Information-based functional brain mapping -- Kriegeskorte et al. 103 (10): 3863 Data Supplement - HTML Page - index.htslp -- Proceedings of the National Academy of Sciences

Kriegeskorte et al. 10.1073/pnas.0600244103.

Supporting Information

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Supporting Figure 3
Supporting Text
Supporting Figure 4

Supporting Figure 3

Fig. 3. Simulated fMRI data, statistical maps. Unthresholded mapping results obtained with different statistics for the simulated fMRI data. This figure promotes an intuitive understanding of the quantitative ROC results presented in Fig. 1. All maps show the central slice of the simulated 3D volume. (Top Left) The regions containing the simulated effect patterns. Functional contrast to noise varies horizontally, region size vertically within the slice (blue axes; see Methodological Details). (Top Right) The t map obtained by conventional voxelwise-univariate contrast analysis (condition 1 versus condition 2) performed on unsmoothed data. Note that this approach does not highlight the regions very clearly, even for high contrast-to-noise ratios. (Center Left) The absolute t map. Large effect regions of higher contrast to noise are visually apparent here. When the same map (absolute t) is computed for smoothed data (Center Right), some correct hot spots remain, but many incorrect ones appear in random locations outside the effect regions. This reflects the fact that smoothing removes the information in the high-spatial-frequency band of the effects, i.e., adjacent opposite effects cancel out. Smoothing the absolute t map (instead of the data) provides a much better map (Bottom Left), which correctly highlights even smaller regions of lower contrast to noise. This reflects the fact that adjacent subtle effects now accrue (instead of canceling when they have opposite signs in the t map). The absolute t map has been smoothed by convolution with a sphere of 4-mm radius. Equivalently, this map can be thought of as the result of spherical-searchlight mapping, where the value at each voxel is the average absolute t value within the spherical neighborhood. An even better map is obtained by spherical-searchlight mapping using the Mahalanobis distance between the activity patterns within the spherical neighborhood as the statistic at each voxel (Bottom Right). The Mahalanobis map as well was obtained using a spherical searchlight of 4-mm radius. These visually apparent results are quantitatively substantiated by the ROC analyses in Fig. 1. The red-green color bar applies to the t map (Top Right). The color scale linearly spans the range from the minimum (negative) to the maximum (positive) value of the t map. The black-orange-yellow-white colorbar at the bottom applies to the lower four maps. The color scale linearly spans the range from 0 to the maximum value of each map. In all statistical maps the effect-region contours are shown in cyan. Two fine points should be noted: (i) Maps very similar to the Mahalanobis map can be obtained by either squaring each value of the smoothed absolute t map (this does not change the ROC) or by smoothing the map of squared t values. However, visual inspection with thresholds and ROC analysis reveal that the Mahalanobis map is superior to both of these alternatives. This indicates that the lower bias of the noise model implicit to the Mahalanobis map (i.e., a multinormal model) is worth its cost in terms of variance for the present combination of searchlight dimensionality and degrees of freedom. (ii) (Middle Right) Smoothing has been performed by convolution of each data volume with an 8-mm full-width-at-half-maximum Gaussian. Similar results are obtained using a 4-mm-radius sphere, i.e., the same spatial integration window used to obtain the maps of the bottom row.

Supporting Figure 4

Fig. 4. Real fMRI data, control analysis. Comparison of voxels marked in activation- (green) and information-based (red) mapping analyses. Voxels marked in both maps are shown in yellow. Fig. 4 replicates the comparison shown in Fig. 2 D and E for the same subject with one modification: Instead of using the false discovery rate (FDR) threshold obtained separately for each map, the FDR threshold obtained for the activation-based map (P = 0.0032) has been used for both maps. As a result, fewer voxels than before are marked in the information-based map and the expected FDR is lower than 5% for that map (conservative). Note that this does not entail a substantial change to the information-based map or the comparison (refer to Fig. 2 D and E for details.)

Supporting Text
Conventional Aspects of the Analyses.
Preprocessing of real functional MRI (fMRI) data.
The fMRI data sets were subjected to a series of preprocessing operations: (i) slice-scan-time adjustment, (ii) head-motion correction, (iii) removal of temporal drifts of frequencies below 0.009 Hz, and (iv) selection of brain voxels (those shown as anatomical background in Fig. 2) for mapping analyses and false discovery rate (FDR) thresholding. Steps i-iii were performed by using the brainvoyager 2000 software package (Brain Innovation, Maastricht, The Netherlands; Version 4.8). Step iv was performed in matlab (MathWorks, Natick, MA) by thresholding the spatially smoothed temporal average of the fMRI data. Design-matrix construction and linear modeling of real fMRI data.
In both the activation- and the information-based analyses, we assumed an instantaneous rectangular neural response to the stimuli and obtained hemodynamic response predictors from a linear model (1). The design matrix included these cognitive predictors along with six head-motion-parameter time courses, the global spatial-mean time course, and a confound-mean predictor. The activation-based analysis consisted in standard univariate linear regression and contrast t analysis. All activation- and information-based analyses were performed using custom software developed in matlab. Receiving-operator characteristic (ROC) analysis of statistical maps from simulated fMRI data.
We use ROC analysis to quantify how well different local effect statistics distinguish between the effect regions and the surrounding pure noise. An ROC depicts the tradeoff relation between sensitivity and specificity as the threshold is varied over the complete range of map values. In Fig. 1 B and C, the area under the ROC is used as a summary measure indicating to what extent high sensitivity and specificity can simultaneously be achieved, i.e., the quality of the effect statistic. More precisely, the area under the ROC represents three intuitively meaningful quantities: (i) the average sensitivity across all specificities, (ii) the average specificity across all sensitivities and (iii) the probability that upon drawing a random effect-region voxel and a random pure-noise voxel, the effect-region voxel will have the higher effect statistic. If the area under the ROC is 1, the effect statistic allows perfect classification of effect-region and pure-noise voxels by choice of an appropriate threshold. If the area under the ROC is 0.5, then the statistic does not order effect-region and pure-noise voxels better than chance.

1. Boynton, G. M., Engel, S. A., Glover, G. H. & Heeger, D. J. (1996) J. Neurosci. 16, 4207-4221.