Supplementary Data Supplementary Materials and Methods Step-by-step description of principal component-orthogonalization technique Below is a step-by-step description of the principal component (PC)-orthogonalization technique introduced in this article. Step 1: Conducted the multiple linear regression general linear model (GLM) with ordinary least squares (OLS) method with AFNI s 3dDeconvolve program. Y n = b 0 þ + k b k S kn þ e n, (1) where Y n is the nth time point of the voxel signal time-series, b 0 is the mean baseline, b k is the amplitude of the kth stimulus condition, S kn is the model signal of the kth stimulus condition at the nth time point, and + k denotes summation over k stimuli. e n is the nth time point of the GLM OLS regression residuals time-series. The four-dimensional (4D) data set of e n is termed RSDL. Similarly, the 4D residuals data set of the generalized least squares (GLS) estimation of Equation (1) is called RSDL GLS. GLS regression was performed with the 3dDeconvolve and 3dREMLfit programs in analysis of functional neuroimages (AFNI). Step 2: Performed principal component analysis (PCA) decomposition of the RSDL data set with AFNI s 3dpc program. Since the length of the modeled time-series was 203, this yielded 203 three-dimensional (3D) spatial PCs and 203 onedimensional (1D) eigen-time-series. Step 3: Performed GLM in Equation (1) with OLS regression with simultaneous orthogonalization of the top 40, 70, 80, and 100 PCs from Step 2. Y n = b 0 þ + r b r PC rn þ + k b k S kn þ e pcn, (2) where b r is the estimated coefficient of the rth PC eigentime-series and e pcn is the nth time point of the resultant PC-orthogonalized GLM. + r denotes summation over r PCs. For the case of PC orthogonalization with 80 PCs, e pcn is termed RSDL-ort80PC. Supplementary Results First-level residuals normality test results Supplementary Figure S1 shows the maps of nonwhite voxels (in red) as assessed by the Anderson Darling test for normality (obtained through application of AFNI s 3dNormalityTest program) for the RSDL GLS data sets for two representative subjects, overlaid on the gray-scale map of voxel time-series standard deviations of the corresponding RSDL GLS data sets. From Supplementary Figure S1A and B, it is apparent that departures from normality are often seen in residuals voxel time-series exhibiting high variance, for example, large sinuses. Amplification of detection power in PC orthogonalization Supplementary Figure S2 shows the variation in the amplification of detection power of the PC orthogonalization technique over conventional GLM with OLS approach, across the brain. It displays maps of ratio of Body condition z- statistic obtained with the PC orthogonalization technique to the Body z-statistic obtained with conventional GLM using OLS regression. The highest amplification is seen in large sinuses. Furthermore, gray matter areas exhibit appreciably more amplification than white matter regions. Effects of PC orthogonalization on brain activation maps Supplementary Figure S3 shows the average (across 21 subjects; for representational purposes) Body-Object contrast z-statistic obtained through conventional GLM with OLS approach (Supplementary Fig. S3A) and PCorthogonalized GLM using the top 80 PCs of the RSDL data sets. The data have been clustered at cluster detection threshold p < 0.001 and minimum cluster size = 20 voxels, rendering the maps in Supplementary Figure 1A and B significant at family-wise error (FWE) a < 0.05 and FWE a < 0.001, respectively. One can see that the PC-orthogonalized GLM reveals a larger cluster of body-part-specific activation in extrastriate body area. Displaying representative group independent components analysis maps Supplementary Figure S4 depicts the spatial maps of four independent components (ICs) obtained from group independent components analysis (ICA)-decomposition of the 21 subjects RSDL data sets. These results were obtained by applying Melodic ICA program (Beckmann et al., 2005) in the FMRIB software library (FSL) software suite (Smith et al., 2004). The data from the 21 subjects RSDL data sets were temporally concatenated, and FSL s probabilistic ICA algorithm (Beckmann and Smith, 2004) was applied on the resultant data set. The number of ICs to extract was estimated automatically by the Melodic program through the Laplace approximation to the posterior distribution of the model evidence (Beckmann and Smith, 2004). The data set mask input into the Melodic program comprised voxels common to all 21 subjects echo-planar imaging brain mask. Melodic estimated 21 ICs. Supplementary Figure S4 depicts maps of three ICs corresponding to well-known brain function networks (Smith et al., 2009): default mode network (DMN), cingulo-opercular and attention network, and somatosensory network; and one IC that depicts signal artifacts arising from cerebrospinal fluid (CSF) fluctuations in the ventricles and large sinuses.
Displaying Representative PCs Supplementary Figure S5 shows PCA component strength maps of three representative PCs from three subjects obtained from PC decomposition of the RSDL data set. The strength of a given PC at a given RSDL data voxel was the amount of signal in that voxel residuals time-series that was linearly related to the corresponding PC eigentime-series. This was quantified by the t-statistic of the regression coefficient obtained with ordinary linear least squares regression analysis. Supplementary Figure S4 displays a PC that exhibits significant linear (negative) relationship with DMN; another PC showing significant activation in cingulo-opercular and superior parietal premotor networks; and one PC that is severely contaminated by motion and physiological artifacts. Supplementary References Beckmann CF, DeLuca M, Devlin JT, Smith SM. 2005. Investigations into resting-state connectivity using independent component analysis. Philos Trans R Soc Lond B Biol Sci 360:1001 1013. Beckmann CF, Smith SM. 2004. Probabilistic independent component analysis for functional magnetic resonance imaging. IEEE Trans Med Imaging 23:137 152. Smith SM, Fox PT, Miller KL, Glahn DC, Fox PM, Mackay CE, et al. 2009. Correspondence of the brain s functional architecture during activation and rest. Proc Natl Acad Sci U S A 106:13040 13045. Smith SM, Jenkinson M, Woolrich MW, Beckmann CF, Behrens TE, Johansen-Berg H, et al. 2004. Advances in functional and structural MR image analysis and implementation as FSL. Neuroimage 23 Suppl 1:S208 S219.
SUPPLEMENTARY FIG. S1. Maps of voxels (in red) whose residuals time-series exhibit significant ( p < 0.05) departures from normality as assessed by the AD test, overlaid on gray-scale images of the standard deviation of the corresponding residuals time-series, of the RSDL GLS data sets of two representative subjects (A, B). AD, Anderson Darling.
SUPPLEMENTARY FIG. S2. Maps of the ratio of Body z-statistic obtained with the optimal PC-orthogonalized GLM to that of the Body Z-statistic obtained with the conventional GLM using the OLS approach. GLM, general linear model; OLS, ordinary least squares; PC, principal component.
SUPPLEMENTARY FIG. S3. Average (across 21 subjects) of first-level GLM Body-Object t-contrast (converted to standard normal z-statistic) thresholded CDT p < 0.001 and cluster size 20 voxels using conventional GLM with OLS approach (A) and the PC-orthogonalized GLM analysis (B). CDT, cluster detection threshold.
SUPPLEMENTARY FIG. S4. Spatial maps of four ICs obtained through group ICA decomposition of the RSDL data set depicting default mode network, cingulo-opercular network, somatosensory network, and cerebrospinal fluid (CSF) fluctuations in ventricles and sinuses, respectively. IC, independent component; ICA, independent components analysis.
SUPPLEMENTARY FIG. S5. PCA component strength maps denoting the significance (t-statistic) of the linear regression coefficient assessing the presence of signal represented by the corresponding PC time-series in voxels across the brain. (A) Shows prominent DMN loading (negative); (B) contains cingulo-opercular and superior parietal premotor networks; (C) is contaminated by motion and physiological artifacts. DMN, default mode network; PC, principal component; PCA, principal component analysis.