law behavior across all eight patients and investigated scales.Longer phase-locking intervals become more probable during attacks, destroying the original scale-free property.
- Adaptive SOC model: The model produces a PLI power-law at the self-organized connectivity Kc = 3.1, whereas distributions away from Kc deviate from power-law behavior.The ordered-phase distribution shifts toward larger PLI, resembling the pattern observed during epileptic seizures.
- Human observations: Power-law scaling of PLI is conserved before seizure onset but is lost relatively abruptly when seizures begin.This loss occurs despite declining phase-locking measures before onset, indicating that criticality persists until seizure onset according to the PLI criterion.
- Clinical relevance: PLI-based seizure precursors may appear earlier through declining synchronization, but their sensitivity and specificity were not statistically validated in this study.The authors state that validating the measure’s usefulness and performance was beyond the article’s scope.
- Interpretation: A seizure-associated deviation from the PLI power law corresponds to a shift away from balanced critical dynamics and provides direct in vivo evidence linking impaired criticality to pathology.Related in vitro findings associate excess excitation with destroyed power-law avalanche distributions and larger avalanche sizes.
- Interpretation: The authors suggest that failure of adaptive interplay between neuronal activity and network topology leads to pathological, overly synchronized activity and loss of criticality.The abrupt loss of the power-law distribution at seizure onset is interpreted as evidence that adaptive SOC fails beyond a threshold.