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Determination of information flow direction among brain structures by a modified directed transfer function (dDTF) method
Abstract
A modification of directed transfer function-direct DTF-is proposed for the analysis of direct information transfer among brain structures on the basis of local field potentials (LFP). Comparison of results obtained by the analysis of simulated and experimental data with a new dDTF and DTF method is shown. A new measure to estimate direct causal relations between signals is defined. The present results demonstrate the effectiveness of the new dDTF method and indicate that the dDTF method can be used to obtain the reliable patterns of connections between various brain structures.
... The Granger causality measure is a mainly descriptive tool that captures influence and interconnection among time series. A popular variant of Granger causality, direct directed transfer function (dDTF) [8], [25] distinguishes between direct and indirect interconnections between two nodes by multiplying the directed transfer function (DTF, the normalized transfer function between the two nodes) by the partial coherence between them in the frequency domain. We are motivated here by understanding to what extent the reconstruction results obtained via methods that build on Granger causality are sensitive to the presence of latent nodes. ...
... The indirect interactions represented by dashed edges in these plots imply the presence of latent nodes. For comparison, we have also used the brain connectivity estimator technique called direct directed transfer function (dDTF) measure [8], [25] from neuroscience to identify direct connections between nodes. This technique is a refinement of the directed transfer function (DTF) approach, which instead cannot distinguish between direct and indirect connections. ...
... We take the first 13 EEG channels corresponding to the fronto-temporal cortical areas (shown as blue squares in Fig. 10(a)) as the manifest nodes and the remaining channels as well as the truly hidden brain regions (the ones not probed in the test) as the latent nodes. In the following, we present the results of identifying the direct and indirect connections among the manifest nodes using the LSAR method as well as the dDTF algorithm [8], [25] and the S+L algorithm of [22]. For each method, we only keep the edges whose identified weights are above a certain threshold θ (which we choose as a proportional constant α ∈ (0, 1) times the largest edge weight in the network). ...
We consider linear time-invariant networks with unknown topology where only a manifest subset of the nodes can be directly actuated and measured while the state of the remaining latent nodes and their number are unknown. Our goal is to identify the transfer function of the manifest subnetwork and determine whether interactions between manifest nodes are direct or mediated by latent nodes. We show that, if there are no inputs to the latent nodes, the manifest transfer function can be approximated arbitrarily well in the H-infinity norm sense by the transfer function of an auto-regressive model and present a least-squares estimation method to construct the auto-regressive model from measured data. We show that the least-squares auto-regressive method guarantees an arbitrarily small H-infinity norm error in the approximation of the manifest transfer function, exponentially decaying once the model order exceeds a certain threshold. Finally, we show that when the latent subnetwork is acyclic, the proposed method achieves perfect identification of the manifest transfer function above a specific model order as the length of the data increases. Various examples illustrate our results.
... The spatial task was conducted in a virtual reality (VR) environment with an omnidirectional treadmill to simulate real-world navigation. To analyze neural synchronization and coordination during these social interactions and their relationship with dyadic task performance, we used various intra-and inter-brain connectivity measures, namely phase locking value (PLV) [36], corrected imaginary PLV (ciPLV) [37], weighted phase lag index (wPLI) [38], and directed transfer function (dDTF) [39]. Each measure provided a unique perspective on the complex interplay of neural activities between individuals in collaborative settings. ...
... Three measures of functional connectivity, namely PLV [36], ciPLV [37], and wPLI [38], were used to examine intra-and inter-brain connections. In addition, dDTF [39] was used to assess causality within and between brains, providing a comprehensive view of functional and effective connectivity (Fig. 4C). These connectivity analyses were conducted across a spectrum of EEG frequency bands, including delta (1-3 Hz), theta (4-7 Hz), alpha (8-12 Hz), beta (13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30), and gamma (31)(32)(33)(34)(35)(36)(37)(38)(39)(40)(41)(42)(43)(44)(45)(46)(47)(48)(49)(50). ...
... In addition, dDTF [39] was used to assess causality within and between brains, providing a comprehensive view of functional and effective connectivity (Fig. 4C). These connectivity analyses were conducted across a spectrum of EEG frequency bands, including delta (1-3 Hz), theta (4-7 Hz), alpha (8-12 Hz), beta (13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30), and gamma (31)(32)(33)(34)(35)(36)(37)(38)(39)(40)(41)(42)(43)(44)(45)(46)(47)(48)(49)(50). Moreover, we determined the relationship between intra-/inter-brain couplings and task performance metrics (follower's post-test scores and completion times). ...
Navigating through a physical environment to reach a desired location involves a complex interplay of cognitive, sensory, and motor functions. When navigating with others, experiencing a degree of behavioral and cognitive synchronization is both natural and ubiquitous. This synchronization facilitates a harmonious effort toward achieving a common goal, reflecting how individuals instinctively align their actions and thoughts in collaborative settings. Collaborative spatial tasks, which are crucial in daily and professional settings, require coordinated navigation and problem-solving skills. This study explores the neural mechanisms underlying such tasks by using hyperscanning electroencephalography (EEG) technology to examine brain dynamics in dyadic route planning within a virtual reality setting. By analyzing intra- and inter-brain couplings across delta, theta, alpha, beta, and gamma EEG bands using both functional and effective connectivity measures, we identified significant neural synchronization patterns associated with collaborative task performance in both leaders and followers. Functional intra-brain connectivity analyses revealed distinct neural engagement across EEG frequency bands, with increased delta couplings observed in both leaders and followers. Theta connectivity was particularly enhanced in followers, whereas the alpha band exhibited divergent patterns that indicate role-specific neural strategies. Inter-brain analysis revealed increased delta causality between interacting members but decreased theta and gamma couplings from followers to leaders. Additionally, inter-brain analysis indicated decreased couplings in faster-performing dyads, especially in theta bands. These insights enhance our understanding of the neural mechanisms driving collaborative spatial navigation and demonstrate the effectiveness of hyperscanning in studying complex brain-to-brain interactions.
... Developing a methodological framework for studying these effects would allow for a more comprehensive understanding of the neural substrate underlying anxiety and how they may be related to interoceptive processing in the body. Therefore, to investigate the links between the heart and the brain in individuals with high and low anxiety, we here propose a methodological framework relying on full frequency directed transfer function (ffDTF) [45]. Granger causality is a statistical technique that allows inference of causal relationships between time series data [46], such as the heart rate and brain signals acquired during fMRI scans. ...
... Granger causality is a statistical technique that allows inference of causal relationships between time series data [46], such as the heart rate and brain signals acquired during fMRI scans. The ffDTF is a variant of Granger causality that allows for the detection of causal relationships at multiple frequencies [45], [47], providing a more comprehensive picture of the interactions between the heart and the brain. To parcellate the brain into meaningful regions of interests for brain-heart interplay (BHI) analysis, we utilized the AAL2 atlas [48]. ...
... where H ij (f ) is the transfer function from channel j to channel i at frequency f , and k is the total number of channels. The DTF can be normalized for a band of interest to obtain the full frequency DTF (ffDTF) [45]: ...
Brain-heart interactions (BHI) are critical for generating and processing emotions, including anxiety. Understanding specific neural correlates would be instrumental for greater comprehension and potential therapeutic interventions of anxiety disorders. While prior work has implicated the pontine structure as a central processor in cardiac regulation in anxiety, the distributed nature of anxiety processing across the cortex remains elusive. To address this, we performed a whole-brain-heart analysis using the full frequency directed transfer function to study resting-state spectral differences in BHI between high and low anxiety groups undergoing fMRI scans. Our findings revealed a hemispheric asymmetry in low-frequency interplay (0.05 Hz - 0.15 Hz) characterized by ascending BHI to the left insula and descending BHI from the right insula. Furthermore, we provide evidence supporting the “pacemaker hypothesis”, highlighting the pons’ function in regulating cardiac activity. Higher frequency interplay (0.2 Hz - 0.4Hz) demonstrate a preference for ascending interactions, particularly towards ventral prefrontal cortical activity in high anxiety groups, suggesting the heart’s role in triggering a cognitive response to regulate anxiety. These findings highlight the impact of anxiety on BHI, contributing to a better understanding of its effect on the resting-state fMRI signal, with further implications for potential therapeutic interventions in treating anxiety disorders.
... Otherwise, some studies have suggested the neural mechanism of effective connectivity [8,12,[17][18][19][20]. Effective connectivity represents a form of directed connectivity across brain structures, revealing causal interactions between distinct brain regions [10,12]. ...
... In the earlier studies, Granger causality (GC) [21] and its extensions, such as directed transfer function (DTF) [17,19] and partial directed coherence (PDC) [19,22,23], and related concepts such as Transfer entropy (TE), are used to study functional and effective connectivity in cognitive neuroscience [12,[17][18][19]. The GC analysis, however, has some prerequisites for being applied to EEG signals [12], and may not be the best method for calculating the effective connectivity of brainrelated signals, which are nonlinear and non-Gaussian distributions [24,25]. ...
... In the earlier studies, Granger causality (GC) [21] and its extensions, such as directed transfer function (DTF) [17,19] and partial directed coherence (PDC) [19,22,23], and related concepts such as Transfer entropy (TE), are used to study functional and effective connectivity in cognitive neuroscience [12,[17][18][19]. The GC analysis, however, has some prerequisites for being applied to EEG signals [12], and may not be the best method for calculating the effective connectivity of brainrelated signals, which are nonlinear and non-Gaussian distributions [24,25]. ...
A significant issue for traffic safety has been drowsy driving for decades. A number of studies have investigated the effects of acute fatigue on spectral power; and recent research has revealed that drowsy driving is associated with a variety of brain connections in a specific cortico-cortical pathway. In spite of this, it is still unclear how different brain regions are connected in drowsy driving at different levels of daily fatigue. This study identified the brain connectivity-behavior relationship among three different daily fatigue levels (low-, median- and high-fatigue) with the EEG data transfer entropy. According to the results, only low- and medium-fatigue groups demonstrated an inverted U-shaped change in connectivity from high performance to poor behavioral performance. In addition, from low- to high-fatigue groups, connectivity magnitude decreased in the frontal region and increased in the occipital region. These study results suggest that brain connectivity and driving behavior would be affected by different levels of daily fatigue.
... can also be viewed as the spectral coherence of frequency f between i-th and j-th signals, capturing the correlation between the j-th input (column index) and i-th output (row index) of the system. Note that, matrix H(f ) is asymmetric [13], [14], i.e., in general h ij = h ji , which implies the correlation direction. In this way, DTF characterize the directional relationship from channel (contact) j to channel i where i = j. ...
... In this way, DTF characterize the directional relationship from channel (contact) j to channel i where i = j. Usually, DTF value is written in normalized form [13]: ...
... In this work, we choose β band (12 − 30Hz) as primary range, which has been widely studied to characterize seizure patterns [15], [16]. Model order K is empirically chosen 10, as suggested in [11], [13]. ...
... This work presents a network modeling method using SEEG signals to analyze the suspicious EZs. Here, we employ graph model defined by nodes (SEEG contacts), edges (connections between the nodes) and directions (also named causal relation [5]). It has been observed that, epileptiform patterns usually arise from a few spatially-refined zones (e.g., seizure onset zones) at or before clinical onset, and then propagate into larger areas in a temporal order [6]. ...
... For EEG signal analysis, C refers to the number of signal channels (e.g., C = 20 contact points for SEEG in one or more electrodes), and n is the n-th sample. The standard MVAR with order K (i.e., time lag) is written as [5]: ...
... When i = j, i.e., the diagonal elements h ii (f ) is simply the power spectrum for the i-th signal at f frequency [8]. An important property of H(f ) is its asymmetry [5], i.e., in general h ij (f ) = h ji (f ), which implies the directionality of such correlation. In EEG analysis, we can use the value of h ij (f ) to characterize the directional (causal) relationship from channel j to channel i at a specific frequency f . ...
... Using the fitted model, it was possible to compute several connectivity measures [13]: from MVARICA. The noise covariance matrix and the model coefficients were extracted to compute the Coherence [14], Partial Coherence [15], PDC [16], full frequency PDC (ffPDC) [17], PDC factor [16], generalized PDC (gPDC) [18], Direct Transfer Function (DTF) [19], full frequency DTF (ffDTF) [20], dDTF [20], and generalized DTF (gDTF) [21] between all channels in both directions. ...
... Using the fitted model, it was possible to compute several connectivity measures [13]: from MVARICA. The noise covariance matrix and the model coefficients were extracted to compute the Coherence [14], Partial Coherence [15], PDC [16], full frequency PDC (ffPDC) [17], PDC factor [16], generalized PDC (gPDC) [18], Direct Transfer Function (DTF) [19], full frequency DTF (ffDTF) [20], dDTF [20], and generalized DTF (gDTF) [21] between all channels in both directions. ...
In line with our prior research, we aimed to identify and classify biomarkers of major depressive disorder (MDD) using electroencephalography (EEG) in patients and age-matched healthy children and adolescents. To achieve this, resting-state eyes-closed EEG data were pre-processed, and the analysis was performed on a channel-wise and Regions of Interest (ROI)-wise basis. We computed several resting-state Functional Connectivity (rsFC) measurements using a Multivariate Auto-Regressive (MVAR) model. The resulting connectivity measurements were then used to train a Random Forest model. We analyzed the best-performing models to understand the model's decision-making process and identify the learned biomarkers. Overall, the Random Forest model achieved a F1-score of 0.975 and a Matthews Correlation Coefficient (MCC) of 0.970. The model's test scores were highest with Partial Directed Coherence (PDC) and its variants. Additionally, we found that direct measurements, specifically PDC Factor and direct Directed Transfer Function (dDTF), performed better than other variants.
... The MVARICA model was then fitted to the original EEG chunk data [13]. Using the fitted model, it was possible to compute several connectivity measures [15]: from MVARICA, the noise covariance matrix and the model coefficient were extracted to compute the Coherence [16], Partial Coherence [17], PDC [18], ffPDC [19], PDC factor [18], generalized PDC (gPDC) [20], DTF [21], full frequency DTF (ffDTF) [22], direct DTF (dDTF) [22], and generalized DTF (gDTF) [23] between all channels in both directions. ...
... The MVARICA model was then fitted to the original EEG chunk data [13]. Using the fitted model, it was possible to compute several connectivity measures [15]: from MVARICA, the noise covariance matrix and the model coefficient were extracted to compute the Coherence [16], Partial Coherence [17], PDC [18], ffPDC [19], PDC factor [18], generalized PDC (gPDC) [20], DTF [21], full frequency DTF (ffDTF) [22], direct DTF (dDTF) [22], and generalized DTF (gDTF) [23] between all channels in both directions. ...
This research aimed to use the Convolutional Neural Networks (CNN) to identify biomarkers in Children and Adolescents with Major Depressive Disorder (MDD) apart from age-matched healthy young individuals. To achieve this, resting-state eyes-closed electroencephalography (EEG) was pre-processed, and the analysis was performed based on frequency bands and Regions Of Interest (ROI). We computed several resting-state Functional Connectivity (rsFC) measurements using a Multi-Variate Auto-Regressive (MVAR) model. We analyzed the best-performing model to understand the model decision-making process and identify the learned bio-markers. Overall, results achieved an F1-Score of 0.790 and a Mathew Correlation Coefficient (MCC) of 0.745 in the rsFC measurement of full frequency Partial Directed Coherence (ffPDC). We found that Partial Directed Coherence (PDC) performed better than Coherence, Partial Coherence, and Directed Transfer Function (DTF). We also found that the full-frequency version of PDC and DTF outperformed PDC and DTF and their other variants.
... In the analytical phase, the EEG data was segregated into six distinct frequency bands using a specialized filter bank, covering the full frequency spectrum: full band (0.5-45 Hz), delta (0.5-4 Hz), theta (4-8 Hz), alpha (8)(9)(10)(11)(12), beta (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30), and gamma (30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40)(41)(42)(43)(44)(45). An averaging reference operation was subsequently applied across all datasets to ensure analytical consistency and accuracy. ...
... The direct directed transfer function (dDTF), a modification of the DTF method, is especially notable. It incorporates Granger causality principles and allows distinguishing between direct and indirect connections [29]. This study employs the dDTF method for source linkage analysis. ...
Background
Current research on the neurological impact of SARS-CoV-2 primarily focuses on the elderly or severely ill individuals. This study aims to explore the diverse neurological consequences of SARS-CoV-2 infection, with a particular focus on mildly affected children and adolescents.
Methods
A cohort study was conducted to collect pre- and post-infection resting-state electroencephalogram (EEG) data from 185 participants and 181 structured questionnaires of long-term symptoms across four distinct age groups. The goal was to comprehensively evaluate the impact of SARS-CoV-2 infection on these different age demographics. The study analyzed EEG changes of SARS-CoV-2 by potential biomarkers across age groups using both spatial and temporal approaches.
Results
Spatial analysis indicated that children and adolescents exhibit smaller changes in brain network and microstate patterns post-infection, implying a milder cognitive impact. Sequential linear analyses showed that SARS-CoV-2 infection is associated with a marked rise in low-complexity, synchronized neural activity within low-frequency EEG bands. This is evidenced by a significant increase in Hjorth activity within the theta band and Hjorth mobility in the delta band. Sequential nonlinear analysis indicated a significant reduction in the Hurst exponent across all age groups, pointing to increased chaos and complexity within the cognitive system following infection. Furthermore, linear regression analysis based on questionnaires established a significant positive relationship between the magnitude of changes in these neural indicators and the persistence of long-term symptoms post-infection.
Conclusions
The findings underscore the enduring neurological impacts of SARS-CoV-2 infection, marked by cognitive decline and increased EEG disarray. Although children and adolescents experienced milder effects, cognitive decline and heightened low-frequency electrical activity were evident. These observations might contribute to understanding potential anxiety, insomnia, and neurodevelopmental implications.
... dDTF is another effective connectivity method that is linear and parametric and estimates frequency components between two pairs of EEG channels (Mullen 2010;Korzeniewska et al. 2003). This measure can be estimated for j th and i th channels from Eq. (3) ...
... In this research, we estimated three appropriate measures, from linear and nonlinear divisions, dDTF, PDC and TE to represent interactions of EEG signals between SZ patients and healthy participants. These measures had highly effective results in neuroscience studies (Korzeniewska et al. 2003;Astolfi et al. 2007;Vicente et al. 2011;Huang et al. 2015;Phang et al. 2019;Gao et al. 2020;Bagherzadeh et al. 2022). ...
Schizophrenia (SZ) is a serious mental disorder that can mainly be distinguished by symptoms including delusions and hallucinations. This mental disorder makes difficult conditions for the person and her/his relatives. Electroencephalogram (EEG) signal is a sophisticated neuroimaging technique that helps neurologists to diagnose this mental disorder. Estimating and evaluating brain effective connectivity between electrode pairs is an appropriate way of diagnosing brain states in neuroscience studies. In this study, we construct a novel image from multi-channels of EEG based on the fusion of three effective connectivity, partial directed coherence (PDC), and direct directed transfer function (dDTF) and transfer entropy (TE) at three consecutive time windows. Then, this image was used as input of five well-known convolutional neural networks (CNNs) through transfer learning (TL) to learn patterns related to SZ patients to diagnose this disorder from normal participants from two public databases. Also, the majority voting method was used to improve these results based on ensemble results of the five CNNs, i.e., ResNet-50, Inception-v3, DenseNet-201, EfficientNetB0, and NasNet-Mobile. The highest average accuracy, specificity and sensitivity to diagnose SZ patients from healthy participants were obtained using EfficientNetB0 through the Leave-One-Subject-out (LOSO) Cross-Validation criterion equal to 96.67%, 96.23%, 96.82%, 95.15%, 94.42% and 96.28% for the first and second databases, respectively. Also, as we suggested, the ensemble approach of EfficientNetB0, ResNet-50 and NasNet-Mobile increased the accuracy by approximately 3%. Our results show the effectiveness of providing fused images from multichannel EEG signals to the ensemble of CNNs through TL to diagnose SZ than state-of-the-art studies.
... Each matrix element ℎ ( ) can also be viewed as the spectral coherence of frequency between th and th signals, capturing the correlation between the th input (column index) and th output (row index) of the system. Note that, matrix ( ) is asymmetric [33], i.e., in general ℎ ≠ ℎ , which implies the directionality of such correlation. When = , ℎ ( ) is simply the power spectrum for the th signal at frequency [26]. ...
... In this way, DTF characterizes the directional (causal) relationship from channel (contact) to channel where ≠ . Usually, DTF values are written in normalized form [33]: ...
Stereo-electroencephalography is a minimally invasive technique for patients with refractory epilepsy pursuing surgery to reduce or control seizures. Electrodes are implanted based on pre-surgery evaluations and can collect deep brain activities for surgery decisions. This paper presents a methodology to analyze stereo-electroencephalography (SEEG) and assist clinicians by recommending the optimal surgical option and target areas for
focal epilepsy patients. A seizure network (graph) model is proposed to characterize the spatial distribution and
temporal changes of ictal events. The network nodes and edges correspond to specific epileptogenic regions and propagation/impact pathways (weighted by directed transfer function), respectively. We then employ a K-means clustering strategy to group nodes into a few clusters, from which the target surgical areas can be identified. Ten patients with different types of focal seizures were thoroughly analyzed. Promising consistency
between results of our method’s recommendations, clinical decisions and surgery outcomes were observed.
... dDTF is another effective connectivity method that is linear and parametric and estimates frequency components between two pairs of EEG channels (Mullen 2010;Korzeniewska et al. 2003). This measure can be estimated for j th and i th channels from Eq. (3) ...
... In this research, we estimated three appropriate measures, from linear and nonlinear divisions, dDTF, PDC and TE to represent interactions of EEG signals between SZ patients and healthy participants. These measures had highly effective results in neuroscience studies (Korzeniewska et al. 2003;Astolfi et al. 2007;Vicente et al. 2011;Huang et al. 2015;Phang et al. 2019;Gao et al. 2020;Bagherzadeh et al. 2022). ...
... Since this relationship is asymmetric, the direction of the information flow can be determined. To estimate the strength and direction of functional links, the Directed Transfer Function (DTF) was chosen, which is a refined method based on an autoregressive model and generalized onto multiple signals Korzeniewska, Maczak, Kamiski, Blinowska, & Kasicki, 2003). It is characterized by significant advantages over other connectivity measures. ...
... Before the connectivity analysis was run, it was checked whether the remaining amount of data was sufficient for DTF calculations. The following formula was applied: W ≥ 10(pM2/N) where: W -required minimum window length in samples, p -model order, M -number of channels, and N -total number of epochs for all trials within each condition valence (Korzeniewska et al., 2003). The criterion was fulfilled for all subjects. ...
Chronic pain and depression are prevalent and often co-occur. The underlying biological mechanism of their comorbid incidence remains only partly understood. Ineffective emotional control is one of the trans-diagnostic factors between depression and chronic pain and can manifest in the form of Repetitive Negative Thinking (RNT) such as pain catastrophizing or depressive rumination. This thesis aimed to identify common effective connectivity patterns for depressive disorder, endometriosis-related chronic pain, and high RNT tendencies in nonclinical groups, that are related to the impaired emotional regulation of negatively-valenced stimuli. Four EEG experiments were conducted on clinical and nonclinical groups wherein brain activity was measured during induced depressive rumination or pain-related negative imagery. To assess the effective connectivity, the Directed Transfer Function method was used, which is based on Granger causality principles and provides a multivariate estimation of information flow rate and direction. Common effective connectivity patterns in beta oscillations were identified and were related to the dysregulation of the fronto-temporal emotional regulation brain circuit. Emotional regulation abilities could be an important target in therapies and preventive actions for depression and chronic pain.
... dDTF [70] is a method derived from DTF that focuses on the dynamic fitting of Multivariate Autoregressive (MVAR) models to find the most effective connectivity in a frequency domain of EEG, in this study we conducted pairwise analysis of channels (electrodes), and unlike a coherence method, the calculated data is not symmetric (meaning A→B is not equal B→A). ...
This study explores the neural and behavioral consequences of LLM-assisted essay writing. Participants were divided into three groups: LLM, Search Engine, and Brain-only (no tools). Each completed three sessions under the same condition. In a fourth session, LLM users were reassigned to Brain-only group (LLM-to-Brain), and Brain-only users were reassigned to LLM condition (Brain-to-LLM). A total of 54 participants took part in Sessions 1-3, with 18 completing session 4. We used electroencephalography (EEG) to assess cognitive load during essay writing, and analyzed essays using NLP, as well as scoring essays with the help from human teachers and an AI judge. Across groups, NERs, n-gram patterns, and topic ontology showed within-group homogeneity. EEG revealed significant differences in brain connectivity: Brain-only participants exhibited the strongest, most distributed networks; Search Engine users showed moderate engagement; and LLM users displayed the weakest connectivity. Cognitive activity scaled down in relation to external tool use. In session 4, LLM-to-Brain participants showed reduced alpha and beta connectivity, indicating under-engagement. Brain-to-LLM users exhibited higher memory recall and activation of occipito-parietal and prefrontal areas, similar to Search Engine users. Self-reported ownership of essays was the lowest in the LLM group and the highest in the Brain-only group. LLM users also struggled to accurately quote their own work. While LLMs offer immediate convenience, our findings highlight potential cognitive costs. Over four months, LLM users consistently underperformed at neural, linguistic, and behavioral levels. These results raise concerns about the long-term educational implications of LLM reliance and underscore the need for deeper inquiry into AI's role in learning.
... This function represents a linear combination of causal influences along all causal pathways, direct and indirect, beginning at one site and ending at another (Korzeniewska et al., 2008). To distinguish direct from indirect flows, a dDTF is proposed (Korzeniewska et al., 2003). The dDTF method determines the strength and direction of the direct flow of neural activity using DTF combined with partial coherence. ...
... The periods of these epochs are in the range of 280 ms, which is reminiscent of alpha wave periods and generalized brain states, as examined, for example, by Kringelbach and Deco [3,56]. Further work should acquire more data and compare results with existing connectivity methods, such as those described by Wendling [31], the Granger causality, or the multitude of DTFs [57][58][59]. ...
The precise localization of epileptic foci with the help of EEG or iEEG signals is still a clinical challenge with current methodology, especially if the foci are not close to individual electrodes. On the research side, dipole reconstruction for focus localization is a topic of recent and current developments. Relatively low numbers of recording electrodes cause ill-posed and ill-conditioned problems in the inversion of lead-field matrices to calculate the focus location. Estimations instead of tissue conductivity measurements further deteriorate the precision of location tasks. In addition, time-resolved phase shifts are used to describe connectivity. We hypothesize that correlations over runtime approaches might be feasible to predict seizure foci with adequate precision. In a case study on EEG correlation in a healthy subject, we found repetitive periods of alternating high correlation in the short (20 ms) and long (300 ms) range. During these periods, a numerical determination of proportions of predominant latency and, newly established here, directionality is possible, which supports the identification of loops that, according to current opinion, manifest themselves in epileptic seizures. In the future, this latency and directionality analysis could support focus localization via dipole reconstruction using new triangulation calculations.
... DTF provides effective connectivity across multichannel EEG measurements, considered as multivariate data. Regarding Granger causality, the directional flow of the neural information across the cortex is obtained by using DTF [38]. ...
Purpose:The goal of the present study is to quantify the close association between graph theoretic global brain connectivity measures and Alzheimer's Disease (AD) in comparison to Controls. Methods:International Mini-Mental State Examination (MMSE) was used to evaluate cognitive and neuropsychological state of the participants (AD, 12 men, 24 women, mean age = 66.4, sd = 7.9 and controls, 18 men, 11 women, mean age = 67.9, sd = 5.4). There are no comorbidities in patients. Eyes-closed 19-channel surface EEG series were collected from the 2nd Department of Neurology of AHEPA General Hospital of Thessaloniki by experienced neurologists. 2 min long resting-state recordings have been analyzed through non-overlapped sliding window of 1 second and graph theoretical connectivity indices have been estimated by using Directed Transfer Function (DTF) combined with Brain Connectivity Toolbox. EEG recordings and clinical test scores of the individuals were both downloaded from a public dataset on OpenNeuro platform (A dataset of EEG recordings from: Alzheimer's disease, Frontotemporal dementia and Healthy subjects. https:// doi. org/ 10. 18112/ openn euro. ds004 504. v1.0. 7.). Results:AD provided the lower measures in terms of Global Efficiency, Local Efficiency (LE) and Cluster Coefficients. LE estimations provided meaningful and significant statistical difference between patients and controls in theta (4.5-8 Hz), alpha (8.5-12 Hz), beta (12.5-30 Hz), gamma (30.5-45 Hz) sub-bands. Conclusion: The patients provided the lower segregation and integration measures than controls due to loss of connection. AD induces the considerable decrease in segregation. The brain fails to integrate cortical regions into effective networks since there is synaptic disconnection as neuropathology of AD.
... PDC might be interpreted as an indicator of the level of synchronization between two signals in the studied signal set, because the shared influence from all other signals has been removed. Thus, the PDC might be used as a measure of the strength of direct connection between two structures (Korzeniewska et al. 2003;Heyse et al. 2021). ...
To date, it is largely unknown how frequency range of neural oscillations measured with EEG is related to functional connectivity. To address this question, we investigated frequency-dependent directed functional connectivity among the structures of mesial and anterior temporal network including amygdala, hippocampus, temporal pole and parahippocampal gyrus in the living human brain. Intracranial EEG recording was obtained from 19 consecutive epilepsy patients with normal anterior mesial temporal MR imaging undergoing intracranial presurgical epilepsy diagnostics with multiple depth electrodes. We assessed intratemporal bidirectional functional connectivity using several causality measures such as Granger causality (GC), directed transfer function (DTF) and partial directed coherence (PDC) in a frequency-specific way. In order to verify the obtained results, we compared the spontaneous functional networks with intratemporal effective connectivity evaluated by means of SPES (single pulse electrical stimulation) method. The overlap with the evoked network was found for the functional connectivity assessed by the GC method, most prominent in the higher frequency bands (alpha, beta and low gamma), yet vanishing in the lower frequencies. Functional connectivity assessed by means of DTF and PCD obtained a similar directionality pattern with the exception of connectivity between hippocampus and parahippocampal gyrus which showed opposite directionality of predominant information flow. Whereas previous connectivity studies reported significant divergence between spontaneous and evoked networks, our data show the role of frequency bands for the consistency of functional and evoked intratemporal directed connectivity. This has implications for the suitability of functional connectivity methods in characterizing local brain circuits.
... Korzeniewska et al. proposed the full-frequency DTF (ffDTF) [72]. It is calculated with Equation (A4), which normalizes the sum of causal effects from other variables to X i within a specified frequency band. ...
Abstracting causal knowledge from process measurements has become an appealing topic for decades, especially for fault root cause analysis (RCA) based on signals recorded by multiple sensors in a complex system. Although many causality detection methods have been developed and applied in different fields, some research communities may have an idiosyncratic implementation of their preferred methods, with limited accessibility to the wider community. Targeting interested experimental researchers and engineers, this paper provides a comprehensive comparison of data-based causality detection methods in root cause diagnosis across two distinct domains. We provide a possible taxonomy of those methods followed by descriptions of the main motivations of those concepts. Of the two cases we investigated, one is a root cause diagnosis of plant-wide oscillations in an industrial process, while the other is the localization of the epileptogenic focus in a human brain network where the connectivity pattern is transient and even more complex. Considering the differences in various causality detection methods, we designed several sets of experiments so that for each case, a total of 11 methods could be appropriately compared under a unified and reasonable evaluation framework. In each case, these methods were implemented separately and in a standard way to infer causal interactions among multiple variables to thus establish the causal network for RCA. From the cross-domain investigation, several findings are presented along with insights into them, including an interpretative pitfall that warrants caution.
... As potential predictors of treatment response, power features have been utilised (Al-Kaysi et al., 2017;Hasanzadeh et al., 2019;Jaworska et al., 2019;Zhdanov et al., 2020), while connectivity features have been relatively underexamined. Alpha spectral correlation-based connectivity was used to predict rTMS treatment response, achieving 69.30% accuracy (Corlier et al., 2019), and directed transfer function (Korzeniewska et al., 2003) connectivity matrices of EEG bands has been applied to predict treatment remission to selective serotonin reuptake inhibitors (SSRIs) (Mirjebreili et al., 2024). In the present study, the predictive accuracy achieved from EEG band connectivity indicates its feasibility. ...
Aim
To investigate neural oscillatory networks in major depressive disorder (MDD), effects of home-based transcranial direct current stimulation (tDCS) treatment, and potential predictors of treatment remission.
Methods
In a randomised controlled trial (RCT) of home-based tDCS treatment, EEG data were acquired a subset: 21 MDD participants (16 women) (mean age 36.63 ± 9.71 years) in current depressive episode of moderate to severe severity (mean Hamilton Depression Rating Scale (HAMD) score 18.42 ± 1.80). Participants were randomised to either active (n=11) or sham tDCS (n=8). Treatment was home-based tDCS treatment for 10 weeks in a bifrontal montage (anode over left dorsolateral prefrontal cortex) consisting of 5 sessions per week for 3 weeks and 3 sessions per week for 7 weeks. Active tDCS was 2mA and sham tDCS 0mA with brief ramp up and ramp down period to mimic active stimulation. Each session was 30 minutes. Clinical remission was defined as HAMD score ≤ 7. Resting-state EEG data were acquired at baseline, prior to the start of treatment, and at 10-week end of treatment. EEG data were acquired using portable 4-channel EEG device (electrode positions: AF7, AF8, TP9, TP10). EEG band power was extracted for each electrode and functional connectivity phase synchronization by phase locking value (PLV). Deep learning was applied to baseline PLV features to identify predictors of treatment remission.
Results
Main effect of group was observed in gamma PLV in frontal and temporal regions, in which active tDCS treatment group showed higher connectivity as compared to sham group. In active treatment group, significant positive correlations between changes in delta, theta, alpha, and beta PLV and improvement in depression severity were observed. The highest treatment remission prediction was achieved by combining PLV features from theta, alpha, and beta: accuracy 71.94% (sensitivity 52.88%, specificity 83.06%).
Conclusions
Synchronized brain activity across large-scale networks as reflected in gamma PLV is a potential mechanism of active tDCS as compared to placebo-sham tDCS. Baseline resting-state EEG is a potential predictor of treatment remission. Home-based EEG measures are feasible and potentially useful predictors of clinical outcome.
... A connectivity strength was determined by the direct Directed Transfer Function (dDTF) which is a causal estimator in the frequency domain (Korzeniewska et al. 2003). The dDTF is calculated as the product of the full-frequency DTF and partial coherence and thus is resistant to the effects of indirect transmission. ...
Cortical involvements, including those in the sensorimotor, frontal, and occipitoparietal regions, are important mechanisms of neural control in human standing. Previous research has shown that cortical activity and corticospinal excitability vary flexibly in response to postural demand. However, it is unclear how corticocortical and corticomuscular connectivity is dynamically modulated during standing balance and over time. This study investigated the dynamics of this connectivity using electroencephalography (EEG) and electromyography (EMG). The EEG and EMG were measured in different 4 positions: sitting (ST), normal quiet standing (QS), one-leg standing (ON), and standing on a piece of wood (WD). For corticomuscular connectivity, we concentrated on sway-varying connectivity in the timing of peak velocity of postural sway in the anteroposterior direction. For the corticocortical connectivity, the time-varying connectivity was quantified, particularly in the θ-band connectivity which is linked to error identification, using a sliding-window approach. The study found that corticomuscular connectivity from the brain to the lower-limb muscle was strengthened during the sway peak in the γ- and β-frequency bands, while the connectivity strength from the muscle to the brain was decreased in the θ- and α-band. For the time-varying connectivity, the θ-connectivity in all time-epoch was divided into 7 states including both posture-relevant and -irrelevant clusters. In one of the 7 states, the strong connectivity pairs were concentrated in the mid-central region and the proportion of epochs from the ON and WD conditions was significantly higher, indicating a functional role for posture balance. These findings shed light on electrodynamic connectivity which varies in response to postural demand. Those dynamics, particularly in the θ-band connectivity, can be used for ongoing monitoring and/or intervention for postural disability.
... (1) where H(f) is the transfer matrix of the system at a specific frequency and S(f) is the spectral density matrix. We extract five frequency bands for the dDTF measure by averaging the frequency spectrum as follows: delta (2-4), theta (4)(5)(6)(7)(8), alpha (8)(9)(10)(11)(12)(13), beta (13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32), and gamma (32)(33)(34)(35)(36)(37)(38)(39)(40)(41)(42)(43)(44)(45)(46)(47)(48)(49)(50). All steps for dDTF measurement are done in MATLAB software by the Source Information Flow Toolbox (SIFT) version 0.1a 36 . ...
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).
... dDTF is a linear parametric EC measure that estimates common frequency components between two EEG channels [54,55]. dDTF from th channel to th channel is estimated using Eq. ...
The objective of this paper is to develop a novel emotion recognition system from electroencephalogram (EEG) signals using effective connectivity and deep learning methods. Emotion recognition is an important task for various applications such as human-computer interaction and, mental health diagnosis. The paper aims to improve the accuracy and robustness of emotion recognition by combining different effective connectivity (EC) methods and pre-trained convolutional neural networks (CNNs), as well as long short-term memory (LSTM). EC methods measure information flow in the brain during emotional states using EEG signals. We used three EC methods: transfer entropy (TE), partial directed coherence (PDC), and direct directed transfer function (dDTF). We estimated a fused image from these methods for each five-second window of 32-channel EEG signals. Then, we applied six pre-trained CNNs to classify the images into four emotion classes based on the two-dimensional valence-arousal model. We used the leave-one-subject-out cross-validation strategy to evaluate the classification results. We also used an ensemble model to select the best results from the best pre-trained CNNs using the majority voting approach. Moreover, we combined the CNNs with LSTM to improve recognition performance. We achieved the average accuracy and F-score of 98.76%, 98.86%, 98.66 and 98.88% for classifying emotions using DEAP and MAHNOB-HCI datasets, respectively. Our results show that fused images can increase the accuracy and that an ensemble and combination of pre-trained CNNs and LSTM can achieve high accuracy for automated emotion recognition. Our model outperformed other state-of-the-art systems using the same datasets for four-class emotion classification.
... The correct identification of the underlying network depends heavily on the correct estimation of the interdependence. The founding concept of statistical interdependence measures from multivariate time series is the Granger causality [3]: a variable X Granger causes a variable Y if the information in the past of X improves the prediction of Y over the past of Y. Initially, linear Granger causality measures were developed based mainly on vector autoregressive (VAR) models and further extended to the frequency domain [4][5][6][7]. Many non-linear extensions of the Granger causality concept have been developed in the recent years based mainly on information theory [8,9], state-space methods [10,11] and phase synchronization [12][13][14]. ...
One of the most challenging aspects in the study of the complex dynamical systems is the estimation of their underlying, interdependence structure. Being in the era of Big Data, this problem gets even more complicated since more observed variables are available. To estimate direct causality effects in this setting, dimension reduction has to be employed in the Granger causality measure. The measure should also be capable to detect non-linear effects, persistently present in real-world complex systems. The model-free information-based measure of partial mutual information from mixed embedding (PMIME) has been developed to address these issues and it was found to perform well on multivariate time series of moderately high dimension. Here, the problem of forming complex networks from direct, possibly non-linear, high-dimensional time series at the order of hundreds is investigated. The performance of the measure PMIME is tested on two coupled dynamical systems in discrete time (coupled Hénon maps) and continuous time (coupled Mackey–Glass delay differential equations). It is concluded that the correct detection of the underlying causality network depends mainly on the network density rather than on its size (number of nodes). Finally, the effect of network size is investigated in the study of the British stock market in the period around Brexit.
... Elements of the system indicate the causal influence from input to output in concrete frequency [39,40]. Korzeniewska et al. [41] noticed that the DTF values may be high in the parts of the spectrum where the relative power of the signal is very small, making a comparison of outflows at different frequencies. This observation led to the introduction of the full frequency Direct Transfer Function (ffDTF). ...
... The directed transfer function (DTF) extends Granger causality (GC) methods to distinguish causal relationships among signals rather than the relationships of direct and indirect responses, in multivariate time series. The use of direct DTF (dDTF) method in characterizing the direct response in a multivariate time series has been proposed [9]. However, matrix inversion is required in these methods, which may incur a substantial computational cost and affect accuracy [10]. ...
Objective. The study of brain networks has become an influential tool for investigating post-stroke brain function. However, studies on the dynamics of cortical networks associated with muscle activity are limited. This is crucial for elucidating the altered coordination patterns in the post-stroke motor control system. Approach. In this study, we introduced the time-delayed maximal information spectral coefficient (TDMISC) method to assess the local frequency band characteristics (alpha, beta, and gamma bands) of functional corticomuscular coupling (FCMC) and cortico-cortical network parameters. We validated the effectiveness of TDMISC using a unidirectionally coupled Hénon maps model and a neural mass model. Main result. A grip task with 25% of maximum voluntary contraction was designed, and simulation results demonstrated that TDMISC accurately characterizes signals’ local frequency band and directional properties. In the gamma band, the affected side showed significantly strong FCMC in the ascending direction. However, in the beta band, the affected side exhibited significantly weak FCMC in all directions. For the cortico-cortical network parameters, the affected side showed a lower clustering coefficient than the unaffected side in all frequency bands. Additionally, the affected side exhibited a longer shortest path length than the unaffected side in all frequency bands. In all frequency bands, the unaffected motor cortex in the stroke group exerted inhibitory effects on the affected motor cortex, the parietal associative areas, and the somatosensory cortices. Significance. These results provide meaningful insights into neural mechanisms underlying motor dysfunction.
... Following this, we calculated the optimal model order for each participant as an average from the respective trials and performed the final calculation of the multivariate autoregressive models based on this average of optimal model orders (see Table S2 in Supplementary Materials for individual averaged model order). From these coefficients, we derived the full frequency directed transfer function (ffDTF), a directed measure of interaction normalized with respect to all of the frequencies in the predefined frequency interval [35]. For each subject, the mean connectivity matrices over the trials were calculated. ...
Background: Minutes after an injury to the spinal cord, structural and functional reorganization of the connected brain areas may be initiated. Exercise enhances this neuroplasticity in the further course of the condition, which might modulate the connectivity patterns in brain regions responsible for movement execution and imagination. However, connectivity patterns have not been analyzed as a correlate for activity effects on neuroplasticity after spinal cord injury (SCI). We hypothesize that wheelchair sport has a modulating effect on the cortical connectivity in patients with SCI, such that distinguished activity patterns can be observed between sportive and non-sportive individuals with SCI and healthy participants. Methods: Sportive (n = 16) and non-sportive (n = 7) patients with SCI as well as sportive (n = 16) and non-sportive (n = 14) healthy participants were instructed to either observe, imagine, or conduct an observed movement while high-density EEG (HD-EEG) was recorded. Functional connectivity was computed from the recorded signals, and the coefficients were compared between groups and conditions using a non-parametric repeated measures analysis. Results: We found that depending on being sportive or not, patients with SCI and controls would react differently to the conditions, but the effects depended on the location in the brain as well as the analyzed frequency range (p < 0.05). Further analysis indicates that non-sportive patients showed higher connectivity received by the right posterior parietal cortex and a lower connectivity received by the left M1 compared to sportive patients. These effects were mainly observed during movement imagination, not during movement. Sportive and non-sportive participants in the healthy control group showed smaller differences than the patients. Conclusions: The results suggest a modulative effect of sports on connectivity patterns during movement imagination and to some extent during movement. This effect was predominantly found in patients with SCI, and to a lesser extent in healthy participants with opposing connectivity patterns. We suggest that this might be due to increased cortical excitability and the elevated brain derived neurotrophic factor (BDNF) level in patients with SCI that is enhanced by exercise.
... Beat to beat data was resampled into time series uniformly sampled at 4 Hz. Further processing of data was done using GMAC toolbox for spectral granger causality based partial directed coherence [3,18]. Partial Directed Coherence (PDC) was calculated in low frequency domain only (0.04-0.15 Hz) to include only the baroreflex mediated changes through sympathetic stimulation. ...
Non-hypotensive hypovolemia simulated with oscillatory lower body negative pressure in the range of -10 to -20 mmHg is associated with vasoconstriction {increase in total peripheral vascular resistance (TPVR)}. Due to the mechanical stiffening of vessels, there is a disjuncture of mechano-neural coupling at the level of arterial baroreceptors which has not been investigated. The study was designed to quantify both the cardiac and vascular arms of the baroreflex using an approach based on Wiener-Granger causality (WGC) - partial directed coherence (PDC). Thirty-three healthy human volunteers were recruited and continuous heart rate and blood pressure {systolic (SBP), diastolic (DBP), and mean (MBP)} were recorded. The measurements were taken in resting state, at -10 mmHg (level 1) and -15 mmHg (level 2). Spectral causality - PDC was estimated from the MVAR model in the low-frequency band using the GMAC MatLab toolbox. PDC from SBP and MBP to RR interval and TPVR was calculated. The PDC from MBP to RR interval showed no significant change at -10 mmHg and -15 mmHg. No significant change in PDC from MBP to TPVR at -10 mmHg and -15 mmHg was observed. Similar results were obtained for PDC estimation using SBP as input. However, a significant increase in TPVR from baseline at both levels of oscillatory LBNP (p-value <0.001). No statistically significant change in PDC from blood pressure to RR interval and blood pressure to TPVR implies that vasoconstriction is not associated with activation of the arterial baroreflex in ≤-15 mmHg LBNP. Thereby, indicating the role of cardiopulmonary reflexes during the low level of LBNP simulated non-hypotensive hypovolemia.
... synchronic symmetric activity between ROIs and are referred to as non-directed or functional connectivity [128]. Estimators based on Granger's prediction such as partial directed coherence (PDC) [129][130][131], or directed transfer Function (DTF) [132,133] and any of their normalizations describe causal relationships between variables and are referred to as directed or effective connectivity [134]. Connectivity also allows the analysis of brain activity as network topologies, borrowing methods from graph theory [32,134]. ...
Background
Significant clinician training is required to mitigate the subjective nature and achieve useful reliability between measurement occasions and therapists. Previous research supports that robotic instruments can improve quantitative biomechanical assessments of the upper limb, offering reliable and more sensitive measures. Furthermore, combining kinematic and kinetic measurements with electrophysiological measurements offers new insights to unlock targeted impairment-specific therapy. This review presents common methods for analyzing biomechanical and neuromuscular data by describing their validity and reporting their reliability measures.
Methods
This paper reviews literature (2000–2021) on sensor-based measures and metrics for upper-limb biomechanical and electrophysiological (neurological) assessment, which have been shown to correlate with clinical test outcomes for motor assessment. The search terms targeted robotic and passive devices developed for movement therapy. Journal and conference papers on stroke assessment metrics were selected using PRISMA guidelines. Intra-class correlation values of some of the metrics are recorded, along with model, type of agreement, and confidence intervals, when reported.
Results
A total of 60 articles are identified. The sensor-based metrics assess various aspects of movement performance, such as smoothness, spasticity, efficiency, planning, efficacy, accuracy, coordination, range of motion, and strength. Additional metrics assess abnormal activation patterns of cortical activity and interconnections between brain regions and muscle groups; aiming to characterize differences between the population who had a stroke and the healthy population.
Conclusion
Range of motion, mean speed, mean distance, normal path length, spectral arc length, number of peaks, and task time metrics have all demonstrated good to excellent reliability, as well as provide a finer resolution compared to discrete clinical assessment tests. EEG power features for multiple frequency bands of interest, specifically the bands relating to slow and fast frequencies comparing affected and non-affected hemispheres, demonstrate good to excellent reliability for populations at various stages of stroke recovery. Further investigation is needed to evaluate the metrics missing reliability information. In the few studies combining biomechanical measures with neuroelectric signals, the multi-domain approaches demonstrated agreement with clinical assessments and provide further information during the relearning phase. Combining the reliable sensor-based metrics in the clinical assessment process will provide a more objective approach, relying less on therapist expertise. This paper suggests future work on analyzing the reliability of metrics to prevent biasedness and selecting the appropriate analysis.
... Since it makes use of the inverse of the regression matrix, the DTF measure is a linear combination of direct and indirect couplings. The "direct DTF" (dDTF) variant is an alternative that emphasizes direct connections (Korzeniewska et al. 2003). Note that, unlike for GGC, there is no corresponding time-domain connectivity map for PDC or DTF. ...
... describes causal influence of channel j on channel i at frequency f normalized in respect of inflows to the destination channel i. DTF expressed by formula (4) shows not only direct, but also indirect (cascade) flows. To determine only direct flows, direct DTF (dDTF) was introduced 42 . ...
Slow gamma oscillations (20–50 Hz) have been suggested to coordinate information transfer between brain structures involved in memory formation. Whereas the involvement of slow gamma in memory processing was studied by means of correlation between the gamma power and the occurrence of a given event (sharp wave ripples (SWRs), cortical transients), our approach consists of the analysis of the transmission of slow gamma itself. We use the method based on Granger causality principle—direct Directed Transfer Function, which allows to determine directed propagation of brain activity, including bidirectional flows. Four cortical sites along with CA1 ipsi- and contralateral were recorded in behaving wild-type and APP/PS1 mice before and after learning session of a spatial memory task. During slow wave sleep propagation of slow gamma was bidirectional, forming multiple loops of interaction which involved both CA1 and some of cortical sites. In episodes coincident with SWRs the number and strength of connectivity pathways increased in both groups compared to episodes without SWRs. The effect of learning was expressed only in APP/PS1 mice and consisted in strengthening of the slow gamma transmission from hippocampus to cortex as well as between both CA1 which may serve more efficient transmission of information from impaired CA1.
... To estimate the multivariate autoregressive model, partial correlation estimation with unbiased covariance estimates (Marple, 1987) was used, which was shown to be the estimate with the lowest prediction error (Schlögl, 2006). The model order used was p = 2. Based on the estimation of the multivariate autoregressive model, the transfer function and the connectivity measure of the full frequency Directed Transfer Function (ffDTF; Kaminski and Blinowska, 1991;Korzeniewska et al., 2003) were calculated in 0.5 Hz steps from 1 to 49 Hz. The ffDTF is based on the principle of Granger causality (Granger, 1969). ...
Background:
Despite humans frequently performing spontaneous facial self-touches (sFST), the function of this behavior remains speculative. sFST have been discussed in the context of self-regulation, emotional homeostasis, working memory processes, and attention focus. First evidence indicates that sFST and active facial self-touches (aFST) are neurobiologically different phenomena. The aim of the present analysis was to examine EEG-based connectivity in the course of sFST and aFST to test the hypotheses that sFST affect brain network interactions relevant for other than sensorimotor processes.
Methods:
To trigger spontaneous FST a previously successful setting was used: 60 healthy participants manually explored two haptic stimuli and held the shapes of the stimuli in memory for a 14 min retention interval. Afterwards the shapes were drawn on a sheet of paper. During the retention interval, artifact-free EEG-data of 97 sFST by 32 participants were recorded. At the end of the experiment, the participants performed aFST with both hands successively. For the EEG-data, connectivity was computed and compared between the phases before and after sFST and aFST and between the respective before-and the after-phases.
Results:
For the before-after comparison, brainwide distributed significant connectivity differences (p < .00079) were observed for sFST, but not for aFST. Additionally, comparing the before- and after-phases of sFST and aFST, respectively, revealed increased similarity between the after-phases than between the before-phases.
Conclusion:
The results support the assumption that sFST and aFST are neurobiologically different phenomena. Furthermore, the aligned network properties of the after-phases compared to the before-phases indicate that sFST serve self-regulatory functions that aFST do not serve.
Analysis of functional connectivity can provide insights into how the brain performs various cognitive and behavioral tasks as well as the neural mechanisms underlying several pathologies. In this work, we describe a novel approach to estimate functional connectivity from electroencephalography (EEG) data using the concept of coherence potentials (CPs), which are defined as clusters of high-amplitude deflections with similar waveform shapes. We define connectivity measures based on features of CPs, including the time intervals between CP peaks and their co-occurrence on different electrodes or channels. We used EEG data from 25 healthy subjects performing three tasks - resting state (eyes closed and eyes open), working memory and pattern completion tasks to investigate the ability of CP based connectivity measures to distinguish between these tasks. When compared with traditional connectivity measures including several spectral-based measures and mutual information, our results showed that CP based connectivity measures more robustly and significantly distinguished between all the tasks both at group-level and subject-level. In conclusion, CP based EEG connectivity measures provide a reliable way to distinguish between different cognitive task conditions and could pave way in the early detection of neurological disorders such as Alzheimer’s disease that affect various cognitive tasks.
Granger causality (GC) effective connectivity (EC) calculated from electroencephalogram (EEG) signals has been widely used in mental disorder detection. However, the existing methods only take into account linear dynamics or nonlinear dynamics within a single sample, ignoring the nonlinear dynamics shared by the same class of subjects. In this article, a model combining graph neural networks (GNNs) and variational autoencoders (VAEs) is proposed to construct shared latent nonlinear EC from raw EEG signals for depression detection. Several convolution modules and fully connected layers are used in the graph encoding network to learn the embeddings of the connectivity connected by every two EEG channels. In the graph decoding network, a class-specific Gaussian mixture model (GMM) is introduced in the VAEs to model shared dynamics in EC of the same class of subjects, and the shared dynamics combine the encoded embeddings of the EC and the past time series to restore raw EEG signals. Through a node-to-edge encoding process and an edge-to-node decoding process, the shared latent nonlinear EC in EEG signals can ultimately be learned by gradually optimizing the model’s loss function. The performance of the proposed method is verified on several open-accessed datasets. The excellent results prove that the proposed neural networks can learn more generalized nonlinear EC representations, and shared latent dynamics discovery can also help to identify depression better. The code is available at https://github.com/william-yuan2012/DSLNEC-tscausality.
This article proposes a systematic methodological review and objective criticism of existing methods enabling the derivation of time-varying Granger-causality statistics in neuroscience. The increasing interest and the huge number of publications related to this topic calls for this systematic review which describes the very complex methodological aspects. The capacity to describe the causal links between signals recorded at different brain locations during a neuroscience experiment is of primary interest for neuroscientists, who often have very precise prior hypotheses about the relationships between recorded brain signals that arise at a specific time and in a specific frequency band. The ability to compute a time-varying frequency-specific causality statistic is therefore essential. Two steps are necessary to achieve this: the first consists of finding a statistic that can be interpreted and that directly answers the question of interest. The second concerns the model that underlies the causality statistic and that has this time-frequency specific causality interpretation. In this article, we will review Granger-causality statistics with their spectral and time-varying extensions.
Background
Recent advancements in virtual reality (VR) and biofeedback (BF) technologies have opened new avenues for breathing training. Breathing training has been suggested as an effective means for mental disorders, but it is difficult to master the technique at the beginning. VR-BF technologies address the problem of breathing, and visualizing breathing may facilitate the learning of breathing training. This study explores the integration of VR and BF to enhance user engagement in self-help breathing training, which is a multifaceted approach encompassing mindful breathing, guided breathing, and breath counting techniques.
Objective
We identified 3 common breathing training techniques in previous studies, namely mindful breathing, guided breathing, and breath counting. Despite the availability of diverse breathing training methods, their varying effectiveness and underlying neurological mechanisms remain insufficiently understood. We investigated using electroencephalography (EEG) indices across multiple breathing training modalities to address this gap.
Methods
Our automated VR-based breathing training environment incorporated real-time EEG, heart rate, and breath signal BF. We examined 4 distinct breathing training conditions (resting, mindful breathing, guided breathing, and breath counting) in a cross-sectional experiment involving 51 healthy young adults, who were recruited through online forum advertisements and billboard posters. In an experimental session, participants practiced resting state and each breathing training technique for 6 minutes. We then compared the neurological differences across the 4 conditions in terms of EEG band power and EEG effective connectivity outflow and inflow with repeated measures ANOVA and paired t tests.
Results
The analyses included the data of 51 participants. Notably, EEG band power across the theta, alpha, low-beta, high-beta, and gamma bands varied significantly over the entire scalp (t ≥1.96, P values <.05). Outflow analysis identified condition-specific variations in the delta, alpha, and gamma bands (P values <.05), while inflow analysis revealed significant differences across all frequency bands (P values <.05). Connectivity flow analysis highlighted the predominant influence of the right frontal, central, and parietal brain regions in the neurological mechanisms underlying the breathing training techniques.
Conclusions
This study provides neurological evidence supporting the effectiveness of self-help breathing training through the combined use of VR and BF technologies. Our findings suggest the involvement of internal-external attention focus and the dorsal attention network in different breathing training conditions. There is a huge potential for the use of breathing training with VR-BF techniques in terms of clinical settings, the new living style since COVID-19, and the commercial value of introducing VR-BF breathing training into consumer-level digital products. Furthermore, we propose avenues for future research with an emphasis on the exploration of applications and the gamification potential in combined VR and BF breathing training.
Trial Registration
ClinicalTrials.gov NCT06656741; https://clinicaltrials.gov/study/NCT06656741
Cortical mechanism is necessary for human standing control. Previous research has demonstrated that cortical oscillations and corticospinal excitability respond flexibly to postural demands. However, it is unclear how corticocortical and corticomuscular connectivity changes dynamically during standing with spontaneous postural sway and over time. This study investigated the dynamics of sway- and time-varying connectivity using electroencephalography and electromyography. Electroencephalography and electromyography were recorded in sitting position and 3 standing postures with varying base-of-support: normal standing, one-leg standing, and standing on a piece of wood. For sway-varying connectivity, corticomuscular connectivity was calculated based on the timing of peak velocity in anteroposterior sway. For time-varying connectivity, corticocortical connectivity was measured using the sliding-window approach. This study found that corticomuscular connectivity was strengthened at the peak velocity of postural sway in the γ- and β-frequency bands. For time-varying corticocortical connectivity, the θ-connectivity in all time-epoch was classified into 7 clusters including posture-relevant component. In one of the 7 clusters, strong connectivity pairs were concentrated in the mid-central region, and the proportion of epochs under narrow-base standing conditions was significantly higher, indicating a functional role for posture balance. These findings shed light on the connectivity dynamics and cortical oscillation that govern standing balance.
Estimation of mental workload from electroencephalogram (EEG) signals aims to accurately measure the cognitive demands placed on an individual during multitasking mental activities. By analyzing the brain activity of the subject, we can determine the level of mental effort required to perform a task and optimize the workload to prevent cognitive overload or underload. This information can be used to enhance performance and productivity in various fields such as healthcare, education, and aviation. In this paper, we propose a method that uses EEG and deep neural networks to estimate the mental workload of human subjects during multitasking mental activities. Notably, our proposed method employs subject-independent classification. We use the "STEW" dataset, which consists of two tasks, namely "No task" and "simultaneous capacity (SIMKAP)-based multitasking activity". We estimate the different workload levels of two tasks using a composite framework consisting of brain connectivity and deep neural networks. After the initial preprocessing of EEG signals, an analysis of the relationships between the 14 EEG channels is conducted to evaluate effective brain connectivity. This assessment illustrates the information flow between various brain regions, utilizing the direct Directed Transfer Function (dDTF) method. Then, we propose a deep hybrid model based on pre-trained Convolutional Neural Networks (CNN) and Long Short-Term Memory (LSTM) for the classification of workload levels. The accuracy of the proposed deep model achieved 83.12% according to the subject-independent leave-subject-out (LSO) approach. The pre-trained CNN + LSTM approaches to EEG data have been found to be an accurate method for assessing the mental workload.
In this study, we have developed a novel method based on deep learning and brain effective connectivity to classify responders and non-responders to selective serotonin reuptake inhibitors (SSRIs) antidepressants in major depressive disorder (MDD) patients prior to the treatment using EEG signal. The effective connectivity of 30 MDD patients was determined by analyzing their pretreatment EEG signals, which were then concatenated into delta, theta, alpha, and beta bands and transformed into images. Using these images, we then fine tuned a hybrid Convolutional Neural Network that is enhanced with bidirectional Long Short-Term Memory cells based on transfer learning. The Inception-v3, ResNet18, DenseNet121, and EfficientNet-B0 models are implemented as base models. Finally, the models are followed by BiLSTM and dense layers in order to classify responders and non-responders to SSRI treatment. Results showed that the EfficiencyNet-B0 has the highest accuracy of 98.33, followed by DensNet121, ResNet18 and Inception-v3. Therefore, a new method was proposed in this study that uses deep learning models to extract both spatial and temporal features automatically, which will improve classification results. The proposed method provides accurate identification of MDD patients who are responding, thereby reducing the cost of medical facilities and patient care.
Using functional neuroimaging, electrophysiological techniques and neural data processing techniques, neuroscientists have found that mathematically gifted adolescents exhibit unusual neurocognitive features in the activation of task-related brain regions. Hemispheric information interaction, functional reorganization of networks, and utilization of task-related brain regions are beneficial to rapid and efficient task processing. Based on Granger causality channel selection, the transfer entropy (TE) value between effective channels was computed, and the information flow patterns in the directed functional brain networks derived from electroencephalography (EEG) data during deductive reasoning tasks were explored. We evaluated the workspace configuration patterns of the brain network and the global integration characteristics of separated brain regions using node strength, motif, directed clustering coefficient and characteristic path length in the brain networks of mathematically gifted adolescents with effective connectivity. The empirical results demonstrated that a more integrated functional network at the global level and a more efficient clique at the local level support a pattern of workspace configuration in the mathematically gifted brain that is more conducive to task-related information processing.
Practicing mindfulness, focusing attention on the internal and external experiences occurring in the present moment with open and nonjudgement stance, can lead to the development of emotional regulation skills. Yet, the effective connectivity of brain regions during mindfulness has been largely unexplored. Studies have shown that mindfulness practice promotes functional connectivity in practitioners, potentially due to improved emotional regulation abilities and increased connectivity in the lateral prefrontal areas. To examine the changes in effective connectivity due to mindfulness training, we analyzed electroencephalogram (EEG) signals taken before and after mindfulness training, focusing on training-related effective connectivity changes in the frontal area. The mindfulness training group participated in an 8-week mindfulness-based stress reduction (MBSR) program. The control group did not take part. Regardless of the specific mindfulness practice used, low-gamma band effective connectivity increased globally after the mindfulness training. High-beta band effective connectivity increased globally only during Breathing. Moreover, relatively higher outgoing effective connectivity strength was seen during Resting and Breathing and Body-scan. By analyzing the changes in outgoing and incoming connectivity edges, both F7 and F8 exhibited strong parietal connectivity during Resting and Breathing. Multiple regression analysis revealed that the changes in effective connectivity of the right lateral prefrontal area predicted mindfulness and emotional regulation abilities. These results partially support the theory that the lateral prefrontal areas have top-down modulatory control, as these areas have high outflow effective connectivity, implying that mindfulness training cultivates better emotional regulation.
The present study tests the hypothesis that emotions of fear and anger are associated with distinct psychophysiological and neural circuitry according to discrete emotion model due to contrasting neurotransmitter activities, despite being included in the same affective group in many studies due to similar arousal-valance scores of them in emotion models. EEG data is downloaded from OpenNeuro platform with access number of ds002721. Brain connectivity estimations are obtained by using both functional and effective connectivity estimators in analysis of short (2 sec) and long (6 sec) EEG segments across the cortex. In tests, discrete emotions and resting-states are identified by frequency band specific brain network measures and then contrasting emotional states are deep classified with 5-fold cross-validated Long Short Term Memory Networks. Logistic regression modeling has also been examined to provide robust performance criteria. Commonly, the best results are obtained by using Partial Directed Coherence in Gamma (31.5-60.5Hz) sub-bands of short EEG segments. In particular, Fear and Anger have been classified with accuracy of 91.79%. Thus, our hypothesis is supported by overall results. In conclusion, Anger is found to be characterized by increased transitivity and decreased local efficiency in addition to lower modularity in Gamma-band in comparison to fear. Local efficiency refers functional brain segregation originated from the ability of the brain to exchange information locally. Transitivity refer the overall probability for the brain having adjacent neural populations interconnected, thus revealing the existence of tightly connected cortical regions. Modularity quantifies how well the brain can be partitioned into functional cortical regions. In conclusion, PDC is proposed to graph theoretical analysis of short EEG epochs in presenting robust emotional indicators sensitive to perception of affective sounds.
Previous studies have identified several brain regions involved in the sympathetic response and its integration with pain, cognition, emotions and memory processes. However, little is known about how such regions dynamically interact during a sympathetic activation task. In this study, we analyzed EEG activity and effective connectivity during a cold pressor test (CPT). A source localization analysis identified a network of common active sources including the right precuneus (r-PCu), right and left precentral gyri (r-PCG, l-PCG), left premotor cortex (l-PMC) and left anterior cingulate cortex (l-ACC). We comprehensively analyzed the network dynamics by estimating power variation and causal interactions among the network regions through the direct directed transfer function (dDTF). A connectivity pattern dominated by interactions in α (8–12) Hz band was observed in the resting state, with r-PCu acting as the main hub of information flow. After the CPT onset, we observed an abrupt suppression of such α-band interactions, followed by a partial recovery towards the end of the task. On the other hand, an increase of δ-band (1–4) Hz interactions characterized the first part of CPT task. These results provide novel information on the brain dynamics induced by sympathetic stimuli. Our findings suggest that the observed suppression of α and rise of δ dynamical interactions could reflect non-pain-specific arousal and attention-related response linked to stimulus’ salience.
This paper introduces a new frequency-domain approach to describe the relationships (direction of information flow) between multivariate time series based on the decomposition of multivariate partial coherences computed from multivariate autoregressive models. We discuss its application and compare its performance to other approaches to the problem of determining neural structure relations from the simultaneous measurement of neural electrophysiological signals. The new concept is shown to reflect a frequency-domain representation of the concept of Granger causality.
Overnight sleep EEG recorded from 21 derivations was studied for 7 subjects (4 normal and 3 depressive). The multichannel autoregressive model was fitted to all 21 channels simultaneously. Ordinary, multiple and partial coherencies and directed transfer function were estimated for sleep stages and wakefulness. Ordinary coherencies give rather trivial information that coherence decreases with the distance. Partial coherencies revealed specific structure to a large degree repeatable for studied subjects. Study of directed transfer function made possible the identification of main centres from which EEG activity is spreading during sleep. An EEG analysis, based on treating signals as a realization of one process and on simultaneous (not pair-wise) evaluation of time series, offers new possibilities in the investigation of synchronization and functional relations in brains.
The directed transfer function (DTF) method is a multichannel analysis based on an autoregressive model that detects flow of seizure activity. This report extends the application of the DTF method to compare patterns of flow of seizures with different sites of origin. Analysis of a seizure originating from mesial temporal structures is compared with a seizure originating from lateral temporal neocortex; both complex partial seizures were recorded with intracranial electrodes that combine subdural grid arrays and depth electrodes. The DTF method has the potential to determine patterns of flow of activity, including periods when visual analysis of the intracranial ictal EEG may not allow for definitive source localization. The extension of the DTF analyses into integrated DTF (IDTF) formats is also illustrated. When activity of a relatively discrete frequency can be identified, the IDTF analysis facilitates display of patterns of flow of this selected activity.
We consider the question of evaluating causal relations among neurobiological signals. In particular, we study the relation between the directed transfer function (DTF) and the well-accepted Granger causality, and show that DTF can be interpreted within the framework of Granger causality. In addition, we propose a method to assess the significance of causality measures. Finally, we demonstrate the applications of these measures to simulated data and actual neurobiological recordings.
The existence of a prominent electroencephalogram (EEG) activity within the theta frequency range (4–7 Hz) in the hippocampus has been one of the most studied rhythmic activities of the mammalian brain. However, in lower mammals the hippocampal EEG has a wider frequency range and may extend from 3 to 4 Hz up to 10 to 12 Hz. Therefore, it has become current practice to name this EEG activity Rhythmic Slow Activity (RSA), in order to avoid the term theta rhythm, which does not cover the entire frequency range within which the hippocampal EEG of lower animals may fall. Several reviews on RSA, particularly in relation to behavior, have appeared (Ishizuka et al., 1990; Komisaruk, 1977; Lopes da Silva and Arnolds, 1978; Robinson, 1980; Vanderwolf and Robinson, 1981). Robinson (1980) discussed in particular the influence of species differences on RSA. In this respect, a controversial point is whether hippocampal RSA occurs also in humans. Single cases have been reported in which hippocampal RSA was observed in man (Giaquinto, 1973), but Halgren et al. (1985) were not able to find RSA in recordings in humans. However, using spectral analysis, Arnolds et al. (1980) were able to demonstrate RSA in the hippocampus of epileptic patients. This RSA presented a dominant low frequency (about 3–4 Hz), which was modulated with behavior in a similar way as in lower mammals.
The investigation of brain electrical activity is usually approached in one of two ways. In the first approach the methods of analysis of stochastic signals are used to extract the characteristic features of the EEG, without any attempt to elucidate the physiological basis of its generation (Gersh and Yonemoto 1977; Gersh et al. 1977; Bodenstein and Praetorius 1977). In the second approach, models based on the neurophysiological data are created, but very often the results of the modeling are difficult to compare directly with the experimental data and only general features of the EEG are described (Aninos and Zenone 1980; Wilson and Cowan 1973; Zetterberg 1973).
We describe a statistical approach for identifying nonlinearity in time series. The method first specifies some linear process as a null hypothesis, then generates surrogate data sets which are consistent with this null hypothesis, and finally computes a discriminating statistic for the original and for each of the surrogate data sets. If the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data, then the null hypothesis is rejected and nonlinearity is detected. We discuss various null hypotheses and discriminating statistics. The method is demonstrated for numerical data generated by known chaotic systems, and applied to a number of experimental time series which arise in the measurement of superfluids, brain waves, and sunspots; we evaluate the statistical significance of the evidence for nonlinear structure in each case, and illustrate aspects of the data which this approach identifies.
Based on a bidirectional model and the temporal relation of the signals, directed coherence is defined to describe the EEG correlation according to the direction of information transmission in the frequency domain. The interhemispheric directed coherences of EEG pairs in the prefrontal, frontal, central, parietal and occipital cortices were investigated. Statistically, significantly greater right-left directed coherences were found in the parietal and occipital regions than that of the left-right direction for alpha activity. The results indicate different information processing for different frequency bands between the left and right hemispheres, and this can not be derived from the examination of original coherence. This may suggest that the measure of directed coherence can provide more information than that of original coherence.
A method of modified coherence analysis was applied to the interpretation of EEG differences between the frontal and occipital cortex. This paper discusses a bidirectional communication model for the frontal and occipital cortex. Directed coherence method was used to analyze alpha activities over the scalp. The results show that both in the left and right hemisphere, slow waves in the alpha frequency band had high correlation in the frontal-occipital direction, and fast waves had high correlation in the occipital-frontal direction. It may suggest that the structure of information transmission is different for fast and slow waves of alpha rhythm.
The paper describes the method of determining direction and frequency content of the brain activity flow. The method was formulated in the framework of the AR model. The transfer function matrix was found for multichannel EEG process. Elements of this matrix, properly normalized, appeared to be good estimators of the propagation direction and spectral properties of the investigated signals. Simulation experiments have shown that the estimator proposed by us unequivocally reveals the direction of the signal flow and is able to distinguish between direct and indirect transfer of information. The method was applied to the signals recorded in the brain structures of the experimental animals and also to the human normal and epileptic EEG. The sensitivity of the method and its usefulness in the neurological and clinical applications was demonstrated.
A parametric autoregressive model was applied to the multichannel EEG time series. Small statistical fluctuations of the spectral estimates obtained from the short data strings made possible to follow the time changes of the signals. The multiple and partial coherences were calculated for the four channel process and compared with the coherences computed between the pairs of channels. From the study it followed that the partial coherences are the proper measure of the synchronization of brain structures and their intrinsic relationships. The partial phase spectra give the information about the phase delays. The advantages of the parametric description of signals in the frequency domain in respect to the modelling of dynamic systems was pointed out.
EEG interactions of the background among locations can start to change just before epileptiform discharges. Such interactions were investigated with relative power contribution analysis based on a multivariate autoregressive model, which permits determination of multiple causal relations of EEGs among locations. EEGs from F3, F4, P3, P4, T3 and T4 were examined in 10 epileptic patients with asymmetric spike and wave complexes (SWCs). A 12.5-s epoch just before SWCs was divided into stationary segments throughout 6 locations with a segmentation method. In segments long before SWCs, most power at each location was generated from its own location. In segments immediately preceding SWCs, contributions from other locations, particularly from the hemisphere with smaller SWCs, increased. Overall EEG relationships among 6 locations were examined by an entropy which measures the uniformness of the spatial distribution of power contribution. The entropy significantly increased gradually toward SWCs. Our findings demonstrated stronger interactions among locations just before epileptiform discharges, suggesting a transitional state from background EEG to epileptiform discharges.
The relationships among the CA1 field of hippocampus, the entorhinal-piriform area, the subiculum and the lateral septum were studied in various behavioral states in the rat. The EEG signals recorded simultaneously from chronically implanted electrodes were analyzed by means of a multichannel autoregressive (AR) model. Power spectra, ordinary, multiple and partial coherences, and directed transfer functions were calculated. The method of analysis which took into account all signals simultaneously, not pair-wise, made it possible to estimate the spectral characteristics and the directions of the EEG flow between structures. The pattern of the EEG activity propagation depended on the type of behavior, difficulty of the task performed by the animal, and the phase of the trial. Our results not only confirmed the existence of connections between analyzed structures, but also showed that these connections may have different strengths during various types of behavior.
Background activity as well as three kinds of bilateral epileptiform discharges, recorded from the cerebral cortex and hippocampus of freely behaving rats treated with intravenous kainic acid (KA), were analysed by the directed transfer function (DTF) method within multivariate autoregressive modeling of the EEG. This method reveals statistical influence (flow of activity) between brain regions at different frequencies. There was no significant influence between rhythms in different brain regions in the background EEG. Early after KA administration, low frequency rhythms (< 10Hz) in the frontal cortex began to lead slow rhythms in other areas and high frequency rhythms (20-60 Hz), possibly gamma oscillations, intensified in the hippocampus. In spike-wave discharges, frontal cortex led both low and high frequency rhythms. Initially during generalised non-convulsive discharges, slow rhythms originated from frontal cortex and high frequency rhythms from hippocampus while later, slow rhythms as well, often arose from hippocampus. During the convulsive discharge, the flow of activity of dominant slow rhythms repeatedly changed between hippocampus and neocortex, with more frequent dominance of the hippocampus, while hippocampus continued to lead high frequency rhythms. We conclude that KA-induced epileptiform discharges are cortical and hippocampal events, specifically that the frontal cortex is early to express low frequency rhythms and the hippocampus, high frequency rhythms. More generally, the findings suggest that epileptiform discharges result from interacting rhythms of different frequencies that arise from different structures, and that gamma oscillations possibly contribute to widespread synchronisation during some forms of epileptogenesis.
There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recordhag information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalization of this result with the partial cross spectrum is suggested.The object of this paper is to throw light on the relationships between certain classes of econometric models involving feedback and the functions arising in spectral analysis, particularly the cross spectrum and the partial cross spectrum. Causality and feedback are here defined in an explicit and testable fashion. It is shown that in the two-variable case the feedback mechanism can be broken down into two causal relations and that the cross spectrum can be considered as the sum of two cross spectra, each closely connected with one of the causations. The next three sections of the paper briefly introduce those aspects of spectral methods, model building, and causality which are required later. Section IV presents the results for the two-variable case and Section V generalizes these results for three variables.
The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum information theoretical criterion (AIC) estimate (MAICE) which is designed for the purpose of statistical identification is introduced. When there are several competing models the MAICE is defined by the model and the maximum likelihood estimates of the parameters which give the minimum of AIC defined by AIC = (-2)log-(maximum likelihood) + 2(number of independently adjusted parameters within the model). MAICE provides a versatile procedure for statistical model identification which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure. The practical utility of MAICE in time series analysis is demonstrated with some numerical examples.
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