Semi-blind ICA of fmri: a method for utilizing hypothesis-derived time courses in a spatial ICA analysis

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1 NeuroImage 25 (2005) Semi-blind ICA of fmri: a method for utilizing hypothesis-derived time courses in a spatial ICA analysis V.D. Calhoun, a,b,c, * T. Adali, d M.C. Stevens, a,b K.A. Kiehl, a,b and J.J. Pekar e,f a Olin Neuropsychiatry Research Center, Institute of Living, Hartford, CT 06106, USA b Department of Psychiatry, Yale University, New Haven, CT 06520, USA c Department of Psychiatry, Johns Hopkins University, Baltimore, MD 21205, USA d Department of CSEE, University of Maryland Baltimore Country, Baltimore, MD 21250, USA e Department of Radiology, Johns Hopkins University, Baltimore, MD 21205, USA f FM Kirby Research Center for Functional Brain Imaging, Kennedy Krieger Institute, Baltimore, MD 21205, USA Received 10 June 2004; revised 2 December 2004; accepted 7 December 2004 Independent component analysis (ICA) is a data-driven approach utilizing high-order statistical moments to find maximally independent sources that has found fruitful application in functional magnetic resonance imaging (fmri). Being a blind source separation technique, ICA does not require any explicit constraints upon the fmri time courses. However, for some fmri data analysis applications, such as for the analysis of an event-related paradigm, it would be useful to flexibly incorporate paradigm information into the ICA analysis. In this paper, we present an approach for constrained or semi-blind ICA (sbica) analysis of event-related fmri data by imposing regularization on certain estimated time courses using the paradigm information. We demonstrate the performance of our approach using both simulations and fmri data from a three-stimulus auditory oddball paradigm. Simulation results suggest that (1) a regression approach slightly outperforms ICA when prior information is accurate and ICA outperforms the general linear model (GLM)-based approach when prior information is not completely accurate, (2) prior information improves the robustness of ICA in the presence of noise, and (3) ICA analysis using prior information with temporal constraints can outperform a regression approach when the prior information is not completely accurate. Using fmri data, we compare a regression-based conjunction analysis of target and novel stimuli, both of which elicit an orienting response, to an sbica approach utilizing both the target and novel stimuli to constrain the ICA time courses. Results show similar positive associations for both GLM and sbica, but sbica detects additional negative associates consistent with regions implicated in a default mode of brain activity. This suggests that task-related default mode decreases have a more bcomplexq signal that benefits from a flexible modeling approach. Compared with a traditional GLM approach, the sbica approach provides a flexible way to analyze fmri data that reduces the assumptions placed upon the hemodynamic response of the brain. The advantages and limitations of our technique * Corresponding author. Olin Neuropsychiatry Research Center, Institute of Living, 200 Retreat Avenue, Hartford, CT 06106, USA. address: vince.calhoun@yale.edu (V.D. Calhoun). Available online on ScienceDirect ( are discussed in detail in the manuscript to provide guidelines to the reader for developing useful applications. The use of prior time course information in a spatial ICA analysis, which combines elements of both a regression approach and a blind ICA approach, may prove to be a useful tool for fmri analysis. D 2004 Elsevier Inc. All rights reserved. Keywords: fmri; Functional; Brain; Independent component analysis; ICA Introduction Independent component analysis (ICA) is a data-driven approach that has been used to extract linearly mixed maximally independent components and their dual time courses from fmri data (McKeown et al., 1998). The majority of ICA of fmri proceeds by extracting spatially independent sources, although temporal ICA is also used (Biswal and Ulmer, 1999). Specifically, for spatial ICA, we assume the fmri data contains a set of sources (images) that have been linearly bmixedq by their fmri time courses. The problem then becomes one of bunmixingq the fmri data sources. ICA has been shown to be useful for characterizing data sets for which a specific a priori model is not available (Calhoun et al., 2002) or even to generate or improve upon models of neuronal function (Seifritz et al., 2002). However, a limitation of the existing ICA models that have been applied to fmri data is the lack of ability to incorporate information about the fmri paradigm into the algorithm. Because ICA is a blind source separation technique, no information is assumed about the time courses. Paradigm information is typically applied after the ICA algorithm in selecting the components of interest through sorting the component time courses according to some spatial or temporal criteria (Nakada et al., 2000). Such approaches aid in the interpretation of the output but do not directly utilize paradigm /$ - see front matter D 2004 Elsevier Inc. All rights reserved. doi: /j.neuroimage

2 528 V.D. Calhoun et al. / NeuroImage 25 (2005) information in the unmixing process. Another approach attempts to recombine components using the available paradigm information (McKeown, 2000). Such an approach, though useful, is a two-stage process and does not utilize the paradigm information directly in the ICA algorithm. Recent work has suggested that the real potential of ICA methods for fmri analysis will increase if prior information, when available, is incorporated into the estimation scheme (Suzuki et al., 2002). Since, in such cases, the motivation is to explicitly assume some information about the underlying sources or the mixing coefficients, the approach may be called semi-blind ICA (sbica). The challenge in such methods is how to incorporate the available information. Stone et al. presented a method that attempts to use a criterion that jointly determines spatial and temporal independent components, called spatiotemporal ICA, or incorporate skew symmetric source distributions as a more realistic fmri assumption (Stone et al., 2002). Suzuki et al. have also explored skew-symmetric distributions (Suzuki et al., 2002). Information about spatially varying hemodynamic delays has also been utilized to decrease bias in estimated ICA sources (Calhoun et al., 2003). The incorporation of prior information has been demonstrated in a Bayesian framework, in which available information is used to form prior probabilities about the sources (Choudrey and Roberts, 2001; Knuth, 1999; Rowe, 2000). Such approaches tend to be complex and computationally expensive, a major concern given the large size of fmri data sets. When working with a specific area such as fmri, a good number of additional assumptions are needed in order to derive the final form. In contrast, ICA constraints may be applied directly using an approach based upon Lagrange multipliers in which constraints are applied directly to the sources (Lu and Rajapakse, 2003). Lu and Rajapakse demonstrate their method on fmri by assuming temporal independence and constraining the time courses with a task-related reference function (Lu and Rajapakse, 2001). In our case, we are interested in performing spatial ICA, but applying constraints to the time courses (i.e., the mixing matrix). An aspect of ICA that has not yet been fully explored is the incorporation of constraints upon specific components, which are known to have particular properties (and not imposing these constraints upon other components whose properties are either different or not known). For example, it is well known that ICA components may be task-related, transiently task-related, physiology-related, artifact-related, etc. (Calhoun et al., 2004a). Most of the artifactual or physiologic components are not well suited to constraining due to a lack of prior information about these signals; thus, the algorithm must be able to bblindlyq detect such signals. The ability to incorporate prior information directly into the algorithm has several potential advantages. First, the performance of the algorithm may improve by incorporating information that is known about the time course into the algorithm. Secondly, components that are constrained to have a particular time course can be directly compared in an analysis of multiple data sets (e.g., a group analysis). Such comparisons are currently possible by manually sorting and combining (Calhoun et al., 2001a) or by estimating a single group mixing matrix or source matrix and back-reconstructing individual time courses and images (Calhoun et al., 2001b; Svensen et al., 2002). Although ICA can be useful to examine changes in events distributed over time (Duann et al., 2002), an additional motivation for our approach is that ICA is not well suited to the analysis of fmri data from event-related experiments that benefit from the ability to isolate activity closely related to specific events. In this paper, we demonstrate a simple but effective approach for incorporating information about the fmri paradigm into an ICA algorithm based upon the infomax principle (Bell and Sejnowski, 1995). We propose a component-selective constraint of the ICA model mixing matrix such that one or more specific components are constrained to be bcloseq to a paradigm-derived time course. The degree of closeness is specified by the user based upon amount of confidence placed in the information provided. Using simulations, we compare our sbica approach to standard ICA and also to a linear regression-based analysis. Finally, we demonstrate the performance on two runs of fmri data collected on 20 participants performing an event-related auditory oddball experiment. The auditory oddball elicits an attention orienting response that has been examined using fmri (Kiehl et al., 2001; Muller et al., 2003; Stevens et al., 2000). In this paper, hemodynamic correlations with target and novel stimuli were investigated in detail. In the current analysis, we were interested in detecting activity related to both target and novel activity. The target/novelrelated activity can be examined in the context of the GLM with a conjunction analysis (Price and Friston, 1997). However, such an approach is limited by fairly stringent modeling assumption. We were thus interested in how the results of sbica compared to more commonly employed conjunction analysis. We hypothesized that certain regions would be revealed by the sbica analysis as involved in the orienting response but not detected by the GLM analysis. Specifically, we predicted that higher order information integrative regions such as prefrontal and parietal cortex (which may be expected to have more bcomplexq fmri time courses and thus be more divergent from a simple predictive model) would be detected using sbica (Cohen et al., 1994). We also expected some regions in which the GLM model would slightly outperform the sbica analysis (specifically temporal lobe regions that fit the GLM model well, but slightly less well for the ICA analyses). Theory The ICA model, as typically applied to fmri data, assumes that the images x k for k =1,..., K time points may be described by C spatially independent sources s i for i =1,..., C, which are linearly mixed by coefficients a j where j =1,..., C. Assuming less sources that time points (C b K) and writing in matrix form, we have RX = AS where R is a C K data compression matrix, X is the K V data, A is the C C mixing matrix, and S is the C V source matrix, where V is the number of voxels. Typically, data compression is employed using principal component analysis (PCA) (McKeown et al., 1998). For the moment, we will assume no data compression. The source estimates are then written as U = A 1 X = WX. The independence among the sources may be maximized using an approach based upon the infomax principle (Bell and Sejnowski, 1995). This approach proceeds by maximization of the joint output entropy of sources passed through a non-linear squashing function. Using a gradient ascent approach leads to an iterative equation Dto update the weights as: W i ¼ W i 1 þ DW ð1þ

3 V.D. Calhoun et al. / NeuroImage 25 (2005) The update for the infomax using natural gradient is given by (Amari et al., 1996): DW ¼ g I þ JðuÞu H W ð2þ where the non-linearity is chosen as tanh (u) and J (u) = 2tanh (u). Such an approach has been shown to be equivalent to a maximum likelihood approach when the derivative of the non-linearity matches the assumed source density (Cardoso, 1997). Our approach involved constraining the columns of the A matrix (W 1 ) such that they are bcloseq to pre-specified time courses at each update of the weight algorithm. We utilize correlation as the distance metric (although other metrics, such as Kullback Leibler divergence, could be used instead). The tolerance for each constraint is specified in a C 1 vector t containing a tolerance value for each column of the mixing matrix and an R K design matrix D i for each column i of A (i.e., each component) containing R regressors, each with unit norm, as well as an N K design matrix common to all components, N, containing N nuisance criteria (e.g., intercept and drift terms). The D i matrix thus contains the prior information about the fmri time courses for each component i. At each iteration of the algorithm, alternating with the infomax update steps, we compute a multiple regression of the K (R + N) matrix K i ¼ D T i upon the N estimated columns of A (the fmri time courses) to produce the (R + N) 1 parameter estimates: D i N i ¼ K T i K 1K T i i a i ; and apply the distance criteria: q i ¼ corr D T i D i; a i to update the weights as follows: a i ¼ q izt i a i q i bt i a i þ c D T i D i þ N T ð5þ m i a i using a correction factor c to enforce the constraint. For time courses below the correlation tolerance t i, we are thus maximizing the independence of the sources while constraining the time courses to be close to a predictive model such that a i N T N i = D T i D i where the left side of the equation is the time course for component i (after removing the nuisance terms) and the right side is the predictive model. At each iteration, if the estimated time course is too far from the assumed shape, this approach bcorrects Q the estimated time course using the available prior information. If c = 0 then there is no correction applied, whereas if c = 1 then the time course is corrected to the shape of the constraining design matrix, exactly. A choice of c around 0.5 provides a balance between these two extremes. This correction is only applied if the regressor is below the correlation tolerance, t i, and most of the components will surpass the threshold (because little is known about the shape of their time courses and no constraint is applied and thus the correlation threshold t i is set to zero for these components). In this case, the lower part of the update equation (Eq. (5)) not computed. Since at initialization of the algorithm most of the weights will be random, prior information is used to improve convergence for the sources for which prior information is to be incorporated. Specifically, for the columns of interest (those which have a nonzero correlation threshold), the columns of A are resorted (and the sources are recomputed) such that the update constraint will be applied to the columns of A that have the highest correlation with the ð3þ ð4þ constraint time courses. This will prevent a situation in which one of the unconstrained time courses randomly correlates well with a constrained time course. In this case the algorithm would in the best case be quite far from a stable solution (since the bwrongq column of A would be highly correlated with the constraint) and in the worst case would be more likely to find a local minimum. Since we have prior information about some of the time courses, resorting is a simple and inexpensive way to minimize these potential problems. In the event of data compression, the A matrix will be rectangular and the analysis above can proceed by using the pseudo-inverse of A instead of the inverse. Methods Simulations In order to examine the performance of the sbica approach, we performed two simulations. For the first simulation, we generated two bknownq time courses and 58 bunknownq time courses and mixed together 60 simulated spatial sources using these time courses. We then added Gaussian noise, resulting in several contrast-to-noise ratios for the known sources (CNR = 0.15, 0.46, or 1.38). Finally, we unmixed the sources using the sbica algorithm with varying amounts of constraint. This enabled us to examine the impact of the constraint upon the estimated time courses under different noise conditions. The second simulation (see Fig. 3) was a comparison of the maps and time courses for the sbica approach and a typical GLM analysis, when the prior information about one of two time courses of interest is not correct. For this simulation two spatial sources were generated (borders outlined in cyan or magenta) and a data set was generated using the bactualq or btrueq time courses (plotted in white) and other unknown time courses (randomly generated). For the unknown time courses the tolerance criteria was set to zero, i.e., q = 0. In addition, two predicted time courses (plotted in yellow) were generated. The first predicted time course was identical to the actual time course whereas the second predicted time course resembled the actual but did not adequately capture some of the features of the time course. The ICA algorithm time courses were then initialized using these two predicted time courses. To account for the impact of the initial conditions, 30 ICA estimations were performed and the average is presented in the results. Participants Participants were recruited via advertisements, presentations at local universities, and by word-of-mouth. Twenty healthy participants each provided written, informed, IRB approved consent at Hartford Hospital. Prior to inclusion in the study, potential participants were screened to ensure they were free from DSMIV Axis I or Axis II psychopathology. All participants had normal hearing (assessed by self-report) and were able to perform the oddball task successfully (to discriminate between the tones) during practice prior to the scanning session. Auditory oddball paradigm Two runs of auditory stimuli were presented to each participant by a computer stimuli presentation system (VAPP: psychiatry.ubc.ca/vapp/) via insert earphones embedded within 30

4 530 V.D. Calhoun et al. / NeuroImage 25 (2005) Fig. 1. Auditory oddball paradigm. The standard stimulus was a 500 Hz tone, the target stimulus was a 1000 Hz tone, and the novel stimuli consisted of nonrepeating random digital noises (e.g., tone sweeps, whistles). Each stimulus had duration 200 ms, the target and novel stimuli each occurred with a probability of 0.10; the non-target stimuli occurred with a probability of The stimulus duration was 200 ms with a 1000, 1500, or 2000 ms inter-stimulus interval. db sound attenuating MR-compatible headphones. The standard stimulus was a 500 Hz tone, the target stimulus was a 1000 Hz tone, and the novel stimuli consisted of non-repeating random digital noises (e.g., tone sweeps, whistles) (Fig. 1). The target and novel stimuli each occurred with a probability of 0.10; the nontarget stimuli occurred with a probability of The stimulus duration was 200 ms with a 1000, 1500, or 2000 ms interstimulus interval. All stimuli were presented at approximately 80 decibels above the standard threshold of hearing (80 db SPL). All participants reported that they could hear the stimuli and discriminate them from the background scanner noise. The intervals between stimuli of interest (i.e., target and novel stimuli) were allocated in a pseudorandom manner to ensure that these stimuli had equal probability of occurring at 0, 1/3, and 2/3 after Fig. 2. Simulation results for three different noise levels and four weight settings. In each box shown is the time courses resulting from two simulated taskrelated components for three different contrast to noise ratios (CNR). The constraints are either weak (tolerance = 0.25), strong (tolerance = 0.7), or full (tolerance = 1.0). Stronger constraints result in time courses that are closer to the task-related time courses.

5 V.D. Calhoun et al. / NeuroImage 25 (2005) the beginning of a 1500 ms image acquisition period. Because of this, the hemodynamic response to each type of stimulus of interest was sampled uniformly at 500 ms intervals. An MRI-compatible fiberoptic response device (Lightwave Medical, Vancouver, BC) was used to acquire behavioral responses. Prior to entry into the scanning room, each participant performed a practice block of 10 trials to ensure understanding of the instructions. The participants were instructed to respond as quickly and accurately as possible with their right index finger every time they heard the target stimulus and not to respond to the non-target stimuli nor the novel stimuli. The stimulus paradigm utilized to collect new data at the Olin center was slightly modified from those in Kiehl et al. (2001) (Kiehl and Liddle, 2001). The modification made involved changing the event times such that the target, novel, and standard stimuli in order to increase their orthogonality. Also, the stimulus frequencies were slightly modified in order to be audible in the 3T scanner environment. Imaging parameters Scans were acquired at the Olin Neuropsychiatry Research Center at the Institute of Living on a Siemens Allegra 3T dedicated head scanner equipped with 40 mt/m gradients and a standard quadrature head coil. The functional scans were acquired using gradient echo echo planar imaging with the following parameters (repeat time (TR) = 1.50 s, echo time (TE) = 27 ms, field of view = 24 cm, acquisition matrix = 64 64, flip angle = 608, slice thickness = 4 mm, gap = 1 mm, 29 slices, ascending acquisition). Six bdummyq scans were performed at the beginning to allow for longitudinal equilibrium, after which the paradigm was automatically triggered to start by the scanner. Fig. 3. Comparison of ICA, sbica, and GLM analyses. Three analyses (averaged over 30 initial condition settings) at two CNR levels are presented. The right side of Fig. 2 shows a comparison of the spatial maps of the sbica analysis with a GLM analysis. Original activation boundaries for two temporally distinct activations are outlined in cyan and magenta. The sbica time courses are presented in cyan and magenta on the left side of the figure along with the predicted (yellow) and actual (white) waveforms. For C/R 1 the predicted and actual time courses are identical whereas for C/R 2, there is a mismatch. In the high noise situation, constrained ICA is more robust to noise and performs better than the GLM for the mismatched case and almost as well as the GLM for the matched case.

6 532 V.D. Calhoun et al. / NeuroImage 25 (2005) Data analysis Preprocessing Data were preprocessed using SPM2 (Worsley and Friston, 1995). Images were realigned using INRIalign a motion correction algorithm unbiased by local signal changes (Freire and Mangin, 2001; Freire et al., 2002). Data were spatially normalized into the standard Montreal Neurological Institute space (Friston et al., 1995), spatially smoothed with a mm full width at half-maximum Gaussian kernel. A fifth-order IIR Butterworth low-pass filter of 0.16 Hz was applied to remove any high-frequency noise associated with alterations in the applied radio frequency field. The data were slightly subsampled to mm, resulting in voxels. For display, even slices 8 38 are presented. GLM analysis Data for each subject were analyzed by multiple regression incorporating regressors for the novel, target, and standard stimuli and their temporal derivatives plus an intercept term. Regressors were created by modeling the stimuli as delta functions convolved with the default SPM2 hemodynamic response function and also including the temporal derivative of this function. Only correct responses were modeled. A second-level conjunction analysis between the target and novel stimuli was then performed (Price and Friston, 1997) using the amplitude estimates from the first-level analysis following amplitude bias correction by the derivative terms (Calhoun et al., 2004b). A conjunction analysis was performed to examine activity associated with both the target and novel stimuli and for comparison with the sbica approach constrained by the target and novel stimuli. ICA analysis We performed ICA on all in-brain voxels using the sbica algorithm implemented in a Matlab toolbox (Egolf et al., 2004). For the fmri data we were interested in modeling regions that are associated with the target and novel stimuli. Regressors for both stimuli were generated in the standard way by convolution with the SPM hemodynamic response function. We then created a design matrix D 1 for component 1 which had two columns, one containing the target stimuli regressor and one containing the novel stimuli regressor. Two nuisance regressors, contained in N, were used: an intercept regressor and a linear drift Fig. 4. Comparison of ICA and sbica for non-constrained source. Comparison of source separation results for (a) blind ICA, (b) semi-blind ICA, and (c) the ground truth. The constrained time course (tc 2) and spatial map (map 2) show market improvement and the unconstrained source is not adversely affected.

7 V.D. Calhoun et al. / NeuroImage 25 (2005) regressor. The data for each of the 20 participants were each reduced to 30 dimensions using PCA, followed by a sbica analysis with c = 0.5 and using q i=1 = 0.45 for the novel/target component and q ip1 = 0 for the remainder of the components (i.e., one component was constrained to fit well to the target/ novel design matrix). The component images were then calibrated to the raw data so the intensity values were in units of percent signal change from the mean. Briefly, the components are calibrated using linear regression, i.e., the estimated ICA time course is treated as the model and fit to the raw data. This fit is used to scale the component images into units that reflect the deviation of the data from the mean and enables a second-level random effects analysis to be performed (Calhoun et al., 2001c). The target/novel constrained component was extracted for each of the 20 participants. Following this, a voxelwise random effects analysis was performed on the component image by entering the component images into a one sample t test. A direct comparison of the GLM and ICA results was performed using a paired t test between the two analysis approaches. For both the GLM and ICA analyses a corrected threshold of q b 0.05, which controls for the false discovery rate (FDR), was used (Genovese et al., 2002). Results Simulation 1 Fig. 2 shows simulation results for the two bknownq time courses under three different noise levels. Four different weight combinations are shown ranging from no constraint, i.e., standard ICA with initialization of the mixing matrix (Fig. 2a; blue and magenta curves; q = 0) to full constraint (Fig. 2d, magenta curve; q =1,k = 1). Clearly, the more weight given to a known time courses the more the resulting ICA-estimated time courses resemble the original. In this simulation, the constraint was based upon perfect prior information, so any variation about the estimated time course is due to fitting the noise. Note that even for a weak constraint (Fig. 2b, magenta curve) the time courses estimate improves considerably. Simulation 2 The right side of Fig. 3 shows a comparison of the spatial maps of the sbica analysis with a GLM analysis. Two different bactivationsq are presented in the same image, with original boundaries outlined in cyan and magenta. These activations Fig. 5. Comparison of ICA and sbica in one participant. Results for task-related component for blind ICA (left) and sbica (right). ICA tends to capture primarily temporal lobe regions and is not highly task related. The correlation with the novel/target regressor is significantly increased (0.51 vs. 0.33) for the sbica analysis.

8 534 V.D. Calhoun et al. / NeuroImage 25 (2005) Fig. 6. Results from auditory oddball GLM and sbica group analyses. SPM conjunction analysis between novels and targets (left) and sbica component for the novel/target constrained component (right). Both analyses are FDR corrected at P b were smooth and thus represent a range of spatially varying contrast-to-noise (CNR) values with the highest being in the middle of the activation and the lowest on the edge. The sbica time courses are presented on the left side of the figure and are plotted in cyan and magenta. Also shown are the predicted (yellow) and actual (white) waveforms for component (C, in the ICA case) or regressor (R, in the GLM case) 1 and 2 (C/R 1 and C/R 2). For C/R 1 the predicted and actual time courses are identical, whereas for C/R 2 the predicted time course is a smooth function with two modeled events while the actual time courses have additional modulations and the delay for the second event is slightly earlier than predicted. In all cases, the algorithm converged. A question that arose was whether the sbica constraint would negatively impact the unconstrained components. To test this, we performed an additional simulation. Fig. 4 shows blind ICA (Fig. 4a), semi-blind ICA (Fig. 4b), and ground truth (Fig. 4c) time courses and images for two sources. The data set consisted of a image with 60 time points containing 40 simulated sources. The data were first reduced to 40 dimensions using PCA, then processed using our sbica algorithm using the same parameters as for the fmri data analysis. One of the sources (colored in magenta) was constrained for the sbica analysis and another one, overlapping with the constrained source (colored in cyan) and correlated temporally with a value of 0.46, was not constrained. The semiblind ICA results (Fig. 4b) show marked improvement for the Fig. 7. Comparison of sbica time courses and target/novel regressors. For the first run, the group averaged sbica time course (yellow) is plotted with the target (cyan) and novel (magenta) regressors.

9 V.D. Calhoun et al. / NeuroImage 25 (2005) constrained source and no apparent degrading of for the unconstrained source. fmri experiments On the auditory oddball task, performance was as follows: reaction time F ms, accuracy for target detection 99.6 F 0.54%, novel false alarms 0.46 F 0.28%, standard false alarms 0.15 F 0.10%. A comparison of ICA and sbica for one participant is presented in Fig. 5. For the blind ICA analysis the component of interest was selected by performing a multiple regression of the target/novel regressor upon the ICA time courses. The component that was most highly correlated with this regressor was selected. The blind ICA tends to capture temporal lobe regions into a separate component but is not strongly correlated with the task. The sbica approach also includes motor and parietal regions and the correlation value is significantly higher (0.51 vs. 0.33), as expected. The fmri results for the GLM conjunction analysis (left) and the sbica analysis (right) are presented in Fig. 6 (FDR corrected q b 0.05). Large portions of temporal lobe, motor and supplemental motor cortices, and thalamus are active. For the sbica analysis, a slightly greater spatial extent in activated regions is observed as well as additional negatively correlated parietal regions. The average correlation with the target/novel regressor across the 20 participants and 2 runs was q = The average time course for run 1 is presented in Fig. 7 (yellow curve) along with the regressor for target stimuli (cyan) and that for the novel stimuli (magenta). The average ratio of target to novel stimuli weights estimated by the sbica approach was 1.7; thus, the target stimuli were contributing about 2/3 of the amplitude to the final component and the novel stimuli about 1/3 of the amplitude on average (although the relative weight contributions are allowed to vary between participants since both target and novel regressors are contained in the design matrix, D 1 ). This is also evident from Fig. 7 since the estimated time course most resembles the target stimuli regressor. A direct comparison of the GLM and the sbica results using a paired t test are presented in Fig. 8 thresholded at FDR corrected q b Talairach coordinates for the difference between the GLM and sbica approaches are presented in Table 1. Discussion We have demonstrated an approach for incorporating information about the fmri paradigm into an ICA analysis. The proposed algorithm has a number of advantages over blind ICA or GLM approaches. Simulation results illustrate three key points. First, in the low noise case (Fig. 3a), both the GLM and ICA do well when the predicted information is perfect, with the GLM slightly outperforming ICA (additional voxels detected on the edge of the activation). However, when the predicted information is not correct the ICA approach does a much better job of estimating the time courses and the activated regions (as expected). Secondly, in the high noise case (Fig. 3b), the GLM model was found to be more robust whereas the ICA results show considerable degradation. Thirdly, in high noise situation (Fig. 3c) the sbica approach shows improved performance over the GLM when the prior information is not accurate (C/R 2) and Fig. 8. Direct comparison of sbica and GLM group results. A paired t test comparison of the GLM and sbica results (FDR corrected P b 0.05). Regions where sbica is greater than GLM are indicted in red and regions where GLM is greater than sbica are indicated in blue. similar performance for C/R 1. These results suggest that in high noise situations prior information is crucial to the success of ICA. Additionally, we demonstrate that, even in high noise situations, if the predicted waveforms are not correct, ICA can outperform the GLM when prior information is effectively incorporated into the analysis. For fmri analyses, sbica thus provides a flexible fit to the fmri time course rather than a rigid constraint and is thus able to gracefully handle departures from the predicted time course. It is thus useful in situations where small departures from the predicted model are expected. Additionally, the inclusion of the other, unconstrained components in the analysis provides a type of noise filtering of the data (these components may of course be utilized in a typical, ICA exploratory approach if desired; Bannister et al., 2001). Thirdly, since the components are constrained, they can now be readily compared in a group analysis (for more exploratory ICA group analysis approaches, see Calhoun et al., 2001b; Svensen et al., 2002). Finally, the sbica approach provides a representative time course, which may be useful for interpretation and/or subsequent analyses. Each of the three approaches has different advantages and disadvantages. A comparison of some of the properties of the GLM, blind ICA, and semi-blind ICA approaches is provided in Table 2. There are several parameters that must be selected for our sbica approach, including the correlation tolerance for each component i, t i, the prior information time courses, D i, and the correction amount c i. In practice we have found good results by setting the correction amount to 0.5, thereby allowing the algorithm learn the true shape of the time courses from the data.

10 536 V.D. Calhoun et al. / NeuroImage 25 (2005) Table 1 Talairach coordinates for ICA and GLM target analyses Area Brodmann L/R volume (cc) L/R random effects: Max T (x,y,z) Positive (sbica N GLM) Precuneus 23,31,7,19 2.5/ (0, 57,19)/4.1 (6, 60,20) Medial frontal gyrus 11,25,10,9,8,6 2.6/ ( 6,29, 12)/5.5 (3,34, 12) Superior frontal gyrus 6,10,9,8,11 0.4/ ( 21,52, 13)/4.7 (12,18,71) Posterior cingulate 23,30,31,29 0.6/ (0, 54,19)/5.0 (6, 54,19) Anterior cingulate 24,32,10,25,42,9 3.9/ ( 6,29, 6)/4.7 (3,35, 7) Parahippocampal gyrus 19,37,36,30 0.2/ ( 21, 47,2)/4.0 (21, 47, 8) Cuneus 30,7,19,17,18 0.5/ ( 24, 78,9)/3.4 (12, 58,11) Superior parietal lobule 7 0.0/ (0, 67,59)/3.2 (6, 64,53) Middle temporal gyrus 21,20,39 0.6/ ( 59, 27, 9)/4.7 (56, 32, 8) Fusiform gyrus 37,19 0.2/ ( 36, 53, 7)/4.1 (24, 50, 8) Lingual gyrus 19,18,17 0.1/ ( 21, 79,1)/3.3 (18, 47,2) Middle frontal gyrus 8,11,9,10 0.3/ ( 21,49, 13)/3.2 (18,34,37) Subcallosal gyrus 11,25,47 0.4/na 5.8 ( 12,26, 11)/na Inferior frontal gyrus 47,11,25 0.3/ ( 12,29, 12)/3.0 (48,31, 12) Middle occipital gyrus 19,18 0.3/ ( 27, 78,15)/2.7 (27, 78,23) Caudate 0.3/na 4.5 ( 12,26, 6)/na Postcentral gyrus 3,5,7 0.3/ ( 15, 40,71)/2.6 (12, 55,64) Cingulate gyrus / (0, 57,25)/3.8 (3, 60,25) Negative (GLM N sbica) Lingual gyrus 18,19,17 6.8/ (0, 81,7)/3.6 (0, 79,1) Cuneus 18,17,23,30,19 6.4/ (0, 78,15)/4.1 (3, 81,15) Superior temporal gyrus 22,21,41,42,38,29 5.9/ ( 59, 12,1)/3.3 (53, 20,7) Thalamus 2.1/ (0, 23,12)/3.5 (3, 17,1) Middle temporal gyrus 21,22 1.5/na 4.2 ( 56, 9, 5)/na Parahippocampal gyrus /na 3.8 ( 15, 53, 7)/na Middle occipital gyrus 18,19 0.2/ ( 27, 93,10)/3.7 (27, 93,10) Posterior cingulate 30,23,31 0.6/ ( 3, 69,12)/3.0 (3, 25,18) Precentral gyrus 6,4 0.0/2.1 na/3.1 (33, 20,70) Postcentral gyrus 3,1 0.0/0.4 na/2.8 (33, 29,68) Precuneus /na 3.5 ( 6, 69,20)/na Transverse temporal gyrus 42,41 0.5/ ( 59, 17,12)/2.8 (53, 20,12) Medial frontal gyrus 11,10 0.2/ (0,55, 13)/2.9 (6,55, 13) Voxels above the threshold for Fig. 8 were converted to Talairach coordinates and entered into a database to provide anatomic and functional labels for the left (L) and right (R) hemispheres. The volume of activated voxels in each area is provided in cubic centimeters (cc). Within each area, the maximum t value and its coordinate are provided. The tolerance criteria, t i, are only non-zero for components that have available prior information. We chose standardized units of correlation in order to enable an intuition about selecting this parameter. If the tolerance is close to one, then the advantages of having a flexible modeling approach will not be utilized. If the tolerance is close to zero, then the algorithm becomes a standard ICA approach. We have found good results on the oddball data by adjusting the tolerance criteria to a moderate value in order to provide a balance between the two extremes. Finally, the time courses, D i, can be derived in the standard way by convolving the idealized paradigm regressors with a hemodynamic response function. While the GLM conjunction analysis of the fmri data provides a way to examine target/novel activity, such an approach utilizes a Table 2 Comparison of GLM, ICA, and sbica approaches Traditional GLM Blind ICA Semi-blind ICA Hypothesis-driven Not hypothesis-driven Hypothesis-driven (for constrained components) Not data-driven Data-driven Data-driven (for unconstrained components) a Sensitive to incorrect model specification No model Sensitivity to incorrect model specification can be controlled No representative time course Representative time course Representative time course No sorting required Component sorting required No component sorting required (for constrained components) Relies on prior information No prior information utilized Can utilize prior information More robust to noise Less robust to noise Robustness to noise can be controlled Univariate Multivariate Multivariate Group analysis straightforward Group analysis not straightforward Group analysis straightforward (for constrained components) An examination of how the GLM, ICA, and sbica approaches behave along several dimensions. a In this paper, we did not exploit the information contained in the unconstrained components...to do so would be similar to the examination/sorting of components in a blind ICA approach (McKeown et al., 1998).

11 V.D. Calhoun et al. / NeuroImage 25 (2005) fairly stringent modeling approach. Though some flexibility is provided by the incorporation of the temporal derivative, we were interested in whether additional regions were not being detected due to departures from the predictive model. Additionally, we were interested in examining a representative time course for the conjoined result. The sbica approach provides a natural way to allow departures from the model while still constraining the final estimation to be close. The sbica algorithm is thus used to perform a bselectiveq time course shaping by selecting a relatively sparse set of regions that contribute significantly to the time course data-derived bmodelq. On the whole, the GLM and ICA results for the component of interest were similar but not identical. Consistent with our hypothesis, frontal and parietal regions were detected by the sbica approach but not by the GLM approach. However these regions were also found to be negatively associated with the task. The negative correlation is consistent with regions implicated in the socalled bdefault modeq network, which are typically found to be negatively correlated with the presented task (Raichle et al., 2001). However, more work is required to examine whether there is a relationship between these regions and a default mode network. In some regions, the GLM approach was found to be greater than the sbica approach, although mostly in regions in the temporal lobe and thalamus, which were also detected by the sbica approach. This may reflect the improved detection power of the GLM model when the data are close to the predicted model. The only region that was increased for the GLM but not detected for sbica was the primary visual cortex. This region exhibited significant departures from the HRF model, enough so to be separated into a different, unconstrained component. We have previously found transient activation in similar regions (Calhoun et al., 2001b). The sbica approach we have presented attempts to find a solution that maximizes the spatial independence of the component images while simultaneously maintaining task-related time course(s) that closely fits the paradigm. There is thus a competition between the spatial and temporal dimension. It is thus important, when constraining more than one component, to select temporal constraints that are expected to be reasonably spatially independent (perhaps ascertained by a previous GLM analysis). For example, it is not reasonable to attempt to constrain two components, once with the target stimulus and one with the novel stimulus since it is well known that these stimuli elicit largely overlapping responses in temporal lobe, thalamus, and parietal lobe (Kiehl et al., 2001). Because the assumption of spatial independence is violated in such a situation (Calhoun et al., 2001d), the sbica algorithm would not be expected to perform well under such constraints. Standard limitations of the GLM are also relevant in this situation, for example, it is not reasonable to constrain two components if both time courses are highly collinear. Limitations of our approach include the need to select additional parameters, although an advantage is that post hoc sorting of components is not required. In future work we hope to extend our approach to adaptively determine the tolerance criteria as well as to analyze the tradeoffs between the spatial independence constraint and the time courses constraint. Additionally, in this study both the GLM and ICA analyses were performed using the same preprocessing (motion correction, smoothing, etc.) as in (Calhoun et al., 2004b). However, differences in these preprocessing stages can affect the results for both the GLM and sbica analysis and can be analyzed in a framework as in (Calhoun et al., 2004a). Conclusions We have demonstrated an approach for performing semi-blind ICA of fmri data in order to utilized prior information about the paradigm time courses in the algorithm. Our approach requires no post hoc sorting of components (for the constrained components), appears to improve the robustness of ICA in the presence of noise and enables a flexible, yet constrained hemodynamic model while also producing an estimated fmri time course. This method enables control over various aspects of fmri modeling and thus is a complement to the existing approaches for fmri data analysis such as the GLM and blind ICA. Acknowledgments We would like to thank the research staff at the Olin Neuropsychiatry Research Center who helped collect and process the data. 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