Multivariate Analysis of fmri Group Data Using Independent Vector Analysis

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1 Multivariate Analysis of fmri Group Data Using Independent Vector Analysis Jong-Hwan Lee 1, Te-Won Lee 2, Ferenc A. Jolesz 1, and Seung-Schik Yoo 1,3 1 Department of Radiology, Brigham and Women s Hospital, Harvard Medical School, MA, USA jhlee@bwh.harvard.edu 2 Institute of Neural Computation, University of California at San Diego, La Jolla, CA, USA 3 Dept. of BioSystems, Korea Advanced Insitute of Science and Techonology, Daejeon, Korea Abstract. A multivariate non-parametric approach for the processing of fmri group data is important to address variability of hemodynamic responses across subjects, sessions, and brain regions. Independent component analysis (ICA) has a limitation during the inference of group effects due to a permutation problem of independent components. In order to address this limitation, we present an independent vector analysis (IVA) for the processing of fmri group data. Compared to the ICA, the IVA offers an extra dimension for the dependent parameters, which can be assigned for the automated grouping of dependent activation patterns across subjects. The IVA was applied to the fmri data obtained from 12 subjects performing a left-hand motor task. In comparison with conventional univariate methods, IVA successfully characterized the group-representative activation time courses (as component vectors) without extra data processing schemes to circumvent the permutation problem, while effectively detecting the areas with hemodynamic responses deviating from canonical, model-driven ones. Keywords: Independent Vector Analysis, fmri, Neuroimaging, Group Study, Multivariate Analysis. 1 Introduction Functional MRI (fmri) measures the blood-oxygenation-level-dependent (BOLD) signal changes associated with neural activity. Thus, temporal dynamics of the BOLD signal (time series; TS), called as hemodynamic response function (HRF), is the key element in analyzing fmri data. Typically, univariate approaches such as the generalized linear model (GLM) or regression analysis, are performed to estimate the conformity of a measured voxel-wise BOLD TS to the fixed, canonical HRF [1]. However, the BOLD TS may not be fully appreciated from the univariate methods due to the variations across subjects, scans, and brain regions [2]. ICA [3], as one of the multivariate approaches, has provided flexibility in data processing compared to the hypothesis-driven, univariate methods. Such flexibility applies especially when observed hemodynamic responses deviated from expected (hypothesized) HRF [4]. Task-related activation components, often similar in their M.E. Davies et al. (Eds.): ICA 2007, LNCS 4666, pp , Springer-Verlag Berlin Heidelberg 2007

2 634 J.-H. Lee et al. spatial/temporal patterns across subjects/sessions, may not be inherently generalized from individual to group level analysis since the ICA algorithm permutes the order of output components. Therefore, the task-related components across subjects/sessions were manually inspected and grouped in the previous study [5]. This method may require careful selection of the component-of-interest from the large number of subjects/sessions. In the present study, we propose a novel fmri analysis method for group processing based on independent vector analysis (IVA) [6]. IVA was originally proposed to address the limitation of the conventional ICA approach during the blind source/signal separation (BSS) in the frequency domain (i.e. permutation of extracted independent components across frequency bins). IVA correctly indexed the independent components (ICs) that were identified during the BSS in the frequency domain by utilizing the mutual dependency among the extracted ICs across frequency bins. Intuitively, the IVA model offers an extra dimension for processing dependent components, compared to the ICA model. In the fmri study, this extra dimension can be assigned for automated grouping of similar IC maps across subjects. Fundamentally, IVA is an extension of ICA, whereby the component of an input and an output stage forms a vector (instead of a scalar value as in the case of ICA). IVA assumes and, therefore, attempts to increase independency across output vector components, while maintaining dependency among scalar elements within each vector. The dependency in the fmri study is analogous to mutual activation patterns across the subjects, comparable to the group trend in similar spatial activation patterns. Using the IVA algorithm, the spatially-similar trend in activation maps across subjects (dependent, thus representing group-trend) can be derived as the output vector components. As a result, one can avoid the complications of manual selection of task-related IC maps/time-courses (TCs) across subjects, thus rendering the whole process user-independent. In order to show the utility of the proposed method, we implemented and applied the IVA algorithm to analyze fmri data of a left-hand motor clenching task using a short-time trial-based paradigm design. The obtained result was compared with the result from the generalized linear model (GLM) in SPM2 (Wellcome Department of Imaging Neuroscience, University College London, London, UK; 2 Methods 2.1 IVA Model and Learning Algorithm Figure 1 shows a schematic diagram of concurrent synthesis (generative) and analysis models for group data processing using IVA. In the synthesis model, the weighting values at the v th voxels associated with IC maps (assuming mutual dependence across subjects) were grouped into a single vector array assuming the spatial similarity across the subjects. Through the mixing matrix A (TCs represented by each column), the arrays of these vectors are linearly combined to form sets of other vector arrays (equal to the number of temporal points of the BOLD TS), each containing the measured BOLD signal from a specific (v th ) voxel location across all of the subjects. In the analysis model, the unknown weighting values (also associated with IC map) can be estimated via a corresponding unmixing matrix W. The matrix W can be

3 Multivariate Analysis of fmri Group Data Using Independent Vector Analysis 635 obtained by applying a learning rule to increase independence among output vector arrays (thus, sorting out the activation patterns). This is accompanied by maintaining dependence of weighting values within each output vector array, thus deriving mutual activations across the subjects for group inference. Fig. 1. The schematic diagrams of synthesis and analysis models for fmri group data pro- (1) ( M ) (1) ( M ) = a, L, a w = w, L, w. cessing using independent vector analysis. a [ ] and [ ] ji From the synthesis model in Fig. 1, the measured BOLD TS at the v th voxel of subject m can be represented as ji ji x = A c. (1) Each subject has its own mixing matrix (i.e. TCs) with independent activations (i.e. weighting values associated with IC maps) for the measured BOLD TS and does not share a mixing matrix with other subjects. In addition, the dependence among weighting values across subjects, within each unknown vector component, is assumed by the multivariate probability density function (p.d.f.) (1) ( M ) p( c i ) ( = p( ci, L, ci ) ). The boldface and lightface represent a vector/matrix and scalar value, respectively. The superscript and subscript denote the indices of the subjects and the IC map/fmri volumes, respectively. M is the number of subjects ( m { 1, L, M }), N is the number of fmri volume acquisitions corresponding to the unknown IC maps ( i, j, k { 1, L, N} ), and V is the number of voxels within a brain region ( v { 1, L,V} ). The number of unknown IC maps was assumed to be the same as the number of volume acquisitions in Fig. 1. The assumed number of IC maps can be further reduced using a dimension reduction scheme such as principle component analysis (PCA) [3,5]. Then, by applying an unmixing matrix in the analysis model (i.e. inverse of TCs), the weighting values at the v th voxel (across IC maps) of subject m can be estimated as ˆ ) ( m c = W x. (2) kj kj kj

4 636 J.-H. Lee et al. In order to derive learning algorithm, as presented in [6], the Kullback-Leibler (KL) divergence was adopted as a measure of independence of output vector components. Also, variance-dependent multivariate p.d.f. was utilized as a measure of dependence among elements within output vector component. By following the procedure in [6], (m) the algorithm for calculating an update term, Δ W corresponding to the unmixing matrix of the subject m, can be derived as T ( ) [ I ϕ( cˆ )( cˆ ) ] W, m Δ W (3) [ ] T where I is an identity matrix ( N N ), (m) ϕ( c ˆ ) = ϕ( cˆ 1 ) L ϕ( cˆ N ), and M ( l) 2 ϕ ( cˆ ( )) = ˆ ( ) = ˆ k v ck v c ( ). l 1 k v Applying Eq. (3), the unmixing matrix can be iteratively updated for the data from all voxels ( v = 1, L, V ). The only difference compared to the Infomax-based ICA (for the processing of a single subject data [3]) is the application of a nonlinear function ϕ ( cˆ ) (c.f. score function in ICA), which is dependent across subjects in IVA. 2.2 Application to Trial-Based fmri Data This study was approved by the local Institutional Review Board. Twelve righthanded subjects (aged , 5 females) performed one session of a left hand (LH) clenching (2 times/sec) task based on a short-time trial-based paradigm design (65-sec duration excluding 10-sec of dummy scans; task onset occurred at 15-sec followed by a 3-sec task-period). For the start/end of the task, a pre-recorded sound cue was played to the subject in the MRI system via an auditory headset (Avotec, Jensen Beach, FL). The fmri data was obtained in a 3-Tesla clinical scanner (Signa VH, GE Medical Systems) using a single channel, standard birdcage, head coil. To obtain functional data, an EPI sequence was applied to image most of the brain volume (13 axial slices, flip angle=80, TE/TR=40/1000msec, 64 frequency and phase encoding: in-plane voxels, 5mm thickness with a 1mm gap, 240mm square field-of-view) for detection of the BOLD TS associated with neural activity. Prior to group processing, individual EPI data was standardized to the MNI (Montreal Neurological Institute) space by following preprocessing steps in SPM2 (i.e. in order: slice timing correction, realignment, normalization, and spatial smoothing using an 8mm full-width-at-half-maximum 3-D Gaussian kernel). Before processing using IVA algorithm, a PCA-based dimension reduction scheme [3,5] was applied to reduce the number of IC maps/tcs to 50. The sum of corresponding 50 eigenvalues was more than 99% of a sum of total 65 eigenvalues for each subject. Using the IVA algorithm in Eq. (3) to a normalized set of dimension-reduced fmri group data, a semi-batch learning scheme [3] was applied to update the unmixing matrix of each subject. A batch of a mm 3 isotropic cluster (5 5 5=125 voxels due to the 2 2 2mm 3 isotropic voxel) was used, assuming dependencies of neural activations within this cluster across subjects. The learning rate (η ) was set to 10-3 throughout iterations. The iteration was stopped when a ratio of weight change ( ) ( ( ) m η ΔW m W ) was stabilized ( ~ ). After the algorithm converged, the resulting IC map (i.e. weighting values of TC) was transformed into a z-scored map by subtracting a mean value and dividing by the standard deviation [3].

5 Multivariate Analysis of fmri Group Data Using Independent Vector Analysis 637 Sign ambiguity of IC maps/tcs that typically arise from ICA-based methods [3, 4, 5, 7] also applied to the case of IVA. In IVA, the voxel-wise correlation coefficients between (1) the IC z-map within the activated regions ( z >threshold) and (2) the original fmri volumes were utilized. If the averaged (across time points) value of the correlation coefficients was negative, the sign of the IC z-map (& corresponding TC) was inverted. In order to find task-related components, a spatial sorting scheme was employed, whereby a voxel-wise correlation value between the sign-corrected IC z-map and cross-correlation (CC) map (obtained from the temporal correlation coefficients using the task-related canonical HRF) was regarded as the degree of task relevance of each IC z-map for each subject. This similarity measure (i.e. the voxel-wise correlation value) was then averaged across all subjects for each output vector array of IVA and subsequently sorted in descending order. The resulting five most task-related IC z-maps across subjects were processed using one-sample t-test implemented in SPM2 by considering a random effect (RFX) model [8]. These resulting task-related group activation maps of IVA were compared to the group activation map of GLM obtained from SPM2. After obtaining a group inference, the group activation maps were qualitatively compared in terms of location of activation. The areas with an activation volume greater than 5 5 5mm 3 (p<10-3 ) were identified and labeled from the Brodmann s Area (BA) and Automated Anatomical Labeling (AAL) templates (provided by MRIcro; 3 Results Figure 2 shows the task-related group activation maps obtained from GLM and IVA. In the results of GLM (Fig.2A), which is a univariate approach, a single task-related group activation map was acquired. In the results of IVA, the 5 most task-related components were selected after the reordering of output components based on the spatial sorting strategy explained in Section 2.2. The group activations (p<10-2 ~ p<10-7 ) were coded with a color gradient. The labeled anatomical areas of the group activations were listed in Table 1. From the analysis by GLM, the directly task-related areas (e.g. right primary motor area: M1, supplementary motor area: SMA, primary sensory area: S1, and cingulate gyrus) and paradigm-related areas (auditory; superior temporal) showed more significant activations compared to basal ganglia (caudate/putamen/pellidum) and thalamus (see Fig. 2A). In the results of IVA, the task-related activations (e.g. the right M1, SMA, S1, cingulate gyrus, and sup./mid. temporal gyrus) were extracted as the 1 st task-related group activation map ĉ 1. The group activations in the remaining components were dominant in the primary auditory area ( ĉ ), basal ganglia & thalamus ( 2 ĉ 3 ), inf. frontal & insular cortex ( ĉ ), and mid. 4 frontal & cingulate gyrus ( ĉ 5 ). From the comparison of group activation maps between GLM and IVA (Fig. 2), some of the activations revealed by IVA were underestimated by GLM. For example, the size of activated regions obtained in the auditory area by GLM (examples were shown with green circles in Fig. 2A) was reduced compared to the area detected by IVA (marked as green in Fig. 2B). Also, the activations in the basal ganglia/thalamus

6 638 J.-H. Lee et al. identified from IVA (blue area in Fig. 2B) were not detected when processed with GLM (examples were shown with blue circles in Fig. 2A). Fig. 2. Group activation maps obtained by (A) GLM and (B) IVA methods. For IVA, five most task-related component maps ( cˆ 1 ~ cˆ 5 ) were color-coded. Table 1. The strongly activated cortical areas inside group activation map. If any activated cluster (p<10-3) was bigger than 5 5 5mm3, the center of this cluster was registered using BA and AAL indices (provided by MRIcro; GLM Left-Hemisphere Inf. frontal / SMA / Insula / Mid. Cingulate / S1 / SupraMarginal / Sup. Temp. *BA: 6, 23, 24, 32, 42, 47, 48 Right-Hemisphere M1 / Inf. Frontal / SMA / Insula / Mid. Cingulate / S1 / Parietal (Sup., Inf) / SupraMarginal / Sup. Temp. *BA: 2, 3, 4, 6, 8, 23, 24, 32, 38, 40, 42, 44, 47, 48 c 1 : SMA / Mid. Cingulate / S1 / SupraMarginal / Temp. (Sup., Mid.) *BA: 3, 6, 8, 22, 23, 24, 32, 41, 42, 48 c 1 : M1 / Frontal (Sup., Mid.) / SMA / Mid. Cingulate / S1 / Parietal (Sup., Inf) / SupraMarginal / Sup. Temp. *BA: 2, 3, 4, 6, 23, 24, 32, 40, 48 c 2 : Insula / SupraMarginal / Heschl / Temporal (Sup., Mid.) *BA: 22, 42, 48 c 3 IVA : Frontal (Sup., Inf.) / Insula / Hippocampus / Amygdala / Putamen / Pallidum / Thalamus / Heschl / Sup.Temp. *BA: 11, 20, 25, 34, 38, 47, 48 c 2 : Heschl / Sup. Temp. *BA: 22, 48 c 3 : Insula / Hippocampus / Amygdala / Caudate / Putamen / Pallidum Thalamus *BA: 11, 20, 27, 34, 37, 38, 48 / c 4 / *BA: 6, 48 : Inf. Frontal / Insula SupraMarginal / Putamen / Heschl *BA: 45, 47, 48 c 5 : Mid. Frontal / Cingulate (Ant., Mid.) c 5 : / Sup. Temp. Sup. Temp. *BA: 24, 32, 48 c 4 : Inf. Frontal / Insula / Putamen *BA: 24, 32, 38, 45, 46 Insula / Cingulate (Ant., Mid.) /

7 Multivariate Analysis of fmri Group Data Using Independent Vector Analysis 639 We conjectured that the differences in activation maps between GLM and IVA were caused by the individual differences in temporal patterns of hemodynamic responses from the areas. Therefore, individual differences in the obtained TCs were further compared across subjects (Note that the TC represents a dominant feature of the BOLD TS corresponding to the activated voxels in the IC map). Figure 3 shows the individual TCs corresponding to three highly task-related group activation maps ĉ in Fig. 2B) by IVA. Here, we adopted the convention introduced by Duann et ( 1 ĉ ~ 3 al., [8], whereby the normalized TC (0~1) was coded in gray scale (black: 0 & white: 1) so that relative amplitudes can be readily discriminated within/across subjects. First of all, the TCs (Fig. 3A) corresponding to the 1 st (highly) task-related group activation map ĉ was in good agreement with the hypothesized HRF in GLM (yellow box: 1 task-related period; correlation coefficient between the averaged TC across subjects and the hypothesized HRF: 0.88). On the other hand, the TCs (Fig. 3B&C) corresponding to ĉ 2 & ĉ 3 showed some degree of variations in peak position within the task-related period. It is also notable that additional peaks during rest-periods were observed (examples are shown with arrows) with reduced correlation coefficients of 0.56 & 0.63, compared to the ĉ. Because of these large variations between the actual 1 hemodynamic responses (analogous to TCs) and the hypothesized HRF across subjects, the activations in the corresponding areas may not be detected by GLM. Fig. 3. Image plots of TCs across subjects corresponding to 3 highly task-related group activation maps ( ĉ ~ 1 ĉ 3 ). Each TC was normalized between 0 (black) and 1 (white). A yellow box indicates the period of task-related response. Green arrows indicate examples of the peaks during the rest-period. The plots in the bottom are the hypothesized HRF (green line), along with the averaged TC (blue line), and standard deviations (red bars) across all subjects. A correlation coefficient between the averaged TC and the hypothesized HRF is shown in the topright corner of each averaged time plot. A task-period (3-sec) is marked with thick black bar. 4 Conclusion In this study, we have proposed the use of IVA to infer the group-activation pattern from fmri data. The IVA algorithm was applied for multiple subjects BOLD signals

8 640 J.-H. Lee et al. and the spatially-similar trend in activation maps across subjects (dependent, thus representing group-trend) were derived as the output vector components. From the application of the proposed method to fmri data, the resulting IC maps/tcs of individual subjects provided reliable task-related information for a further group level inference. In addition, IVA provided more robust activation patterns than GLM (based on the hypothesized univariate HRF), especially when the HRF deviated from the hypothesized HRF (e.g. from the basal ganglia/thalamus). These results show the feasibility of IVA to be used in fmri group studies as potential alternative to conventional univariate approach. The proposed model may also be adopted to find out multivariate common activation patterns across multiple trials/sessions from a single subject data by substituting the index of a subject for the index of a trial/session. The IVA approach demands computational load since an individual unmixing matrix is iteratively trained using the results from other subjects (represented as nonlinear function, ϕ ( cˆ )), and thus, all of the unmixing matrices should be parallely updated. This increased computational demand can be alleviated by the increasing hardware memory. In order to achieve the fully-automated group processing using IVA, elaborate sets of optimization in terms of learning parameters and sorting schemes (for the selection of task-related features) are needed. Acknowledgments. This work was partially supported in part by grants from NIH (R01-NS to Yoo, SS and NIH U41RR to Jolesz FA). References 1. Worsley, K.J., Friston, K.J.: Analysis of fmri time-series revisited again. Neuroimage. 2, (1995) 2. Aguirre, G.K., Zarahn, E., D Esposito, M.: The variability of human, BOLD hemodynamic responses. NeuroImage 8, (1998) 3. McKeown, M.J., Makeig, S., Brown, G.G., Jung, T.P., Kindermann, S.S., Bell, A.J., Sejnowski, T.J.: Analysis of fmri data by blind separation into independent spatial components. Hum. Brain Mapp. 6, (1998) 4. Quigley, M.A., Haughton, V.M., Carew, J., Cordes, D., Moritz, C.H., Meyerand, M.E.: Comparison of independent component analysis and conventional hypothesis-driven analysis for clinical functional MR image processing. AJNR Am. J. Neuroradiol. 23, (2002) 5. Calhoun, V.D., Adali, T., McGinty, V.B., Pekar, J.J., Watson, T.D., Pearlson, G.D.: fmri activation in a visual-perception task: network of areas detected using the generalized linear model and independent component analysis. Neuroimage 14, (2001) 6. Kim, T.S., Attias, H.T., Lee, S.Y., Lee, T.W.: Blind source separation exploiting higherorder frequency dependencies. IEEE Trans. Audio, Speech and Language Process. 15, (2007) 7. Duann, J.R., Jung, T.P., Kuo, W.J., Yeh, T.C., Makeig, S., Hsieh, J.C., Sejnowski, T.J.: Single-trial variability in event-related BOLD signals. Neuroimage 15, (2002) 8. Friston, K.J., Holmes, A.P., Worsley, K.J.: How many subjects constitute a study? Neuroimage 10, 1 5 (1999)