IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE MARCH/APRIL 2006

Exploratory Analysis ofBrain Connectivity with ICA

Deriving Functional ConnectivityWithout a Prior Model

BY JAGATH C. RAJAPAKSE,CHOONG LEONG TAN,XUEBIN ZHENG, SUSANTA MUKHOPADHYAY,AND KANYAN YANG

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Covariance-based methods of exploration of func-tional connectivity of the brain from functionalmagnetic resonance imaging (fMRI) experiments,such as principal component analysis (PCA) and

structural equation modeling (SEM), used earlier to deter-mine interactions among brain regions of neural systems,require a priori knowledge such as an anatomical model toinfer functional connectivity. We introduce a hybrid method,combining independent component analysis (ICA) and SEM,which is capable of deriving functional connectivity in anexploratory manner without the need of a prior model. Thespatial ICA (SICA) derives independent neural systems orsources involved in task-related brain activation, while anautomated method based on the SEM finds the structure ofthe connectivity among the elements in independent neuralsystems. Unlike earlier second-order approaches, the task-related neural systems derived from the ICA provide brainconnectivity in the complete statistical sense. We illustratethe use and efficacy of our approach on two fMRI datasetsobtained from a visual task and a language reading task.

fMRI exploits the changes of magnetic properties of oxy-genated hemoglobin, caused by neuronal activation of thebrain [1]. An important area of current research in fMRI is todetermine the brain voxels or regions that are activated dur-ing a functional task and to infer how these regions effective-ly interact among one another to execute the particular task.In this context, activated brain regions are modeled as nodesin graphs, and the interactions are represented by thestrengths of the edges.

In the hypothesis-driven approach, the detection of activa-tion is usually done by statistically comparing hemodynamicresponse corresponding to each brain voxel with each of theinput stimuli, assuming that the voxels indexing the brainregions participating in the sensory or cognitive processingof the given experimental tasks and control tasks show dif-ferent fMRI signals levels. The simplest of these approachesis the correlation analysis [2]. Analyses of variance/covariancetest the signal at each voxel by using univariate measures,e.g., t-tests or F-tests, under the null hypothesis that the teststatistics are distributed under a known probability distribu-tion, usually a Gaussian. In order to correct for multiplecomparisons and spatial correlations, the statistical maps are

further analyzed using random fields [3], [4]; the Gaussianrandom fields are used in the popular statistical parametricmapping (SPM) approach [3]. One drawback of thisapproach is that the analyses of the spatial correlations aredone independently after the analyses in the temporaldomain; a spatio-temporal analysis, where spatial and tempo-ral analyses are done simultaneously, is often desired infMRI [5]. fMRI data are corrupted by physiological noise,such as heart beat, respiration, and blood flow, and electronicnoise of the scanners [6]. They are further confounded by thevariation in the baseline magnetization of the scanner [7] andthe subject’s head motion [8]. Therefore, prior to the applica-tion of the simple correlation analysis or SPM analysis,fMRI data are required to be preprocessed using appropriatefiltering techniques and corrected for artifacts.

ICA separates the underlying sources in a signal that aremutually independent in the complete statistical sense fromtheir linear mixtures [9]–[12]. Recently, ICA has beenapplied to analyze fMRI data in two different ways: SICAand temporal ICA (TICA) [13]–[16]. FMRI data is decom-posed into a set of spatially independent components (ICs)in SICA, whereas the TICA decomposes the data into a setof temporal ICs. In this article, we focus on SICA, whichhas been shown to be capable of separating the componentsof interest that are due to task-related brain activation fromother components that are due to interferences and artifacts[13]. It is, therefore, unnecessary to preprocess fMRI databefore the detection of brain activation by using ICA.Furthermore, the analysis of fMRI with the ICA is spatio-temporal. Recent experiments and results have indicatedthat ICA can be used to reliably separate fMRI datasets intomeaningful constituent components, including consistentlyand transiently task-related physiological changes, nontask-related physiological phenomena, and machine or move-ment artifacts [13], [15], [16]. The task-related componentscan be attributed to independent brain processes or neuralsources underlying the brain activation.

An analysis of brain function in terms of networks, ratherthan single regions, is necessary to fully grasp the complexi-ties associated with cognition [17]–[19]. There is mountingevidence that dynamic patterns generated by brain networksunderlie all of cognition and perception. Connectionist and

IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE MARCH/APRIL 2006 103

imaging approaches for understanding the integration mech-anism of brain function have grown over the past decade.The distributed brain systems associated with performance ofa verbal fluency task were first identified in a nondirectedcorrelational analysis of neurophysiological data obtainedwith position emission tomography (PET) [20]. The recentadvances in functional brain imaging and image analyseshave paved the way to investigate the brain function in termsof neural systems rather than individual regions involved in asensory or cognitive task [20]–[24]. A neural system consistsof a set of neural elements, i.e., individual brain voxels orregions of connected voxels, collectively involved in a par-ticular brain process.

The traditional method to access functional connectivitymaps of the brain for a specific region of interest in fMRI isto evaluate the covariance with a seed voxel. One or a smallcluster of voxels whose averaged time course serves as a ref-erence model for the cross-correlation analysis with theremaining brain voxels is chosen, yielding a spatial zero-lagcross-correlation map [25]–[27]. The information aboutneural interactions is more effectively extracted through thedecomposition of interregional covariances of activity. Suchanalyses use a recursive PCA, which suggests that the vari-ance in neurophysiological measurements could be account-ed for by a few principal components [20], [28]. Hierarchicalclustering has also been used in the resting state measure-ments to assess networks of functional connectivity; it doesnot require specifying the number of clusters [29].

SEM is commonly used for the analysis of the effectiveconnectivity among brain regions. McIntosh and Gonzalez-Lima [22] first described SEM and applied for network analy-sis of vision tasks using PET experiments. Other researchershave later used SEM for network analysis of brain regionsinvolved in particular brain events or brain lesions [23],[30]–[33]. Recently, Bullmore et al. showed how to searchfor the best fitting model from an fMRI dataset [24].However, SEM is only confirmatory in the sense that it isonly capable of reaffirming or refuting the connectivity of analready known a priori model, which is often under anatomi-cal constraints. The use of anatomical data is further compli-cated by the fact that much of the data have been obtained instudies of monkeys, and it is not always certain which area toinclude, especially if the brain regions are involved in func-tions unique to humans, such as language [24].

Biswal [25] first observed the activation in the motorcortices in the resting brain or the default state of the brainin an fMRI experiment. Although the resting state, bydefault, means the uncontrolled state, there are potentialadvantages to investigating the functional connectivity thatdoes not require a focal task. It has been recently observedthat, in the default mode, the left precentral gyrus has ahigh correlation to the postcentral gyrus and small region ofthe left hemisphere thalamus [26], and cortical neuronsbelonging to specific but spatially separated functionalclusters have shown correlated patterns of spontaneousactivity over time [34], [35].

The aim of this article is to extract independent neural sys-tems involved in fMRI experiment tasks by using ICA. Theconnectivity among the different brain regions activated byindependent neural sources is then determined by usingcovariance analysis, such as SEM. The main contribution ofthis work is that, to explore the connectivity patterns among

brain regions, a prior model of connectivity such as ananatomical model is not needed. In that sense, our approachto finding brain connectivity is exploratory.

Detection of Brain Activation with ICAIn fMRI, a series of T∗

2 weighted MR brain images is obtainedat regular intervals while a subject is performing a sensory,motor, or cognitive task in the scanner. Therefore, the func-tional magnetic resonance (fMR) images are inherently spatio-temporal. Let us denote the spatio-temporal matrix of noisyfMRI data by X = [x1x2 . . . xm]T , where the vectorxj = (xj1, xj2, . . . xjn)

T represents the jth scan (i.e., the brainimage taken at jth instance of time) in which xji is the mea-sured intensity value of ith brain voxel of the jth scan; the fMRimage taken during the experiment is presumed to consist of mscans, each containing the intensities of n brain voxels. ThefMR image is given by a matrix X of size mxn of intensities.

SICAThe application of ICA for the analysis of fMRI presumesthat the multifocal brain areas activated by the performanceof a psychomotor task are unrelated to the brain areas whosesignals are affected by artifacts and noises. Each of the indi-vidual neural sources underlying the performance of the taskis represented by one or more spatial ICs in SICA and isassociated with a single task-related time course and a com-ponent map.

The SICA decomposes the fMRI signal into a linear com-bination of IC maps and their corresponding time courses[13] as follows:

X = MC, (1)

where C = [c1c2 . . . ck]T denotes the matrix of size kxn ofcomponent maps and M = [m1 m2 . . . mk] denotes the mixingmatrix of size m × k for corresponding time courses; the vec-tor ml denotes the time course related to the spatial compo-nent map cl, which indicates the amount of contribution ofcomponent cl to the fMRI data; k(≤m) denotes the total num-ber of components, at most one Gausssian, that generate theobserved fMRI data. The matrix M, a full column rank m × kmatrix, represents the linear mixing of the sources embeddedin the observed fMRI data. The mixing is pressumed to beinstantaneous, i.e., there is no time delay between the events ofthe neural sources in the brain and the observed signals. Letthe component map cl = (cl1, cl2, . . . cln)

T , where cli repre-sents the intensity corresponding to the ith brain voxel site ofthe lth component map and the time courseml = (ml1, ml2, . . . mlm)T , where mlj represents the amplitudeof the jth instance of the time series. By convention, theabove decomposition in (1) is referred to as SICA, where thevoxel intensities of each of the component maps are placedin separate rows of matrix C and each column of M repre-sents a time course of the corresponding components.

The basic linear model assumed in the SICA of fMRI isgiven by

x̃i = Mc̃i + φi, (2)

where the time series x̃i = (x1i, x2i, . . . xmi)T ∈ Rm of activa-

tion, corresponding to the brain voxel i, is presumed to be azero mean vector (which may be obtained by subtracting the

104 IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE MARCH/APRIL 2006

mean of the time series from each element) and the elementsof the time series c̃i = (c1i, c2i, . . . cki)

T ∈ Rk indicates thecontribution of each component map to the activation timeseries; φi ∈ Rm indicates the noise embedded in the timeseries x̃i. By repeating (2) for all time series relating to allbrain voxels and writing them in a matrix format, (1) can bederived. The challenge of identifying brain signal sourcescan be posed as the realization of source components cl forl = 1, 2, . . . , k, given the observations xj for j = 1, 2, . . . , m,

with an unknown mixing matrix M. If no further assumptionsare made, the noise can be considered as a source signal com-ponent and hence is generally included in the decompositionof the SICA, i.e., (1).

The matrix of component maps is determined by multiply-ing the observed data matrix X by a demixing matrix W:

C = WX, (3)

where W is the Moore-Penrose generalized matrix pseudo-inverse of the mixing matrix M, given by W = (MTM)−1MT.We use the fast ICA algorithm [36] to determine theunknown demixing matrix and to decompose the observedfMRI signals into statistical IC maps.

Derivation of ICs From the perspective of information theory, the estimation ofstatistical ICs is equivalent to the minimization of mutualinformation. The main objective is to find the most non-Gaussian [9] directions in the experimentally obtaineddataset. Based on this idea, a contrast function may bederived and optimized so that the source signals are separat-ed to be maximally independent.

The current algorithms for deriving the ICs can loosely beclassified into two categories. One category contains adap-tive algorithms generally based on stochastic gradient meth-ods and implemented in neural networks [10], [11]. Theneural adaptive algorithms exhibit slow convergence andtheir convergence depends crucially on the correct choice ofthe learning rate parameters. The second category relies onbatch computation by optimizing some relevant criterionfunctions [37].

The fast ICA algorithm is a fast and efficient approach tocomputing the demixing matrix W in (3) based on the conceptof mutual information [36]. If c = (c1, c2, . . . ck)

T denotes thevector of components, the differential entropy H of the vectorc of components, having density f(·) is defined as follows:

H(c) =∫

f(c)log f(c)dc. (4)

From the fundamental concept of information theory, itsknown that given a set of random variables of equal vari-ances, the entropy of the variable that follows a Gaussiandistribution, has the largest entropy [38]. Therefore, the rela-tive values of entropy give a measure of non-Gaussianity.Thus, an alternative measure of non-Gaussianity [9] isdefined in terms of negentropy as

J(c) = H(cGauss) − H(c), (5)

where cGauss is a Gaussian random vector of the same covari-ance matrix as c. This value is always nonnegative for non-Gaussian and zero for a Gaussian. Using the concept of

differential entropy, one can define the mutual information Ibetween the k components cl for l = 1, 2, . . . k [9]:

I(c1, c2, . . . ck) = J(c) −k∑

l=1

J(cl). (6)

As mutual information is a natural measure of the depen-dence between random variables, the ICs in a fast ICA canbe determined by minimizing the mutual information of thetransformed components by the demixing matrix W of (3). Itis evident that minimizing the mutual information in c findsthe direction of maximim negentropy. We extract all thecomponents, i.e., the complete ICA, and select the task-relat-ed components belonging to different neural systems.

Selection of Task-Related ComponentsThe SICA has been recently adopted to separate the indepen-dent sources in fMRI data, and previous experiments havedemonstrated its feasibility in extracting the task-related com-ponents and discarding other artifacts and noises. Therefore,the decomposition by ICA provides us with an accurate pic-ture of brain voxels and regions that are activated by neuralsources without any interference from artifacts [13].However, the identification of the task-related activationmaps from others was performed only by observing the corre-sponding time courses in a supervised manner. In order tofind the components that are related to the neural sources acti-vated by particular brain processes or phenomena, we firstattempt to detect and remove the component maps of uninter-esting signals. The identification of components representingGaussian noise could be based on a fourth-order statistic, kur-tosis κ . An important feature of kurtosis is that it is the sim-plest statistical quantity for indicating the non-Gaussianity ofa random variable [39]. Due to the Gaussianity of randomnoises and the specificity of spatial distributions of usefulbrain signals, the component maps of neural sources in fMRIusually have a kurtosis value far greater than zero. Therefore,the kurtosis of a component map is used to remove noisycomponents from the potential activation maps.

After the number of component maps is reduced by themeasurement of kurtosis, the activation maps are extractedby observing the correlation between the input stimuli andthe time courses of the remaining non-Gaussian componentmaps. The voxels whose signals have significant correlationabove a preselected threshold with input stimuli are desig-nated as areas of activation. However, if the task involvesindependent neural systems or sources, the task-relatedcomponents appear in different component maps. Once thetask-related component maps are extracted from the ICA-separated component maps, to extract the voxels of signifi-cant activation at a particular significant level, z-statisticalmaps are generated under the null hypothesis of no activa-tion. The voxels whose absolute z-scores are greater thansome threshold of significance, i.e., p-value, are consideredto be activated voxels.

Functional ConnectivityA neural system is unique as it is composed of numerous inter-connected neural elements ranging from single neurons toentire ensembles across brain areas. The communicationsamong and along neural elements underlie the brain function.Hitherto, basically three kinds of connectivities have drawnthe attention of scientists and researchers in brain studies [20]:

IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE MARCH/APRIL 2006 105

➤ anatomical connectivity: determined by the neuroanatomicalorganization of clusters of cortical areas of the brain, whichgives the topology of the anatomical structure of the brain

➤ functional connectivity: defined as the temporal correlationbetween pairs of neurophysiological (functional) measure-ments of different brain areas

➤ effective connectivity: defined as an influence of one brain ele-ment on another element through an anatomical model from adirect or indirect connecton. The effective connectivity maynot always be through a direct link, but may be through indi-rect links (a series of connections via different brain elements).As the functional connectivity is defined on pairwise cor-

relation coefficients, the above connectivity is actuallyreferred to as functional connectivity in the second-order sta-tistical sense. The functional connectivity is thus representedby uncorrelated neural systems, within which there are sig-nificant temporal correlations among the activated neuralelements. The eigenimage analysis offers a method of deter-mining second-order functional connectivity of the brain,while SEM offers further quantification of brain regionsinvolved in the functional connectivity.

Eigenimage AnalysisThe PCA, also referred to as eigenimage analysis, offers aneffective way to analyze the second-order functional connec-tivity [20], [28]. The eigenimage analysis decomposes fMRIinto a series of orthogonal images that embody in a decreasingmanner the amounts of the functional connectivity. Thecovariance matrix R of fMRI data can be expressed as follows

R =k∑

l=1

λleleTl + δ, (7)

where only k(<n) number of eigenvalues are significantlylarge, el = (el1, el 2, . . . el n)

T denotes the lth eigenimage inwhich eli is the ith element of the lth eigenimage, and δdenotes the negligible residual covariance. The value of kcan be found using a method described in [40].

If the (i1, i2)th element of the covariance matrix R is ri1 i 2 ,from eigenimage decomposition,

ri1,i 2 ≈ λ1ei11ei 21. (8)

If ri1 i 2 is significantly large, either ei11, ei 21, or both are large.Since the diagonal elements of R must be 1 and e2

i11 and e2i21

must be approximately equal to 1, both ei11 and ei 21 shouldbe significant. Therefore, the element ri1 i 2 of the covariancematrix R is significantly large. There is a significant func-tional connectivity, in the second-order statistical sense,between the neural element i1 and i2 of the brain. The voxelshaving high intensity in eigenimages with large eigenvaluescorrespond to highly correlated voxels or are connected inthe second-order sense. Therefore, all of the first k ≤ neigenvectors corresponding to relatively high eigenvalueswould represent the functional connectivity.

However, the eigenimage analysis only provides anapproximate pattern of functional connectivity measured bya relatively high value of second-order correlation as, besidesthe neural sources in fMRI, there exist other confoundingartifacts and noises that are not orthogonal to the connectivitypatterns. Since the subtle signal changes coming from neural

activity may be vulnerable to various kinds of artifacts andnoises, the high correlation value may arise from a connec-tivity of interfering signals other than the neural sources.

Structural Equation ModelingThe SEM provides a method to represent the covariancestructure of a set of variables. The fundamental hypothesis inthe structural equation procedure is that the correlation matrixof the fMRI data, R, is a function of a set of parameters, θ . Inmodeling fMRI data, the theoretically anticipated connectionsbetween brain regions are written down in the form of a pathmodel matrix, K = {θi, j}p×p, where p is the number of activat-ed brain elements and {ri|i = 1, 2 . . . p} denotes the set ofneural elements activated in a neural system.

The data model is written as a set of simultaneous regres-sion equations [41]:

v = Kv + ϕ, (9)

where v = (v1, v2, . . . vp)T denotes the vector of regional

variances and ϕ = (ϕ1, ϕ2, . . . ϕp)T denotes the vector of

residual variances. Equation (6) can be rearranged to showthat v = (I − K)−1ϕ and the correlation matrix R̂ predictedby the path model are given by

R̂ = (I − K)−1ϕϕT((I − K)−1)T. (10)

Assuming that the pairwise correlations between the princi-pal eigen time series of the brain elements significantly con-stitute the interregional correlation matrix R, the residualvariance for each region is estimated as

φi = 1 − λ2i∑p

j= i λ2j

, (11)

where φi denotes the residual variance of the region ri and λj

denotes the jth eigenvalue of the correlation matrix.The objective is to find the estimates of the nonzero path

coefficients that minimize a measure of discrepancy betweenthe observed correlation matrix, R and the correlation matrixpredicted by the path model R̂. Instead of minimizing func-tions of observed and predicted individual correlation values,the SEM is derived by minimizing the discrepancy betweenthe observed interregional correlation matrix and the correla-tion matrix predicted by the model [42].

An automated search for the best fitting model, as proposedby Bullmore et al. [24], is adopted to find the best neural sys-tem with the path coefficients θi, j representing the influencefrom the region rj onto the region ri. The estimates of the pathcoefficients are found by iteratively minimizing the maxi-mum likelihood (ML) discrepancy function F [24], [41]:

F = log|R̂| − tr(RR̂−1) − log|R| − q, (12)

where |·| denotes the determinant and tr(·) denotes the traceof a matrix; the number of nonzero path coefficients in thematrix is denoted by q. Under the null hypothesis H0 : R̂ = R,the value of F multiplied by β − 1, where β is the number ofindependent observations on each variable, is approximatelydistributed as χ2 on 1

2 p(p + 1) − q degrees of freedom.Given by Bullmore et al. [24], the automated search for the

best fitting model starts from the worst fitting model (the nullmodel in which all path coefficients are constrained or set to

106 IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE MARCH/APRIL 2006

zero). The algorithm computes the Lagrangian multiplier (LM)for each constrained coefficient and allows the coefficient withthe maximum LM to be nonzero. Bullmore also suggested aparameter, say, Akaikes’s information criterion, A:

A = χ2q + 2q. (13)

As path coefficients are unconstrained, Chi-square for themodel with q nonzero paths χ2

q will decrease and 2q willincrease. If the decrement χ2 − χ2

q+1 < 2, then A will have aminimum at q, and this can be taken as an operational defini-tion of the best model.

Higher-Order Functional Connectivity with ICAThe SICA decomposes fMR images into components thatare independent in the complete statistical sense. The acti-vated neural elements in each task-related component mapdefine an independent neural system in the higher-orderstatistical sense. ➤ Higher-order functional connectivity is defined by neural

systems within which different neural elements, i.e., voxelsor regions, are activated by the same dependency of tempo-ral variation in the complete statistical sense.Once the neural systems involved in a functional task are

identified by SICA, the connected neural elements are identi-fied by the values of their intensities of the component maps.The following theorem allows us to determine the connectedneural elements in a neural system. ➤ Theorem: For a certain time course ml related to a neural

source, indexed by l, the functional connectivity is givenby a set of voxels {vi : |cli | > α, i = 1, 2, . . . n} , wherecl = (cl1, cl 2, . . . cln)

T is a vector representing the lthcomponent map given by the SICA, α is a preselectedthreshold value, determining the significance of the con-nectivity at a given p-value, and |·| stands for theabsolute value of the variable.

➤ Proof: Let us consider the lth component map cl that ispresumed to be task-related and its corresponding timecourse ml = (m1l, mm2 l, . . . mml)

T . Under the null hypothe-sis of no activation, the component maps are presumed tohave independently and identically distributed Gaussiannoise intensities, in which cli represents the relative contri-butions of the source signals of the image intensities at aparticular voxel i. The voxels whose absolute z-score sta-tistics are greater than some threshold α relating to a sig-nificance level, p-value, violating the null-hypothesis, isconsidered as active voxels within that component.Negative z-scores indicate voxels whose fMRI signals aremodulated opposite to the time course of activation for thatcomponent. In accordance with the definition of higher-order functional connectivity, all the activated voxels in acomponent map constitute a neural system that showsfunctional connectivity in the higher-order statistical sense.In SICA, the voxel values for each of the component

maps are placed in separate rows of matrix C, and each col-umn of M represents a time course of the correspondingcomponent map. The activated neural elements in the com-ponent map derived from the above ICA procedure are fullydependent, allowing us to investigate the functional connec-tivity of the brain in higher-order statistical sense. Unlikethe definition of second-order functional connectivity,which measures the correlation between neural elements,

the higher-order connectivity is a dependency between neur-al elements due to a certain brain process or phenomena.Hence, the brain process is characterized by a definite timecourse representing a neural source.

There are two advantages of yielding higher-order func-tional connectivity by using ICA. The first is that the resultsare unaffected by any confounding factors, which has been amajor concern in the previous work of connectivity analysisby using fMRI data. This advantage can be finely realized bythe ICA, which is capable of separating the mixed fMRI sig-nals into different artifacts and neural sources. Secondly, theconnectivity is investigated in a complete statistical sense,i.e., the neural elements are connected by any order statistics,which may highlight connectivities that are not shown byconsidering only second-order statistics.

When fMRI data are decomposed by ICA, the task-relatedactivation may appear in more than one component map,indicating that the input stimuli are processed by indepen-dent brain processes or the data are generated by independentneural sources. The correlation between the activated brainelements in these component maps could then be found byusing other methods, such as SEM, to observe the correla-tions among the activated neural elements.

Experiments and Results

Visual Task

DataThe images were obtained in visual stimulation task using aFLASH protocol at the Magnetic Resonance Imaging (MRI)Centre of the Max-Planck-Institute of CognitiveNeuroscience. While a subject was performing the experi-ment, three to six two-dimensional (2-D) T∗

2 -weightedimages, each with 64 scans, were acquired using a gradient-echo FLASH sequence (TR = 80.5 ms: TE = 40 ms:matrix = 128 × 64; the image matrices were zero-filled toobtain 128 × 128 images with a spatial resolution of1.953 × 1.953 mm2; slice thickness = 5 mm and 2-mm gap).The corresponding 2-D anatomical slices were also acquiredwith a T1-weighted IR RARE sequence (TI = 900 ms; TR =40 ms; TE = 3,900 ms; matrix = 512 × 512) in the sameexperimental session. In all experiments, ON and OFF stimuliwere presented at a rate of 5.162 s/sample. Each stimulationperiod had four successive stimulation ON states followed byfour stimulation OFF states. An 8-Hz alternating checkerboardpattern with a central fixation point was projected on an LCDsystem, and subjects were asked to fixate on the point duringthe stimulation. The stimulations were repeated for eightcycles (total experimental time = 5.5 min). For further infor-mation about the experimental procedure, see [43].

Activation DetectionThe detection of activation for each subject was preformedseparately, and the connectivity maps derived were averagedacross the subjects. The fMRI scans were decomposed into62 IC maps by SICA. An empirically determined thresholdof kurtosis value κ = 5.0 was applied to remove the noisysources, and the correlation with the input stimulus was mea-sured to pick out the components of neural activations. Thetask-related component maps obtained for a representativesubject are shown in Figure 1.

IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE MARCH/APRIL 2006 107

Each component map indicated a single brain region ofactivation, which had a significant correlation value with thestimulation time series (cor > 0.1): 1) primary visual senso-ry (PVS) area (BA17), 2) right primary somatomotor(RPSA) area (BA4), and 3) left primary somatomotor(LPSA) area (BA17).

Connectivity AnalysisThe time series of each activated region was obtained from thecorresponding column of the mixing matrix M multiplied bythe averaged intensity of the corresponding component map.According to (1), if a component map showing task-relatedactivation is cl and its correspondingtime course is ml, then the temporalpattern of response in this region iscomputed from 1/N

∑ni=1;|cli|>α climl ,

where N is the number of activatedvoxels and corresponds to a p-value =0.05. The residual variance for eachregion was estimated by the total vari-ance of the region.

The automated search of best fittingmodel was performed on the temporalresponse patterns of the three regions.χ2 value, p-value, and Akaike’s infor-mation criterion fit index for eachmodel in the model search are shownin Figure 2. The χ2 value monotoni-cally decreases as the number ofnonzero path coefficients increasefrom zero to three. The p-value forChi-square has a maximum whenq = 2, and Akaike’s information crite-rion has a minimum when q = 2.Thus, the best model, in terms of max-imum probability and minimum cost,has q = 2 nonzero path coefficients.The path model result is shown inFigure 3(a). A confirmatory SEMmodel was also derived starting from afully connected model for each subjectand then averaged to obtain the finalfunctional connectivity map, which isshown in Figure 3(b). As seen fromFigure 2, the fully connected modelwith q = 3 nonzero path coefficientshas a lower fit index of P-value.

ResultsThe best model of q = 2 paths clearlyconforms to the process of theoretical-ly preferred model. Since the stimuliused in this experiment were all visualpatterns, the main input region is PVSarea, and a connection is drawn direct-ly forward from PVS to RPSA andfrom PVS to LPSA, respectively tomodel the process of visual sensoryand psychomotor operation. Botheffects are looked on as direct effects.This may be understood as a simplemodel of an inner visual circuit or

neural network. PVS is putatively responsible for receivingand analyzing the input from peripheral visual stimuli andthen directing the signals to the contralateral primarysomatomotor areas.

English Reading Task

DataThe data was collected from a previous study investigatingneural substrates of silent reading of English, Pinying, andChinese tasks, involving early Chinese-English bilingualtenth graders [44]. Subjects were asked to silently read

Fig. 2. Measures of model goodness for a series of automatically specified pathmodels: (a) χ2-value, (b) p-value, and (c) Akaike’s information criterion against theincreasing number of nonzero path coefficients obtained in the visual task.

Fig. 1. The three task-related component maps derived using SICA for a representativesubject whose time courses showed significant correlation with the visual stimulus; col-ored voxels demonstrate significantly activated regions: (a) primary visual sensory cor-tex, (b) right primary somatosensory area, and (c) left primary somatosensory area.

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English words with Indian-Tamil fonts (not familiar to thispopulation) serving as controls. An eight-block design (fourON/four OFF; ABABABAB), where epochs of activationwere alternated with epochs of rest, was used. A set ofEnglish words is divided over four blocks of 25 stimuli each.Sixty-four words from the Indian-Tamil language dividedinto four blocks of 16 were used. Each language readingblock lasted 30 s, while the control blocks lasted 20 s each.Each word stem remained on the screen for 1,200 ms with nointerstimulus interval.

Brain MRI scans were obtained on a magnet operatingat 2.0 T (Bruker, Germany). Axial T1-weighted imageswere acquired to define the anterior-posterior commissur-al (AC-PC) plane. Functional MR images were acquiredusing a T2∗ -weighted echo-planar imaging (EPI)sequence (TR = 2,000 ms, TE = 60 ms, flip angle 90◦

matrix size = 128 × 128, field of view = 230 × 230 mm,100 measurements). Seventeen axial slices, each having athickness of 6 mm and parallel to the AC-PC plane, wereacquired to cover the whole brain during each measure-ment. On the same occasion, sagittal or axial 3-D T1-weighted images by using a spoilt gradient echo (SPGR)sequence (TR = 11.4 ms, TE = 4.4 ms, FA = 15◦ FOV= 200 × 200 mm, matrix size = 256 × 256, slab thickness= 170 mm, voxel size = 0.66 × 0.77 × 1.55 mm3 ) wereacquired for structural overlay.

Activation DetectionAfter excluding the first eight dummy scans (16 s) in eachsession (during which magnetization steady state was beingreached), 60 scans were used for SICA. The fMRI scanswere decomposed into 57 IC maps. A threshold of kurtosisvalue κ = 5.0 was applied to remove the noisy sources, andcorrelation analysis technique was employed to pick out thecomponents of neural activations. All subjects showed fourmain ICA components that had significant correlation valueswith the stimulation time series (cor > 0.1), each exhibitingone region of significant activation at a threshold determinedby a p-value = 0.05: 1) the left superior parietal cortex(SPC); 2) the left inferior frontal cortex (IFC); 3) the anteriorcingulate cortex (ACC); and 4) the right middle temporalcortex (MTC). The four component maps of a representativesubject are shown in Figure 4.

Connectivity AnalysisThe time series of each region were obtained similar to thevisual task. The automated search of the best fitting modelwas also performed on the data of four regions. The p-valuefor χ2 value has a maximum when q = 3, and Akaike’sinformation criterion has a minimum when q = 3. The finalfunctional connectivity map was obtained by averaging theindividual connectivity maps across subjects.

ResultsThe best model, in terms of maximumprobability and minimum cost, asdepicted in Figure 5, has q = 3. TheIFG and ACC have been known to beinvolved in language processing in theliterature. MTG is heavily involved inword comprehension and retrieval.The SPG is known to be involved withattention of visual spatial tasks. Thecurrent task is visually challenging,and hence substantial attention isrequired from the subject.

Conclusions and DiscussionWe demonstrated that ICA finds high-er-order connectivities underlyingbrain regions in fMRI. The signalchanges in fMRI are subtle and inter-fered with other artifacts and randomnoises. PCA is unable to thoroughlyanalyze the connectivity without beingaffected by additive confounds, as thecorrelation between voxels is comput-ed from the mixed value of intensities.

Fig. 3. The path model for the fMRI data from visual experiment: (a) best fitted modelhaving q = 2 nonzero path coefficients and (b) a confirmatory model derived fromfully connected edges.

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The use of anatomical data is further complicated

by the fact that much of it has been obtained

in studies of monkeys, and it is not always

certain which area to include.

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However, ICA technique is capable of decomposing the fMRimages into a number of independent source signals, whichcould purely be artifacts, noises, or neural sources, and,hence, the neural source componentsare noise-free.

The different eigenimages extract-ed from PCA represent uncorrelatedneural systems. However, ICA aimsat separating the fMR images basedon a maximum independence criteri-on among different components,which is a stronger property thanuncorrelatedness. Due to the spatialindependence of different sourcesunderlying fMRI datasets, ICA couldperform a better separation of thesesignals and give a pattern of func-tional connectivity closer to thesources than those given by PCA.

Functional connectivity is often theresult of neuronal interactions alonganatomical or structural connections;in some cases of task-involved experi-ments, some connectivity may be dueto common input from an externalneuronal or stimulus source. Thus,after captured in fMR images, thisconnectivity is more likely to bedemonstrated with the same neuralsource signal or component, whichwas known as an activation map inprevious studies [13]. Other compo-nents obtained in decomposition offMR images may also be related toconnected components.

On the other hand, higher-orderconnectivity could not take the placeof second-order connectivity. It isbelieved that second-order connec-tivity still takes the dominant role inanalyzing brain interactions within aneural system. A neural system isusually composed of a number of brain regions that areresponsible for a certain brain function. In a certain neuralsystem, most connected regions could be interpreted by atemporal correlation, as they are involved in the samebrain function. However, it is not required and not realis-tic that the connected regions should have the samedependency of temporal variation. In that sense, higher-order connectivity is a much stronger property than sec-ond-order connectivity.

In such cases, an objective- or data-driven method is supe-rior to a purely theoretical or confirmatory approach. ICA isessentially an exploratory technique since no constraints or apriori information is placed on the system. This method canbe used to select regions that appear to be operating as afunctional unit. A significant correlation with the stimulationtime series can provide clues for regions that must be includ-ed in a structural equation model. Spatial ICA based on thespatial independence of components in fMRI data gives theunderlying spatial patterns of voxel intensities and suggestsregions that may be part of a functional system. Although the

correlation-based approaches to activation detection is possi-ble for detecting activated areas in the brain, it can only pro-vide the significance for an activated region, not the exact

Fig. 4. Component maps from ICA whose time series showed significantly correlatedregion with the input stimulation; colored voxels demonstrate significantly activatedregions. (a) The left superior parietal gyrus (SPG). (b) The left inferior frontal gyrus (IFG).(c) The anterior cingulate cortex (ACC). (d) The right middle temporal gyrus (MTG).

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Fig. 5. The path model for fMRI data obtained in silent read-ing of English words with Tamil words (unfamiliar to the sub-ject) used as a controlled task. The best fitted model wasgiven when q = 3.

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information of activation intensity. However, ICA has beendemonstrated as a more powerful method, not only for find-ing activation maps but for extracting intensity values fromthe component maps as well, due to its ability to separateactivation maps from artifacts and noises.

The amalgamation with Bullmore’s automated search forbest path model [24] provides a picture as to possible func-tional influences that could best account for the interactionsamong this brain operation network. This approach is indeeda significant step from conventionally confirmatoryapproaches in SEM, where a theory-constrained model isbeing modulated by evaluating the modification of paths andomission of regions. Although it has been concluded thatpath analysis methods could provide a realistic picture of theinteractions of brain activity and behavior, there is still noevidence for a direct, anatomical connection between theregions in question, especially the mechanisms underlyingbrain lesions or mental disorders, which could not beaccounted for by theoretical presumptions.

Our modeling approach, however, is not undoubtedly goodenough to find a irrefutable path model for an fMRI dataset.Questions still exist regarding the dependence of the p-valueon asymptotic distributional assumptions and of other detailsof the analysis, such as prior estimation of residual variancesand effective degrees of freedom. Theoretically, the anatomi-cal network may serve as a balance for validating theexploratory models. But it is affirmative that our approachwill have significant potentials in looking into unpredictableand abnormal events in brain functions.

AcknowledgmentsThe visual data was collected when J. C. Rajapakse was a vis-iting scientist at the Max-Planck-Institute of CognitiveNeuroscience, Leipzig, Germany. The English reading taskdata was provided by Dr. Y.Y. Sitoh of National NeuroscienceInstitute, Singapore. This work was partially supported by agrant to J.C. Rajapakse from Ministry of Education (MOE)and Agency of Science, Technology and Research (A*Star),Singapore, (A*Star ref. number: 0221010017).

Jagath C. Rajapakse is an associate pro-fessor in the School of ComputerEngineering (SCE) and the DeputyDirector of the BioInformatics ResearchCentre (BIRC) at the Nanyang Tech-nological University (NTU), Singapore.He is presently a visiting professor to theBiological Engineering Division,

Massachusetts Institute of Technology (MIT). He received aB.Sc. (Eng.) degree with first class honors in electronic andtelecommunication engineering from the University ofMoratuwa, Sri Lanka, and M.Sc. and Ph.D. degrees in elec-trical and computer engineering from the State University ofNew York at Buffalo. Before joining NTU, he was a visitingfellow at the National Institute of Mental Health, Bethesda,Maryland, and a visiting scientist at the Max-Planck-Institute of Cognitive Neuroscience, Leipzig, Germany.

The mission of Dr. Rajapakse's research is to investigatethe neural correlates and the genetic mechanisms of humanbrain function and disease by using neuroimaging and bioin-formatics approaches, leading to new therapies and drugs forbrain disease. He has authored more than 175 research publi-

cations in refereed journals, conference proceedings, andbooks in the fields of brain imaging, computational biology,and machine learning. His current research projects are sup-ported by grants from NTU, the Ministry of Education(MOE), the Science and Engineering Research Council(SERC), and the Bio-Medical Research Council (BMRC) ofthe Agency of Science and Technology for Research(A*Star), and National Grid Office (NGO), Singapore, andthe Singapore-MIT Alliance (Computation and SystemsBiology program).

Choong Leong Tan is a senior managerwith mTouche (Singapore) Pte Ltd, a lead-ing publicly-listed research and develop-ment company in southeast Asia. He isresponsible for its daily information tech-nology operations in the Asia region,including research in the fields oftelecommunication and product develop-

ment of mTouche's messaging platforms.He joined mTouche (Singapore) Pte Ltd in 2005. Before

joining mTouche he was a research fellow with theBioInfomatics Research Centre of the NanyangTechnological University of Singapore (NTU). During histwo-year tenure there, he was the project leader, leading agroup of researchers and Ph.D. candidates on an neu-roimaging project funded by the Agency of Science andTechnology for Research (A*Star). He received his doctorof philosophy in 2003 from NTU through a researchscholarship. His research was on magnetic resonanceimaging (MRI). Before that, he obtained his bachelor ofapplied science (in computer engineering) with honors in1998 through the accelerated honors program with NTUand was awarded the Postgraduate Training Initiativescholarship.

Zheng Xuebin is a Ph.D. student in theBioInformatics Research Centre (BIRC)under the School of Computer Engineering(SCE) at Nanyang TechnologicalUniversity, Singapore. He received a B.Sc.degree in electronics from the Universityof Central Lancashire, the UnitedKingdom, and an M.Sc. degree in

Telecommunications from the Queen's University of Belfast,the United Kingdom. His research deals with brain imagingand machine learning for the study of human neural systems.He developed graphical techniques for brain connectivityanalysis based on neuroimaging data.

Susanta Mukhopadhyay is a researchfellow at the BioInformatics ResearchCentre, School of Computer Engineering,Nanyang Technological University,Singapore. He received a B.Sc.(Hons) inphysics from Presidency College,Calcutta, India, and B.Tech. and M.Tech.degrees in radiophysics and electronics

from the University of Calcutta, India. He received a Ph.D.in computer science from Indian Statistical Institute,Calcutta, in 2003. His Ph.D. work was related to multiscaleimage processing under the framework of mathematical

IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE MARCH/APRIL 2006

IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE MARCH/APRIL 2006 111

morphology. He worked as a research associate at theBurnham Institute, La Jolla, California, from 2001–2003.

Kanyang Yang is currently a softwareengineer in the Shanghai Business Group,Kure Computing Center Co., Ltd. Hisresponsibilities include scheduling pro-jects of software development, designingand developing, and communicating andcoordinating between customers and engi-neers in both China and Japan. He

received a B.Sc. degree in computer science from FudanUniversity, China, and an M.Eng. degree in computer engi-neering from Nanyang Technological University, Singapore.His M.Eng. research was the analysis of brain connectivitywith independent component analysis (ICA). His main con-tributions include the restoration of fMRI dataset using anICA algorithm, developing the concept of higher-order func-tional connectivity in the human brain with the ICA tech-nique, and proposing an exploratory approach to modelingeffective connectivity in the human brain.

Address for Correspondence: Jagath C. Rajapakse,BioInformatics Research Centre, School of ComputerEngineering, Nanyang Technological University, N4-2a32 50Nanyang Avenue, Singapore 639798. Phone: +65 67905802.Fax: +65 67906559. E-mail: asjagath@ntu.edu.sg.

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