A conditional Granger causality model approach for group analysis in functional magnetic resonance imaging

Granger causality model (GCM) derived from multivariate vector autoregressive models of data has been employed to identify effective connectivity in the human brain with functional magnetic resonance imaging (fMRI) and to reveal complex temporal and spatial dynamics underlying a variety of cognitive processes. In the most recent fMRI effective connectivity measures, pair-wise GCM has commonly been applied based on single-voxel values or average values from special brain areas at the group level. Although a few novel conditional GCM methods have been proposed to quantify the connections between brain areas, our study is the first to propose a viable standardized approach for group analysis of fMRI data with GCM. To compare the effectiveness of our approach with traditional pair-wise GCM models, we applied a well-established conditional GCM to preselected time series of brain regions resulting from general linear model (GLM) and group spatial kernel independent component analysis of an fMRI data set in the temporal domain. Data sets consisting of one task-related and one resting-state fMRI were used to investigate connections among brain areas with the conditional GCM method. With the GLM-detected brain activation regions in the emotion-related cortex during the block design paradigm, the conditional GCM method was proposed to study the causality of the habituation between the left amygdala and pregenual cingulate cortex during emotion processing. For the resting-state data set, it is possible to calculate not only the effective connectivity between networks but also the heterogeneity within a single network. Our results have further shown a particular interacting pattern of default mode network that can be characterized as both afferent and efferent influences on the medial prefrontal cortex and posterior cingulate cortex. These results suggest that the conditional GCM approach based on a linear multivariate vector autoregressive model can achieve greater accuracy in detecting network connectivity than the widely used pair-wise GCM, and this group analysis methodology can be quite useful to extend the information obtainable in fMRI.     

Investigating the neural basis for fMRI-based functional connectivity in a blocked design: application to interregional correlations and psycho-physiological interactions

This paper investigates how well different kinds of fMRI functional connectivity analysis reflect the underlying interregional neural interactions. This is hard to evaluate using real experimental data where such relationships are unknown. Rather, we use a biologically realistic neural model to simulate both neuronal activities and multiregional fMRI data from a blocked design. Because we know how every element in the model is related to every other element, we can compare functional connectivity measurements across different spatial and temporal scales. We focus on (1) psycho-physiological interaction (PPI) analysis, which is a simple brain connectivity method that characterizes the activity in one brain region by the interaction between another region's activity and a psychological factor, and (2) interregional correlation analysis. We investigated the neurobiological underpinnings of PPI using simulated neural activities and fMRI signals generated by a large-scale neural model that performs a visual delayed match-to-sample task. Simulated fMRI data are generated by convolving integrated synaptic activities (ISAs) with a hemodynamic response function. The simulation was done under three task conditions: high-attention, low-attention and a control task ('passive viewing'). We investigated how biological and scanning parameters affect PPI and compared these with functional connectivity measures obtained using correlation analysis. We performed correlational and PPI analyses with three types of time-series data: ISA, fMRI and deconvolved fMRI (which yields estimated neural signals) obtained using a deconvolution algorithm. The simulated ISA can be considered as the 'gold standard' because it represents the underlying neural activity. Our main findings show (1) that evaluating the change in an interregional functional connection using the difference in regression coefficients (as is essentially done in the PPI method) produces results that better reflect the underlying changes in neural interrelationships than does evaluating the functional connectivity difference as a change in correlation coefficient; (2) that using fMRI and deconvolved fMRI data led to similar conclusions in the PPI-based functional connectivity results, and these generally agreed with the nature of the underlying neural interactions; and (3) the functional connectivity correlation measures often led to different conclusions regarding significance for different scanning and hemodynamic parameters, but the significances of the PPI regression parameters were relatively robust. These results highlight the way in which neural modeling can be used to help validate the inferences one can make about functional connectivity based on fMRI data.     

Estimation of the effective and functional human cortical connectivity with structural equation modeling and directed transfer function applied to high-resolution EEG

Different brain imaging devices are presently available to provide images of the human functional cortical activity, based on hemodynamic, metabolic or electromagnetic measurements. However, static images of brain regions activated during particular tasks do not convey the information of how these regions are interconnected. The concept of brain connectivity plays a central role in the neuroscience, and different definitions of connectivity, functional and effective, have been adopted in literature. While the functional connectivity is defined as the temporal coherence among the activities of different brain areas, the effective connectivity is defined as the simplest brain circuit that would produce the same temporal relationship as observed experimentally among cortical sites. The structural equation modeling (SEM) is the most used method to estimate effective connectivity in neuroscience, and its typical application is on data related to brain hemodynamic behavior tested by functional magnetic resonance imaging (fMRI), whereas the directed transfer function (DTF) method is a frequency-domain approach based on both a multivariate autoregressive (MVAR) modeling of time series and on the concept of Granger causality.

This study presents advanced methods for the estimation of cortical connectivity by applying SEM and DTF on the cortical signals estimated from high-resolution electroencephalography (EEG) recordings, since these signals exhibit a higher spatial resolution than conventional cerebral electromagnetic measures. To estimate correctly the cortical signals, we used a subject's multicompartment head model (scalp, skull, dura mater, cortex) constructed from individual MRI, a distributed source model and a regularized linear inverse source estimates of cortical current density. Before the application of SEM and DTF methodology to the cortical waveforms estimated from high-resolution EEG data, we performed a simulation study, in which different main factors (signal-to-noise ratio, SNR, and simulated cortical activity duration, LENGTH) were systematically manipulated in the generation of test signals, and the errors in the estimated connectivity were evaluated by the analysis of variance (ANOVA). The statistical analysis returned that during simulations, both SEM and DTF estimators were able to correctly estimate the imposed connectivity patterns under reasonable operative conditions, that is, when data exhibit an SNR of at least 3 and a LENGTH of at least 75 s of nonconsecutive EEG recordings at 64 Hz of sampling rate.

Hence, effective and functional connectivity patterns of cortical activity can be effectively estimated under general conditions met in any practical EEG recordings, by combining high-resolution EEG techniques and linear inverse estimation with SEM or DTF methods. We conclude that the estimation of cortical connectivity can be performed not only with hemodynamic measurements, but also with EEG signals treated with advanced computational techniques.     

A novel approach for fMRI data analysis based on the combination of sparse approximation and affinity propagation clustering

Clustering analysis has been widely used to detect the functional connectivity from functional magnetic resonance imaging (fMRI) data. However, it has some limitations such as enormous computer memory requirement, and difficulty in estimating the number of clusters. In this study, in order to effectually resolve the deficiencies mentioned above, we have proposed a novel approach (SAAPC) for fMRI data analysis, which combines sparsity, an effective assumption for analyzing fMRI signal, with affinity propagation clustering (APC).     

Combining independent component analysis and correlation analysis to probe interregional connectivity in fMRI task activation datasets

A new approach in studying interregional functional connectivity using functional magnetic resonance imaging (fMRI) is presented. Functional connectivity may be detected by means of cross correlating time course data from functionally related brain regions. These data exhibit high temporal coherence of low frequency fluctuations due to synchronized blood flow changes. In the past, this fMRI technique for studying functional connectivity has been applied to subjects that performed no prescribed task ("resting" state). This paper presents the results of applying the same method to task-related activation datasets. Functional connectivity analysis is first performed in areas not involved with the task. Then a method is devised to remove the effects of activation from the data using independent component analysis (ICA) and functional connectivity analysis is repeated. Functional connectivity, which is demonstrated in the "resting brain," is not affected by tasks which activate unrelated brain regions. In addition, ICA effectively removes activation from the data and may allow us to study functional connectivity even in the activated regions.     

静息状态下脑功能连接的磁共振成像研究

静息状态下脑功能连接的磁共振成像研究近年来取得了迅猛发展. 通过对fMRI信号低频涨落成分的同步性分析,可以得到大脑静息态任意脑区的功能连接和多套网络系统,其中“默认网络”的发现可能为人脑固有网络的研究提供新的思路. 而静息态网络与解剖连接之间可能存在的对应,以及在神经精神疾病患者脑中性质和连接的异常改变,使其具有重要的研究和临床应用价值. 该文总结了静息状态功能磁共振成像的主要研究成果,对静息状态脑功能网络的发现和发展、研究方法、各网络及其特点以及在临床方面的应用进行简单的介绍和分析.     

Hierarchical clustering to measure connectivity in fMRI resting-state data

Low frequency oscillations, which are temporally correlated in functionally related brain regions, characterize the mammalian brain, even when no explicit cognitive tasks are performed. Functional connectivity MR imaging is used to map regions of the resting brain showing synchronous, regional and slow fluctuations in cerebral blood flow and oxygenation. In this study, we use a hierarchical clustering method to detect similarities of low-frequency fluctuations. We describe one measure of correlations in the low frequency range for classification of resting-state fMRI data. Furthermore, we investigate the contribution of motion and hardware instabilities to resting-state correlations and provide a method to reduce artifacts. For all cortical regions studied and clusters obtained, we quantify the degree of contamination of functional connectivity maps by the respiratory and cardiac cycle. Results indicate that patterns of functional connectivity can be obtained with hierarchical clustering that resemble known neuronal connections. The corresponding voxel time series do not show significant correlations in the respiratory or cardiac frequency band.     

Independent component model of the default-mode brain function: combining individual-level and population-level analyses in resting-state fMRI

Resting-state functional magnetic resonance imaging (RS-fMRI) is a technique used to investigate the spontaneous correlations of blood-oxygen-level-dependent signals across different regions of the brain. Using functional connectivity tools, it is possible to investigate a specific RS-fMRI network, referred to as "default-mode" (DM) network, that involves cortical regions deactivated in fMRI experiments with cognitive tasks. Previous works have reported a significant effect of aging on DM regions activity. Independent component analysis (ICA) is often used for generating spatially distributed DM functional connectivity patterns from RS-fMRI data without the need for a reference region. This aspect and the relatively easy setup of an RS-fMRI experiment even in clinical trials have boosted the combined use of RS-fMRI and ICA-based DM analysis for noninvasive research of brain disorders. In this work, we considered different strategies for combining ICA results from individual-level and population-level analyses and used them to evaluate and predict the effect of aging on the DM component. Using RS-fMRI data from 20 normal subjects and a previously developed group-level ICA methodology, we generated group DM maps and showed that the overall ICA-DM connectivity is negatively correlated with age. A negative correlation of the ICA voxel weights with age existed in all DM regions at a variable degree. As an alternative approach, we generated a distributed DM spatial template and evaluated the correlation of each individual DM component fit to this template with age. Using a "leave-one-out" procedure, we discuss the importance of removing the bias from the DM template-generation process.     

Functional connectivity in the rat brain: a complex network approach

Functional connectivity analyses of fMRI data can provide a wealth of information on the brain functional organization and have been widely applied to the study of the human brain. More recently, these methods have been extended to preclinical species, thus providing a powerful translational tool. Here, we review methods and findings of functional connectivity studies in the rat. More specifically, we focus on correlation analysis of pharmacological MRI (phMRI) responses, an approach that has enabled mapping the patterns of connectivity underlying major neurotransmitter systems in vivo. We also review the use of novel statistical approaches based on a network representation of the functional connectivity and their application to the study of the rat brain functional architecture.     

Multivariate Gaussian Copula Mutual Information to Estimate Functional Connectivity with Less Random Architecture

Recognition of a brain region’s interaction is an important field in neuroscience. Most studies use the Pearson correlation to find the interaction between the regions. According to the experimental evidence, there is a nonlinear dependence between the activities of different brain regions that is ignored by Pearson correlation as a linear measure. Typically, the average activity of each region is used as input because it is a univariate measure. This dimensional reduction, i.e., averaging, leads to a loss of spatial information across voxels within the region. In this study, we propose using an information-theoretic measure, multivariate mutual information (mvMI), as a nonlinear dependence to find the interaction between regions. This measure, which has been recently proposed, simplifies the mutual information calculation complexity using the Gaussian copula. Using simulated data, we show that the using this measure overcomes the mentioned limitations. Additionally using the real resting-state fMRI data, we compare the level of significance and randomness of graphs constructed using different methods. Our results indicate that the proposed method estimates the functional connectivity more significantly and leads to a smaller number of random connections than the common measure, Pearson correlation. Moreover, we find that the similarity of the estimated functional networks of the individuals is higher when the proposed method is used.     

Biophysical and neural basis of resting state functional connectivity: Evidence from non-human primates

Functional MRI (fMRI) has evolved from simple observations of regional changes in MRI signals caused by cortical activity induced by a task or stimulus, to task-free acquisitions of images in a resting state. Such resting state signals contain low frequency fluctuations which may be correlated between voxels, and strongly correlated regions are deemed to reflect functional connectivity within synchronized circuits. Resting state functional connectivity (rsFC) measures have been widely adopted by the neuroscience community, and are being used and interpreted as indicators of intrinsic neural circuits and their functional states in a broad range of applications, both basic and clinical. However, there has been relatively little work reported that validates whether inter-regional correlations in resting state fluctuations of fMRI (rsfMRI) signals actually measure functional connectivity between brain regions, or to establish how MRI data correlate with other metrics of functional connectivity. In this mini-review, we summarize recent studies of rsFC within mesoscopic scale cortical networks (100 μm–10 mm) within a well defined functional region of primary somatosensory cortex (S1), as well as spinal cord and brain white matter in non-human primates, in which we have measured spatial patterns of resting state correlations and validated their interpretation with electrophysiological signals and anatomic connections. Moreover, we emphasize that low frequency correlations are a general feature of neural systems, as evidenced by their presence in the spinal cord as well as white matter. These studies demonstrate the valuable role of high field MRI and invasive measurements in an animal model to inform the interpretation of human imaging studies.     

Functional MRI and multivariate autoregressive models

Connectivity refers to the relationships that exist between different regions of the brain. In the context of functional magnetic resonance imaging (fMRI), it implies a quantifiable relationship between hemodynamic signals from different regions. One aspect of this relationship is the existence of small timing differences in the signals in different regions. Delays of 100 ms or less may be measured with fMRI, and these may reflect important aspects of the manner in which brain circuits respond as well as the overall functional organization of the brain. The multivariate autoregressive time series model has features to recommend it for measuring these delays and is straightforward to apply to hemodynamic data. In this review, we describe the current usage of the multivariate autoregressive model for fMRI, discuss the issues that arise when it is applied to hemodynamic time series and consider several extensions. Connectivity measures like Granger causality that are based on the autoregressive model do not always reflect true neuronal connectivity; however, we conclude that careful experimental design could make this methodology quite useful in extending the information obtainable using fMRI.     

Anatomical correlates of the functional organization in the human occipitotemporal cortex

The connectivity between functionally distinct areas in the human brain is unknown because of the limitations posed by current postmortem anatomical labeling techniques. Diffusion tensor imaging (DTI) has previously been used to define large white matter tracts based on well-known anatomical landmarks in the living human brain. In the present study, we used DTI coupled with functional magnetic resonance imaging (fMRI) to assess neuronal connections between human striate and functionally defined extrastriate ventral cortical areas. Functional areas were identified with conventional fMRI mapping procedures and then used as seeding points in a DTI analysis to ascertain connectivity patterns between cortical areas, thus yielding the pattern of connections between human occipitoventral visual areas in vivo.     

A SVM-based quantitative fMRI method for resting-state functional network detection

Resting-state functional magnetic resonance imaging (fMRI) aims to measure baseline neuronal connectivity independent of specific functional tasks and to capture changes in the connectivity due to neurological diseases. Most existing network detection methods rely on a fixed threshold to identify functionally connected voxels under the resting state. Due to fMRI non-stationarity, the threshold cannot adapt to variation of data characteristics across sessions and subjects, and generates unreliable mapping results. In this study, a new method is presented for resting-state fMRI data analysis. Specifically, the resting-state network mapping is formulated as an outlier detection process that is implemented using one-class support vector machine (SVM). The results are refined by using a spatial-feature domain prototype selection method and two-class SVM reclassification. The final decision on each voxel is made by comparing its probabilities of functionally connected and unconnected instead of a threshold. Multiple features for resting-state analysis were extracted and examined using an SVM-based feature selection method, and the most representative features were identified. The proposed method was evaluated using synthetic and experimental fMRI data. A comparison study was also performed with independent component analysis (ICA) and correlation analysis. The experimental results show that the proposed method can provide comparable or better network detection performance than ICA and correlation analysis. The method is potentially applicable to various resting-state quantitative fMRI studies.     

Fine-scale functional connectivity in somatosensory cortex revealed by high-resolution fMRI

High-resolution functional magnetic resonance imaging (fMRI) at high field (9.4 T) has been used to measure functional connectivity between subregions within the primary somatosensory (SI) cortex of the squirrel monkey brain. The hand-face region within the SI cortex of the squirrel monkey has been previously well mapped with functional imaging and electrophysiological and anatomical methods, and the orderly topographic map of the hand region is characterized by a lateral to medial representation of individual digits in four subregions of areas 3a, 3b, 1 and 2. With submillimeter resolution, we are able to detect not only the separate islands of activation corresponding to vibrotactile stimulations of single digits but also, in subsequent acquisitions, the degree of correlation between voxels within the SI cortex in the resting state. The results suggest that connectivity patterns are very similar to stimulus-driven distributions of activity and that connectivity varies on the scale of millimeters within the same primary region. Connectivity strength is not a reflection of global larger-scale changes in blood flow and is not directly dependent on distance between regions. Preliminary electrophysiological recordings agree well with the fMRI data. In human studies at 7 T, high-resolution fMRI may also be used to identify the same subregions and assess responses to sensory as well as painful stimuli, and to measure connectivity dynamically before and after such stimulations.     

Single-subject manual independent component analysis and resting state fMRI connectivity outcomes in patients with juvenile absence epilepsy

The quality of fMRI data impacts functional connectivity measures and consequently, the decisions that clinicians and researchers make regarding functional connectivity interpretation. The present study used resting state fMRI to investigate resting state network connectivity in a sample of patients with Juvenile Absence Epilepsy. Single-subject manual independent component analysis was used in two levels, whereby all noise components were removed, and cerebrospinal fluid pulsation components only were isolated and removed. Improved temporal signal to noise ratios and functional connectivity metrics were observed in each of the cleaning levels for both epilepsy and control cohorts. Results showed full, single-subject manual independent component analysis reduced the number of functional connectivity correlations and increased the strength of these correlations. Similar effects were also observed for the cerebrospinal fluid pulsation only cleaned data relative to the uncleaned, and fully cleaned data. Single-subject manual independent component analysis coupled with short TR multiband acquisition can significantly improve the validity of findings derived from fMRI data sets.     

Disrupted functional connectivity in social anxiety disorder: a resting-state fMRI study

Dysfunction of the corticolimbic circuitry has been highlighted in social anxiety disorder (SAD) during social stimuli. However, few studies have investigated functional connectivity in SAD during the resting state, which may improve our understanding of SAD pathophysiology. The aim of this study was to investigate whether whole-brain functional connectivity might be aberrant in SAD patients, and if so, whether these changes are related to the measured clinical severity. Seventeen SAD patients and 19 healthy controls participated in resting-state functional magnetic resonance imaging. The brain was first divided into 90 paired brain regions and functional connectivity was then estimated by temporal correlation between each of these regions. Furthermore, connections that were significantly disrupted in SAD patients were correlated with clinical severity measured using the Liebowitz Social Anxiety Scale. Compared with healthy controls, SAD patients showed decreased positive connections within the frontal lobe and decreased negative connections between the frontal and occipital lobes. In particular, the weaker negative connections between the frontal lobe, which mainly involved the right median prefrontal cortex, and the occipital lobe had a significant positive correlation with the severity of SAD symptoms. The results support the hypothesis that some abnormalities of functional connectivity exist in SAD patients, which relate to the frontal cortex and occipital cortex. In addition, decreased functional connectivity between the frontal and occipital lobes and within the frontal lobe might be related to abnormal information processing and reflect disturbed neural organization resulting in defective social cognition, which could represent an early imaging biomarker for SAD.     

Images-based suppression of unwanted global signals in resting-state functional connectivity studies

Correlated fluctuations of low-frequency fMRI signal have been suggested to reflect functional connectivity among the involved regions. However, large-scale correlations are especially prone to spurious global modulations induced by coherent physiological noise. Cardiac and respiratory rhythms are the most offending component, and a tailored preprocessing is needed in order to reduce their impact. Several approaches have been proposed in the literature, generally based on the use of physiological recordings acquired during the functional scans, or on the extraction of the relevant information directly from the images. In this paper, the performances of the denoising approach based on general linear fitting of global signals of noninterest extracted from the functional scans were assessed. Results suggested that this approach is sufficiently accurate for the preprocessing of functional connectivity data.     

A simple and fast technique for on-line fMRI data analysis

In the present work a simple technique for fMRI data analysis is presented. Artifacts due to random and stimulus-correlated motions are corrected without image registration procedures. The first step of our procedure is the calculation of the raw activation map by correlation analysis. The task related motion artifacts arise at the tissue interfaces, including vessels: when image intensity gradient is calculated the high values correspond to interface regions. To eliminate stimulus-correlated motion artifacts the intensity gradient image, obtained from the fMRI data set, is compared to the raw activation map. Since small random motions decrease the value of the correlation coefficient (R) of the external pixels of the activation areas, in the last step of our analysis procedures the clusters are extended to connected pixels having R values smaller than the defined threshold. Each cluster is expanded until the R value of the cluster average intensity is kept constant. The procedure has been tested with both GRE and EPI studies. The presented approach is a fast and robust technique useful for preliminary or on-line analysis of fMRI data.     

The role of nonlinearity in computing graph-theoretical properties of resting-state functional magnetic resonance imaging brain networks

In recent years, there has been an increasing interest in the study of large-scale brain activity interaction structure from the perspective of complex networks, based on functional magnetic resonance imaging (fMRI) measurements. To assess the strength of interaction (functional connectivity, FC) between two brain regions, the linear (Pearson) correlation coefficient of the respective time series is most commonly used. Since a potential use of nonlinear FC measures has recently been discussed in this and other fields, the question arises whether particular nonlinear FC measures would be more informative for the graph analysis than linear ones. We present a comparison of network analysis results obtained from the brain connectivity graphs capturing either full (both linear and nonlinear) or only linear connectivity using 24 sessions of human resting-state fMRI. For each session, a matrix of full connectivity between 90 anatomical parcel time series is computed using mutual information. For comparison, connectivity matrices obtained for multivariate linear Gaussian surrogate data that preserve the correlations, but remove any nonlinearity are generated. Binarizing these matrices using multiple thresholds, we generate graphs corresponding to linear and full nonlinear interaction structures. The effect of neglecting nonlinearity is then assessed by comparing the values of a range of graph-theoretical measures evaluated for both types of graphs. Statistical comparisons suggest a potential effect of nonlinearity on the local measures-clustering coefficient and betweenness centrality. Nevertheless, subsequent quantitative comparison shows that the nonlinearity effect is practically negligible when compared to the intersubject variability of the graph measures. Further, on the group-average graph level, the nonlinearity effect is unnoticeable.