Seizure Cycles under Pharmacotherapy.

OBJECTIVE: This study was undertaken to determine the effects of antiseizure medications (ASMs) on multidien (multiday) cycles of interictal epileptiform activity (IEA) and seizures and evaluate their potential clinical significance. METHODS: We retrospectively analyzed up to 10 years of data from 88 of the 256 total adults with pharmacoresistant focal epilepsy who participated in the clinical trials of the RNS System, an intracranial device that keeps records of IEA counts. Following adjunctive ASM trials, we evaluated changes over months in (1) rates of self-reported disabling seizures and (2) multidien IEA cycle strength (spectral power for periodicity between 4 and 40 days). We used a survival analysis and the receiver operating characteristics to assess changes in IEA as a predictor of seizure control. RESULTS: Among 56 (33.3%) of the 168 adjunctive ASM trials suitable for analysis, ASM introduction was followed by an average 50 to 70% decrease in multidien IEA cycle strength and a concomitant 50 to 70% decrease in relative seizure rate for up to 12 months. Individuals with a ≥50% decrease in IEA cycle strength in the first 3 months of an ASM trial had a higher probability of remaining seizure responders (≥50% seizure rate reduction, p < 10-7) or super-responders (≥90%, p < 10-8) over the next 12 months. INTERPRETATION: In this large cohort, a decrease in multidien IEA cycle strength following initiation of an adjunctive ASM correlated with seizure control for up to 12 months, suggesting that fluctuations in IEA mirror "disease activity" in pharmacoresistant focal epilepsy and may have clinical utility as a biomarker to predict treatment response. ANN NEUROL 2024;95:743-753.

Neural manifolds carry reactivation of phonetic representations during semantic processing.

Traditional models of speech perception posit that neural activity encodes speech through a hierarchy of cognitive processes, from low-level representations of acoustic and phonetic features to high-level semantic encoding. Yet it remains unknown how neural representations are transformed across levels of the speech hierarchy. Here, we analyzed unique microelectrode array recordings of neuronal spiking activity from the human left anterior superior temporal gyrus, a brain region at the interface between phonetic and semantic speech processing, during a semantic categorization task and natural speech perception. We identified distinct neural manifolds for semantic and phonetic features, with a functional separation of the corresponding low-dimensional trajectories. Moreover, phonetic and semantic representations were encoded concurrently and reflected in power increases in the beta and low-gamma local field potentials, suggesting top-down predictive and bottom-up cumulative processes. Our results are the first to demonstrate mechanisms for hierarchical speech transformations that are specific to neuronal population dynamics.

Learning to generalize seizure forecasts.

OBJECTIVE: Epilepsy is characterized by spontaneous seizures that recur at unexpected times. Nonetheless, using years-long electroencephalographic (EEG) recordings, we previously found that patient-reported seizures consistently occur when interictal epileptiform activity (IEA) cyclically builds up over days. This multidien (multiday) interictal-ictal relationship, which is shared across patients, may bear phasic information for forecasting seizures, even if individual patterns of seizure timing are unknown. To test this rigorously in a large retrospective dataset, we pretrained algorithms on data recorded from a group of patients, and forecasted seizures in other, previously unseen patients. METHODS: We used retrospective long-term data from participants (N = 159) in the RNS System clinical trials, including intracranial EEG recordings (icEEG), and from two participants in the UNEEG Medical clinical trial of a subscalp EEG system (sqEEG). Based on IEA detections, we extracted instantaneous multidien phases and trained generalized linear models (GLMs) and recurrent neural networks (RNNs) to forecast the probability of seizure occurrence at a 24-h horizon. RESULTS: With GLMs and RNNs, seizures could be forecasted above chance in 79% and 81% of previously unseen subjects with a median discrimination of area under the curve (AUC) = .70 and .69 and median Brier skill score (BSS) = .07 and .08. In direct comparison, individualized models had similar median performance (AUC = .67, BSS = .08), but for fewer subjects (60%). Moreover, calibration of pretrained models could be maintained to accommodate different seizure rates across subjects. SIGNIFICANCE: Our findings suggest that seizure forecasting based on multidien cycles of IEA can generalize across patients, and may drastically reduce the amount of data needed to issue forecasts for individuals who recently started collecting chronic EEG data. In addition, we show that this generalization is independent of the method used to record seizures (patient-reported vs. electrographic) or IEA (icEEG vs. sqEEG).

Seizure forecasting: Bifurcations in the long and winding road.

To date, the unpredictability of seizures remains a source of suffering for people with epilepsy, motivating decades of research into methods to forecast seizures. Originally, only few scientists and neurologists ventured into this niche endeavor, which, given the difficulty of the task, soon turned into a long and winding road. Over the past decade, however, our narrow field has seen a major acceleration, with trials of chronic electroencephalographic devices and the subsequent discovery of cyclical patterns in the occurrence of seizures. Now, a burgeoning science of seizure timing is emerging, which in turn informs best forecasting strategies for upcoming clinical trials. Although the finish line might be in view, many challenges remain to make seizure forecasting a reality. This review covers the most recent scientific, technical, and medical developments, discusses methodology in detail, and sets a number of goals for future studies.

Imagined speech can be decoded from low- and cross-frequency intracranial EEG features.

Reconstructing intended speech from neural activity using brain-computer interfaces holds great promises for people with severe speech production deficits. While decoding overt speech has progressed, decoding imagined speech has met limited success, mainly because the associated neural signals are weak and variable compared to overt speech, hence difficult to decode by learning algorithms. We obtained three electrocorticography datasets from 13 patients, with electrodes implanted for epilepsy evaluation, who performed overt and imagined speech production tasks. Based on recent theories of speech neural processing, we extracted consistent and specific neural features usable for future brain computer interfaces, and assessed their performance to discriminate speech items in articulatory, phonetic, and vocalic representation spaces. While high-frequency activity provided the best signal for overt speech, both low- and higher-frequency power and local cross-frequency contributed to imagined speech decoding, in particular in phonetic and vocalic, i.e. perceptual, spaces. These findings show that low-frequency power and cross-frequency dynamics contain key information for imagined speech decoding.

Forecasting seizure risk in adults with focal epilepsy: a development and validation study.

BACKGROUND: People with epilepsy are burdened with the apparent unpredictability of seizures. In the past decade, converging evidence from studies using chronic EEG (cEEG) revealed that epileptic brain activity shows robust cycles, operating over hours (circadian) and days (multidien). We hypothesised that these cycles can be leveraged to estimate future seizure probability, and we tested the feasibility of forecasting seizures days in advance. METHODS: We did a feasibility study in distinct development and validation cohorts, involving retrospective analysis of cEEG data recorded with an implanted device in adults (age ≥18 years) with drug-resistant focal epilepsy followed at 35 centres across the USA between Jan 19, 2004, and May 18, 2018. Patients were required to have had 20 or more electrographic seizures (development cohort) or self-reported seizures (validation cohort). In all patients, the device recorded interictal epileptiform activity (IEA; ≥6 months of continuous hourly data), the fluctuations in which helped estimate varying seizure risk. Point process statistical models trained on initial portions of each patient's cEEG data (both cohorts) generated forecasts of seizure probability that were tested on subsequent unseen seizure data and evaluated against surrogate time-series. The primary outcome was the percentage of patients with forecasts showing improvement over chance (IoC). FINDINGS: We screened 72 and 256 patients, and included 18 and 157 patients in the development and validation cohorts, respectively. Models incorporating information about multidien IEA cycles alone generated daily seizure forecasts for the next calendar day with IoC in 15 (83%) patients in the development cohort and 103 (66%) patients in the validation cohort. The forecasting horizon could be extended up to 3 days while maintaining IoC in two (11%) of 18 patients and 61 (39%) of 157 patients. Forecasts with a shorter horizon of 1 h, possible only for electrographic seizures in the development cohort, showed IoC in all 18 (100%) patients. INTERPRETATION: This study shows that seizure probability can be forecasted days in advance by leveraging multidien IEA cycles recorded with an implanted device. This study will serve as a basis for prospective clinical trials to establish how people with epilepsy might benefit from seizure forecasting over long horizons. FUNDING: None. VIDEO ABSTRACT.

Robustness of connectome harmonics to local gray matter and long-range white matter connectivity changes.

Recently, it has been proposed that the harmonic patterns emerging from the brain's structural connectivity underlie the resting state networks of the human brain. These harmonic patterns, termed connectome harmonics, are estimated as the Laplace eigenfunctions of the combined gray and white matters connectivity matrices and yield a connectome-specific extension of the well-known Fourier basis. However, it remains unclear how topological properties of the combined connectomes constrain the precise shape of the connectome harmonics and their relationships to the resting state networks. Here, we systematically study how alterations of the local and long-range connectivity matrices affect the spatial patterns of connectome harmonics. Specifically, the proportion of local gray matter homogeneous connectivity versus long-range white-matter heterogeneous connectivity is varied by means of weight-based matrix thresholding, distance-based matrix trimming, and several types of matrix randomizations. We demonstrate that the proportion of local gray matter connections plays a crucial role for the emergence of wide-spread, functionally meaningful, and originally published connectome harmonic patterns. This finding is robust for several different cortical surface templates, mesh resolutions, or widths of the local diffusion kernel. Finally, using the connectome harmonic framework, we also provide a proof-of-concept for how targeted structural changes such as the atrophy of inter-hemispheric callosal fibers and gray matter alterations may predict functional deficits associated with neurodegenerative conditions.

Chance and risk in epilepsy.

PURPOSE OF REVIEW: Epilepsy is a dynamical disorder of the brain characterized by sudden, seemingly unpredictable transitions to the ictal state. When and how these transitions occur remain unresolved questions in neurology. RECENT FINDINGS: Modelling work based on dynamical systems theory proposed that a slow control parameter is necessary to explain the transition between interictal and ictal states. Recently, converging evidence from chronic EEG datasets unravelled the existence of cycles of epileptic brain activity at multiple timescales - circadian, multidien (over multiple days) and circannual - which could reflect cyclical changes in a slow control parameter. This temporal structure of epilepsy has theoretical implications and argues against the conception of seizures as completely random events. The practical significance of cycles in epilepsy is highlighted by their predictive value in computational models for seizure forecasting. SUMMARY: The canonical randomness of seizures is being reconsidered in light of cycles of brain activity discovered through chronic EEG. This paradigm shift motivates development of next-generation devices to track more closely fluctuations in epileptic brain activity that determine time-varying seizure risk.

Ensembling crowdsourced seizure prediction algorithms using long-term human intracranial EEG.

Seizure prediction is feasible, but greater accuracy is needed to make seizure prediction clinically viable across a large group of patients. Recent work crowdsourced state-of-the-art prediction algorithms in a worldwide competition, yielding improvements in seizure prediction performance for patients whose seizures were previously found hard to anticipate. The aim of the current analysis was to explore potential performance improvements using an ensemble of the top competition algorithms. The results suggest that minor increments in performance may be possible; however, the outcomes of statistical testing limit the confidence in these increments. Our results suggest that for the specific algorithms, evaluation framework, and data considered here, incremental improvements are achievable but there may be upper bounds on machine learning-based seizure prediction performance for some patients whose seizures are challenging to predict. Other more tailored approaches that, for example, take into account a deeper understanding of preictal mechanisms, patient-specific sleep-wake rhythms, or novel measurement approaches, may still offer further gains for these types of patients.

Intracortical neural activity distal to seizure-onset-areas predicts human focal seizures.

The apparent unpredictability of epileptic seizures has a major impact in the quality of life of people with pharmacologically resistant seizures. Here, we present initial results and a proof-of-concept of how focal seizures can be predicted early in advance based on intracortical signals recorded from small neocortical patches away from identified seizure onset areas. We show that machine learning algorithms can discriminate between interictal and preictal periods based on multiunit activity (i.e. thresholded action potential counts) and multi-frequency band local field potentials recorded via 4 X 4 mm2 microelectrode arrays. Microelectrode arrays were implanted in 5 patients undergoing neuromonitoring for resective surgery. Post-implant analysis revealed arrays were outside the seizure onset areas. Preictal periods were defined as the 1-hour period leading to a seizure. A 5-minute gap between the preictal period and the putative seizure onset was enforced to account for potential errors in the determination of actual seizure onset times. We used extreme gradient boosting and long short-term memory networks for prediction. Prediction accuracy based on the area under the receiver operating characteristic curves reached 90% for at least one feature type in each patient. Importantly, successful prediction could be achieved based exclusively on multiunit activity. This result indicates that preictal activity in the recorded neocortical patches involved not only subthreshold postsynaptic potentials, perhaps driven by the distal seizure onset areas, but also neuronal spiking in distal recurrent neocortical networks. Beyond the commonly identified seizure onset areas, our findings point to the engagement of large-scale neuronal networks in the neural dynamics building up toward a seizure. Our initial results obtained on currently available human intracortical microelectrode array recordings warrant new studies on larger datasets, and open new perspectives for seizure prediction and control by emphasizing the contribution of multiscale neural signals in large-scale neuronal networks.

Uncovering low-dimensional structure in high-dimensional representations of long-term recordings in people with epilepsy.

Effective representations of recordings of epileptic activity for seizure prediction are high-dimensional, which prevents their visualization. Here we introduce and evaluate methods to find low-dimensional (2D or 3D) descriptors of these high-dimensional representations, which are amenable for visualization. Once low-dimensional descriptors are found, it is useful to identify structure in them. We evaluate clustering algorithms to automatically identify this structure. In addition, typical recordings of epileptic activity are long, extending for several days or weeks. We present and assess extensions of the previous methods to handle large datasets.

Ongoing intracortical neural activity predicts upcoming interictal epileptiform discharges in human epilepsy.

Interictal epileptiform discharges (IEDs) are a hallmark of focal epilepsies. Most previous studies have focused on whether IED events increase seizure likelihood or, on the contrary, act as a protective mechanism. Here, we study instead whether IED events themselves can be predicted based on measured ongoing neural activity. We examined local field potentials (LFPs) and multi-unit activity (MUA) recorded via intracortical 10 × 10 (4 × 4 mm) arrays implanted in two patients with pharmacologically resistant seizures. Seizures in one patient (P1) were characterized by low-voltage fast-activity (LVFA), and IEDs occurred as isolated (100 - 200 ms) spike-wave events. In the other patient (P2), seizures were characterized by complex spike-wave discharges (2 - 3 Hz) and IEDs consisted of bursts of ~ 2 - 3 spike-wave discharges each lasting ~ 300 - 500 ms. We used extreme gradient boosting (XGBoost) classifiers for IED prediction. Inputs to the classifiers consisted of LFP power spectra; In addition, counts of MUA (1-ms and 100-ms time bins) and envelope, as well as leading eigenvalues/eigenvectors of MUA correlation matrices were used as features. Features were computed from moving short-time windows (1 second) immediately preceding IED events (0.3 - 0.5 preictal gap). Classifiers allowed successful IED prediction in both patients, with better results in the case of IED occurring in the LVFA case (area under ROC curve: 0.86). In comparison, LFP features performed comparatively for P1 datasets, while MUA appeared not predictive in the case of P2. Our preliminary results suggest that features of ongoing activity, predictive of upcoming IED events, can be identified based on intracortical recordings, and warrant further investigation in larger datasets. We expect this type of prediction analyses to contribute to a better understanding of the mechanisms underlying the generation of IED events and their contribution to seizure onset.

Epilepsyecosystem.org: crowd-sourcing reproducible seizure prediction with long-term human intracranial EEG.

Accurate seizure prediction will transform epilepsy management by offering warnings to patients or triggering interventions. However, state-of-the-art algorithm design relies on accessing adequate long-term data. Crowd-sourcing ecosystems leverage quality data to enable cost-effective, rapid development of predictive algorithms. A crowd-sourcing ecosystem for seizure prediction is presented involving an international competition, a follow-up held-out data evaluation, and an online platform, Epilepsyecosystem.org, for yielding further improvements in prediction performance. Crowd-sourced algorithms were obtained via the 'Melbourne-University AES-MathWorks-NIH Seizure Prediction Challenge' conducted at kaggle.com. Long-term continuous intracranial electroencephalography (iEEG) data (442 days of recordings and 211 lead seizures per patient) from prediction-resistant patients who had the lowest seizure prediction performances from the NeuroVista Seizure Advisory System clinical trial were analysed. Contestants (646 individuals in 478 teams) from around the world developed algorithms to distinguish between 10-min inter-seizure versus pre-seizure data clips. Over 10 000 algorithms were submitted. The top algorithms as determined by using the contest data were evaluated on a much larger held-out dataset. The data and top algorithms are available online for further investigation and development. The top performing contest entry scored 0.81 area under the classification curve. The performance reduced by only 6.7% on held-out data. Many other teams also showed high prediction reproducibility. Pseudo-prospective evaluation demonstrated that many algorithms, when used alone or weighted by circadian information, performed better than the benchmarks, including an average increase in sensitivity of 1.9 times the original clinical trial sensitivity for matched time in warning. These results indicate that clinically-relevant seizure prediction is possible in a wider range of patients than previously thought possible. Moreover, different algorithms performed best for different patients, supporting the use of patient-specific algorithms and long-term monitoring. The crowd-sourcing ecosystem for seizure prediction will enable further worldwide community study of the data to yield greater improvements in prediction performance by way of competition, collaboration and synergism.10.1093/brain/awy210_video1awy210media15817489051001.

Predicting the spatiotemporal diversity of seizure propagation and termination in human focal epilepsy.

Recent studies have shown that seizures can spread and terminate across brain areas via a rich diversity of spatiotemporal patterns. In particular, while the location of the seizure onset area is usually invariant across seizures in an individual patient, the source of traveling (2-3 Hz) spike-and-wave discharges during seizures can either move with the slower propagating ictal wavefront or remain stationary at the seizure onset area. Furthermore, although many focal seizures terminate synchronously across brain areas, some evolve into distinct ictal clusters and terminate asynchronously. Here, we introduce a unifying perspective based on a new neural field model of epileptic seizure dynamics. Two main mechanisms, the co-existence of wave propagation in excitable media and coupled-oscillator dynamics, together with the interaction of multiple time scales, account for the reported diversity. We confirm our predictions in seizures and tractography data obtained from patients with pharmacologically resistant epilepsy. Our results contribute toward patient-specific seizure modeling.

Anatomic consistencies across epilepsies: a stereotactic-EEG informed high-resolution structural connectivity study.

See Bernasconi (doi:10.1093/brain/awx229) for a scientific commentary on this article. Drug-resistant localization-related epilepsies are now recognized as network diseases. However, the exact relationship between the organization of the epileptogenic network and brain anatomy overall remains incompletely understood. To better understand this relationship, we studied structural connectivity obtained from diffusion weighted imaging in patients with epilepsy using both stereo-electroencephalography (SEEG)-determined epileptic brain regions and whole-brain analysis. High resolution structural connectivity analysis was applied in 15 patients with drug-resistant localization-related epilepsies and 36 healthy control subjects to study structural connectivity changes in epilepsy. Two different methods of structural connectivity analysis were carried out using diffusion weighted imaging, one focusing on the relationship between epileptic regions determined by SEEG investigations and one blinded to epileptic regions looking at whole-brain connectivity. First, we performed zone-based analysis comparing structural connectivity findings in patients and controls within and between SEEG-defined zones of interest. Next, we performed whole-brain structural connectivity analysis in all subjects and compared findings to the same SEEG-defined zones of interest. Finally, structural connectivity findings were correlated against clinical features. Zone-based analysis revealed no significant decreased structural connectivity within nodes of the epilepsy network at the group level, but did demonstrate significant structural connectivity differences between nodes of the epileptogenic network (regions involved in seizures generation and propagation) and the remaining of the brain in patients compared to controls. Whole-brain analyses showed a total of 133 clusters of significantly decreased structural connectivity across all patients. One cluster of significantly increased structural connectivity was identified in a single patient. Clusters of decreased structural connectivity showed topographical preference for both the salience and default mode networks despite clinical heterogeneity within our patient sample. Correlation analysis did not reveal any significant findings regarding either the effect of age at disease onset, disease duration or post-surgical outcome on structural connectivity. Taken together, this work demonstrates that structural connectivity disintegration targets distributed functional networks while sparing the epilepsy network.

Individual brain structure and modelling predict seizure propagation.

See Lytton (doi:10.1093/awx018) for a scientific commentary on this article.Neural network oscillations are a fundamental mechanism for cognition, perception and consciousness. Consequently, perturbations of network activity play an important role in the pathophysiology of brain disorders. When structural information from non-invasive brain imaging is merged with mathematical modelling, then generative brain network models constitute personalized in silico platforms for the exploration of causal mechanisms of brain function and clinical hypothesis testing. We here demonstrate with the example of drug-resistant epilepsy that patient-specific virtual brain models derived from diffusion magnetic resonance imaging have sufficient predictive power to improve diagnosis and surgery outcome. In partial epilepsy, seizures originate in a local network, the so-called epileptogenic zone, before recruiting other close or distant brain regions. We create personalized large-scale brain networks for 15 patients and simulate the individual seizure propagation patterns. Model validation is performed against the presurgical stereotactic electroencephalography data and the standard-of-care clinical evaluation. We demonstrate that the individual brain models account for the patient seizure propagation patterns, explain the variability in postsurgical success, but do not reliably augment with the use of patient-specific connectivity. Our results show that connectome-based brain network models have the capacity to explain changes in the organization of brain activity as observed in some brain disorders, thus opening up avenues towards discovery of novel clinical interventions.

Heterogeneity of time delays determines synchronization of coupled oscillators.

Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial distribution of time delays with regard to synchronization, by decomposing it into patterns and therefore reducing the stability analysis into the tractable problem of a finite set of delay-coupled differential equations. We analyze delay-structured networks of phase oscillators and we find that, depending on the heterogeneity of the delays, the oscillators group in phase-shifted, anti-phase, steady, and non-stationary clusters, and analytically compute their stability boundaries. These results find direct application in the study of brain oscillations.

How do parcellation size and short-range connectivity affect dynamics in large-scale brain network models?

Recent efforts to model human brain activity on the scale of the whole brain rest on connectivity estimates of large-scale networks derived from diffusion magnetic resonance imaging (dMRI). This type of connectivity describes white matter fiber tracts. The number of short-range cortico-cortical white-matter connections is, however, underrepresented in such large-scale brain models. It is still unclear on the one hand, which scale of representation of white matter fibers is optimal to describe brain activity on a large-scale such as recorded with magneto- or electroencephalography (M/EEG) or functional magnetic resonance imaging (fMRI), and on the other hand, to which extent short-range connections that are typically local should be taken into account. In this article we quantified the effect of connectivity upon large-scale brain network dynamics by (i) systematically varying the number of brain regions before computing the connectivity matrix, and by (ii) adding generic short-range connections. We used dMRI data from the Human Connectome Project. We developed a suite of preprocessing modules called SCRIPTS to prepare these imaging data for The Virtual Brain, a neuroinformatics platform for large-scale brain modeling and simulations. We performed simulations under different connectivity conditions and quantified the spatiotemporal dynamics in terms of Shannon Entropy, dwell time and Principal Component Analysis. For the reconstructed connectivity, our results show that the major white matter fiber bundles play an important role in shaping slow dynamics in large-scale brain networks (e.g. in fMRI). Faster dynamics such as gamma oscillations (around 40 Hz) are sensitive to the short-range connectivity if transmission delays are considered.

Whole-brain analytic measures of network communication reveal increased structure-function correlation in right temporal lobe epilepsy.

The in vivo structure-function relationship is key to understanding brain network reorganization due to pathologies. This relationship is likely to be particularly complex in brain network diseases such as temporal lobe epilepsy, in which disturbed large-scale systems are involved in both transient electrical events and long-lasting functional and structural impairments. Herein, we estimated this relationship by analyzing the correlation between structural connectivity and functional connectivity in terms of analytical network communication parameters. As such, we targeted the gradual topological structure-function reorganization caused by the pathology not only at the whole brain scale but also both in core and peripheral regions of the brain. We acquired diffusion (dMRI) and resting-state fMRI (rsfMRI) data in seven right-lateralized TLE (rTLE) patients and fourteen healthy controls and analyzed the structure-function relationship by using analytical network communication metrics derived from the structural connectome. In rTLE patients, we found a widespread hypercorrelated functional network. Network communication analysis revealed greater unspecific branching of the shortest path (search information) in the structural connectome and a higher global correlation between the structural and functional connectivity for the patient group. We also found evidence for a preserved structural rich-club in the patient group. In sum, global augmentation of structure-function correlation might be linked to a smaller functional repertoire in rTLE patients, while sparing the central core of the brain which may represent a pathway that facilitates the spread of seizures.

•rTLE patients exhibit increased mean search information compared controls.•Structural search information best predicts functional connectivity in both groups.•Whole brain structure-function correlation is increased in rTLE patients.•Structure-function correlation differs in brain periphery but not in the rich club.