Brain health in diverse settings: How age, demographics and cognition shape brain function.

Diversity in brain health is influenced by individual differences in demographics and cognition. However, most studies on brain health and diseases have typically controlled for these factors rather than explored their potential to predict brain signals. Here, we assessed the role of individual differences in demographics (age, sex, and education; n = 1298) and cognition (n = 725) as predictors of different metrics usually used in case-control studies. These included power spectrum and aperiodic (1/f slope, knee, offset) metrics, as well as complexity (fractal dimension estimation, permutation entropy, Wiener entropy, spectral structure variability) and connectivity (graph-theoretic mutual information, conditional mutual information, organizational information) from the source space resting-state EEG activity in a diverse sample from the global south and north populations. Brain-phenotype models were computed using EEG metrics reflecting local activity (power spectrum and aperiodic components) and brain dynamics and interactions (complexity and graph-theoretic measures). Electrophysiological brain dynamics were modulated by individual differences despite the varied methods of data acquisition and assessments across multiple centers, indicating that results were unlikely to be accounted for by methodological discrepancies. Variations in brain signals were mainly influenced by age and cognition, while education and sex exhibited less importance. Power spectrum activity and graph-theoretic measures were the most sensitive in capturing individual differences. Older age, poorer cognition, and being male were associated with reduced alpha power, whereas older age and less education were associated with reduced network integration and segregation. Findings suggest that basic individual differences impact core metrics of brain function that are used in standard case-control studies. Considering individual variability and diversity in global settings would contribute to a more tailored understanding of brain function.

EEG functional connectivity as a Riemannian mediator: An application to malnutrition and cognition.

Mediation analysis assesses whether an exposure directly produces changes in cognitive behavior or is influenced by intermediate "mediators". Electroencephalographic (EEG) spectral measurements have been previously used as effective mediators representing diverse aspects of brain function. However, it has been necessary to collapse EEG measures onto a single scalar using standard mediation methods. In this article, we overcome this limitation and examine EEG frequency-resolved functional connectivity measures as a mediator using the full EEG cross-spectral tensor (CST). Since CST samples do not exist in Euclidean space but in the Riemannian manifold of positive-definite tensors, we transform the problem, allowing for the use of classic multivariate statistics. Toward this end, we map the data from the original manifold space to the Euclidean tangent space, eliminating redundant information to conform to a "compressed CST." The resulting object is a matrix with rows corresponding to frequencies and columns to cross spectra between channels. We have developed a novel matrix mediation approach that leverages a nuclear norm regularization to determine the matrix-valued regression parameters. Furthermore, we introduced a global test for the overall CST mediation and a test to determine specific channels and frequencies driving the mediation. We validated the method through simulations and applied it to our well-studied 50+-year Barbados Nutrition Study dataset by comparing EEGs collected in school-age children (5-11 years) who were malnourished in the first year of life with those of healthy classmate controls. We hypothesized that the CST mediates the effect of malnutrition on cognitive performance. We can now explicitly pinpoint the frequencies (delta, theta, alpha, and beta bands) and regions (frontal, central, and occipital) in which functional connectivity was altered in previously malnourished children, an improvement to prior studies. Understanding the specific networks impacted by a history of postnatal malnutrition could pave the way for developing more targeted and personalized therapeutic interventions. Our methods offer a versatile framework applicable to mediation studies encompassing matrix and Hermitian 3D tensor mediators alongside scalar exposures and outcomes, facilitating comprehensive analyses across diverse research domains.

Automatic quality control of the numerical accuracy of EEG lead fields.

Precise individualized EEG source localization is predicated on having accurate subject-specific Lead Fields (LFs) obtained from their Magnetic Resonance Images (MRI). LF calculation is a complex process involving several error-prone steps that start with obtaining a realistic head model from the MRI and finalizing with computationally expensive solvers such as the Boundary Element Method (BEM) or Finite Element Method (FEM). Current Big-Data applications require the calculation of batches of hundreds or thousands of LFs. LF. Quality Control is conventionally checked subjectively by experts, a procedure not feasible in practice for larger batches. To facilitate this step, we introduce the Lead Field Automatic-Quality Control Index (LF-AQI) that flags LF with potential errors. We base our LF-AQI on the assumption that LFs obtained from simpler head models, i.e., the homogeneous head model LF (HHM-LF) or spherical head model LF (SHM-LF), deviate only moderately from a "good" realistic test LF. Since these simpler LFs are easier to compute and check for errors, they may serve as "reference LF" to detect anomalous realistic test LF. We investigated this assumption by comparing correlation-based channel ρmin(ref,test)and source τmin(ref,test) similarity indices (SI) between "gold standards," i.e., very accurate FEM and BEM LFs, and the proposed references (HHM-LF and SHM-LF). Surprisingly we found that the most uncomplicated possible reference, HHM-LF had high SI values with the gold standards-leading us to explore further use of the channel ρmin(HHM-LF,test)and source τmin(HHM-LF,test)SI as a basis for our LF-AQI. Indeed, these SI successfully detected five simulated scenarios of LFs artifacts. This result encouraged us to evaluate the SI on a large dataset and thus define our LF-AQI. We thus computed the SI of 1251 LFs obtained from the Child Mind Institute (CMI) MRI dataset. When ρmin(HHM-LF,test)and source τmin(HHM-LF,test) were plotted for all test subjects on a 2D space, most were tightly clustered around the median of a high similarity centroid (HSC), except for a smaller proportion of outliers. We define the LF-AQI for a given LF as the log Euclidean distance between its SI and the HSC median. To automatically detect outliers, the threshold is at the 90th percentile of the CMI LF-AQIs (-0.9755). LF-AQI greater than this threshold flag individual LF to be checked. The robustness of this LF-AQI screening was checked by repeated out-of-sample validation. Strikingly, minor corrections in re-processing the flagged cases eliminated their status as outliers. Furthermore, the "doubtful" labels assigned by LF-AQI were validated by neuroscience students using a Likert scale questionnaire designed to manually check the LF's quality. Item Response Theory (IRT) analysis was applied to the questionnaire results to compute an optimized model and a latent variable θ for that model. A linear mixed model (LMM) between the θ and LF-AQI resulted in an effect with a Cohen's d value of 1.3 and a p-value <0.001, thus validating the correspondence of LF-AQI with the visual quality control. We provide an open-source pipeline to implement both LF calculation and its quality control to allow further evaluation of our index.

Accurate and Efficient Simulation of Very High-Dimensional Neural Mass Models with Distributed-Delay Connectome Tensors.

This paper introduces methods and a novel toolbox that efficiently integrates high-dimensional Neural Mass Models (NMMs) specified by two essential components. The first is the set of nonlinear Random Differential Equations (RDEs) of the dynamics of each neural mass. The second is the highly sparse three-dimensional Connectome Tensor (CT) that encodes the strength of the connections and the delays of information transfer along the axons of each connection. To date, simplistic assumptions prevail about delays in the CT, often assumed to be Dirac-delta functions. In reality, delays are distributed due to heterogeneous conduction velocities of the axons connecting neural masses. These distributed-delay CTs are challenging to model. Our approach implements these models by leveraging several innovations. Semi-analytical integration of RDEs is done with the Local Linearization (LL) scheme for each neural mass, ensuring dynamical fidelity to the original continuous-time nonlinear dynamic. This semi-analytic LL integration is highly computationally-efficient. In addition, a tensor representation of the CT facilitates parallel computation. It also seamlessly allows modeling distributed delays CT with any level of complexity or realism. This ease of implementation includes models with distributed-delay CTs. Consequently, our algorithm scales linearly with the number of neural masses and the number of equations they are represented with, contrasting with more traditional methods that scale quadratically at best. To illustrate the toolbox's usefulness, we simulate a single Zetterberg-Jansen and Rit (ZJR) cortical column, a single thalmo-cortical unit, and a toy example comprising 1000 interconnected ZJR columns. These simulations demonstrate the consequences of modifying the CT, especially by introducing distributed delays. The examples illustrate the complexity of explaining EEG oscillations, e.g., split alpha peaks, since they only appear for distinct neural masses. We provide an open-source Script for the toolbox.

Early protein energy malnutrition impacts life-long developmental trajectories of the sources of EEG rhythmic activity.

Protein Energy Malnutrition (PEM) has lifelong consequences on brain development and cognitive function. We studied the lifelong developmental trajectories of resting-state EEG source activity in 66 individuals with histories of Protein Energy Malnutrition (PEM) limited to the first year of life and in 83 matched classmate controls (CON) who are all participants of the 49 years longitudinal Barbados Nutrition Study (BNS). qEEGt source z-spectra measured deviation from normative values of EEG rhythmic activity sources at 5-11 years of age and 40 years later at 45-51 years of age. The PEM group showed qEEGt abnormalities in childhood, including a developmental delay in alpha rhythm maturation and an insufficient decrease in beta activity. These profiles may be correlated with accelerated cognitive decline.

Harmonized-Multinational qEEG norms (HarMNqEEG).

This paper extends frequency domain quantitative electroencephalography (qEEG) methods pursuing higher sensitivity to detect Brain Developmental Disorders. Prior qEEG work lacked integration of cross-spectral information omitting important functional connectivity descriptors. Lack of geographical diversity precluded accounting for site-specific variance, increasing qEEG nuisance variance. We ameliorate these weaknesses. (i) Create lifespan Riemannian multinational qEEG norms for cross-spectral tensors. These norms result from the HarMNqEEG project fostered by the Global Brain Consortium. We calculate the norms with data from 9 countries, 12 devices, and 14 studies, including 1564 subjects. Instead of raw data, only anonymized metadata and EEG cross-spectral tensors were shared. After visual and automatic quality control, developmental equations for the mean and standard deviation of qEEG traditional and Riemannian DPs were calculated using additive mixed-effects models. We demonstrate qEEG "batch effects" and provide methods to calculate harmonized z-scores. (ii) We also show that harmonized Riemannian norms produce z-scores with increased diagnostic accuracy predicting brain dysfunction produced by malnutrition in the first year of life and detecting COVID induced brain dysfunction. (iii) We offer open code and data to calculate different individual z-scores from the HarMNqEEG dataset. These results contribute to developing bias-free, low-cost neuroimaging technologies applicable in various health settings.

Causal effects of cingulate morphology on executive functions in healthy young adults.

In this study, we want to explore evidence for the causal relationship between the anatomical descriptors of the cingulate cortex (surface area, mean curvature-corrected thickness, and volume) and the performance of cognitive tasks such as Card Sort, Flanker, List Sort used as instruments to measure the executive functions of flexibility, inhibitory control, and working memory. We have performed this analysis in a cross-sectional sample of 899 healthy young subjects of the Human Connectome Project. To the best of our knowledge, this is the first study using causal inference to explain the relationship between cingulate morphology and the performance of executive tasks in healthy subjects. We have tested the causal model under a counterfactual framework using stabilized inverse probability of treatment weighting and marginal structural models. The results showed that the posterior cingulate surface area has a positive causal effect on inhibition (Flanker task) and cognitive flexibility (Card Sort). A unit increase (+1 mm2 ) in the posterior cingulate surface area will cause a 0.008% and 0.009% increase from the National Institute of Health (NIH) normative mean in Flankers (p-value <0.001), and Card Sort (p-value 0.005), respectively. Furthermore, a unit increase (+1 mm2 ) in the anterior cingulate surface area will cause a 0.004% (p-value <0.001) and 0.005% (p-value 0.001) increase from the NIH normative mean in Flankers and Card Sort. In contrast, the curvature-corrected-mean thickness only showed an association for anterior cingulate with List Sort (p = 0.034) but no causal effect.

Neural alterations in working memory of mild-moderate TBI: An fMRI study in Malaysia.

Working memory (WM) encompasses crucial cognitive processes or abilities to retain and manipulate temporary information for immediate execution of complex cognitive tasks in daily functioning such as reasoning and decision-making. The WM of individuals sustaining traumatic brain injury (TBI) was commonly compromised, especially in the domain of WM. The current study investigated the brain responses of WM in a group of participants with mild-moderate TBI compared to their healthy counterparts employing functional magnetic resonance imaging. All consented participants (healthy: n = 26 and TBI: n = 15) performed two variations of the n-back WM task with four load conditions (0-, 1-, 2-, and 3-back). The respective within-group effects showed a right hemisphere-dominance activation and slower reaction in performance for the TBI group. Random-effects analysis revealed activation difference between the two groups in the right occipital lobe in the guided n-back with cues, and in the bilateral occipital lobe, superior parietal region, and cingulate cortices in the n-back without cues. The left middle frontal gyrus was implicated in the load-dependent processing of WM in both groups. Further group analysis identified that the notable activation changes in the frontal gyri and anterior cingulate cortex are according to low and high loads. Though relatively smaller in scale, this study was eminent as it clarified the neural alterations in WM in the mild-moderate TBI group compared to healthy controls. It confirmed the robustness of the phenomenon in TBI with the reproducibility of the results in a heterogeneous non-Western sample.

Cancer Segmentation by Entropic Analysis of Ordered Gene Expression Profiles.

The availability of massive gene expression data has been challenging in terms of how to cure, process, and extract useful information. Here, we describe the use of entropic measures as discriminating criteria in cancer using the whole data set of gene expression levels. These methods were applied in classifying samples between tumor and normal type for 13 types of tumors with a high success ratio. Using gene expression, ordered by pathways, results in complexity-entropy diagrams. The map allows the clustering of the tumor and normal types samples, with a high success rate for nine of the thirteen, studied cancer types. Further analysis using information distance also shows good discriminating behavior, but, more importantly, allows for discriminating between cancer types. Together, our results allow the classification of tissues without the need to identify relevant genes or impose a particular cancer model. The used procedure can be extended to classification problems beyond the reported results.

WeBrain: A web-based brainformatics platform of computational ecosystem for EEG big data analysis.

The current evolution of 'cloud neuroscience' leads to more efforts with the large-scale EEG applications, by using EEG pipelines to handle the rapidly accumulating EEG data. However, there are a few specific cloud platforms that seek to address the cloud computational challenges of EEG big data analysis to benefit the EEG community. In response to the challenges, a WeBrain cloud platform (https://webrain.uestc.edu.cn/) is designed as a web-based brainformatics platform and computational ecosystem to enable large-scale EEG data storage, exploration and analysis using cloud high-performance computing (HPC) facilities. WeBrain connects researchers from different fields to EEG and multimodal tools that have become the norm in the field and the cloud processing power required to handle those large EEG datasets. This platform provides an easy-to-use system for novice users (even no computer programming skills) and provides satisfactory maintainability, sustainability and flexibility for IT administrators and tool developers. A range of resources are also available on https://webrain.uestc.edu.cn/, including documents, manuals, example datasets related to WeBrain, and collected links to open EEG datasets and tools. It is not necessary for users or administrators to install any software or system, and all that is needed is a modern web browser, which reduces the technical expertise required to use or manage WeBrain. The WeBrain platform is sponsored and driven by the China-Canada-Cuba international brain cooperation project (CCC-Axis, http://ccc-axis.org/), and we hope that WeBrain will be a promising cloud brainformatics platform for exploring brain information in large-scale EEG applications in the EEG community.

Neurodevelopmental effects of childhood malnutrition: A neuroimaging perspective.

Approximately one in five children worldwide suffers from childhood malnutrition and its complications, including increased susceptibility to inflammation and infectious diseases. Due to improved early interventions, most of these children now survive early malnutrition, even in low-resource settings (LRS). However, many continue to exhibit neurodevelopmental deficits, including low IQ, poor school performance, and behavioral problems over their lifetimes. Most studies have relied on neuropsychological tests, school performance, and mental health and behavioral measures. Few studies, in contrast, have assessed brain structure and function, and to date, these have mainly relied on low-cost techniques, including electroencephalography (EEG) and evoked potentials (ERP). The use of more advanced methods of neuroimaging, including magnetic resonance imaging (MRI) and functional near-infrared spectroscopy (fNIRS), has been limited by cost factors and lack of availability of these technologies in developing countries, where malnutrition is nearly ubiquitous. This report summarizes the current state of knowledge and evidence gaps regarding childhood malnutrition and the study of its impact on neurodevelopment. It may help to inform the development of new strategies to improve the identification, classification, and treatment of neurodevelopmental disabilities in underserved populations at the highest risk for childhood malnutrition.

Brain status modeling with non-negative projective dictionary learning.

Accurate prediction of individuals' brain age is critical to establish a baseline for normal brain development. This study proposes to model brain development with a novel non-negative projective dictionary learning (NPDL) approach, which learns a discriminative representation of multi-modal neuroimaging data for predicting brain age. Our approach encodes the variability of subjects in different age groups using separate dictionaries, projecting features into a low-dimensional manifold such that information is preserved only for the corresponding age group. The proposed framework improves upon previous discriminative dictionary learning methods by incorporating orthogonality and non-negativity constraints, which remove representation redundancy and perform implicit feature selection. We study brain development on multi-modal brain imaging data from the PING dataset (N = 841, age = 3-21 years). The proposed analysis uses our NDPL framework to predict the age of subjects based on cortical measures from T1-weighted MRI and connectome from diffusion weighted imaging (DWI). We also investigate the association between age prediction and cognition, and study the influence of gender on prediction accuracy. Experimental results demonstrate the usefulness of NDPL for modeling brain development.

Crystallized and fluid intelligence are predicted by microstructure of specific white-matter tracts.

Studies of the neural basis of intelligence have focused on comparing brain imaging variables with global scales instead of the cognitive domains integrating these scales or quotients. Here, the relation between mean tract-based fractional anisotropy (mTBFA) and intelligence indices was explored. Deterministic tractography was performed using a regions of interest approach for 10 white-matter fascicles along which the mTBFA was calculated. The study sample included 83 healthy individuals from the second wave of the Cuban Human Brain Mapping Project, whose WAIS-III intelligence quotients and indices were obtained. Inspired by the "Watershed model" of intelligence, we employed a regularized hierarchical Multiple Indicator, Multiple Causes model (MIMIC), to assess the association of mTBFA with intelligence scores, as mediated by latent variables summarizing the indices. Regularized MIMIC, used due to the limited sample size, selected relevant mTBFA by means of an elastic net penalty and achieved good fits to the data. Two latent variables were necessary to describe the indices: Fluid intelligence (Perceptual Organization and Processing Speed indices) and Crystallized Intelligence (Verbal Comprehension and Working Memory indices). Regularized MIMIC revealed effects of the forceps minor tract on crystallized intelligence and of the superior longitudinal fasciculus on fluid intelligence. The model also detected the significant effect of age on both latent variables.

The Statistics of EEG Unipolar References: Derivations and Properties.

In this brief communication, which complements the EEG reference review (Yao et al. in Brain Topogr, 2019), we provide the mathematical derivations that show: (1) any EEG reference admits the general form of a linear transformation of the ideal multichannel EEG potentials with reference to infinity; (2) the average reference (AR), the reference electrode standardization technique (REST), and its regularized version (rREST) are solving the linear inverse problems that can be derived from both the maximum likelihood estimate (MLE) and the Bayesian theory; however, REST is based on more informative prior/constraint of volume conduction than that of AR; (3) we show for the first time that REST is also a unipolar reference (UR), allowing us to define a general family of URs with unified notations; (4) some notable properties of URs are 'no memory', 'rank deficient by 1', and 'orthogonal projector centering'; (5) we also point out here, for the first time, that rREST provides the optimal interpolating function that can be used when the reference channel is missing or the 'bad' channels are rejected. The derivations and properties imply that: (a) any two URs can transform to each other and referencing with URs multiple times will not accumulate artifacts; (b) whatever URs the EEG data was previously transformed with, the minimum norm solution to the reference problem will be REST and AR with and without modeling volume conduction, respectively; (c) the MLE and the Bayesian theory show the theoretical optimality of REST. The advantages and limitations of AR and REST are discussed to guide readers for their proper use.

Critical Comments on EEG Sensor Space Dynamical Connectivity Analysis.

Many different analysis techniques have been developed and applied to EEG recordings that allow one to investigate how different brain areas interact. One particular class of methods, based on the linear parametric representation of multiple interacting time series, is widely used to study causal connectivity in the brain. However, the results obtained by these methods should be interpreted with great care. The goal of this paper is to show, both theoretically and using simulations, that results obtained by applying causal connectivity measures on the sensor (scalp) time series do not allow interpretation in terms of interacting brain sources. This is because (1) the channel locations cannot be seen as an approximation of a source's anatomical location and (2) spurious connectivity can occur between sensors. Although many measures of causal connectivity derived from EEG sensor time series are affected by the latter, here we will focus on the well-known time domain index of Granger causality (GC) and on the frequency domain directed transfer function (DTF). Using the state-space framework and designing two simulation studies we show that mixing effects caused by volume conduction can lead to spurious connections, detected either by time domain GC or by DTF. Therefore, GC/DTF causal connectivity measures should be computed at the source level, or derived within analysis frameworks that model the effects of volume conduction. Since mixing effects can also occur in the source space, it is advised to combine source space analysis with connectivity measures that are robust to mixing.

ERP Source Analysis Guided by fMRI During Familiar Face Processing.

Event related potentials (ERPs) provide precise temporal information about cognitive processing, but with poor spatial resolution, while functional magnetic resonance imaging (fMRI) reliably identifies brain areas involved, but with poor temporal resolution. Here we use fMRI to guide source localization of the ERPs at different times for studying the temporal dynamics of the neural system for recognizing familiar faces. fMRI activation areas were defined in a previous experiment applying the same paradigm used for ERPs. The Bayesian model averaging (BMA) method was used to estimate the generators of the ERPs to unfamiliar, visually familiar, and personally-familiar faces constraining the model by fMRI activation results. For this, higher prior probabilities in the solution space were assigned to the fMRI-defined regions, which included face-selective areas and other areas related to "person knowledge" retrieval. Source analysis was carried out in three-time windows: early (150-210 ms), middle (300-380 ms) and late (460-580 ms). The early and middle responses were generated in fMRI-defined areas for all face categories, while these areas do not contribute to the late response. Different areas contributed to the generation of the early and middle ERPs elicited by unfamiliar faces: fusiform (Fus), inferior occipital, superior temporal sulcus and the posterior cingulate (PC) cortices. For familiar faces, the contributing areas were Fus, PC and anterior temporal areas for visually familiar faces, with the addition of the medial orbitofrontal areas and other frontal structures for personally-significant faces. For both unfamiliar and familiar faces, more extended and reliable involvement of contributing areas were obtained for the middle compare with early time window. Our fMRI guide ERP source analysis suggested the recruitment of person-knowledge processing areas as early as 150-210 ms after stimulus onset during recognition of personally-familiar faces. We concluded that fMRI-constrained BMA source analysis provide information regarding the temporal-dynamics in the neural system for cognitive processsing.

EECoG-Comp: An Open Source Platform for Concurrent EEG/ECoG Comparisons-Applications to Connectivity Studies.

Electrophysiological Source Imaging (ESI) is hampered by lack of "gold standards" for model validation. Concurrent electroencephalography (EEG) and electrocorticography (ECoG) experiments (EECoG) are useful for this purpose, especially primate models due to their flexibility and translational value for human research. Unfortunately, there is only one EECoG experiments in the public domain that we know of: the Multidimensional Recording (MDR) is based on a single monkey ( www.neurotycho.org ). The mining of this type of data is hindered by lack of specialized procedures to deal with: (1) Severe EECoG artifacts due to the experimental produces; (2) Sophisticated forward models that account for surgery induced skull defects and implanted ECoG electrode strips; (3) Reliable statistical procedures to estimate and compare source connectivity (partial correlation). We provide solutions to the processing issues just mentioned with EECoG-Comp: an open source platform ( https://github.com/Vincent-wq/EECoG-Comp ). EECoG lead fields calculated with FEM (Simbio) for MDR data are also provided and were used in other papers of this special issue. As a use case with the MDR, we show: (1) For real MDR data, 4 popular ESI methods (MNE, LCMV, eLORETA and SSBL) showed significant but moderate concordance with a usual standard, the ECoG Laplacian (standard partial [Formula: see text]); (2) In both monkey and human simulations, all ESI methods as well as Laplacian had a significant but poor correspondence with the true source connectivity. These preliminary results may stimulate the development of improved ESI connectivity estimators but require the availability of more EECoG data sets to obtain neurobiologically valid inferences.

Mapping Brain Activity with Electrocorticography: Resolution Properties and Robustness of Inverse Solutions.

Electrocorticography (ECoG) is an electrophysiological technique that records brain activity directly from the cortical surface with high temporal (ms) and spatial (mm) resolution. Its major limitations are in the high invasiveness and in the restricted field-of-view of the electrode grid, which partially covers the cortex. To infer brain activity at locations different from just below the electrodes, it is necessary to solve the electromagnetic inverse problem. Limitations in the performance of source reconstruction algorithms from ECoG have been, to date, only partially addressed in the literature, and a systematic evaluation is still lacking. The main goal of this study is to provide a quantitative evaluation of resolution properties of widely used inverse methods (eLORETA and MNE) for various ECoG grid sizes, in terms of localization error, spatial dispersion, and overall amplitude. Additionally, this study aims at evaluating how the use of simultaneous electroencephalography (EEG) affects the above properties. For these purposes, we take advantage of a unique dataset in which a monkey underwent a simultaneous recording with a 128 channel ECoG grid and an 18 channel EEG grid. Our results show that, in general conditions, the reconstruction of cortical activity located more than 1 cm away from the ECoG grid is not accurate, since the localization error increases linearly with the distance from the electrodes. This problem can be partially overcome by recording simultaneously ECoG and EEG. However, this analysis enlightens the necessity to design inverse algorithms specifically targeted at taking into account the limited field-of-view of the ECoG grid.

Which Reference Should We Use for EEG and ERP practice?

Which reference is appropriate for the scalp ERP and EEG studies? This unsettled problem still inspires unceasing debate. The ideal reference should be the one with zero or constant potential but unfortunately it is well known that no point on the body fulfills this condition. Consequently, more than ten references are used in the present EEG-ERP studies. This diversity seriously undermines the reproducibility and comparability of results across laboratories. A comprehensive review accompanied by a brief communication with rigorous derivations and notable properties (Hu et al. Brain Topogr, 2019. https://doi.org/10.1007/s10548-019-00706-y ) is thus necessary to provide application-oriented principled recommendations. In this paper current popular references are classified into two categories: (1) unipolar references that construct a neutral reference, including both online unipolar references and offline re-references. Examples of unipolar references are the reference electrode standardization technique (REST), average reference (AR), and linked-mastoids/ears reference (LM); (2) non-unipolar references that include the bipolar reference and the Laplacian reference. We show that each reference is derived with a different assumption and serves different aims. We also note from (Hu et al. 2019) that there is a general form for the reference problem, the 'no memory' property of the unipolar references, and a unified estimator for the potentials at infinity termed as the regularized REST (rREST) which has more advantageous statistical evidence than AR. A thorough discussion of the advantages and limitations of references is provided with recommendations in the hope to clarify the role of each reference in the ERP and EEG practice.

Multi-subject hierarchical inverse covariance modelling improves estimation of functional brain networks.

A Bayesian model for sparse, hierarchical, inver-covariance estimation is presented, and applied to multi-subject functional connectivity estimation in the human brain. It enables simultaneous inference of the strength of connectivity between brain regions at both subject and population level, and is applicable to fMRI, MEG and EEG data. Two versions of the model can encourage sparse connectivity, either using continuous priors to suppress irrelevant connections, or using an explicit description of the network structure to estimate the connection probability between each pair of regions. A large evaluation of this model, and thirteen methods that represent the state of the art of inverse covariance modelling, is conducted using both simulated and resting-state functional imaging datasets. Our novel Bayesian approach has similar performance to the best extant alternative, Ng et al.'s Sparse Group Gaussian Graphical Model algorithm, which also is based on a hierarchical structure. Using data from the Human Connectome Project, we show that these hierarchical models are able to reduce the measurement error in MEG beta-band functional networks by 10%, producing concomitant increases in estimates of the genetic influence on functional connectivity.