Principle of structural equation modeling for exploring functional interactivity within a putative network of interconnected brain areas

Functional neuroimaging first allowed researchers to describe the functional segregation of regionally activated areas during a variety of experimental tasks. More recently, functional integration studies have described how these functionally specialized areas, interact within a highly distributed neural network. When applied to the field of neurosciences, structural equation modeling (SEM) uses theoretical and/or empirical hypotheses to estimate the effects of an experimental task within a putative network. SEM represents a linear technique for multivariate analysis of neuroimaging data and has been developed to simultaneously examine ratios of multiple causality in an experimental design; the method attempts to explain a covariance structure within an anatomical constrained model. This method, when combined with the concept of effective connectivity, can provide information on the strength and direction of the functional interactions that take place between identified brain regions of a putative network.     

Rate dependence of human visual cortical response due to brief stimulation: an event-related fMRI study

The human brain response to a wide range of visual stimulus rates presented over a prolonged time period has been investigated by various neuroimaging techniques. However, to date, no imaging study has been performed to study the dynamic human brain response to various stimulus rates when presented in a short time. This report describes activation in the human brain due to brief visual stimulus presentation (1 s) for stimulus rates varying from 1 to 20 Hz using event-related functional MRI (fMRI). Our results show that the amplitude of the fMRI response increases with the stimulus frequency and plateaus at 6 Hz. This finding differs slightly from the results of previous blocked task paradigm experiments (with a longer time of stimulus presentation), in which the response peaks at approximately 8 Hz and then decreases. Our results are in close agreement with previously published psychophysical studies, suggesting that the fMRI signal in this experiment is indicative of cortical activity related to visual processing.     

Investigation of the large-scale functional brain networks modulated by acupuncture

Previous neuroimaging studies have primarily focused on the neural activities involving the acute effects of acupuncture. Considering that acupuncture can induce long-lasting effects, several researchers have begun to pay attention to the sustained effects of acupuncture on the resting brain. Most of these researchers adopted functional connectivity analysis based on one or a few preselected brain regions and demonstrated various function-guided brain networks underlying the specific effect of acupuncture. Few have investigated how these brain networks interacted at the whole-brain level. In this study, we sought to investigate the functional correlations throughout the entire brain following acupuncture at acupoint ST36 (ACUP) in comparison with acupuncture at nearby nonacupoint (SHAM). We divided the whole brain into 90 regions and constructed functional brain network for each condition. Then we examined the network hubs and identified statistically significant differences in functional correlations between the two conditions. Following ACUP, but not SHAM, the limbic/paralimbic regions such as the amygdala, hippocampus and anterior cingulate gyrus emerged as network hubs. For direct comparisons, increased correlations for ACUP compared to SHAM were primarily related with the limbic/paralimbic and subcortical regions such as the insula, amygdala, anterior cingulate gyrus, and thalamus, whereas decreased correlations were mainly related with the sensory and frontal cortex. The heterogeneous modulation patterns between the two conditions may relate to the functional specific modulatory effects of acupuncture. The preliminary findings may help us to better understand the long-lasting effects of acupuncture on the entire resting brain, as well as the neurophysiological mechanisms underlying acupuncture.     

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.     

Community structure and modularity in networks of correlated brain activity

Functional connectivity patterns derived from neuroimaging data may be represented as graphs or networks, with individual image voxels or anatomically-defined structures representing the nodes, and a measure of correlation between the responses in each pair of nodes determining the edges. This explicit network representation allows network-analysis approaches to be applied to the characterization of functional connections within the brain. Much recent research in complex networks has focused on methods to identify community structure, i.e. cohesive clusters of strongly interconnected nodes. One class of such algorithms determines a partition of a network into 'sub-networks' based on the optimization of a modularity parameter, thus also providing a measure of the degree of segregation versus integration in the full network. Here, we demonstrate that a community structure algorithm based on the maximization of modularity, applied to a functional connectivity network calculated from the responses to acute fluoxetine challenge in the rat, can identify communities whose distributions correspond to anatomically meaningful structures and include compelling functional subdivisions in the brain. We also discuss the biological interpretation of the modularity parameter in terms of segregation and integration of brain function.     

In vivo mapping of functional domains and axonal connectivity in cat visual cortex using magnetic resonance imaging

Noninvasive cognitive neuroimaging studies based on functional magnetic resonance imaging (fMRI) are of ever-increasing importance for basic and clinical neurosciences. The explanatory power of fMRI could be greatly expanded, however, if the pattern of the neuronal circuitry underlying functional activation could be made visible in an equally noninvasive manner. In this study, blood oxygenation level-dependent (BOLD)-based fMRI and diffusion tensor imaging (DTI) were performed in the same cat visual cortex, and the foci of fMRI activation utilized as seeding points for 3D DTI fiber reconstruction algorithms, thus providing the map of the axonal circuitry underlying visual information processing. The methods developed in this study will lay the foundation for in vivo neuroanatomy and the ability for noninvasive longitudinal studies of brain development.     

Characterization of BOLD-fMRI signal during a verbal fluency paradigm in patients with intracerebral tumors affecting the frontal lobe

Previous studies have indicated that the BOLD-fMRI signal can be modified by tumor processes in close vicinity to functional brain areas. This effect has been investigated primarily for the perirolandic area but there is only a limited number of studies concerning frontal cortical regions. Therefore, the aim of the current study was to characterize BOLD-fMRI signal and activation patterns in patients with frontal brain tumors while performing a verbal fluency task. Six patients (ages 31-56 years) suffering from frontal (5 left sided and 1 right sided) intracerebral tumors were examined with fMRI while performing a verbal fluency task in a blocked paradigm design. Eight healthy volunteers served as the control group. The patients (5 right and 1 left handed) demonstrated left frontal activation which could be clearly located outside the tumor area and adjacent edema with varying degrees of additional right frontal activation. In the predominant left frontal activation cluster, the mean voxel based z-score and cluster size were not statistically different between patients and controls. The present fMRI study is indicating that language related BOLD signal changes in the frontal cortex of patients with tumors close to functional areas were comparable to the signal in normal controls. Additionally, the temporal hemodynamic response characteristic was comparable in both groups. This is an important finding consistent with PET results and corroborates the feasibility of functional mapping approaches in patients with tumors affecting the frontal lobe. Additional studies investigating alterations of the hemodynamic response depending on tumor location and histology are required in order to further elucidate the association between pathophysiology and BOLD fMRI signal.     

Sexual dimorphism in the human brain: evidence from neuroimaging

In recent years, more and more emphasis has been placed on the investigation of sex differences in the human brain. Noninvasive neuroimaging techniques represent an essential tool in the effort to better understand the effects of sex on both brain structure and function. In this review, we provide a comprehensive summary of the findings that were collected in human neuroimaging studies in vivo thus far: we explore sexual dimorphism in the human brain at the level of (1) brain structure, in both gray and white matter, observed by voxel-based morphometry (VBM) and diffusion tensor imaging (DTI), respectively; (2) baseline neural activity, studied using resting-state functional magnetic resonance imaging (rs-fMRI) and positron emission tomography (PET); (3) neurochemistry, visualized by means of neuroreceptor ligand PET; and (4) task-related neural activation, investigated using fMRI. Functional MRI findings from the literature are complemented by our own meta-analysis of fMRI studies on sex-specific differences in human emotional processing. Specifically, we used activation likelihood estimation (ALE) to provide a quantitative approach to mapping the consistency of neural networks involved in emotional processing across studies. The presented evidence for sex-specific differences in neural structure and function highlights the importance of modeling sex as a contributing factor in the analysis of brain-related data.     

Registering and analyzing rat fMRI data in the stereotaxic framework by exploiting intrinsic anatomical features

The value of analyzing neuroimaging data on a group level has been well established in human studies. However, there is no standard procedure for registering and analyzing functional magnetic resonance imaging (fMRI) data into common space in rodent fMRI studies. An approach for performing rat imaging data analysis in the stereotaxic framework is presented. This method is rooted in the biological observation that the skull shape and size of rat brain are essentially the same as long as their weights are within certain range. Registration is performed using rigid-body transformations without scaling or shearing, preserving the unique properties of the stable shape and size inherent in rat brain structure. Also, it does not require brain tissue masking and is not biased towards surface coil sensitivity profile. A standard rat brain atlas is used to facilitate the identification of activated areas in common space, allowing accurate region of interest analysis. This technique is evaluated from a group of rats (n=11) undergoing routine MRI scans; the registration accuracy is estimated to be within 400 μm. The analysis of fMRI data acquired with an electrical forepaw stimulation model demonstrates the utility of this technique. The method is implemented within the Analysis of Functional NeuroImages (AFNI) framework and can be readily extended to other studies.     

Integration of EEG source imaging and fMRI during continuous viewing of natural movies

Electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) are noninvasive neuroimaging tools which can be used to measure brain activity with excellent temporal and spatial resolution, respectively. By combining the neural and hemodynamic recordings from these modalities, we can gain better insight into how and where the brain processes complex stimuli, which may be especially useful in patients with different neural diseases. However, due to their vastly different spatial and temporal resolutions, the integration of EEG and fMRI recordings is not always straightforward. One fundamental obstacle has been that paradigms used for EEG experiments usually rely on event-related paradigms, while fMRI is not limited in this regard. Therefore, here we ask whether one can reliably localize stimulus-driven EEG activity using the continuously varying feature intensities occurring in natural movie stimuli presented over relatively long periods of time. Specifically, we asked whether stimulus-driven aspects in the EEG signal would be co-localized with the corresponding stimulus-driven BOLD signal during free viewing of a movie. Secondly, we wanted to integrate the EEG signal directly with the BOLD signal, by estimating the underlying impulse response function (IRF) that relates the BOLD signal to the underlying current density in the primary visual area (V1). We made sequential fMRI and 64-channel EEG recordings in seven subjects who passively watched 2-min-long segments of a James Bond movie. To analyze EEG data in this natural setting, we developed a method based on independent component analysis (ICA) to reject EEG artifacts due to blinks, subject movement, etc., in a way unbiased by human judgment. We then calculated the EEG source strength of this artifact-free data at each time point of the movie within the entire brain volume using low-resolution electromagnetic tomography (LORETA). This provided for every voxel in the brain (i.e., in 3D space) an estimate of the current density at every time point. We then carried out a correlation between the time series of visual contrast changes in the movie with that of EEG voxels. We found the most significant correlations in visual area V1, just as seen in previous fMRI studies (Bartels A, Zeki, S, Logothetis NK. Natural vision reveals regional specialization to local motion and to contrast-invariant, global flow in the human brain. Cereb Cortex 2008;18(3):705–717), but on the time scale of milliseconds rather than of seconds. To obtain an estimate of how the EEG signal relates to the BOLD signal, we calculated the IRF between the BOLD signal and the estimated current density in area V1. We found that this IRF was very similar to that observed using combined intracortical recordings and fMRI experiments in nonhuman primates. Taken together, these findings open a new approach to noninvasive mapping of the brain. It allows, firstly, the localization of feature-selective brain areas during natural viewing conditions with the temporal resolution of EEG. Secondly, it provides a tool to assess EEG/BOLD transfer functions during processing of more natural stimuli. This is especially useful in combined EEG/fMRI experiments, where one can now potentially study neural-hemodynamic relationships across the whole brain volume in a noninvasive manner.     

Improving the resolution of functional brain imaging: analyzing functional data in anatomical space

The accurate mapping of functional magnetic resonance imaging (fMRI) activations to anatomical structures is critical for fMRI studies of brain organization. In the commonly used functional space analysis method, functional images are realigned to a functional reference image and processed in low-resolution functional space. The average functional activations are then projected into high-resolution anatomical space for visualization. Here, we describe a new technique, anatomical space analysis (ASA), whereby low-resolution functional images are first coregistered and resampled directly into high-resolution anatomical space with all subsequent data processing performed in high-resolution space. A major advantage of ASA is that minor scanner sampling instabilities and small head movements can increase spatial resolution by providing multiple samples of the relationship between functional and anatomical space. Both simulations and analyses of real fMRI data show that ASA improves the precision, objectivity and reproducibility of functional brain mapping.     

Real-time functional magnetic resonance imaging: methods and applications

Functional magnetic resonance imaging (fMRI) has been limited by time-consuming data analysis and a low signal-to-noise ratio, impeding online analysis. Recent advances in acquisition techniques, computational power and algorithms increased the sensitivity and speed of fMRI significantly, making real-time analysis and display of fMRI data feasible. So far, most reports have focused on the technical aspects of real-time fMRI (rtfMRI). Here, we provide an overview of the different major areas of applications that became possible with rtfMRI: online analysis of single-subject data provides immediate quality assurance and functional localizers guiding the main fMRI experiment or surgical interventions. In teaching, rtfMRI naturally combines all essential parts of a neuroimaging experiment, such as experimental design, data acquisition and analysis, while adding a high level of interactivity. Thus, the learning of essential knowledge required to conduct functional imaging experiments is facilitated. rtfMRI allows for brain-computer interfaces (BCI) with a high spatial and temporal resolution and whole-brain coverage. Recent studies have shown that such BCI can be used to provide online feedback of the blood-oxygen-level-dependent signal and to learn the self-regulation of local brain activity. Preliminary evidence suggests that this local self-regulation can be used as a new paradigm in cognitive neuroscience to study brain plasticity and the functional relevance of brain areas, even being potentially applicable for psychophysiological treatment.     

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.     

Background and evoked activity and their interaction in the human brain

Most functional neuroimaging studies have investigated brain activity evoked by certain types of stimulation or tasks. In recent years, resting brain activity and its influence on evoked activity has become accessible for investigation. However, despite numerous studies on background and evoked activities, either observed with vascular (functional magnetic resonance imaging, positron emission tomography, optical) or electrophysiological (electroencephalography, magnetoencephalography) or a combination of both methods, so far, there is no generally accepted view concerning both the precise meaning of background activity and its relationship to evoked activity. In this article, we give an overview of the current knowledge on this issue and we review recent studies examining the influence of ongoing activity on behavioral responses and the relationship between ongoing and evoked activity.     

Partial least squares for discrimination in fMRI data

Multivariate methods for discrimination were used in the comparison of brain activation patterns between groups of cognitively normal women who are at either high or low Alzheimer's disease risk based on family history and apolipoprotein-E4 status. Linear discriminant analysis (LDA) was preceded by dimension reduction using principal component analysis (PCA), partial least squares (PLS) or a new oriented partial least squares (OrPLS) method. The aim was to identify a spatial pattern of functionally connected brain regions that was differentially expressed by the risk groups and yielded optimal classification accuracy. Multivariate dimension reduction is required prior to LDA when the data contain more feature variables than there are observations on individual subjects. Whereas PCA has been commonly used to identify covariance patterns in neuroimaging data, this approach only identifies gross variability and is not capable of distinguishing among-groups from within-groups variability. PLS and OrPLS provide a more focused dimension reduction by incorporating information on class structure and therefore lead to more parsimonious models for discrimination. Performance was evaluated in terms of the cross-validated misclassification rates. The results support the potential of using functional magnetic resonance imaging as an imaging biomarker or diagnostic tool to discriminate individuals with disease or high risk.     

A generation-attraction model for renewable energy flows in Italy: A complex network approach

In recent years, in Italy, the trend of the electricity demand and the need to connect a large number of renewable energy power generators to the power-grid, developed a novel type of energy transmission/distribution infrastructure. The Italian Transmission System Operator (TSO) and the Distribution System Operator (DSO), worked on a new infrastructural model, based on electronic meters and information technology. In pursuing this objective it is crucial importance to understand how even more larger shares of renewable energy can be fully integrated, providing a constant and reliable energy background over space and time. This is particularly true for intermittent sources as photovoltaic installations due to the fine-grained distribution of them across the Country. In this work we use an over-simplified model to characterize the Italian power grid as a graph whose nodes are Italian municipalities and the edges cross the administrative boundaries between a selected municipality and its first neighbours, following a Delaunay triangulation. Our aim is to describe the power flow as a diffusion process over a network, and using open data on the solar irradiation at the ground level, we estimate the production of photovoltaic energy in each node. An attraction index was also defined using demographic data, in accordance with average per capita energy consumption data. The available energy on each node was calculated by finding the stationary state of a generation-attraction model.     

Long-term variability of global statistical properties of epileptic brain networks

We investigate the influence of various pathophysiologic and physiologic processes on global statistical properties of epileptic brain networks. We construct binary functional networks from long-term, multichannel electroencephalographic data recorded from 13 epilepsy patients, and the average shortest path length and the clustering coefficient serve as global statistical network characteristics. For time-resolved estimates of these characteristics we observe large fluctuations over time, however, with some periodic temporal structure. These fluctuations can--to a large extent--be attributed to daily rhythms while relevant aspects of the epileptic process contribute only marginally. Particularly, we could not observe clear cut changes in network states that can be regarded as predictive of an impending seizure. Our findings are of particular relevance for studies aiming at an improved understanding of the epileptic process with graph-theoretical approaches.     

Decreased Resting-State Functional Complexity in Elderly with Subjective Cognitive Decline

Individuals with subjective cognitive decline (SCD) are at high risk of developing preclinical or clinical state of Alzheimer’s disease (AD). Resting state functional magnetic resonance imaging, which can indirectly reflect neuron activities by measuring the blood-oxygen-level-dependent (BOLD) signals, is promising in the early detection of SCD. This study aimed to explore whether the nonlinear complexity of BOLD signals can describe the subtle differences between SCD and normal aging, and uncover the underlying neuropsychological implications of these differences. In particular, we introduce amplitude-aware permutation entropy (AAPE) as the novel measure of brain entropy to characterize the complexity in BOLD signals in each brain region of the Brainnetome atlas. Our results demonstrate that AAPE can reflect the subtle differences between both groups, and the SCD group presented significantly decreased complexities in subregions of the superior temporal gyrus, the inferior parietal lobule, the postcentral gyrus, and the insular gyrus. Moreover, the results further reveal that lower complexity in SCD may correspond to poorer cognitive performance or even subtle cognitive impairment. Our findings demonstrated the effectiveness and sensitiveness of the novel brain entropy measured by AAPE, which may serve as the potential neuroimaging marker for exploring the subtle changes in SCD.     

Working Memory Decline in Alzheimer’s Disease Is Detected by Complexity Analysis of Multimodal EEG-fNIRS

Alzheimer’s disease (AD) is characterized by working memory (WM) failures that can be assessed at early stages through administering clinical tests. Ecological neuroimaging, such as Electroencephalography (EEG) and functional Near Infrared Spectroscopy (fNIRS), may be employed during these tests to support AD early diagnosis within clinical settings. Multimodal EEG-fNIRS could measure brain activity along with neurovascular coupling (NC) and detect their modifications associated with AD. Data analysis procedures based on signal complexity are suitable to estimate electrical and hemodynamic brain activity or their mutual information (NC) during non-structured experimental paradigms. In this study, sample entropy of whole-head EEG and frontal/prefrontal cortex fNIRS was evaluated to assess brain activity in early AD and healthy controls (HC) during WM tasks (i.e., Rey–Osterrieth complex figure and Raven’s progressive matrices). Moreover, conditional entropy between EEG and fNIRS was evaluated as indicative of NC. The findings demonstrated the capability of complexity analysis of multimodal EEG-fNIRS to detect WM decline in AD. Furthermore, a multivariate data-driven analysis, performed on these entropy metrics and based on the General Linear Model, allowed classifying AD and HC with an AUC up to 0.88. EEG-fNIRS may represent a powerful tool for the clinical evaluation of WM decline in early AD.     

Understanding the Variability in Graph Data Sets through Statistical Modeling on the Stiefel Manifold

Network analysis provides a rich framework to model complex phenomena, such as human brain connectivity. It has proven efficient to understand their natural properties and design predictive models. In this paper, we study the variability within groups of networks, i.e., the structure of connection similarities and differences across a set of networks. We propose a statistical framework to model these variations based on manifold-valued latent factors. Each network adjacency matrix is decomposed as a weighted sum of matrix patterns with rank one. Each pattern is described as a random perturbation of a dictionary element. As a hierarchical statistical model, it enables the analysis of heterogeneous populations of adjacency matrices using mixtures. Our framework can also be used to infer the weight of missing edges. We estimate the parameters of the model using an Expectation-Maximization-based algorithm. Experimenting on synthetic data, we show that the algorithm is able to accurately estimate the latent structure in both low and high dimensions. We apply our model on a large data set of functional brain connectivity matrices from the UK Biobank. Our results suggest that the proposed model accurately describes the complex variability in the data set with a small number of degrees of freedom.