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Evolving networks in the human epileptic brain
Klaus Lehnertz, Gerrit Ansmann, Stephan Bialonski, Henning Dickten, Christian Geier, Stephan Porz
TL;DR
Because seizure onset is increasingly linked to networks of brain regions rather than simple focal or generalized categories, understanding epilepsy requires capturing changing brain interactions. This review surveys methods for inferring and characterizing evolving epileptic networks and evidence spanning seconds to weeks. Within a Watts–Strogatz interpretation, the reviewed findings describe seizure-related shifts in functional topology and fluctuations during seizure-free periods that largely track daily rhythms.
Problem
Seizure onset is increasingly linked to networks of brain regions rather than simple focal or generalized categories, making the evolving interactions relevant to understanding epileptic dynamics.
Source: §I · p. 1Method
The review surveys methods for inferring functional networks from neural time series and characterizing evolving epileptic networks, alongside conceptual developments and findings across timescales.
Source: §I · pp. 1–2, §II · p. 2, B. Estimating interactions from time… · p. 3Results
Within a Watts–Strogatz interpretation, seizure topology shifts from more random toward more regular and back, while seizure-free network-property fluctuations largely track daily rhythms.
Source: §V · p. 7Takeaways & Limitations
These findings may offer clues about seizure self-termination and network control, potentially informing research into alternative therapeutic options.
Source: §V · p. 7The review’s scope inevitably means some contributions may be over- or underemphasized depending on the points made in the text.
Source: §V · p. 7
Abstract
from arXiv · showhide
Network theory provides novel concepts that promise an improved characterization of interacting dynamical systems. Within this framework, evolving networks can be considered as being composed of nodes, representing systems, and of time-varying edges, representing interactions between these systems. This approach is highly attractive to further our understanding of the physiological and pathophysiological dynamics in human brain networks. Indeed, there is growing evidence that the epileptic process can be regarded as a large-scale network phenomenon. We here review methodologies for inferring networks from empirical time series and for a characterization of these evolving networks. We summarize recent findings derived from studies that investigate human epileptic brain networks evolving on timescales ranging from few seconds to weeks. We point to possible pitfalls and open issues, and discuss future perspectives.
I. INTRODUCTION
Seizures are increasingly understood as emerging from networks of brain regions, whose interactions can change across physiological and pathological conditions. This review surveys methods for inferring and characterizing those evolving networks and findings across timescales from seconds to weeks.
I. INTRODUCTION
- Seizure onset within networks of brain regions challenges simple focal-versus-generalized categories and supports a new approach to seizure classification.The review describes epileptic networks as functionally connected cortical and subcortical structures that may also sustain normal activity between seizures.Source: §I · p. 1
- Epileptic brain networks are functional networks of interacting regions whose edges may change with physiological and pathophysiological conditions.The review frames seizures as large-scale network phenomena arising amid normal and abnormal brain functions.Source: §I · p. 1
- The review surveys methods for inferring and characterizing evolving epileptic networks, summarizes findings across seconds-to-weeks timescales, and identifies open issues and future perspectives.It also notes the need for new curative treatments because seizures remain poorly controlled for about 30% of patients despite maximal medical management.Source: §I · pp. 1–2
II. INFERRING FUNCTIONAL BRAIN NETWORKS
Functional brain networks are intended to represent interactions between brain regions, but constructing them requires choosing nodes and inferring edges from measurements. Time-series methods estimate interdependencies because interactions cannot be measured directly and the governing equations are unknown.
II. INFERRING FUNCTIONAL BRAIN NETWORKS
- Functional brain networks are intended to reflect interaction dynamics between brain regions.Identifying nodes and edges is challenging given the brain’s complex structural and functional organization and limitations in assessing it.Source: §II · p. 2
- Brain regions usually serve as network nodes, with sensors placed to capture their dynamics across levels of brain organization.The relevant organization ranges from single neurons and columns to brain regions, lobes, and functional systems.Source: §II · p. 2
- Because interactions cannot be measured directly and governing equations are unknown, time-series analyses estimate linear or nonlinear interdependencies as edges.The underlying interaction equations are not known.Source: §II · p. 2
A. Acquiring time series of neural activity
EEG, MEG, and fMRI provide neural-activity time series with different spatial and temporal resolutions and ways of assigning regions to nodes. EEG and MEG offer millisecond timing, while EEG can record over days to weeks and fMRI offers high spatial but much lower temporal resolution.
A. Acquiring time series of neural activity
- EEG and MEG measure electric and magnetic correlates of neural activity, while fMRI assesses activity indirectly through blood-oxygenation changes.Intracranial EEG can directly record from deeper structures and the brain surface in some patients undergoing presurgical evaluation.Source: A. Acquiring time series of neural… · p. 2
- EEG recordings can extend over days to weeks, capturing a broad range of physiological and pathophysiological activity, and EEG and MEG sample at millisecond resolution.Sensor placement limits spatial resolution; volume conduction and dense sampling can also introduce influences such as transitivity and common sources.Source: A. Acquiring time series of neural… · p. 2
- fMRI provides very high spatial resolution but has temporal resolution orders of magnitude lower than EEG or MEG.Each technique also differs in how brain regions are associated with network nodes.Source: A. Acquiring time series of neural… · p. 2
B. Estimating interactions from time series
Interaction estimators draw on several theoretical traditions, but transitivity and common sources can produce misleading edge estimates, and no approach is commonly accepted. Because most estimators require approximate stationarity, time-resolved sliding windows balance stationarity against statistical accuracy.
B. Estimating interactions from time series
- Estimators of interaction strength and direction draw on synchronization theory, nonlinear dynamics, information theory, statistical physics, and stochastic-process theory.The review highlights recent developments and improvements among these approaches.Source: B. Estimating interactions from time… · p. 2
- Transitivity can produce spurious edges when estimators cannot distinguish direct from indirect interactions, while common sources can inflate interaction-strength estimates.Partialization has been used to address transitivity, but its suitability for empirical data remains unshown; advanced phase-synchronization estimators may help avoid common-source effects.Source: B. Estimating interactions from time… · p. 2
- Sliding-window analysis addresses nonstationarity, trading approximate stationarity against statistical accuracy; windows of several tens of seconds are typically considered acceptable.Each window yields an interaction matrix whose entries estimate an interaction property between pairs of sampled brain regions.Source: B. Estimating interactions from time… · pp. 2–3
C. Constructing functional networks
Functional networks are constructed by converting pairwise interaction estimates into binary or weighted edges, with choices about direction, thresholds, and normalization shaping the resulting network.
C. Constructing functional networks
- Networks may be binary or weighted and undirected or directed, although methods for directed functional networks are few and most characteristics rely on undirected networks.Source: C. Constructing functional networks · p. 3
- Binary networks connect nodes when interaction strength exceeds a threshold or when a statistical test finds the interaction significant.Thresholds may be fixed, examined across a range, or chosen adaptively, including to avoid disconnected networks.Source: C. Constructing functional networks · p. 3
- Weighted networks can assign each edge its interaction strength directly, while normalization can set the mean edge weight to 1.Alternatively, ranks can assign weights from a given distribution to eliminate influences of the estimated-strength distribution.Source: C. Constructing functional networks · p. 3
- For binary networks, edges can be omitted when their interaction estimates are not statistically significant.Source: C. Constructing functional networks · p. 3
III. CHARACTERIZING NETWORKS
Graph-theoretic methods characterize functional networks, drawing on both established and newer measures.
III. CHARACTERIZING NETWORKS
- Graph-theoretic methods are used to characterize functional networks.Source: §III · p. 3
- Some methods originated in social network analysis in the 1970s and were later refined for use across scientific fields.Source: §III · p. 3
- The review focuses on characteristics most commonly used for epileptic brain networks, while noting that many other measures and modifications exist.Source: §III · p. 3
A. Network characteristics
The reviewed network characteristics describe node connectivity, local clustering, paths, and synchronization, but their interpretation can be affected by network construction and spurious interactions.
A. Network characteristics
- Degree counts a node’s neighbors in a binary network, and nodes with many connections are treated as hubs and assumed more important.Source: A. Network characteristics · pp. 3–4
- Clustering measures how often a node’s neighbors connect to one another, but weighted generalizations may fail for complete networks as weights approach zero.Common sources and estimators unable to distinguish direct from indirect interactions can also artificially increase clustering.Source: A. Network characteristics · p. 3
- In weighted networks, shortest-path edge length is usually the inverse of edge weight; disconnected pairs make the mean shortest path infinite.Efficiency or a construction scheme that prevents disconnected networks can address this issue, while spurious shortcuts may underestimate paths.Source: A. Network characteristics · pp. 3–4
- Assortativity measures whether connected nodes have similar degree, but common sources can make a dissortative structure appear assortative.Source: A. Network characteristics · p. 4
- Synchronizability describes the stability of a network’s globally synchronized state, with the eigenratio indicating instability above a threshold given node dynamics.The terminology is inconsistent: synchronizability has been used for both the eigenratio and its inverse.Source: A. Network characteristics · p. 4
- Centralities estimate node importance; degree centrality uses degree or strength, and highly connected nodes are called hubs.Source: A. Network characteristics · p. 4
- Closeness centrality is the inverse of a node’s average shortest-path distance to all other nodes, or may be estimated over only reachable nodes.Source: A. Network characteristics · p. 4
- Betweenness centrality counts shortest paths between other nodes that pass through a given node.The path count is represented by ηjl(i).Source: A. Network characteristics · p. 4
B. Normalizations and null models
Null models help distinguish network characteristics from influences such as edge count, average interaction strength, and weight distributions.
B. Normalizations and null models
- For binary networks, random graphs with the same edge count provide a baseline for characteristics, and further null models can also constrain node degrees or more complex properties.Expected values can be known analytically or estimated using Monte Carlo surrogates.Source: B. Normalizations and null models · p. 4
- For weighted networks, null models can preserve weights or node strengths to assess characteristics against influences including edge-weight dispersion.Some weighted characteristics may be dominated by the maximum edge weight or the standard deviation of edge weights.Source: B. Normalizations and null models · p. 4
- An alternative is to compare the complete analysis procedure with results from null-model time series.Source: B. Normalizations and null models · p. 4
IV. CHARACTERIZING EVOLVING EPILEPTIC NETWORKS
Studies report seizure-linked shifts in functional topology and substantial variation in network properties outside seizures. Long-term observations reveal daily rhythms, while structural findings suggest alterations extending beyond the epileptogenic lesion.
Structural alterations
- MRI studies report structural abnormalities extending beyond possible epileptogenic lesions, although findings are inconsistent across studies.These changes usually evolve much more slowly than epileptic discharges and seizures.Source: §IV · p. 5
Functional alterations
- Across focal, absence, and status epilepticus studies, null-model-normalized clustering and mean shortest path length show a concave-like evolution from random before seizures to regular during seizures, then random at ending or after.In 100 seizures from 60 patients, eigenratio significantly increased during seizures and decreased before seizure end.Source: §IV · p. 5
- During seizures, node centralities may change, but their highest values are not necessarily confined to the epileptic focus and results vary by centrality.Reported patterns include increased betweenness and degree centrality at seizure onset, and decreasing betweenness toward seizure end.Source: §IV · p. 5
Long-term functional alterations
- In 13 patients monitored for more than 2100 h, clustering and path length fluctuated largely with daily rhythms, while seizure-scale processes contributed less.Some patients also showed contributions on timescales longer than a day, possibly associated with anticonvulsant medication changes.Source: §IV · p. 5
- Pre-seizure network changes pointed to a loss of functional long-range connections, but whether these changes distinguish seizure-promoting configurations remains unresolved.The authors state that it remains to be shown whether the changes allow unequivocal judgment about whether a more random configuration promotes seizure generation.Source: §IV · p. 6
- In a 24-hour study of six patients, sparse, fractured, modular networks showed large fluctuations alongside edge structures persisting over roughly 100 seconds.Those persistent structures appeared consistently across cognitive states and recording days.Source: §IV · p. 6
- Long-term node centralities fluctuate, and the epileptic focus is not consistently the most important node; earlier focus-centrality findings may reflect shorter recordings.Preliminary observations also suggest daily rhythms in these fluctuations.Source: §IV · p. 6, Figure 1 · p. 6
V. CONCLUSION AND OUTLOOK
The review synthesizes methods and findings on evolving human epileptic brain networks across timescales from seconds to days and weeks. It reports seizure-related topology shifts and substantial seizure-free fluctuations, while emphasizing open questions and the need for further work.
V. CONCLUSION AND OUTLOOK
- The review covers evolving networks from seconds to days and weeks, while acknowledging that its scope may over- or underemphasize some contributions.It calls for more work to understand seizure-free interval dynamics.Source: §V · pp. 6–7
- During seizures, functional topology shifts from more random to more regular and back, with highest resilience and least synchronous-state stability in the more regular phase.During seizure-free intervals, large network-property fluctuations are largely attributable to daily rhythms, which may confound study of seizure generation.Source: §V · p. 7
- Computational epilepsy models may add insight, and simulations emphasize complex network topology and interactions with neuronal properties in seizure-like activity.The cited simulations address initiation, spread, and termination.Source: §V · p. 7