Automatic identification of functional clusters in FMRI data using spatial dependence

In independent component analysis (ICA) of functional magnetic resonance imaging (fMRI) data, extracting a large number of maximally independent components provides a detailed functional segmentation of brain. However, such high-order segmentation does not establish the relationships among different brain networks, and also studying and classifying components can be challenging. In this study, we present a multidimensional ICA (MICA) scheme to achieve automatic component clustering. In our MICA framework, stable components are hierarchically grouped into clusters based on higher order statistical dependence--mutual information--among spatial components, instead of the typically used temporal correlation among time courses. The final cluster membership is determined using a statistical hypothesis testing method. Since ICA decomposition takes into account the modulation of the spatial maps, i.e., temporal information, our ICA-based approach incorporates both spatial and temporal information effectively. Our experimental results from both simulated and real fMRI datasets show that the use of spatial dependence leads to physiologically meaningful connectivity structure of brain networks, which is consistently identified across various ICA model orders and algorithms. In addition, we observe that components related to artifacts, including cerebrospinal fluid, arteries, and large draining veins, are grouped together and encouragingly distinguished from other components of interest.     

Probabilistic framework for brain connectivity from functional MR images

This paper unifies our earlier work on detection of brain activation (Rajapakse and Piyaratna, 2001) and connectivity (Rajapakse and Zhou, 2007) in a probabilistic framework for analyzing effective connectivity among activated brain regions from functional magnetic resonance imaging (fMRI) data. Interactions among brain regions are expressed by a dynamic Bayesian network (DBN) while contextual dependencies within functional images are formulated by a Markov random field. The approach simultaneously considers both the detection of brain activation and the estimation of effective connectivity and does not require a priori model of connectivity. Experimental results show that the present approach outperforms earlier fMRI analysis techniques on synthetic functional images and robustly derives brain connectivity from real fMRI data.     

Group replicator dynamics: a novel group-wise evolutionary approach for sparse brain network detection

Functional magnetic resonance imaging (fMRI) is increasingly used for studying functional integration of the brain. However, large inter-subject variability in functional connectivity, particularly in disease populations, renders detection of representative group networks challenging. In this paper, we propose a novel technique, "group replicator dynamics" (GRD), for detecting sparse functional brain networks that are common across a group of subjects. We extend the replicator dynamics (RD) approach, which we show to be a solution of the nonnegative sparse principal component analysis problem, by integrating group information into each subject's RD process. Our proposed strategy effectively coaxes all subjects' networks to evolve towards the common network of the group. This results in sparse networks comprising the same brain regions across subjects yet with subject-specific weightings of the identified brain regions. Thus, in contrast to traditional averaging approaches, GRD enables inter-subject variability to be modeled, which facilitates statistical group inference. Quantitative validation of GRD on synthetic data demonstrated superior network detection performance over standard methods. When applied to real fMRI data, GRD detected task-specific networks that conform well to prior neuroscience knowledge.     

Group Study of Simulated Driving fMRI Data by Multiset Canonical Correlation Analysis

In this work, we apply a novel statistical method, multiset canonical correlation analysis (M-CCA), to study a group of functional magnetic resonance imaging (fMRI) datasets acquired during simulated driving task. The M-CCA method jointly decomposes fMRI datasets from different subjects/sessions into brain activation maps and their associated time courses, such that the correlation in each group of estimated activation maps across datasets is maximized. Therefore, the functional activations across all datasets are extracted in the order of consistency across different dataset. On the other hand, M-CCA preserves the uniqueness of the functional maps estimated from each dataset by avoiding concatenation of different datasets in the analysis. Hence, the cross-dataset variation of the functional activations can be used to test the hypothesis of functional-behavioral association. In this work, we study 120 simulated driving fMRI datasets and identify parietal-occipital regions and frontal lobe as the most consistently engaged areas across all the subjects and sessions during simulated driving. The functional-behavioral association study indicates that all the estimated brain activations are significantly correlated with the steering operation during the driving task. M-CCA thus provides a new approach to investigate the complex relationship between the brain functions and multiple behavioral variables, especially in naturalistic tasks as demonstrated by the simulated driving study.     

Neural networks approach to clustering of activity in fMRI data

Clusters of correlated activity in functional magnetic resonance imaging data can identify regions of interest and indicate interacting brain areas. Because the extraction of clusters is computationally complex, we apply an approximative method which is based on artificial neural networks. It allows one to find clusters of various degrees of connectivity ranging between the two extreme cases of cliques and connectivity components. We propose a criterion which allows to evaluate the relevance of such structures based on the robustness with respect to parameter variations. Exploiting the intracluster correlations, we can show that regions of substantial correlation with an external stimulus can be unambiguously separated from other activity.     

Kernel Granger Causality Mapping Effective Connectivity on fMRI Data

Although it is accepted that linear Granger causality can reveal effective connectivity in functional magnetic resonance imaging (fMRI), the issue of detecting nonlinear connectivity has hitherto not been considered. In this paper, we address kernel Granger causality (KGC) to describe effective connectivity in simulation studies and real fMRI data of a motor imagery task. Based on the theory of reproducing kernel Hilbert spaces, KGC performs linear Granger causality in the feature space of suitable kernel functions, assuming an arbitrary degree of nonlinearity. Our results demonstrate that KGC captures effective couplings not revealed by the linear case. In addition, effective connectivity networks between the supplementary motor area (SMA) as the seed and other brain areas are obtained from KGC.      

Convolution Power Spectrum Analysis for fMRI Data Based on Prior Image Signal

Functional MRI (fMRI) data-processing methods based on changes in the time domain involve, among other things, correlation analysis and use of the general linear model with statistical parametric mapping (SPM). Unlike conventional fMRI data analysis methods, which aim to model the blood-oxygen-level-dependent (BOLD) response of voxels as a function of time, the theory of power spectrum (PS) analysis focuses completely on understanding the dynamic energy change of interacting systems. We propose a new convolution PS (CPS) analysis of fMRI data, based on the theory of matched filtering, to detect brain functional activation for fMRI data. First, convolution signals are computed between the measured fMRI signals and the image signal of prior experimental pattern to suppress noise in the fMRI data. Then, the PS density analysis of the convolution signal is specified as the quantitative analysis energy index of BOLD signal change. The data from simulation studies and in vivo fMRI studies, including block-design experiments, reveal that the CPS method enables a more effective detection of some aspects of brain functional activation, as compared with the canonical PS SPM and the support vector machine methods. Our results demonstrate that the CPS method is useful as a complementary analysis in revealing brain functional information regarding the complex nature of fMRI time series.      

A Connectivity-Based Method for Defining Regions-of-Interest in fMRI Data

In this paper, we describe a new methodology for defining brain regions-of-interset (ROIs) in functional magnetic resonance imaging (fMRI) data. The ROIs are defined based on their functional connectivity to other ROIs, i.e., ROIs are defined as sets of voxels with similar connectivity patterns to other ROIs. The method relies on 1) a spatially regularized canonical correlation analysis for identifying maximally correlated signals, which are not due to correlated noise; 2) a test for merging ROIs which have similar connectivity patterns to the other ROIs; and 3) a graph-cuts optimization for assigning voxels to ROIs. Since our method is fully connectivity-based, the extracted ROIs and their corresponding time signals are ideally suited for a subsequent brain connectivity analysis.      

Electrophysiological imaging of brain activity and connectivity-challenges and opportunities

Unlocking the dynamic inner workings of the brain continues to remain a grand challenge of the 21st century. To this end, functional neuroimaging modalities represent an outstanding approach to better understand the mechanisms of both normal and abnormal brain functions. The ability to image brain function with ever increasing spatial and temporal resolution has made a significant leap over the past several decades. Further delineation of functional networks could lead to improved understanding of brain function in both normal and diseased states. This paper reviews recent advancements and current challenges in dynamic functional neuroimaging techniques, including electrophysiological source imaging, multimodal neuroimaging integrating fMRI with EEG/MEG, and functional connectivity imaging.     

Analysis of fMRI data using improved self-organizing mapping and spatio-temporal metric hierarchical clustering

The self-organizing mapping (SOM) and hierarchical clustering (HC) methods are integrated to detect brain functional activation; functional magnetic resonance imaging (fMRI) data are first processed by SOM to obtain a primary merged neural nodes image, and then by HC to obtain further brain activation patterns. The conventional Euclidean distance metric was replaced by the correlation distance metric in SOM to improve clustering and merging of neural nodes. To improve the use of spatial and temporal information in fMRI data, a new spatial distance (node coordinates in the 2-D lattice) and temporal correlation (correlation degree of each time course in the exemplar matrix) are introduced in HC to merge the primary SOM results. Two simulation studies and two in vivo fMRI data that both contained block-design and event-related experiments revealed that brain functional activation can be effectively detected and that different response patterns can be distinguished using these methods. Our results demonstrate that the improved SOM and HC methods are clearly superior to the statistical parametric mapping (SPM), independent component analysis (ICA), and conventional SOM methods in the block-design, especially in the event-related experiment, as revealed by their performance measured by receiver operating characteristic (ROC) analysis. Our results also suggest that the proposed new integrated approach could be useful in detecting block-design and event-related fMRI data.      

Conditional Correlation as a Measure of Mediated Interactivity in fMRI and MEG/EEG

Many measures have been proposed so far to extract brain functional interactivity from functional magnetic resonance imaging (fMRI) and magnetoencephalography/electroencephalography (MEG/EEG) data sets. Unfortunately, none has been able to provide a relevant, self-contained, and common definition of brain interaction. In this paper, we propose a first step in this direction. We first introduce a common terminology together with a cross-modal definition of interaction. In this setting, we investigate the commonalities shared by some measures of interaction proposed in the literature. We show that temporal correlation, nonlinear correlation, mutual information, generalized synchronization, phase synchronization, coherence, and phase locking value (PLV) actually measure the same quantity (namely correlation) when one is investigating linear interactions between independently and identically distributed Gaussian variables. We also demonstrate that these data-driven measures can only partly account for the interaction patterns that can be expressed by the effective connectivity of structural equation modeling (SEM) . To bridge this gap, we suggest the use of conditional correlation, which is shown to be related to mediated interaction.     

Using replicator dynamics for analyzing fMRI data of the human brain

The understanding of brain networks becomes increasingly the focus of current research. In the context of functional magnetic resonance imagery (fMRI) data of the human brain, networks have been mostly detected using standard clustering approaches. In this work, we present a new method of detecting functional networks using fMRI data. The novelty of this method is that these networks have the property that every network member is closely connected with every other member. This definition might to be better suited to model important aspects of brain activity than standard cluster definitions. The algorithm that we present here is based on a concept from theoretical biology called "replicator dynamics."     

Joint modeling of anatomical and functional connectivity for population studies

We propose a novel probabilistic framework to merge information from diffusion weighted imaging tractography and resting-state functional magnetic resonance imaging correlations to identify connectivity patterns in the brain. In particular, we model the interaction between latent anatomical and functional connectivity and present an intuitive extension to population studies. We employ the EM algorithm to estimate the model parameters by maximizing the data likelihood. The method simultaneously infers the templates of latent connectivity for each population and the differences in connectivity between the groups. We demonstrate our method on a schizophrenia study. Our model identifies significant increases in functional connectivity between the parietal/posterior cingulate region and the frontal lobe and reduced functional connectivity between the parietal/posterior cingulate region and the temporal lobe in schizophrenia. We further establish that our model learns predictive differences between the control and clinical populations, and that combining the two modalities yields better results than considering each one in isolation.     

Sparse brain network recovery under compressed sensing

Partial correlation is a useful connectivity measure for brain networks, especially, when it is needed to remove the confounding effects in highly correlated networks. Since it is difficult to estimate the exact partial correlation under the small- n large- p situation, a sparseness constraint is generally introduced. In this paper, we consider the sparse linear regression model with a l(1)-norm penalty, also known as the least absolute shrinkage and selection operator (LASSO), for estimating sparse brain connectivity. LASSO is a well-known decoding algorithm in the compressed sensing (CS). The CS theory states that LASSO can reconstruct the exact sparse signal even from a small set of noisy measurements. We briefly show that the penalized linear regression for partial correlation estimation is related to CS. It opens a new possibility that the proposed framework can be used for a sparse brain network recovery. As an illustration, we construct sparse brain networks of 97 regions of interest (ROIs) obtained from FDG-PET imaging data for the autism spectrum disorder (ASD) children and the pediatric control (PedCon) subjects. As validation, we check the network reproducibilities by leave-one-out cross validation and compare the clustered structures derived from the brain networks of ASD and PedCon.     

Removal of spurious coherence in MEG source-space coherence analysis

Source-space coherence analysis has become a popular method to estimate functional connectivity based on MEG/EEG. Source-space analysis involves solving the inverse problem, estimating the time courses of specific brain regions, and then examining the coherence between activities at different brain regions. However, source-space coherence analysis can be confounded by spurious coherence caused due to the leakage properties of the inverse algorithm employed. Such spurious coherence is typically manifested as an artifactual large peak around the seed voxel, called seed blur, in the resulting coherence images. This seed blur often obscures important details of brain interactions. This paper proposes the use of the imaginary part of the coherence to remove the spurious coherence caused by the leakage of an imaging algorithm. We present a theoretical analysis that explains how the use of imaginary part can remove this spurious coherence. We then present results from both computer simulations and experiments using resting-state MEG data which demonstrate the validity of our analysis.     

Contextual modeling of functional MR images with conditional random fields

This paper presents a conditional random field (CRF) approach to fuse contextual dependencies in functional magnetic resonance imaging (fMRI) data for the detection of brain activation. The interactions among both activation (activated/inactive) labels and observed data of brain voxels are unified in a probabilistic framework based on the CRF, where the interaction strength can be adaptively adjusted in terms of the data similarity of neighboring sites. Compared to earlier detection methods, including statistical parametric mapping and Markov random field, the proposed method avoids the suppression of high frequency information and relaxes the strong assumption of conditional independence of observed data. Experimental results show that the proposed approach effectively integrates contextual constraints within the detection process and robustly detects brain activities from fMRI data.     

A Bayesian hierarchical correlation model for fMRI cluster analysis

Data-driven cluster analysis is potentially suitable to search for, and discriminate between, distinct response signals in blood oxygenation level-dependent functional magnetic resonance imaging (BOLD fMRI), which appear during cerebrovascular disease. In contrast to model-driven methods, which test for a particular BOLD signal whose shape must be given beforehand, data-driven methods generate a set of BOLD signals directly from the fMRI data by clustering voxels into groups with correlated time signals. Here, we address the problem of selecting only the clusters that represent genuine responses to the experimental stimulus by modeling the correlation structure of the clustered data using a Bayesian hierarchical model. The model is empirically justified by demonstrating the hierarchical organization of the voxel correlations after cluster analysis. BOLD signal discrimination is demonstrated using: 1) simulations that contain multiple pathological BOLD response signals; and 2) fMRI data acquired during an event-related motor task. These demonstrations are compared with results from a model-driven method based on the general linear model. Our simulations show that the data-driven method can discriminate between the BOLD response signals, while the model-driven method only finds one signal. For fMRI, the data-driven method distinguishes between the BOLD signals appearing in the sensorimotor cortex and those in basal ganglia and putamen, while the model-driven method combines these signals into one activation map. We conclude that the proposed data-driven method provides an objective framework to identify and discriminate between distinct BOLD response signals.     

A Geometric Interpretation of Fading in Wireless Networks: Theory and Applications

In wireless networks with random node distribution, the underlying point process model and the channel fading process are usually considered separately. A unified framework is introduced that permits the geometric characterization of fading by incorporating the fading process into the point process model. Concretely, assuming nodes are distributed in a stationary Poisson point process in ${BBR}^d$ , the properties of the point processes that describe the path loss with fading are analyzed. The main applications are single-hop connectivity and broadcasting.      

A model selection method for nonlinear system identification based FMRI effective connectivity analysis

In this paper a model selection algorithm for a nonlinear system identification method is proposed to study functional magnetic resonance imaging (fMRI) effective connectivity. Unlike most other methods, this method does not need a pre-defined structure/model for effective connectivity analysis. Instead, it relies on selecting significant nonlinear or linear covariates for the differential equations to describe the mapping relationship between brain output (fMRI response) and input (experiment design). These covariates, as well as their coefficients, are estimated based on a least angle regression (LARS) method. In the implementation of the LARS method, Akaike's information criterion corrected (AICc) algorithm and the leave-one-out (LOO) cross-validation method were employed and compared for model selection. Simulation comparison between the dynamic causal model (DCM), nonlinear identification method, and model selection method for modelling the single-input-single-output (SISO) and multiple-input multiple-output (MIMO) systems were conducted. Results show that the LARS model selection method is faster than DCM and achieves a compact and economic nonlinear model simultaneously. To verify the efficacy of the proposed approach, an analysis of the dorsal and ventral visual pathway networks was carried out based on three real datasets. The results show that LARS can be used for model selection in an fMRI effective connectivity study with phase-encoded, standard block, and random block designs. It is also shown that the LOO cross-validation method for nonlinear model selection has less residual sum squares than the AICc algorithm for the study.