Brain connectivity measure — the direct transfer function — advantages and weak points

Event Abstract Back to Event Weak brain connectivity and causality measures A. Perovic1*, W. Klonowski2, W. Duch3, Z. Djordjevic1 and A. Jovanovic1 1 Aston University , Wellcome trust laboratory for MEG studies, United Kingdom 2 Polish Academy of Sciences, Lab. Biosignal Analysis Fundamentals, Nalecz Institute of Biocybernetics and Biomedical Engineering, Poland 3 Nicolaus Copernicus University, Department of Informatics, Poland Aim: We are investigating brain connectivity in cases when causality measures become unstable or are close to zero. This is of interest in the BCI based on inner tunes and music. Methods: Two brain loci might be functionally related while majority of local processing is mutually non related. Such relation among the brain signal sources we call weak connectivity. While in case of imagined motor activity brain connectivity patterns are often related to prominent brain signal features engaging larger relative energy, when dealing with high frequency bands related to imagined tunes and music the situation is opposite, becoming elusive for the established connectivity criteria. By their nature these phenomena are related to weak energy features. The recorded brain signals contain other important components, a number of which corresponds to local area processing. This reduces the causality measures values approaching that of level of noise, thus establishing the connectivity patterns by usual means becomes harder or impossible. We are investigating different causality measures behaviour in such situations, showing that some of them differ substantially and propose the alternative method of weak linear dependence, described partially in 1,2,3, which is useful in this context. Results: We established the instability of causality criteria in experiments related to weak connectivity and proposed alternative methods to establish weak connectivity in the case of inner tunes and inner music. Conclusion: We expect that the Weak connectivity pattern is present in a number of brain states involved in cognitive tasks.

Brain connectivity is often considered in terms of the communication between functionally distinct brain regions. Many studies have investigated the extent to which patterns of coupling strength between multiple neural populations relates to behaviour. For example, studies have used 'functional connectivity fingerprints' to characterise individuals' brain activity. Here, we investigate the extent to which the exact spatial arrangement of cortical regions interacts with measures of brain connectivity. We find that the shape and exact location of brain regions interact strongly with the modelling of brain connectivity, and present evidence that the spatial arrangement of functional regions is strongly predictive of non-imaging measures of behaviour and lifestyle. We believe that, in many cases, cross-subject variations in the spatial configuration of functional brain regions are being interpreted as changes in functional connectivity. Therefore, a better understanding of these effects is important when interpreting the relationship between functional imaging data and cognitive traits.

Electroencephalographic (EEG) signals recorded from the scalp surface are generally highly correlated. Each channel is a linear mixture of concurrently active brain and non-brain electrical sources whose activities are volume conducted to the scalp electrodes with broadly overlapping patterns (Nunez et al., 1997). This property is particularly relevant to connectivity analyses, which seek to detect and characterize active interactions between brain regions. Therefore, meaningful connectivity patterns can be derived only from measures of cortical source activities and not directly from EEG channel activities (Michel and Murray, 2012). However, this poses a serious problem, since estimating the nature, number, brain (or non-brain) locations, and time courses of the active sources contributing to the scalp EEG is not straightforward (Baillet et al., 2001). Several methods have been proposed to estimate source activities from multi-channel EEG recordings, thereby removing the confounding effects of volume conduction. These methods can be grouped into three categories: (a) simple spatial filters that seek to reduce correlations between scalp channels based on idealized assumptions; (b) more complex spatial filters that seek to estimate net activities within ROIs based on detailed neurophysiological head models; and (c) blind spatial source separation methods that seek to separately identify source signals by exploiting source signal information differences. Whereas simple spatial filters such as bipolar derivations and Laplacian filters can reduce, to some extent, correlations among scalp-recorded channels (Fisch, 2012), more sophisticated spatial filtering methods use inverse imaging methods to estimate the time courses of cortical sources in given or estimated region of interest (ROI) (Baillet et al., 2001). Blind source separation techniques, in particular independent component analysis, by contrast, learn spatial filters from the EEG time courses that separate the data into constituent independent source activities. Their corresponding brain (or non-brain) locations can then be estimated using neurophysiological inverse imaging methods (Makeig et al., 1996; Jung et al., 2001; Delorme et al., 2012). Vector autoregressive (VAR) models are versatile tools for analyzing multivariate time series, including multi-channel EEG or multivariate source activities. VAR models predict current values of time series from their recent past (Lutkepohl, 2005). Importantly, they can be used to derive various electrophysiological connectivity measures (Schlogl and Supp, 2006). Volume conduction in biological tissue can be modeled as instantaneous propagation of activity from sources to recording channels. The resulting zero-phase connectivity may be treated as noise added to lagged connectivity patterns of interest. Although some measures, including the imaginary part of the coherency (Nolte et al., 2004), are insensitive to zero-phase connectivity, measures derived from VAR model coefficients do not include such zero-phase terms. Thus, volume conduction effects are not accounted for by the model and affect the correlation structure of the model residuals, which are normally assumed to be uncorrelated. Popular connectivity measures derived from VAR models include the Directed Transfer Function (DTF) (Kaminski and Blinowska, 1991) and the Partial Directed Coherence (PDC) (Baccala and Sameshima, 2001). Whereas the PDC is defined in terms of the system matrix (a frequency domain representation of the VAR model), the DTF is based on the inverse of the system matrix. Viewing lagged dependencies between source signals as information flow, the DTF may be said to be normalized by the inflow of information to some sink, while the PDC is normalized by the outflow of information from some source. As we will demonstrate below, both the DTF and the PDC are indeed adversely affected by volume conduction from multiple sources to the scalp electrodes, in contrast to the claim of Kaminski and Blinowska in their recent opinion article (Kaminski and Blinowska, 2014). Thus, in general direct application of connectivity measures to scalp EEG signals produces less than accurate results and also does not allow their clear interpretation in terms of underlying source dynamics.

Comparative performance evaluation of data-driven causality measures applied to brain networks

Autism is a neurodevelopmental disorder that has been associated with atypical brain functioning. Functional connectivity MRI (fcMRI) studies examining neural networks in autism have seen an exponential rise over the last decade. Such investigations have led to the characterization of autism as a distributed neural systems disorder. Studies have found widespread cortical underconnectivity, local overconnectivity, and mixed results suggesting disrupted brain connectivity as a potential neural signature of autism. In this review, we summarize the findings of previous fcMRI studies in autism with a detailed examination of their methodology, in order to better understand its potential and to delineate the pitfalls. We also address how a multimodal neuroimaging approach (incorporating different measures of brain connectivity) may help characterize the complex neurobiology of autism at a global level. Finally, we also address the potential of neuroimaging-based markers in assisting neuropsychological assessment of autism. The quest for a neural marker for autism is still ongoing, yet new findings suggest that aberrant brain connectivity may be a promising candidate.

A new method (Event-Related Causality, ERC) is proposed for the investigation of functional interactions between brain regions during cognitive processing. ERC estimates the direction, intensity, spectral content, and temporal course of brain activity propagation within a cortical network. ERC is based upon the short-time directed transfer function (SDTF), which is measured in short EEG epochs during multiple trials of a cognitive task, as well as the direct directed transfer function (dDTF), which distinguishes direct interactions between brain regions from indirect interactions via brain regions. ERC uses new statistical methods for comparing estimates of causal interactions during prestimulus "baseline" epochs and during poststimulus "activated" epochs in order to estimate event-related increases and decreases in the functional interactions between cortical network components during cognitive tasks. The utility of the ERC approach is demonstrated through its application to human electrocorticographic recordings (ECoG) of a simple language task. ERC analyses of these ECoG recordings reveal frequency-dependent interactions, particularly in high gamma (>60 Hz) frequencies, between brain regions known to participate in the recorded language task, and the temporal evolution of these interactions is consistent with the putative processing stages of this task. The method may be a useful tool for investigating the dynamics of causal interactions between various brain regions during cognitive task performance.

Emerging hypotheses suggest that efficient cognitive functioning requires the integration of separate, but interconnected cortical networks in the brain. Although task-related measures of brain activity suggest that a frontoparietal network is associated with the control of attention, little is known regarding how components within this distributed network act together or with other networks to achieve various attentional functions. This review considers both functional and structural studies of brain connectivity, as complemented by behavioral and task-related neuroimaging data. These studies show converging results: The frontal and parietal cortical regions are active together, over time, and identifiable frontoparietal networks are active in relation to specific task demands. However, the spontaneous, low-frequency fluctuations of brain activity that occur in the resting state, without specific task demands, also exhibit patterns of connectivity that closely resemble the task-related, frontoparietal attention networks. Both task-related and resting-state networks exhibit consistent relations to behavioral measures of attention. Further, anatomical structure, particularly white matter pathways as defined by diffusion tensor imaging, places constraints on intrinsic functional connectivity. Lastly, connectivity analyses applied to investigate cognitive differences across individuals in both healthy and diseased states suggest that disconnection of attentional networks is linked to deficits in cognitive functioning, and in extreme cases, to disorders of attention. Thus, comprehensive theories of visual attention and their clinical translation depend on the continued integration of behavioral, task-related neuroimaging, and brain connectivity measures.

Brain connectivity measures have been identified as effective feature extraction tools for the classification of EEG data. However, there exist certain theoretical limitations in the computation of brain networks. First, bivariate models of brain connectivity are incapable of handling the multivariate nature of brain connections. Second, multivariate brain connectivity models are typically based on regression models. These regression models are associated with stationary assumptions, which do not hold for EEG data. To solve this problem, the authors propose clustering as a tool to perform multivariate brain connectivity analysis. Extended variants of Fuzzy c-means and self-organizing map-based clustering are proposed to compute brain networks, which are subsequently used as features for mental imagery detection. Experiments undertaken demonstrate the superiority of the proposed brain network features over its traditional counterparts.KeywordsBrain networksClusteringFuzzy C meansNeuromarketingMultivariate connectivitySelf-organizing mapsSupport vector machine

The goal of the present study is to propose the use of global connectivity measures as quantitative indicators of long-term medication in pediatric patients with Attention-Deficit-Hyperactivity Disorder, combined type (ADHD-C). For this purpose, graph theoretical brain connectivity indices are computed from connectivity estimations across eyes-opened resting-state EEG recordings measured before and after the treatment with osmotic release oral system-methylphenidate for a month in 18 boys (aged between 7–12 years). In order to present the reliable results, neurofunctional correlations are firstly estimated in time (Pearson Correlation (PC), Spearman Correlation), frequency (Directed Transfer Function, Partial Directed Coherence) and phase (Phase Locking Value, Phase Lag Index) domains in between short segments of 2sec over single trials of 1min. Later, transitivity, clustering coefficients, assortativity, global efficiency and modularity are computed from EEG based connectivity matrices produced by each approach. Since the highest classification accuracy of 83.79% is provided by PC, statistical tests (one-way Anova, pair-wise multiple comparison) and step-wise logistic regression modelling are all examined to detect significant differences between pre- and post- treatment relevant connectivity measures. Statistical boxplots are also shown, as well. Overall results reveal that global brain connectivity can be increased by long-term medication in pediatric ADHD-C in terms of increased segregation & resilience. This is the first study to demonstrate that long-term medication can normalize the functional brain connectivity in ADHD, which is characterized by decreased connectivity compared to controls.

Despite the recent literature on sex-related anatomic, maturational and functional brain differences, the study of significant individual developments in math learning and achievement has scarcely approached this perspective. We aimed to compare the influence of sex in functional brain connectivity and behavioral measures in a numerical comparison task. Therefore, a group of school children with ages from 8 to 11 years old was evaluated during a number comparison task. Even though the behavioral performance was similar across the sexes, males distinctly showed a significant correlation between their math WRAT-4 scores and the number of correct responses in the experimental task and working memory scores. Besides, the analysis of the concurrent EEG during task performance showed that males comparatively had a greater brain left intra-hemispheric connectivity, as well as greater interhemispheric connectivity, particularly in Theta and Alpha bands during task performing -as compared to resting-. In contrast, females showed a significantly different decrement of brain connectivity in the Alpha band from resting to task performing. Present results are interpreted as probably reflecting sex-related maturational dissimilarities in neurodevelopment, along with the progressive development of more efficient cognitive strategies, processes running not necessarily parallel in both sexes. 

Cannabis is often consumed in polysubstance contexts, yet research comparing its isolated use to polydrug use is limited. Such comparisons are essential for understanding substance-specific versus interactive effects on brain activity. This study investigates how cannabis-only and polydrug use relate to alterations in resting-state EEG functional connectivity, using the Directed Transfer Function (DTF) to assess frequency-specific information flow in the brain. Three age- and sex-matched groups were studied: individuals with cannabis-only use (n=27), polydrug use (n=29), and non-drug-using controls (n=30). Resting-state EEG was recorded under eyes-open and eyes-closed conditions. DTF was applied to quantify directed connectivity and frequency-dependent propagation of neural signals across brain regions. Individuals with cannabis-only use exhibited localized changes in neural propagation, particularly in frontal areas and within theta, beta, and gamma bands, while alpha-band activity remained relatively stable. In contrast, individuals with polydrug use showed more widespread and complex alterations in connectivity, including reduced alpha activity and increased frontal and prefrontal engagement, suggesting heightened excitation and possible compensatory mechanisms. This study is the first to characterize frequency-specific EEG connectivity patterns associated with cannabis and polydrug use. The findings highlight the importance of studying substance use patterns and considering cannabis within a polysubstance context. A longitudinal study is needed to assess the effects of use duration, frequency, and dosage.

This paper presents comparison of brain connectivity estimators of distracted drivers and non-distracted drivers based on statistical analysis. Twelve healthy volunteers with more than one year of driving experience participated in this experiment. Lane-keeping tasks and the Math problem-solving task were introduced in the experiment and EEGs (electroencephalogram) were used to record the brain waves. Granger-Geweke causality (GGC), directed transfer function (DTF) and partial directed coherence (PDC) brain connectivity estimation methods were used in brain connectivity analysis. Correlation test and a student's t-test were conducted on the connectivity matrixes. Results show a significant difference between the mean of distracted drivers and non-distracted driver's brain connectivity matrixes. GGC and DTF methods student's t-tests shows a p-value below 0.05 with the correlation coefficients varying from 0.62 to 0.38. PDC connectivity estimation method does not show a significant difference between the connectivity matrixes means unless it is compared with lane keeping task and the normal driving task. Furthermore, it shows a strong positive correlation between the connectivity matrixes.

Mental workload refers to the cognitive effort required to perform tasks, and it is an important factor in various fields, including system design, clinical medicine, and industrial applications. In this paper, we propose innovative methods to assess mental workload from EEG data that use effective brain connectivity for the purpose of extracting features, a hierarchical feature selection algorithm to select the most significant features, and finally machine learning models. We have used the Simultaneous Task EEG Workload (STEW) dataset, an open-access collection of raw EEG data from 48 subjects. We extracted brain-effective connectivities by the direct directed transfer function and then selected the top 30 connectivities for each standard frequency band. Then we applied three feature selection algorithms (forward feature selection, Relief-F, and minimum-redundancy-maximum-relevance) on the top 150 features from all frequencies. Finally, we applied sevenfold cross-validation on four machine learning models (support vector machine (SVM), linear discriminant analysis, random forest, and decision tree). The results revealed that SVM as the machine learning model and forward feature selection as the feature selection method work better than others and could classify the mental workload levels with accuracy equal to 89.53% (± 1.36).

eConnectome: A MATLAB toolbox for mapping and imaging of brain functional connectivity

Autism spectrum disorder (ASD) is a neurodevelopmental condition affecting about 1 in 100 children and is currently incurable. ASD represents a challenge to traditional methods of assessment and diagnosis, and it has been suggested that direct measures of brain activity and connectivity between brain regions during demanding tasks represents a potential pathway to building more accurate models of underlying brain function and ASD. One of the key behavioural diagnostic indicators of ASD consists of sensory features (SF), often characterised by over- or under-reactivity to environmental stimuli. SF are associated with behavioural difficulties that impede social and education success in these children as well as anxiety and depression. This review examines the previous literature on the measurement of EEG connectivity and SF observed in individuals with ASD.