Estimation Of Effective Connectivity Research Articles

Transformer-aided dynamic causal model for scalable estimation of effective connectivity

Abstract Dynamic Causal Models (DCMs) in functional Magnetic Resonance Imaging (fMRI) decipher causal interactions, known as Effective Connectivity, among neuronal populations. However, their utility is often constrained by computational limitations, restricting analysis to a small subset of interacting brain areas, typically fewer than 10, thus lacking scalability. While the regression DCM (rDCM) has emerged as a faster alternative to traditional DCMs, it is not without its limitations, including the linearization of DCM terms, reliance on a fixed Hemodynamic Response Function (HRF), and an inability to accommodate modulatory influences. In response to these challenges, we propose a novel hybrid approach named Transformer encoder DCM decoder (TREND), which combines a Transformer encoder with state-of-the-art physiological DCM (P-DCM) as decoder. This innovative method addresses the scalability issue while preserving the nonlinearities inherent in DCM equations. Through extensive simulations, we validate TREND’s efficacy by demonstrating its ability to accurately predict effective connectivity values with dramatically reduced computational time relative to original P-DCM even in networks comprising up to, for instance, 100 interacting brain regions. Furthermore, we showcase TREND on an empirical fMRI dataset demonstrating the superior accuracy and/or speed of TREND compared with other DCM variants. In summary, by amalgamating P-DCM with Transformer, we introduce and validate a pioneering approach for determining effective connectivity values among brain regions, extending its applicability seamlessly to large-scale brain networks.

Impact of data processing varieties on DCM estimates of effective connectivity from task-fMRI.

Effective connectivity (EC) refers to directional or causal influences between interacting neuronal populations or brain regions and can be estimated from functional magnetic resonance imaging (fMRI) data via dynamic causal modeling (DCM). In contrast to functional connectivity, the impact of data processing varieties on DCM estimates of task-evoked EC has hardly ever been addressed. We therefore investigated how task-evoked EC is affected by choices made for data processing. In particular, we considered the impact of global signal regression (GSR), block/event-related design of the general linear model (GLM) used for the first-level task-evoked fMRI analysis, type of activation contrast, and significance thresholding approach. Using DCM, we estimated individual and group-averaged task-evoked EC within a brain network related to spatial conflict processing for all the parameters considered and compared the differences in task-evoked EC between any two data processing conditions via between-group parametric empirical Bayes (PEB) analysis and Bayesian data comparison (BDC). We observed strongly varying patterns of the group-averaged EC depending on the data processing choices. In particular, task-evoked EC and parameter certainty were strongly impacted by GLM design and type of activation contrast as revealed by PEB and BDC, respectively, whereas they were little affected by GSR and the type of significance thresholding. The event-related GLM design appears to be more sensitive to task-evoked modulations of EC, but provides model parameters with lower certainty than the block-based design, while the latter is more sensitive to the type of activation contrast than is the event-related design. Our results demonstrate that applying different reasonable data processing choices can substantially alter task-evoked EC as estimated by DCM. Such choices should be made with care and, whenever possible, varied across parallel analyses to evaluate their impact and identify potential convergence for robust outcomes.

MetaCAE: Causal autoencoder with meta-knowledge transfer for brain effective connectivity estimation

Using machine learning methods to estimate brain effective connectivity networks from functional magnetic resonance imaging (fMRI) data has gradually become one of the hot subjects in the fields of neuroscience. In particular, the encoder–decoder based methods can effectively extract the connections in fMRI time series, which have achieved promising performance. However, these methods generally use Granger causality model, which may identify false directions due to the non-stationary characteristic of fMRI data. Additionally, fMRI datasets have limited sample sizes, which significantly constrains the development of these methods. In this paper, we propose a novel brain effective connectivity estimation method based on causal autoencoder with meta-knowledge transfer, called MetaCAE. The proposed approach employs a causal autoencoder (CAE) to extract causal dependencies from non-stationary fMRI time series, and leverages meta-knowledge transfer to improve the estimation accuracy on small-sample data. More specifically, MetaCAE first employs a temporal convolutional encoder to extract non-stationary temporal information from fMRI time series. Then it uses a structural equation model-based decoder to decode causal relationships between brain regions. Finally, it utilizes a model-agnostic meta-learning method to learn the meta-knowledge of the shared brain effective connectivity among different subjects, and transfers the meta-knowledge to the CAE to enhance its estimation ability on small-sample fMRI data. Comprehensive experiments on both simulated and real-world data demonstrate the efficacy of MetaCAE in estimating brain effective connectivity.

Effective Connectivity Estimation by a Hybrid Neural Network, Empirical Wavelet Transform, and Bayesian Optimization.

Accurately measuring nonlinear effective connectivity is a crucial step in investigating brain functions. Brain signals like EEG is nonstationary. Many effective connectivity methods have been proposed but they have drawbacks in their models such as a weakness in proposing a way for hyperparameter and time lag selection as well as dealing with non-stationarity of the time series. This paper proposes an effective connectivity model based on a hybrid neural network model which uses Empirical Wavelet Transform (EWT) and a long short-term memory network (LSTM). The best hyperparameters and time lag are selected using Bayesian Optimization (BO). Due to the importance of generalizability in neural networks and calculating GC, an algorithm was proposed to choose the best generalizable weights. The model was evaluated using simulated and real EEG data consisting of attention deficit hyperactivity disorder (ADHD) and healthy subjects. The proposed model's performance on simulated data was evaluated by comparing it with other neural networks, including LSTM, CNN-LSTM, GRU, RNN, and MLP, using a Blocked cross-validation approach. GC of the simulated data was compared with GRU, linear Granger causality (LGC), Kernel Granger Causality (KGC), Partial Directed Coherence (PDC), and Directed Transfer Function (DTF). Our results demonstrated that the proposed model was superior to the mentioned models. Another advantage of our model is robustness against noise. The results showed that the proposed model can identify the connections in noisy conditions. The comparison of the effective connectivity of ADHD and the healthy group showed that the results are in accordance with previous studies.

Amortization Transformer for Brain Effective Connectivity Estimation from fMRI Data.

Using machine learning methods to estimate brain effective connectivity networks from functional magnetic resonance imaging (fMRI) data has garnered significant attention in the fields of neuroinformatics and bioinformatics. However, existing methods usually require retraining the model for each subject, which ignores the knowledge shared across subjects. In this paper, we propose a novel framework for estimating effective connectivity based on an amortization transformer, named AT-EC. In detail, AT-EC first employs an amortization transformer to model the dynamics of fMRI time series and infer brain effective connectivity across different subjects, which can train an amortized model that leverages the shared knowledge from different subjects. Then, an assisted learning mechanism based on functional connectivity is designed to assist the estimation of the brain effective connectivity network. Experimental results on both simulated and real-world data demonstrate the efficacy of our method.

A spectral sampling algorithm in dynamic causal modelling for resting-state fMRI.

Resting-state functional magnetic resonance imaging (rs-fMRI) is widely utilized to study the directed influences among neural populations which were called effective connectivity (EC), and the spectral dynamic causal modelling (spDCM) is the state-of-the-art framework to identify them. However, spDCM used variational Laplace to approximate the posterior density by maximizing the free energy, which might underestimate the variability of posterior density and get locked to the local minima. A spectral sampling algorithm (SS-DCM) was proposed to improve the estimation accuracy of the dynamic causal model for rs-fMRI. In SS-DCM, a naïve Bayesian model was constructed in the spectral domain, which described the probabilistic relationship between the sampled parameters and cross spectra of the observed blood oxygen level-dependent signals, and the parameters were sampled using randomly walked Markov Chain Monto Carlo scheme. The root mean square errors of the estimation of EC and hemodynamic parameters of SS-DCM, spDCM and generalized filter scheme were compared in the synthetic data, and SS-DCM was the most accurate and stable. A comparative evaluation using empirical rs-fMRI data was performed to study the EC pattern of the default mode network and compare the accuracy of classification between typically developed subjects and inattentive attention deficit and hyperactivity disorder patients. The results showed high consistency of positivity and negativity of EC between spDCM and SS-DCM, and SS-DCM also provided higher classification accuracy. It is highlighted that SS-DCM improves the accuracy of the estimation of EC and provides accurate information of discrepancies between diseased and healthy subjects using rs-fMRI.

Efficient Estimation of Time-Dependent Brain Functional Connectivity Using Anatomical Connectivity Constraints

There is ongoing interest in the dynamics of resting state brain networks (RSNs) as potential predictors of cognitive and behavioural states. Multivariate Autoregressors (MAR) are used to model regional brain activity as a linear combination of past activity in other regions. The coefficients of the MAR are taken as estimates of effective brain connectivity. However, assumption of stationarity, and the large number of coefficients renders the MAR impractical for estimating brain networks from standard neuroimaging time-series of limited durations. We propose HsMM-MAR-AC, a novel sparse hybrid discrete-continuous model for the efficient estimation of time-dependent effective brain networks from non-stationary brain activity time-series. Discrete quasi-stationary Brain States, and the fast switching between them, are modelled by a Hidden semi-Markov Model whose continuous emissions are drawn from a sparse MAR. The coefficients of the MAR are restricted by Anatomical Brain Connectivity information in two ways: 1) Effective direct connectivity between two brain regions is only considered if the corresponding anatomical connection exists; and 2) the autoregressors lag associated with each connection is based on the fiber length between the two regions, such that only one lag per connection is estimated. We test the accuracy of HsMM-MAR-AC in recovering simulated resting state networks of various durations, and at different thresholds of anatomical restrictions. We demonstrate that HsMM-MAR-AC recovers the RSNs more accurately than the benchmark method of the sliding window, with as little as 4 minutes of data. We also show that when the anatomical restrictions are relaxed, longer time-series are needed to estimate the networks, and became computationally unfeasible without anatomical restrictions. HsMM-MAR-AC offers an efficient model for estimating time-dependent Effective Connectivity from neuroimaging data that exploits the advantages of Hidden Markov and MAR models without identifiability problems, excessive demand on data collection, or unnecessary computational effort.

A novel method for efficient estimation of brain effective connectivity in EEG

Background and Objective: Brain connectivity plays a pivotal role in understanding the brain’s information processing functions by providing various details including magnitude, direction, and temporal dynamics of inter-neuron connections. While the connectivity may be classified as structural, functional and causal, a complete in-vivo directional analysis is guaranteed by the latter and is referred to as Effective Connectivity (EC). Two most widely used EC techniques are Directed Transfer Function (DTF) and Partial Directed Coherence (PDC) which are based on multivariate autoregressive models. The drawbacks of these techniques include poor frequency resolution and the requirement for experimental approach to determine signal normalization and thresholding techniques in identifying significant connectivities between multivariate sources.Methods: In this study, the drawbacks of DTF and PDC are addressed by proposing a novel technique, termed as Efficient Effective Connectivity (EEC), for the estimation of EC between multivariate sources using AR spectral estimation and Granger causality principle. In EEC, a linear predictive filter with AR coefficients obtained via multivariate EEG is used for signal prediction. This leads to the estimation of full-length signals which are then transformed into frequency domain by using Burg spectral estimation method. Furthermore, the newly proposed normalization method addressed the effect on each source in EEC using the sum of maximum connectivity values over the entire frequency range. Lastly, the proposed dynamic thresholding works by subtracting the first moment of causal effects of all the sources on one source from individual connections present for that source.Results: The proposed method is evaluated using synthetic and real resting-state EEG of 46 healthy controls. A 3D-Convolutional Neural Network is trained and tested using the PDC and EEC samples. The result indicates that compared to PDC, EEC improves the EEG eye-state classification accuracy, sensitivity and specificity by 5.57%, 3.15% and 8.74%, respectively.Conclusion: Correct identification of all connections in synthetic data and improved resting-state classification performance using EEC proved that EEC gives better estimation of directed causality and indicates that it can be used for reliable understanding of brain mechanisms. Conclusively, the proposed technique may open up new research dimensions for clinical diagnosis of mental disorders.

Sustained attention induces altered effective connectivity of the ascending thalamo-cortical relay in obsessive-compulsive disorder.

Abnormal function of the thalamo-cortical relay is considered a hallmark of obsessive-compulsive disorder (OCD) and aberrant network interactions may underpin many of the clinical and cognitive symptoms that characterize the disorder. Several statistical approaches have been applied to in vivo fMRI data to support the general loss of thalamo-cortical connectivity in OCD. However, (a) few studies have assessed the contextual constraints under which abnormal network interactions arise or (b) have used methods of effective connectivity to understand abnormal network interactions. Effective connectivity is a particularly valuable method as it describes the putative causal influences that brain regions exert over each other, as opposed to the largely statistical consistencies captured in functional connectivity techniques. Here, using dynamic causal modeling (DCM), we evaluated how attention demand induced inter-group differences (HC ≠ OCD) in effective connectivity within a motivated thalamo-cortical network. Of interest was whether these effects were observed on the ascending thalamo-cortical relay, essential for the sensory innervation of the cortex. fMRI time series data from sixty-two participants (OCD, 30; HC, 32) collected using an established sustained attention task were submitted to a space of 162 competing models. Across the space, models distinguished between competing hypotheses of thalamo-cortical interactions. Bayesian model selection (BMS) identified marginally differing likely generative model architectures in OCD and HC groups. Bayesian model averaging (BMA), was used to weight connectivity parameter estimates across all models, with each parameter weighted by each model’s posterior probability, thus providing more stable estimates of effective connectivity. Inferential statistical analyses of estimated parameters revealed two principal results: (1) Significantly reduced intrinsic connectivity of the V1 → SPC pathway in OCD, suggested connective weakness in the early constituents of the dorsal visual pathway; (2) More pertinent with the discovery possibilities afforded by DCM, sustained attention in OCD patients induced significantly reduced contextual modulation of the ascending relay from the thalamus to the prefrontal cortex. These results form an important complement to our understanding of the contextual bases of thalamo-cortical network deficits in OCD, emphasizing vulnerability of the ascending relay.

A strategy of model space search for dynamic causal modeling in task fMRI data exploratory analysis.

Dynamic causal modeling (DCM) is a tool used for effective connectivity (EC) estimation in neuroimage analysis. But it is a model-driven analysis method, and the structure of the EC network needs to be determined in advance based on a large amount of prior knowledge. This characteristic makes it difficult to apply DCM to the exploratory brain network analysis. The exploratory analysis of DCM can be realized from two perspectives: one is to reduce the computational cost of the model; the other is to reduce the model space. From the perspective of model space reduction, a model space exploration strategy is proposed, including two algorithms. One algorithm, named GreedyEC, starts with reducing EC from full model, and the other, named GreedyROI, start with adding EC from one node model. Then the two algorithms were applied to the task state functional magnetic resonance imaging (fMRI) data of visual object recognition and selected the best DCM model from the perspective of model comparison based on Bayesian model compare method. Results show that combining the results of the two algorithms can further improve the effect of DCM exploratory analysis. For convenience in application, the algorithms were encapsulated into MATLAB function based on SPM to help neuroscience researchers to analyze the brain causal information flow network. The strategy provides a model space exploration tool that may obtain the best model from the perspective of model comparison and lower the threshold of DCM analysis.

Meditation-induced effects on whole-brain structural and effective connectivity

In the past decades, there has been a growing scientific interest in characterizing neural correlates of meditation training. Nonetheless, the mechanisms underlying meditation remain elusive. In the present work, we investigated meditation-related changes in functional dynamics and structural connectivity (SC). For this purpose, we scanned experienced meditators and control (naive) subjects using magnetic resonance imaging (MRI) to acquire structural and functional data during two conditions, resting-state and meditation (focused attention on breathing). In this way, we aimed to characterize and distinguish both short-term and long-term modifications in the brain’s structure and function. First, to analyze the fMRI data, we calculated whole-brain effective connectivity (EC) estimates, relying on a dynamical network model to replicate BOLD signals’ spatio-temporal structure, akin to functional connectivity (FC) with lagged correlations. We compared the estimated EC, FC, and SC links as features to train classifiers to predict behavioral conditions and group identity. Then, we performed a network-based analysis of anatomical connectivity. We demonstrated through a machine-learning approach that EC features were more informative than FC and SC solely. We showed that the most informative EC links that discriminated between meditators and controls involved several large-scale networks mainly within the left hemisphere. Moreover, we found that differences in the functional domain were reflected to a smaller extent in changes at the anatomical level as well. The network-based analysis of anatomical pathways revealed strengthened connectivity for meditators compared to controls between four areas in the left hemisphere belonging to the somatomotor, dorsal attention, subcortical and visual networks. Overall, the results of our whole-brain model-based approach revealed a mechanism underlying meditation by providing causal relationships at the structure-function level.

Increased Basal Ganglia Modulatory Effective Connectivity Observed in Resting-State fMRI in Individuals With Parkinson's Disease.

Alterations to interactions between networked brain regions underlie cognitive impairment in many neurodegenerative diseases, providing an important physiological link between brain structure and cognitive function. Previous attempts to characterize the effects of Parkinson’s disease (PD) on network functioning using resting-state functional magnetic resonance imaging (rs-fMRI), however, have yielded inconsistent and contradictory results. Potential problems with prior work arise in the specifics of how the area targeted by the diseases (the basal ganglia) interacts with other brain regions. Specifically, current computational models point to the fact that the basal ganglia contributions should be captured with modulatory (i.e., second-order) rather than direct (i.e., first-order) functional connectivity measures. Following this hypothesis, a principled but manageable large-scale brain architecture, the Common Model of Cognition, was used to identify differences in basal ganglia connectivity in PD by analyzing resting-state fMRI data from 111 participants (70 patients with PD; 41 healthy controls) using Dynamic Causal Modeling (DCM). Specifically, the functional connectivity of the basal ganglia was modeled as two second-level, modulatory connections that control projections from sensory cortices to the prefrontal cortex, and from the hippocampus and medial temporal lobe to the prefrontal cortex. We then examined group differences between patients with PD and healthy controls in estimated modulatory effective connectivity in these connections. The Modulatory variant of the Common Model of Cognition outperformed the Direct model across all subjects. It was also found that these second-level modulatory connections had higher estimates of effective connectivity in the PD group compared to the control group, and that differences in effective connectivity were observed for all direct connections between the PD and control groups.We make the case that accounting for modulatory effective connectivity better captures the effects of PD on network functioning and influences the interpretation of the directionality of the between-group results. Limitations include that the PD group was scanned on dopaminergic medication, results were derived from a reasonable but small number of individuals and the ratio of PD to healthy control participants was relatively unbalanced. Future research will examine if the observed effect holds for individuals with PD scanned off their typical dopaminergic medications.

Recursive Estimation of Multichannel Autoregressive Processes in Correlated Noise With Joint Instrumental Variable and Bias Compensation

This paper proposes a new recursive algorithm for estimating multichannel autoregressive (AR) processes in spatially correlated noise using joint extended instrumental variable (EIV) and bias compensation (BC). A weighted least squares solution (WLS) for solving the Yule-Walker (YW) equations from EIV and BC is proposed, while the noise covariance parameters is estimated via the least squares method. A splitting approach is proposed for solving this WLS problem based on matrix splitting, and it is further extended to a recursive algorithm, which can be solved via the variable forgetting factor (VFF)-EIV algorithm. A robust smoothing method for estimating the noise parameters and an adaptive model selection method for controlling the BC contribution are proposed for reducing the estimation variance. The validity of the proposed algorithm is evaluated using both synthetic and real data. Experimental results show that the proposed VFF-EBC algorithm gives higher accuracy than conventional recursive least squares (RLS) algorithm and the VFF-EIV method. It also provides faster tracking speed under sudden changes. The proposed method is applied to the BCI competition IV-2b EEG data set on motor imagery tasks for spectrum and effective connectivity estimation. The high-alpha and beta event-related desynchronization associated with the tasks can be clearly revealed. It was also applied to an auditory odd-ball data from the Open-fMRI database.

Promises and pitfalls of topological data analysis for brain connectivity analysis

Developing sensitive and reliable methods to distinguish normal and abnormal brain states is a key neuroscientific challenge. Topological Data Analysis, despite its relative novelty, already generated many promising applications, including in neuroscience. We conjecture its prominent tool of persistent homology may benefit from going beyond analysing structural and functional connectivity to effective connectivity graphs capturing the direct causal interactions or information flows. Therefore, we assess the potential of persistent homology to directed brain network analysis by testing its discriminatory power in two distinctive examples of disease-related brain connectivity alterations: epilepsy and schizophrenia. We estimate connectivity from functional magnetic resonance imaging and electrophysiology data, employ Persistent Homology and quantify its ability to distinguish healthy from diseased brain states by applying a support vector machine to features quantifying persistent homology structure.We show how this novel approach compares to classification using standard undirected approaches and original connectivity matrices. In the schizophrenia classification, topological data analysis generally performs close to random, while classifications from raw connectivity perform substantially better; potentially due to topographical, rather than topological, specificity of the differences. In the easier task of seizure discrimination from scalp electroencephalography data, classification based on persistent homology features generally reached comparable performance to using raw connectivity, albeit with typically smaller accuracies obtained for the directed (effective) connectivity compared to the undirected (functional) connectivity. Specific applications for topological data analysis may open when direct comparison of connectivity matrices is unsuitable - such as for intracranial electrophysiology with individual number and location of measurements. While standard homology performed overall better than directed homology, this could be due to notorious technical problems of accurate effective connectivity estimation.

Regression dynamic causal modeling for resting‐state fMRI

“Resting‐state” functional magnetic resonance imaging (rs‐fMRI) is widely used to study brain connectivity. So far, researchers have been restricted to measures of functional connectivity that are computationally efficient but undirected, or to effective connectivity estimates that are directed but limited to small networks. Here, we show that a method recently developed for task‐fMRI—regression dynamic causal modeling (rDCM)—extends to rs‐fMRI and offers both directional estimates and scalability to whole‐brain networks. First, simulations demonstrate that rDCM faithfully recovers parameter values over a wide range of signal‐to‐noise ratios and repetition times. Second, we test construct validity of rDCM in relation to an established model of effective connectivity, spectral DCM. Using rs‐fMRI data from nearly 200 healthy participants, rDCM produces biologically plausible results consistent with estimates by spectral DCM. Importantly, rDCM is computationally highly efficient, reconstructing whole‐brain networks (>200 areas) within minutes on standard hardware. This opens promising new avenues for connectomics.

Whole-brain estimates of directed connectivity for human connectomics

Connectomics is essential for understanding large-scale brain networks but requires that individual connection estimates are neurobiologically interpretable. In particular, a principle of brain organization is that reciprocal connections between cortical areas are functionally asymmetric. This is a challenge for fMRI-based connectomics in humans where only undirected functional connectivity estimates are routinely available. By contrast, whole-brain estimates of effective (directed) connectivity are computationally challenging, and emerging methods require empirical validation.Here, using a motor task at 7T, we demonstrate that a novel generative model can infer known connectivity features in a whole-brain network (>200 regions, >40,000 connections) highly efficiently. Furthermore, graph-theoretical analyses of directed connectivity estimates identify functional roles of motor areas more accurately than undirected functional connectivity estimates. These results, which can be achieved in an entirely unsupervised manner, demonstrate the feasibility of inferring directed connections in whole-brain networks and open new avenues for human connectomics.

The effect of global signal regression on DCM estimates of noise and effective connectivity from resting state fMRI

The influence of global BOLD fluctuations on resting state functional connectivity in fMRI data remains a topic of debate, with little consensus. In this study, we assessed the effects of global signal regression (GSR) on effective connectivity within and between resting state networks (RSNs) - as estimated with dynamic causal modelling (DCM) for resting state fMRI (rsfMRI). DCM incorporates a forward (generative) model that quantifies the contribution of different types of noise (including global measurement noise), effective connectivity, and (neuro)vascular processes to functional connectivity measurements. DCM analyses were applied to two different designs; namely, longitudinal and cross-sectional designs. In the modelling of longitudinal designs, we considered four extensive longitudinal resting state fMRI datasets with a total number of 20 subjects. In the analysis of cross-sectional designs, we used rsfMRI data from 361 subjects from the Human Connectome Project. We hypothesized that (1) GSR would have no discernible impact on effective connectivity estimated with DCM, and (2) GSR would be reflected in the parameters representing global measurement noise. Additionally, we performed comparative analyses of information gain with and without GSR. Our results showed negligible to small effects of GSR on effective connectivity within small (separately estimated) RSNs. However, although the effect sizes were small, there was substantial to conclusive evidence for an effect of GSR on connectivity parameters. For between-network connectivity, we found two important effects: the effect of GSR on between-network effective connectivity (averaged over all connections) was negligible to small, while the effect of GSR on individual connections was non-negligible. In the cross-sectional (but not in the longitudinal) data, some connections showed substantial to conclusive evidence for an effect of GSR. Contrary to our expectations, we found either no effect (in the longitudinal designs) or a non-specific (cross-sectional design) effect of GSR on parameters characterising (global) measurement noise. Data without GSR were found to be more informative than data with GSR; however, in small resting state networks the precision of posterior estimates was greater after GSR. In conclusion, GSR is a minor concern in DCM studies; however, quantitative interpretation of between-network connections (as opposed to average between-network connectivity) and noise parameters should be treated with some caution. The Kullback-Leibler divergence of the posterior from the prior (i.e., information gain) - together with the precision of posterior estimates - might offer a useful measure to assess the appropriateness of GSR in resting state fMRI.

Deep fuzzy model for non-linear effective connectivity estimation in the intuition of consciousness correlates

The brain connectivity, as a promising technique to explore brain networks during resting-states or cognitive tasks, has been employed remarkably in recent years. The aim of this study is to propose a new approach to improve the Granger causality as one of the fundamental methods for calculation of brain effective connectivity. To this end, we utilized a deep fuzzy structure to model the multivariate autoregressive used in the Granger causality. The proposed model benefits from the hierarchical stacked structure where first – order TSK fuzzy rules are the cores of the network. In the first layer of the stacked structure, the antecedents of the fuzzy rules are extracted from the fuzzy clustering of the input space. For subsequent layers, due to the input perturbation which is caused by the previous layer output, a shuffling approach is adopted. To assess our proposed model, we applied it to two nonlinear synthetic time series and compared it with linear Granger. Results revealed that our model is superior in the detection of effective connectivity. We additionally exploit the pioneer model for one of the controversial concepts in cognitive neuroscience in recent years: the neural correlates of visual consciousness. We applied our method to detect connectivity networks of EEG in consciousness states. Our results demonstrated that the proposed nonlinear connectivity estimator was capable of detecting novel correlates: significant differences have been observed among different states of consciousness, not only in presence of attention, as the linear method detected it, but also in absence of attention.

Effective brain connectivity estimation between active brain regions in autism using the dual Kalman-based method.

Brain connectivity estimation is a useful method to study brain functions and diagnose neuroscience disorders. Effective connectivity is a subdivision of brain connectivity which discusses the causal relationship between different parts of the brain. In this study, a dual Kalman-based method is used for effective connectivity estimation. Because of connectivity changes in autism, the method is applied to autistic signals for effective connectivity estimation. For method validation, the dual Kalman based method is compared with other connectivity estimation methods by estimation error and the dual Kalman-based method gives acceptable results with less estimation errors. Then, connectivities between active brain regions of autistic and normal children in the resting state are estimated and compared. In this simulation, the brain is divided into eight regions and the connectivity between regions and within them is calculated. It can be concluded from the results that in the resting state condition the effective connectivity of active regions is decreased between regions and is increased within each region in autistic children. In another result, by averaging the connectivity between the extracted active sources of each region, the connectivity between the left and right of the central part is more than that in other regions and the connectivity in the occipital part is less than that in others.

Bypassing the volume conduction effect by multilayer neural network for effective connectivity estimation.

Differentiation of real interactions between different brain regions from spurious ones has been a challenge in neuroimaging researches. While using electroencephalographic data, those spurious interactions are mostly caused by the volume conduction (VC) effect between the recording sites. In this study, we address the problem by jointly modeling the causal relationships among brain regions and the mixing effects of volume conduction. The VC effect is formulated with a time-invariant linear equation, and the causal relationships between the brain regions are modeled with a nonlinear multivariate autoregressive process. These two models are simultaneously implemented by a multilayer neural network. The internal hidden layers represent the interactions among the regions, while the external layers are devoted for the relationship between the source activities and observed EEG measurements at the scalp. The causal interactions are estimated by the causality coefficient measure, which is based on the information (weights and parameters) embedded in the network. The proposed method is verified using various simulated data. It is then applied to the real EEG signals collected from a memory retrieval test. The results showed that the method is able to eliminate the volume conduction interferences and consequently leads to higher accuracy in identification of true causal interactions. Graphical abstract The proposed network structure used to simultaneously model the volume conduction and source interactions. By this special structure, we first move from the sensor space to the source space at the first layer. Then, within internal hidden layers, the interactions between the sources are represented in the form of a general (nonlinear) multivariate autoregressive (nMVAR) model. Finally, we return from the source space to the sensor space at the last layer of the network. The proposed method bypasses the effect of volume conduction and causes more accurate connectivity estimation.