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Prioritizing spatial accuracy in high-resolution fMRI data using multivariate feature weight mapping

Prioritizing spatial accuracy in high-resolution fMRI data using multivariate feature weight mapping METHODS ARTICLE published: 16 April 2014 doi: 10.3389/fnins.2014.00066 Prioritizing spatial accuracy in high-resolution fMRI data using multivariate feature weight mapping 1,2 † 1,3 † 4,5 6 Johannes Stelzer * , Tilo Buschmann , Gabriele Lohmann , Daniel S. Margulies , 1 1 Robert Trampel and Robert Turner Department of Neurophysics, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany Danish Research Centre for Magnetic Resonance, Copenhagen University Hospital Hvidovre, Hvidovre, Denmark Department of Diagnostics, Fraunhofer Institute for Cell Therapy and Immunology, Leipzig, Germany Department of Biomedical Magnetic Resonance, University Hospital Tübingen, Tübingen, Germany Magnetic Resonance Center, Max Planck Institute for Biological Cybernetics, Tübingen, Germany Max Planck Research Group for Neuroanatomy and Connectivity, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany Edited by: Although ultra-high-field fMRI at field strengths of 7T or above provides substantial Pedro Antonio Valdes-Sosa, Cuban gains in BOLD contrast-to-noise ratio, when very high-resolution fMRI is required such Neuroscience Center, Cuba gains are inevitably reduced. The improvement in sensitivity provided by multivariate Reviewed by: analysis techniques, as compared with univariate methods, then becomes especially Xi-Nian Zuo, Chinese Academy of welcome. Information mapping approaches are commonly used, such as the searchlight Sciences, China Agustin Lage-Castellanos, Cuban technique, which take into account the spatially distributed patterns of activation in order Neuroscience Center, Cuba to predict stimulus conditions. However, the popular searchlight decoding technique, in *Correspondence: particular, has been found to be prone to spatial inaccuracies. For instance, the spatial Johannes Stelzer, Danish Research extent of informative areas is generally exaggerated, and their spatial configuration Centre for Magnetic Resonance, is distorted. We propose the combination of a non-parametric and permutation-based Copenhagen University Hospital Hvidovre, Kettegaard Allé 30, statistical framework with linear classifiers. We term this new combined method 2650 Hvidovre, Denmark Feature Weight Mapping (FWM). The main goal of the proposed method is to map e-mail: [email protected] the specific contribution of each voxel to the classification decision while including a These authors have contributed correction for the multiple comparisons problem. Next, we compare this new method equally to this work. to the searchlight approach using a simulation and ultra-high-field 7T experimental data. We found that the searchlight method led to spatial inaccuracies that are especially noticeable in high-resolution fMRI data. In contrast, FWM was more spatially precise, revealing both informative anatomical structures as well as the direction by which voxels contribute to the classification. By maximizing the spatial accuracy of ultra-high-field fMRI results, global multivariate methods provide a substantial improvement for characterizing structure-function relationships. Keywords: fMRI, MVPA, searchlight, nonparametric statistics, decoding INTRODUCTION resolution is multivariate pattern recognition analysis (MVPA), The advent of functional magnetic resonance imaging (fMRI) which enables fine-grained components of the brain activity sig- at ultra-high-field strengths allows an impressively fine-grained nal to contribute relevantly (Norman et al., 2006). It is often insight into human cortical function. Modern scanners at 7T or desirable to map the spatial location of discriminating patterns, higher allow researchers to resolve functional data at ever finer or in other words, where in the brain information about the spatial scales, even to the point of resolving individual gray matter experimental condition is present. layers (Polimeni et al., 2010; Trampel et al., 2011). The bene- For this, “information mapping” methods, such as the “search- fits of improved resolution are accompanied by new challenges, light” approach are often employed (Kriegeskorte et al., 2006). however, particularly with regard to data analysis, as it is not The searchlight method attempts to extract the predictive power obvious which analysis technique may best take advantage of the of a small neighborhood of voxels (the searchlight)withregards richer data. For instance, classical activation-based approaches to the stimulus condition, and maps the result of the anal- such as the general linear model (Poline and Brett, 2012) generally ysis back to the center voxel of the searchlight. Repeating rely on spatial smoothing for statistical correction for multi- this procedure over all locations yields an information map ple comparisons, and hence are unable to make appropriate use charting the presence and location of information relating to of the high resolutions. While a more sophisticated approach stimulus condition. It should be noted that the searchlight has been proposed (Harrison et al., 2008) this is computation- method is essentially a local multivariate pattern recognition tech- ally laborious and does not have face validity in terms of actual nique that fails to take into account globally distributed voxel neuroanatomy. A more promising means of exploiting higher patterns. www.frontiersin.org April 2014 | Volume 8 | Article 66 | 1 Stelzer et al. Multivariate feature weight mapping Alternatively, global information maps can be computed task was confirmed using video monitoring. For the analysis in without such spatial preselection of voxels using multivariate our present work, only two conditions were used: Resting (no classifiers with support for high dimensional data or by using task, no hand movement, no motor imagination) and sequen- dimensionality-reduced brain data (e.g., by first performing a tial tapping with four fingers of the right hand to the thumb of principal component analysis). Appropriate classifiers provide the right hand. (The conditions omitted were: Imagined finger information on the contribution of individual features (i.e., voxels tapping without actual finger movement and finger movement without touching the thumb). or principal components) to the classification decision. Mapping this influence back onto the voxel space allows generation of a The experiment was performed with a MAGNETOM 7T whole-brain information map (Mourão-Miranda et al., 2005), scanner (Siemens Healthcare, Erlangen, Germany), using a 24- which delineates the discriminative volume. channel head coil (NOVA Medical Inc., Wilmington MA, USA). Previously, the searchlight method has been reviewed critically The functional scans contained 17–31 axial slices (depending on the grounds of interpretability and with regard to spatial inac- on the subject) covering the left motor cortex (TR = 3300 ms, curacies in the searchlight information maps which obscure the TE = 25 ms, slice thickness 0.75 mm, in plane resolution 0.75 × true local information content (Viswanathan et al., 2012; Etzel 0.75 mm ) using a novel acceleration technique (Heidemann et al., 2013). These shortcomings form the greatest concern with et al., 2012). very high spatial resolution fMRI data, such as that obtainable at Head motion correction was carried out using SPM8 ultra-high-field, as they may well negate the gain in higher spa- (Wellcome Department of Imaging Neuroscience, Institute of tial resolution. In particular, the lower voxel-wise signal-to-noise Neurology, London, UK). Low frequency drifts were removed −1 ratio at very high resolutions requires larger searchlight diameters using a temporal high-pass filter (f = 1/80 s )with highpass to obtain significant results, exacerbating spatial inaccuracies. LIPSIA (Lohmann et al., 2001). Using LIPSIA, a GLM was fitted In the present work, we investigate the quality of the search- to each trial to estimate its β-parameters. We used a gamma- light method as a tool for the analysis of ultra-high-field fMRI function as hemodynamic response function (Glover, 1999). data. As an alternative to the searchlight approach, we present The GLM yielded 15 three-dimensional β-maps per experimen- a global multivariate method adapted from previous work tal condition. The β-parameters were estimated on the z-scored (Mourão-Miranda et al., 2005), which we combine with a non- fMRI time series data (default settings in LIPSIA) and represent parametric solution for the multiple comparison problem (Stelzer the degree of fit between the trial data and the model. et al., 2013). To our knowledge, this is the first implementa- DATA GENERATION FOR SIMULATION tion fully accounting for the multiple comparisons problem, A simulated data set of 30 scans (15 each for class A and B) of one tailored for this widely used multivariate framework for brain “virtual” subject was generated. Each volume (size 66 × 22 × 22 mapping. We compare these two information-mapping methods voxels) was filled with Gaussian noise [∼ N(0, 1)] and smoothed as a means for analyzing ultra-high resolution fMRI and sim- slightly with a Gaussian smoothing kernel (FWHM = 1voxel). ulated data. Noteworthy, while both methods (searchlight and An offset size of 0.5 was added at six locations (three in class A global information maps) incorporate different assumptions and and B, respectively), shaping six half-cubes positioned above and implementations, in research practice the results ultimately are below the centerline of the volume (Figure 3A). Upper half-cubes interpreted in a very similar fashion: Both approaches provide were class A, lower half-cubes were class B. voxel maps, which delineate voxels containing stimulus-relevant The size of the half-cubes varied. The leftmost half-cube had information. a dimension of 6 × 6 × 1 voxels (fine information spread), the second one had a dimension of 6 × 6 × 2 voxels (medium infor- MATERIALS AND METHODS mation spread) and the rightmost half-cube 6 × 6 × 3voxels 7T TAPPING DATA SET (coarseinformation spread). Therewas a4-voxel gapbetween the The ultra-high field fMRI study comprised ten healthy subjects leftmost, a 2-voxel gap between the middle, and no gap between (age range 23–28, right-handed). The study was carried out in the two rightmost half-cubes (see Figure 3A). accordance with the ethics approval from the University of Leipzig and written informed consent was obtained before each study. SEARCHLIGHT DECODING One single subject was selected as representative for visualization. Each voxel of the brain was first scaled to the range [−1, +1]. Per experimental condition, we conducted 15 trials (26.4 s Around every voxel (center voxel), we constructed a spherical each) from four experimental conditions. Trials were presented searchlight that contained every neighbor voxel within a given subsequently (not randomized) in a block design. The basic task radius r (Kriegeskorte et al., 2006; Stelzer et al., 2013). For every was self-paced sequential tapping of four fingers of the right hand searchlight, we trained and cross-validated (“leave 2 out”method) to the thumb at a frequency of about 2 Hz. The first experimental a linear support vector machine (Chang and Lin, 2011). The condition was rest (no movement, no imagination, i.e., base-line center voxel was then associated with the mean cross-validation condition), followed by the imagined finger movement condition. accuracy (i.e., the percentage of correctly predicted labels) and The third and fourth conditions were finger tapping (tapping of later used for brain visualization. four fingers of the right hand to the thumb) and movement of FEATURE WEIGHT MAPPING four fingers as in the previous condition but without thumb con- tact. Due to limitations in scan time there was no rest period in In FWM, the whole brain data was first reduced in dimensional- between subsequent trials. Performance compliance with this easy ity with PCA [dim = df = #samples-1 = 29 (Abdi and Williams, Frontiers in Neuroscience | Brain Imaging Methods April 2014 | Volume 8 | Article 66 | 2 Stelzer et al. Multivariate feature weight mapping 2010)]. The PCA procedure obtained a new representation X function (edf) of cluster sizes. Using this edf, we calculated the of the data matrix X by orthogonally transforming the columns probability of each cluster in the original binarized maps. In the (features) of X into linearly uncorrelated components (principal case of FWM, positive and negative clusters were recovered sepa- components). The principal components were sorted in decreasing rately. The final assessment of cluster p-values was corrected with order by the variance they explain in the data (Abdi and Williams, FDR (Benjamini, 1999; using a cluster p-value of 0.05). 2010). The maximal number of principal components was the ANALYSIS OF SIMULATION DATA maximum of the number of observations and features (more precisely the rank of X, dim = 30). In our data sets, the last com- The analysis was carried out with and without multiple compar- ponent contained no substantial variance and was left out. Hence ison correction. Without multiple comparisons correction, only we always employed every PCA component with the exception of p-value maps were binarized and no further cluster statistics were the last one, corresponding to the number of maximal degrees computed. The remaining voxels were deemed significant. of freedom from the matrix decomposition. The PCA projec- With multiple comparison correction, the entire cluster-based tion was calculated by performing a singular value decomposition analysis (including the empirical cluster-size distribution derived of X. from permuted binarized maps) was repeated for different levels The resulting features were scaled to be within the range of voxel-wise p-value thresholds. Voxels in the remaining clusters were deemed significant. [−1, +1]. A linear support vector machine was then trained using the entire data set (Chang and Lin, 2011), without the applica- Precision is defined as the proportion of true positives and all positives: tion of further cross-validation procedures. Linear support vector machines divide data samples into their classes by constructing a true positives maximally separating hyperplane between the high-dimensional Precision = data points. The hyperplane is established by a set of points true positives + false positives − → − → x and the normal vector w to the hyperplane in the formula − → − → w · x − b = 0. The optimal vector w is calculated by minimiz- Sensitivity is defined as the proportion of voxels in informative − → ing w in the formula y · (w · x − b) ≥ 1with i  {1, ..,n} regions that were discovered significant: i i i and x being the sample vectors from X .The values w are the i i weights given to each feature dimension, (i.e., the principal com- true positives Sensitivity = ponents), and signify the importance of the component in making true positives + false negatives the classification decision. We transform the weights of principal components back to weights of individual voxels by reversing the RESULTS PCA transformation. Note that this procedure solely resulted in 7T DATA SET weights and not in decoding accuracies. The ultra-high resolution 7T finger tapping experiment was analyzed using both the Feature Weight Mapping (FWM) and NON-PARAMETRIC STATISTICS Searchlight Decoding (SLD) method on a single-subject level. We employed permutation tests for assessing statistical signifi- Three axial slices of the results for the analysis are shown in cance (Golland et al., 2005; Mourão-Miranda et al., 2005; Stelzer Figures 1A,B respectively using two different thresholds (the et al., 2013). No spatial smoothing was applied, however due to appropriate threshold for the respective method was chosen based interpolations (motion correction etc.) and the biophysical prop- on simulations in the next section). The searchlight radius was set erties of the BOLD signal, a certain level of intrinsic smoothness to 3 mm. was present in the data. Permutation tests were carried out by ran- The SLD method found the hand knob part of the motor domly shuffling the order of samples within a data set. For SLD, cortex to be significantly discriminative regarding the stimulus permutations were assigned before splitting the data into train- condition (resting vs. finger tapping). Similarly, this region was ing or test sets to ensure no bias due to uneven class distribution. also labeled as discriminative using the FWM method. Each permutation was held fixed for all locations of the search- Furthermore, while the SLD method identified the existence light, preserving spatial correlations. For FWM, permutations and degree of discriminative value of voxels, the FWM method were assigned on the principal component level. also revealed the particular class toward which the voxel influ- For each permutation, an accuracy map (SLD) or weights enced the classification decision. As shown in Figure 1B,regions map (FWM) was computed (cf. two previous sections). The that discriminate toward resting state (blue) and toward tapping empirical p-value of each voxel was then the probability of state (yellow/red) are distinguishable. Effectively, FWM revealed the original accuracy/weight of this voxel in the empirical a finer delineation of smaller cortical structures than SLD. The distribution function given all permutations. FWM method identifies additional regions in the parietal and Using the per-voxel p-value as a threshold map, we binarized frontal cortex as discriminative, while in contrast these regions the original and permuted accuracy or weight-maps. For SLD, remain undetected with the SLD method. Furthermore, the FWM we employed a one-sided (lower than p-value) statistic, for FWM method specifically identifies the cortical sheet, while the SLD we employed a two-sided [lower than p/2 or higher than (1-p/2)] method labels spatially more extended regions reaching deeper statistic. than the cortex, and thus including some white matter. Counting the cluster sizes (six connectivity scheme) in the per- The spatial precision of the SLD method critically depends muted binarized maps, we calculated an empirical distribution on the chosen searchlight radius. Larger searchlight radii return www.frontiersin.org April 2014 | Volume 8 | Article 66 | 3 Stelzer et al. Multivariate feature weight mapping FIGURE 2 | Results of the high resolution 7T finger tapping data set without multiple comparisons correction, using three searchlight radii and the feature weight mapping method. White matter voxels are displayed in false colors (by shifting the color hue by 180 ). Hence the blue tones indicate false positivity. Dark blue tones indicate high decoding accuracies or high feature weights. (A) SLD with a radius of 3 mm. Already at this radius, substantial false positivity is visible on the surface of the cortex on the right side. On the left side, out-of-plane false positivity is visible, as searchlights centered in the selected slice pick up information from the slices below or above. (B) SLD with a radius of 5 mm. The levels of false positivity have increased throughout the entire volume. (C) With a radius of 7 mm, the SLD method results in substantially inaccurate depictions of true information content. (D) Feature weight mapping, to enhance the clarity of the representation only the absolute value of the weights is considered here. The highest (absolute) weights are found within gray matter, while the weights found in white matter are on a low level. SIMULATED DATA Using simulations, we aimed to target how SLD and FWM meth- ods specifically depend on the underlying spatial distribution of FIGURE 1 | Results of the high resolution 7T finger tapping data information. In total, we created three different levels of coarse- set, classifying resting vs. finger tapping with touch. The non-parametric framework (including multiple comparison correction) had ness by structuring information in a specific geometry. The been applied to the searchlight decoding (SLD) and feature weight searchlight radius was set to three voxels. mapping (FWM) methods. (A) SLD method (diameter = 3.75 mm) with The information distribution is depicted in Figure 3A, the vio- a voxel-wise threshold of p = 0.001 (one-sided). (B) FWM method, vox let areas represent informative regions of condition A, while the using a (two-sided) threshold of p = 0.05. vox blue areas represent informative regions of condition B. Qualitative comparison of FWM and SLD accuracy maps where a substantially larger volume is labeled as informative. We depicted three searchlight radii (3, 5, and 7 mil- Figure 3 depicts the results of applying SLD and FWM on the limeter) in Figure 2 and contrasted the results with our proposed prepared simulation data. FWM method. As the two largest searchlight radii failed to reach The SLD method labels most informative regions as significance when including multiple comparisons correction, we significant, while also labeling a considerable number of voxels only show uncorrected accuracy and weight maps. Furthermore, outside the informative regions significant (Figure 3B). for illustrating the degree of voxels labeled informative within The tendency for false-positive labeling was especially promi- white matter, we applied a gray matter mask: the accuracy or nent in the fine and medium distributions, depicted in the left and weight of voxels within white matter is displayed in false colors middle pictures of Figure 3B. Here, the SLD method appeared to (by shifting the color hue by 180 ). We foundthatfor thelarger overestimate the local information content. searchlight radii in Figures 2B,C, a substantial number of white In contrast, the FWM method delineated the informative matter voxels is indicated with the highest accuracies. In con- regions with a high precision (see Figure 3C), and did not label trast, most highly weighted voxels of the FWM method are found voxels outside of the informative regions as discriminative. The within gray matter. number of true positives, however, was smaller compared to Frontiers in Neuroscience | Brain Imaging Methods April 2014 | Volume 8 | Article 66 | 4 Stelzer et al. Multivariate feature weight mapping FIGURE 3 | Analysis of the data simulation (A) Distribution of method corrected with the non-parametric framework (including multiple information, the three violet half-cubes contained class information for comparison correction), using a voxel-wise threshold of p = 0.001 vox condition A, the three blue half-cubes contained class information for (one-sided). (C) Results of FWM method corrected with the class B. In total, three distinct levels of geometry of information non-parametric framework (including multiple comparison correction) using distribution were simulated, the leftmost half-cubes represented a fine a voxel-wise threshold of p = 0.05 (two-sided). The blue-green colors vox information spread, the middle ones an intermediate level and the represent influence toward class B, the red colors for influence toward rightmost half-cubes a coarse information spread. (B) Results of SLD class A. the SLD method, as not all informative voxels were declared achieved up to 100% sensitivity, but at considerable loss of pre- discriminative here. cision, in particular for the fine and intermediate information spreads. Precision and sensitivity We assessed the statistical performance of the SLD and FWM DISCUSSION method by calculating precision and sensitivity curves for each Multivariate analysis techniques are commonly regarded as of the three coarseness levels separately. The analysis was carried promising candidates for analyzing ultra-high-resolution data out with and without application of the multiple comparisons acquired with fMRI.Inour studywecomparedtwo typesof correction. multivariate information mapping techniques; the SLD method The three coarseness simulations are depicted separately in and our newly proposed FWM method. Both methods (SLD Figure 4A (fine information spread), Figure 4B (intermediate) and FWM) aim to determine the local information content in and Figure 4C (coarse information spread). The left charts in the brain responses elicited by different experimental conditions Figure 4 depict the analysis without multiple comparison correc- (hence often termed “information mapping”) and use the same tion while the right charts depict the analysis including multiple underlying non-parametric framework for statistical analysis, comparisons correction. thus both methods are fully comparable. In the case of the uncorrected charts (left) and for both Using ultra-high-field fMRI data and simulations, we found methods, the sensitivity increased for less stringent (i.e., higher) that our new proposed method (FWM) achieves a consider- p-values, while the precision declined. For fine and intermediate ably higher spatial specificity, (that is to say, a higher accuracy information spread the FWM method had a higher precision for in localization and geometry of information) as compared to any given level of sensitivity. Only in the case of coarse informa- SLD. We additionally observed that the results of the searchlight tion spread and low thresholds (corresponding to high sensitivity) approach were systematically inflated and inaccurate. Notably, did the SLD method yield a higher precision. SLD mapped information to non-surface cortex regions con- For any given p-value threshold, the FWM method and SLD sisting of white matter. FWM, on the other hand, specifi- method showed vastly different sensitivity and precision values. cally mapped out the cortical surface. As increasing higher While the FWM method performed very well (i.e., high sensitivity resolution fMRI data become the basis for brain mapping stud- and precision) for relatively high p-values (e.g., p = 0.05), the ies, this methodological attention to anatomical specificity is a vox SLD method performed better in the regime of low p-values necessity. (e.g., p = 0.001). This difference in optimal choices for p-value In the following we discuss the peculiarities and differences of vox thresholds was the motivation for the parameters used for the both information mapping methods in detail. voxel-wise threshold for the fMRI data. When including the multiple comparison correction, the SEARCHLIGHT DECODING precision increased substantially for FWM, achieving almost Given that activity-based information in the BOLD fMRI sig- 100% for most cases. Conversely, this precision gain was not nal is known to be distributed in quite specific types of loca- found with SLD (right charts of Figure 4. At the same time, tion in the brain (i.e., within the cortex, small pial veins and FWM never achieved higher than 90% sensitivity, while SLD subcortical gray matter locations), it should not be surprising that www.frontiersin.org April 2014 | Volume 8 | Article 66 | 5 Stelzer et al. Multivariate feature weight mapping FIGURE 5 | Schematic illustration of the searchlight induced inflations and spatial inaccuracies. (A) Searchlight shape (down-projection to 2D) with a 5-voxel diameter. The violet shaded voxels are located within the searchlight. (B) No voxels carry class information, except the center voxel featuring the green sphere labeled with the letter “i”: this voxel is the sole voxel carrying class information. As a result of the SLD procedure using searchlight decoding (A), many voxels are being labeled as informative (these voxels are depicted in orange). The inflating effect has previously been termed as “needle in the haystack effect” (Viswanathan et al., 2012). (C) Here, no voxels except the two voxels with the green sphere labeled with “i” carry class information. The information carried by one voxel, however, is sufficiently small so that a searchlight has to include both informative voxels in order to be labeled significant. Hence only the voxels in the middle, where the searchlight contains both informative voxels, are labeled informative, resulting in inaccurate and distorted information maps. effect can also be considered in an image containing only two low-informative voxels. The direct area around each voxel will be mapped uninformative by the searchlight approach, and will thus appear as false negative, while those searchlights that con- tain both informative voxels will be labeled informative (depicted in Figure 5C). Thus a distorted picture of the geometry of infor- mation is provided by SLD. Appropriately, this effect had been given the name “haystack in the needle” (Viswanathan et al., 2012). It is easy to see that the latter effect depends on the search- light diameter, as the number of informative voxels monotonically depends on the diameter of the searchlight. However, the effect also depends on the distribution of information and overall geometry. Lastly, the (multivariate) signal to noise ratio presum- ably also plays an important role. Because one main benefit of ultra-high-field fMRI is that it FIGURE 4 | Precision-sensitivity curves for the three different levels of information distribution of the data simulation. The red dots represent allows the study of activations at fine spatial scales (and so help to the FWM method, and the blue dots the SLD method. (A) Precision- establish structure-function relationships), it thus appears ques- Sensitivity for a fine information spread. The left chart is based on tionable whether the searchlight is the optimal method of choice uncorrected voxel p-values (derived from the permutation distribution), the (Kriegeskorte and Bandettini, 2007). right chart depicts results for the full non-parametric multiple comparison The results of our case study and simulations fully supported correction (B) Precision-Sensitivity for an intermediate distribution of information. The left and right charts are as above. (C) Precision-Sensitivity the above considerations with regard to exaggeration of spatial curve for a coarse information spread. The left and right charts are as above. extent and other spatial inaccuracies. The searchlight method indeed yielded inflated estimates of information distribution in both the simulated and ultra-high-field fMRI data set. SLD searchlight information maps may be spatially exaggerated and labeled a high fraction of voxels as informative outside gray distorted. matter areas, obscuring the actual distribution of information Let us consider for example an image containing no signal in the cortex (Figure 2A). This issue becomes especially pre- except one center voxel containing a large amount of class infor- dominant for larger searchlight radii, such as five and seven mation. The resulting searchlight information map (depicted in millimeters (Figures 2B,C). It should be noted that searchlights Figures 5A,B) will label every searchlight location which con- of such dimensions are common practice, or even exceeding tains this center voxel as “informative,” effectively grossly inflating seven millimeters (Soon et al., 2008; Stelzer et al., 2013). The the actual informative regions—thus giving many false positive simulations reflected the same spatial inaccuracies of the search- attributions. In a recent study, this effect has been termed a “nee- light method as found previously in our fMRI data. In here, dle in the haystack effect” (Viswanathan et al., 2012). Another we were able to modify the underlying spatial geometry of the Frontiers in Neuroscience | Brain Imaging Methods April 2014 | Volume 8 | Article 66 | 6 Stelzer et al. Multivariate feature weight mapping true information distribution. We found that the spatial inac- statistical analysis. Ultimately this allows computation of fea- curacies of the resulting information maps were especially vis- ture importance and includes multiple comparison correction. ible in areas of information distributed on small spatial scales The FWM method is tailored for the analysis of extremely high- (Figure 3B). dimensional data such as that produced by high-field fMRI while The effect was especially pronounced in cases where adja- yielding spatially precise information maps. cent informative regions were separated by a small uninformative We found that FWM consistently yielded fine-structured information maps. In 7T fMRI data FWM revealed informative layer (middle column of Figure 3B). Here, the searchlight method labeled the uninformative border region as highly informative. regions precisely within the thickness of the cortex. Compared The issue of exaggeration of spatial extent (“inflation”) may be to SLD, FWM labeled uninformative regions (e.g., within white mitigated by limiting the searchlight only to gray matter voxels matter) much less often as significant. or even directly applying it on the cortical surface (Chen et al., In simulations, it delineated the informative regions precisely. 2011). However, for the surface-based methods, inflation is only Precision and sensitivity curves were generally better for FWM reduced in one of three spatial dimensions; while the spatial accu- than for SLD, when the spatial distribution of information was racy in the direction normal to the cortical surface is improved, within the fine and intermediate information spread range. For the two in-plane dimensions (along the cortical sheet) remain any given value of sensitivity (detected informative volume), inflated and distorted. FWM was more precise than SLD (less false positivity). In the Another issue that needs to be addressed is the claim that the simulations, FWM never reached the highest sensitivity levels searchlight method is only sensitive to local patterns, because (>90%), which were accompanied by an extreme loss in spatial it analyzes only a small neighborhood of voxels at a time. The precision in the SLD method. searchlight method is often considered advantageous when it Another advantage of FWM over SLD is the sign of the comes to fine-grained local representations, where the infor- mapping, which reveals the particular class to which the voxel mation is contained in a small region including only few influences the classifier. For instance, if a voxel activates con- voxels. While this argument may hold for a single search- sistently when in class A but does not activate when in class light location in isolation, the argument does not necessarily B, the resulting weight component would be positive. On the carry over to a searchlight map consisting of many search- other hand, if the voxel activates consistently when in class A but light locations. Due to the inflationary nature of the search- does not activate when in class B, the weight component would light’s information maps, small informative regions will be be determined negative. Hence, the individual weight mapping contained in many searchlight locations. Ultimately, the rep- reveals how the corresponding voxel influences the classification resentation of the information content is hence inflated to a decision depending on the level of activation found in the fea- degree where small representations either fall under the statisti- ture. In an area with positive weights, a high activity level would cal threshold (when including a whole-brain correction) or are influence the classifier to decide on class A, while a low level of grossly overestimated in their spatial extent (see Figures 1, 4). activity would indicate class B. For negative weights, an analogous Furthermore, the intrinsic “smoothing” effect of the search- argument can be made: Here a high level of activity would influ- light method may be severely exacerbated by the inclusion of ence the classifier to decide on class B and a low level of activity spatial smoothing as a post-processing step (e.g., group-level would indicate class A. In contrast, the SLD method is unable to comparisons). deliver such information about the direction of influence for any From a conceptual point of view it can be argued that the given features, as it only determines whether class information is searchlight’s exclusive sensitivity to local patterns may provoke an present or not. unrealistic impression of brain function, given that the brain is In contrast to SLD, FWM is a truly global multivariate a large and massively interconnected network. It is most likely approach, that is, it considers all voxels simultaneously. Since the that the fingerprint of distinct brain states does not solely exist classification has to be computed only once on a relatively small at small spatial scales. Instead, the brain processes information data set (for each permutation), the computational resources nec- on larger spatial dimensions across wide-spread networks. For essary for the non-parametric statistical framework are drastically instance, remote brain areas have been observed to jointly exhibit lower compared to those needed for SLD. Depending on the size patterns of activation governed by long-range neural communica- of the data set in terms of voxels (resolution) and experimental tion (e.g., Laughlin, 2003). Evidently, such large-scale interactions trials, we found that the computation of the permutations in the cannot be captured by the searchlight method. Although some- FWM method was between 5,000 and 30,000 times faster than the times a strictly local investigation at small spatial scales is desired, SLD method. for example in (Diedrichsen et al., 2013), it is not clear that Because the potential for Type I and Type II errors is vastly the searchlight method is even suitable for such studies, given reduced, the interpretability of FWM-generated information its potential for false positive and false negative attributions of maps is much improved as compared with SLD. With FWM, the informative voxels. influence attributed to a given voxel is solely its influence on the classification of that particular voxel. FEATURE WEIGHT MAPPING Contrastingly, in the SLD method the accuracy at a voxel char- The FWM method is a global multivariate information mapping acterizes the aggregate decodability of a neighborhood of voxels technique based on dimensionality reduction, which comprises a around it. 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Neuroimage 78, 1–9. doi: 10.1016/j.neuroimage.2013.03.041 Glover, G. H. (1999). Deconvolution of impulse response in event- Conflict of Interest Statement: The authors declare that the research was con- related BOLD fMRI1. Neuroimage 9, 416–429. doi: 10.1006/nimg.1998. ducted in the absence of any commercial or financial relationships that could be 0419 construed as a potential conflict of interest. Golland, P., Liang, F., Mukherjee, S., and Panchenko, D. (2005). “Permutation tests for classification,” in Information Processing in Medical Imaging, Vol. 3559, eds Received: 10 December 2013; accepted: 21 March 2014; published online: 16 April P. Auer and R. Meir (Berlin; Heidelberg: Springer), 330–341. doi: 10.1007/1150 2014. 3415_34 Citation: Stelzer J, Buschmann T, Lohmann G, Margulies DS, Trampel R and Turner Harrison, L. M., Penny, W., Daunizeau, J., and Friston, K. J. (2008). Diffusion- R (2014) Prioritizing spatial accuracy in high-resolution fMRI data using multivariate based spatial priors for functional magnetic resonance images. Neuroimage 41, feature weight mapping. Front. Neurosci. 8:66. doi: 10.3389/fnins.2014.00066 408–423. doi: 10.1016/j.neuroimage.2008.02.005 This article was submitted to Brain Imaging Methods, a section of the journal Frontiers Heidemann, R. M., Anwander, A., Feiweier, T., Knösche, T. R., and Turner, R. in Neuroscience. (2012). k-space and q-space: combining ultra-high spatial and angular reso- Copyright © 2014 Stelzer, Buschmann, Lohmann, Margulies, Trampel and Turner. lution in diffusion imaging using ZOOPPA at 7T. Curr. Opin. Neurobiol. 60, This is an open-access article distributed under the terms of the Creative Commons 967–978. doi: 10.1016/j.neuroimage.2011.12.081 Attribution License (CC BY). The use, distribution or reproduction in other forums is Kriegeskorte, N., and Bandettini, P. (2007). Analyzing for information, not permitted, provided the original author(s) or licensor are credited and that the original activation, to exploit high-resolution fMRI. Neuroimage 38, 649–662. doi: publication in this journal is cited, in accordance with accepted academic practice. No 10.1016/j.neuroimage.2007.02.022 use, distribution or reproduction is permitted which does not comply with these terms. Frontiers in Neuroscience | Brain Imaging Methods April 2014 | Volume 8 | Article 66 | 8 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Frontiers in Neuroscience Pubmed Central

Prioritizing spatial accuracy in high-resolution fMRI data using multivariate feature weight mapping

Stelzer, Johannes; Buschmann, Tilo; Lohmann, Gabriele; Margulies, Daniel S.; Trampel, Robert; Turner, Robert
Frontiers in Neuroscience , Volume 8 – Apr 16, 2014
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METHODS ARTICLE published: 16 April 2014 doi: 10.3389/fnins.2014.00066 Prioritizing spatial accuracy in high-resolution fMRI data using multivariate feature weight mapping 1,2 † 1,3 † 4,5 6 Johannes Stelzer * , Tilo Buschmann , Gabriele Lohmann , Daniel S. Margulies , 1 1 Robert Trampel and Robert Turner Department of Neurophysics, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany Danish Research Centre for Magnetic Resonance, Copenhagen University Hospital Hvidovre, Hvidovre, Denmark Department of Diagnostics, Fraunhofer Institute for Cell Therapy and Immunology, Leipzig, Germany Department of Biomedical Magnetic Resonance, University Hospital Tübingen, Tübingen, Germany Magnetic Resonance Center, Max Planck Institute for Biological Cybernetics, Tübingen, Germany Max Planck Research Group for Neuroanatomy and Connectivity, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany Edited by: Although ultra-high-field fMRI at field strengths of 7T or above provides substantial Pedro Antonio Valdes-Sosa, Cuban gains in BOLD contrast-to-noise ratio, when very high-resolution fMRI is required such Neuroscience Center, Cuba gains are inevitably reduced. The improvement in sensitivity provided by multivariate Reviewed by: analysis techniques, as compared with univariate methods, then becomes especially Xi-Nian Zuo, Chinese Academy of welcome. Information mapping approaches are commonly used, such as the searchlight Sciences, China Agustin Lage-Castellanos, Cuban technique, which take into account the spatially distributed patterns of activation in order Neuroscience Center, Cuba to predict stimulus conditions. However, the popular searchlight decoding technique, in *Correspondence: particular, has been found to be prone to spatial inaccuracies. For instance, the spatial Johannes Stelzer, Danish Research extent of informative areas is generally exaggerated, and their spatial configuration Centre for Magnetic Resonance, is distorted. We propose the combination of a non-parametric and permutation-based Copenhagen University Hospital Hvidovre, Kettegaard Allé 30, statistical framework with linear classifiers. We term this new combined method 2650 Hvidovre, Denmark Feature Weight Mapping (FWM). The main goal of the proposed method is to map e-mail: [email protected] the specific contribution of each voxel to the classification decision while including a These authors have contributed correction for the multiple comparisons problem. Next, we compare this new method equally to this work. to the searchlight approach using a simulation and ultra-high-field 7T experimental data. We found that the searchlight method led to spatial inaccuracies that are especially noticeable in high-resolution fMRI data. In contrast, FWM was more spatially precise, revealing both informative anatomical structures as well as the direction by which voxels contribute to the classification. By maximizing the spatial accuracy of ultra-high-field fMRI results, global multivariate methods provide a substantial improvement for characterizing structure-function relationships. Keywords: fMRI, MVPA, searchlight, nonparametric statistics, decoding INTRODUCTION resolution is multivariate pattern recognition analysis (MVPA), The advent of functional magnetic resonance imaging (fMRI) which enables fine-grained components of the brain activity sig- at ultra-high-field strengths allows an impressively fine-grained nal to contribute relevantly (Norman et al., 2006). It is often insight into human cortical function. Modern scanners at 7T or desirable to map the spatial location of discriminating patterns, higher allow researchers to resolve functional data at ever finer or in other words, where in the brain information about the spatial scales, even to the point of resolving individual gray matter experimental condition is present. layers (Polimeni et al., 2010; Trampel et al., 2011). The bene- For this, “information mapping” methods, such as the “search- fits of improved resolution are accompanied by new challenges, light” approach are often employed (Kriegeskorte et al., 2006). however, particularly with regard to data analysis, as it is not The searchlight method attempts to extract the predictive power obvious which analysis technique may best take advantage of the of a small neighborhood of voxels (the searchlight)withregards richer data. For instance, classical activation-based approaches to the stimulus condition, and maps the result of the anal- such as the general linear model (Poline and Brett, 2012) generally ysis back to the center voxel of the searchlight. Repeating rely on spatial smoothing for statistical correction for multi- this procedure over all locations yields an information map ple comparisons, and hence are unable to make appropriate use charting the presence and location of information relating to of the high resolutions. While a more sophisticated approach stimulus condition. It should be noted that the searchlight has been proposed (Harrison et al., 2008) this is computation- method is essentially a local multivariate pattern recognition tech- ally laborious and does not have face validity in terms of actual nique that fails to take into account globally distributed voxel neuroanatomy. A more promising means of exploiting higher patterns. www.frontiersin.org April 2014 | Volume 8 | Article 66 | 1 Stelzer et al. Multivariate feature weight mapping Alternatively, global information maps can be computed task was confirmed using video monitoring. For the analysis in without such spatial preselection of voxels using multivariate our present work, only two conditions were used: Resting (no classifiers with support for high dimensional data or by using task, no hand movement, no motor imagination) and sequen- dimensionality-reduced brain data (e.g., by first performing a tial tapping with four fingers of the right hand to the thumb of principal component analysis). Appropriate classifiers provide the right hand. (The conditions omitted were: Imagined finger information on the contribution of individual features (i.e., voxels tapping without actual finger movement and finger movement without touching the thumb). or principal components) to the classification decision. Mapping this influence back onto the voxel space allows generation of a The experiment was performed with a MAGNETOM 7T whole-brain information map (Mourão-Miranda et al., 2005), scanner (Siemens Healthcare, Erlangen, Germany), using a 24- which delineates the discriminative volume. channel head coil (NOVA Medical Inc., Wilmington MA, USA). Previously, the searchlight method has been reviewed critically The functional scans contained 17–31 axial slices (depending on the grounds of interpretability and with regard to spatial inac- on the subject) covering the left motor cortex (TR = 3300 ms, curacies in the searchlight information maps which obscure the TE = 25 ms, slice thickness 0.75 mm, in plane resolution 0.75 × true local information content (Viswanathan et al., 2012; Etzel 0.75 mm ) using a novel acceleration technique (Heidemann et al., 2013). These shortcomings form the greatest concern with et al., 2012). very high spatial resolution fMRI data, such as that obtainable at Head motion correction was carried out using SPM8 ultra-high-field, as they may well negate the gain in higher spa- (Wellcome Department of Imaging Neuroscience, Institute of tial resolution. In particular, the lower voxel-wise signal-to-noise Neurology, London, UK). Low frequency drifts were removed −1 ratio at very high resolutions requires larger searchlight diameters using a temporal high-pass filter (f = 1/80 s )with highpass to obtain significant results, exacerbating spatial inaccuracies. LIPSIA (Lohmann et al., 2001). Using LIPSIA, a GLM was fitted In the present work, we investigate the quality of the search- to each trial to estimate its β-parameters. We used a gamma- light method as a tool for the analysis of ultra-high-field fMRI function as hemodynamic response function (Glover, 1999). data. As an alternative to the searchlight approach, we present The GLM yielded 15 three-dimensional β-maps per experimen- a global multivariate method adapted from previous work tal condition. The β-parameters were estimated on the z-scored (Mourão-Miranda et al., 2005), which we combine with a non- fMRI time series data (default settings in LIPSIA) and represent parametric solution for the multiple comparison problem (Stelzer the degree of fit between the trial data and the model. et al., 2013). To our knowledge, this is the first implementa- DATA GENERATION FOR SIMULATION tion fully accounting for the multiple comparisons problem, A simulated data set of 30 scans (15 each for class A and B) of one tailored for this widely used multivariate framework for brain “virtual” subject was generated. Each volume (size 66 × 22 × 22 mapping. We compare these two information-mapping methods voxels) was filled with Gaussian noise [∼ N(0, 1)] and smoothed as a means for analyzing ultra-high resolution fMRI and sim- slightly with a Gaussian smoothing kernel (FWHM = 1voxel). ulated data. Noteworthy, while both methods (searchlight and An offset size of 0.5 was added at six locations (three in class A global information maps) incorporate different assumptions and and B, respectively), shaping six half-cubes positioned above and implementations, in research practice the results ultimately are below the centerline of the volume (Figure 3A). Upper half-cubes interpreted in a very similar fashion: Both approaches provide were class A, lower half-cubes were class B. voxel maps, which delineate voxels containing stimulus-relevant The size of the half-cubes varied. The leftmost half-cube had information. a dimension of 6 × 6 × 1 voxels (fine information spread), the second one had a dimension of 6 × 6 × 2 voxels (medium infor- MATERIALS AND METHODS mation spread) and the rightmost half-cube 6 × 6 × 3voxels 7T TAPPING DATA SET (coarseinformation spread). Therewas a4-voxel gapbetween the The ultra-high field fMRI study comprised ten healthy subjects leftmost, a 2-voxel gap between the middle, and no gap between (age range 23–28, right-handed). The study was carried out in the two rightmost half-cubes (see Figure 3A). accordance with the ethics approval from the University of Leipzig and written informed consent was obtained before each study. SEARCHLIGHT DECODING One single subject was selected as representative for visualization. Each voxel of the brain was first scaled to the range [−1, +1]. Per experimental condition, we conducted 15 trials (26.4 s Around every voxel (center voxel), we constructed a spherical each) from four experimental conditions. Trials were presented searchlight that contained every neighbor voxel within a given subsequently (not randomized) in a block design. The basic task radius r (Kriegeskorte et al., 2006; Stelzer et al., 2013). For every was self-paced sequential tapping of four fingers of the right hand searchlight, we trained and cross-validated (“leave 2 out”method) to the thumb at a frequency of about 2 Hz. The first experimental a linear support vector machine (Chang and Lin, 2011). The condition was rest (no movement, no imagination, i.e., base-line center voxel was then associated with the mean cross-validation condition), followed by the imagined finger movement condition. accuracy (i.e., the percentage of correctly predicted labels) and The third and fourth conditions were finger tapping (tapping of later used for brain visualization. four fingers of the right hand to the thumb) and movement of FEATURE WEIGHT MAPPING four fingers as in the previous condition but without thumb con- tact. Due to limitations in scan time there was no rest period in In FWM, the whole brain data was first reduced in dimensional- between subsequent trials. Performance compliance with this easy ity with PCA [dim = df = #samples-1 = 29 (Abdi and Williams, Frontiers in Neuroscience | Brain Imaging Methods April 2014 | Volume 8 | Article 66 | 2 Stelzer et al. Multivariate feature weight mapping 2010)]. The PCA procedure obtained a new representation X function (edf) of cluster sizes. Using this edf, we calculated the of the data matrix X by orthogonally transforming the columns probability of each cluster in the original binarized maps. In the (features) of X into linearly uncorrelated components (principal case of FWM, positive and negative clusters were recovered sepa- components). The principal components were sorted in decreasing rately. The final assessment of cluster p-values was corrected with order by the variance they explain in the data (Abdi and Williams, FDR (Benjamini, 1999; using a cluster p-value of 0.05). 2010). The maximal number of principal components was the ANALYSIS OF SIMULATION DATA maximum of the number of observations and features (more precisely the rank of X, dim = 30). In our data sets, the last com- The analysis was carried out with and without multiple compar- ponent contained no substantial variance and was left out. Hence ison correction. Without multiple comparisons correction, only we always employed every PCA component with the exception of p-value maps were binarized and no further cluster statistics were the last one, corresponding to the number of maximal degrees computed. The remaining voxels were deemed significant. of freedom from the matrix decomposition. The PCA projec- With multiple comparison correction, the entire cluster-based tion was calculated by performing a singular value decomposition analysis (including the empirical cluster-size distribution derived of X. from permuted binarized maps) was repeated for different levels The resulting features were scaled to be within the range of voxel-wise p-value thresholds. Voxels in the remaining clusters were deemed significant. [−1, +1]. A linear support vector machine was then trained using the entire data set (Chang and Lin, 2011), without the applica- Precision is defined as the proportion of true positives and all positives: tion of further cross-validation procedures. Linear support vector machines divide data samples into their classes by constructing a true positives maximally separating hyperplane between the high-dimensional Precision = data points. The hyperplane is established by a set of points true positives + false positives − → − → x and the normal vector w to the hyperplane in the formula − → − → w · x − b = 0. The optimal vector w is calculated by minimiz- Sensitivity is defined as the proportion of voxels in informative − → ing w in the formula y · (w · x − b) ≥ 1with i  {1, ..,n} regions that were discovered significant: i i i and x being the sample vectors from X .The values w are the i i weights given to each feature dimension, (i.e., the principal com- true positives Sensitivity = ponents), and signify the importance of the component in making true positives + false negatives the classification decision. We transform the weights of principal components back to weights of individual voxels by reversing the RESULTS PCA transformation. Note that this procedure solely resulted in 7T DATA SET weights and not in decoding accuracies. The ultra-high resolution 7T finger tapping experiment was analyzed using both the Feature Weight Mapping (FWM) and NON-PARAMETRIC STATISTICS Searchlight Decoding (SLD) method on a single-subject level. We employed permutation tests for assessing statistical signifi- Three axial slices of the results for the analysis are shown in cance (Golland et al., 2005; Mourão-Miranda et al., 2005; Stelzer Figures 1A,B respectively using two different thresholds (the et al., 2013). No spatial smoothing was applied, however due to appropriate threshold for the respective method was chosen based interpolations (motion correction etc.) and the biophysical prop- on simulations in the next section). The searchlight radius was set erties of the BOLD signal, a certain level of intrinsic smoothness to 3 mm. was present in the data. Permutation tests were carried out by ran- The SLD method found the hand knob part of the motor domly shuffling the order of samples within a data set. For SLD, cortex to be significantly discriminative regarding the stimulus permutations were assigned before splitting the data into train- condition (resting vs. finger tapping). Similarly, this region was ing or test sets to ensure no bias due to uneven class distribution. also labeled as discriminative using the FWM method. Each permutation was held fixed for all locations of the search- Furthermore, while the SLD method identified the existence light, preserving spatial correlations. For FWM, permutations and degree of discriminative value of voxels, the FWM method were assigned on the principal component level. also revealed the particular class toward which the voxel influ- For each permutation, an accuracy map (SLD) or weights enced the classification decision. As shown in Figure 1B,regions map (FWM) was computed (cf. two previous sections). The that discriminate toward resting state (blue) and toward tapping empirical p-value of each voxel was then the probability of state (yellow/red) are distinguishable. Effectively, FWM revealed the original accuracy/weight of this voxel in the empirical a finer delineation of smaller cortical structures than SLD. The distribution function given all permutations. FWM method identifies additional regions in the parietal and Using the per-voxel p-value as a threshold map, we binarized frontal cortex as discriminative, while in contrast these regions the original and permuted accuracy or weight-maps. For SLD, remain undetected with the SLD method. Furthermore, the FWM we employed a one-sided (lower than p-value) statistic, for FWM method specifically identifies the cortical sheet, while the SLD we employed a two-sided [lower than p/2 or higher than (1-p/2)] method labels spatially more extended regions reaching deeper statistic. than the cortex, and thus including some white matter. Counting the cluster sizes (six connectivity scheme) in the per- The spatial precision of the SLD method critically depends muted binarized maps, we calculated an empirical distribution on the chosen searchlight radius. Larger searchlight radii return www.frontiersin.org April 2014 | Volume 8 | Article 66 | 3 Stelzer et al. Multivariate feature weight mapping FIGURE 2 | Results of the high resolution 7T finger tapping data set without multiple comparisons correction, using three searchlight radii and the feature weight mapping method. White matter voxels are displayed in false colors (by shifting the color hue by 180 ). Hence the blue tones indicate false positivity. Dark blue tones indicate high decoding accuracies or high feature weights. (A) SLD with a radius of 3 mm. Already at this radius, substantial false positivity is visible on the surface of the cortex on the right side. On the left side, out-of-plane false positivity is visible, as searchlights centered in the selected slice pick up information from the slices below or above. (B) SLD with a radius of 5 mm. The levels of false positivity have increased throughout the entire volume. (C) With a radius of 7 mm, the SLD method results in substantially inaccurate depictions of true information content. (D) Feature weight mapping, to enhance the clarity of the representation only the absolute value of the weights is considered here. The highest (absolute) weights are found within gray matter, while the weights found in white matter are on a low level. SIMULATED DATA Using simulations, we aimed to target how SLD and FWM meth- ods specifically depend on the underlying spatial distribution of FIGURE 1 | Results of the high resolution 7T finger tapping data information. In total, we created three different levels of coarse- set, classifying resting vs. finger tapping with touch. The non-parametric framework (including multiple comparison correction) had ness by structuring information in a specific geometry. The been applied to the searchlight decoding (SLD) and feature weight searchlight radius was set to three voxels. mapping (FWM) methods. (A) SLD method (diameter = 3.75 mm) with The information distribution is depicted in Figure 3A, the vio- a voxel-wise threshold of p = 0.001 (one-sided). (B) FWM method, vox let areas represent informative regions of condition A, while the using a (two-sided) threshold of p = 0.05. vox blue areas represent informative regions of condition B. Qualitative comparison of FWM and SLD accuracy maps where a substantially larger volume is labeled as informative. We depicted three searchlight radii (3, 5, and 7 mil- Figure 3 depicts the results of applying SLD and FWM on the limeter) in Figure 2 and contrasted the results with our proposed prepared simulation data. FWM method. As the two largest searchlight radii failed to reach The SLD method labels most informative regions as significance when including multiple comparisons correction, we significant, while also labeling a considerable number of voxels only show uncorrected accuracy and weight maps. Furthermore, outside the informative regions significant (Figure 3B). for illustrating the degree of voxels labeled informative within The tendency for false-positive labeling was especially promi- white matter, we applied a gray matter mask: the accuracy or nent in the fine and medium distributions, depicted in the left and weight of voxels within white matter is displayed in false colors middle pictures of Figure 3B. Here, the SLD method appeared to (by shifting the color hue by 180 ). We foundthatfor thelarger overestimate the local information content. searchlight radii in Figures 2B,C, a substantial number of white In contrast, the FWM method delineated the informative matter voxels is indicated with the highest accuracies. In con- regions with a high precision (see Figure 3C), and did not label trast, most highly weighted voxels of the FWM method are found voxels outside of the informative regions as discriminative. The within gray matter. number of true positives, however, was smaller compared to Frontiers in Neuroscience | Brain Imaging Methods April 2014 | Volume 8 | Article 66 | 4 Stelzer et al. Multivariate feature weight mapping FIGURE 3 | Analysis of the data simulation (A) Distribution of method corrected with the non-parametric framework (including multiple information, the three violet half-cubes contained class information for comparison correction), using a voxel-wise threshold of p = 0.001 vox condition A, the three blue half-cubes contained class information for (one-sided). (C) Results of FWM method corrected with the class B. In total, three distinct levels of geometry of information non-parametric framework (including multiple comparison correction) using distribution were simulated, the leftmost half-cubes represented a fine a voxel-wise threshold of p = 0.05 (two-sided). The blue-green colors vox information spread, the middle ones an intermediate level and the represent influence toward class B, the red colors for influence toward rightmost half-cubes a coarse information spread. (B) Results of SLD class A. the SLD method, as not all informative voxels were declared achieved up to 100% sensitivity, but at considerable loss of pre- discriminative here. cision, in particular for the fine and intermediate information spreads. Precision and sensitivity We assessed the statistical performance of the SLD and FWM DISCUSSION method by calculating precision and sensitivity curves for each Multivariate analysis techniques are commonly regarded as of the three coarseness levels separately. The analysis was carried promising candidates for analyzing ultra-high-resolution data out with and without application of the multiple comparisons acquired with fMRI.Inour studywecomparedtwo typesof correction. multivariate information mapping techniques; the SLD method The three coarseness simulations are depicted separately in and our newly proposed FWM method. Both methods (SLD Figure 4A (fine information spread), Figure 4B (intermediate) and FWM) aim to determine the local information content in and Figure 4C (coarse information spread). The left charts in the brain responses elicited by different experimental conditions Figure 4 depict the analysis without multiple comparison correc- (hence often termed “information mapping”) and use the same tion while the right charts depict the analysis including multiple underlying non-parametric framework for statistical analysis, comparisons correction. thus both methods are fully comparable. In the case of the uncorrected charts (left) and for both Using ultra-high-field fMRI data and simulations, we found methods, the sensitivity increased for less stringent (i.e., higher) that our new proposed method (FWM) achieves a consider- p-values, while the precision declined. For fine and intermediate ably higher spatial specificity, (that is to say, a higher accuracy information spread the FWM method had a higher precision for in localization and geometry of information) as compared to any given level of sensitivity. Only in the case of coarse informa- SLD. We additionally observed that the results of the searchlight tion spread and low thresholds (corresponding to high sensitivity) approach were systematically inflated and inaccurate. Notably, did the SLD method yield a higher precision. SLD mapped information to non-surface cortex regions con- For any given p-value threshold, the FWM method and SLD sisting of white matter. FWM, on the other hand, specifi- method showed vastly different sensitivity and precision values. cally mapped out the cortical surface. As increasing higher While the FWM method performed very well (i.e., high sensitivity resolution fMRI data become the basis for brain mapping stud- and precision) for relatively high p-values (e.g., p = 0.05), the ies, this methodological attention to anatomical specificity is a vox SLD method performed better in the regime of low p-values necessity. (e.g., p = 0.001). This difference in optimal choices for p-value In the following we discuss the peculiarities and differences of vox thresholds was the motivation for the parameters used for the both information mapping methods in detail. voxel-wise threshold for the fMRI data. When including the multiple comparison correction, the SEARCHLIGHT DECODING precision increased substantially for FWM, achieving almost Given that activity-based information in the BOLD fMRI sig- 100% for most cases. Conversely, this precision gain was not nal is known to be distributed in quite specific types of loca- found with SLD (right charts of Figure 4. At the same time, tion in the brain (i.e., within the cortex, small pial veins and FWM never achieved higher than 90% sensitivity, while SLD subcortical gray matter locations), it should not be surprising that www.frontiersin.org April 2014 | Volume 8 | Article 66 | 5 Stelzer et al. Multivariate feature weight mapping FIGURE 5 | Schematic illustration of the searchlight induced inflations and spatial inaccuracies. (A) Searchlight shape (down-projection to 2D) with a 5-voxel diameter. The violet shaded voxels are located within the searchlight. (B) No voxels carry class information, except the center voxel featuring the green sphere labeled with the letter “i”: this voxel is the sole voxel carrying class information. As a result of the SLD procedure using searchlight decoding (A), many voxels are being labeled as informative (these voxels are depicted in orange). The inflating effect has previously been termed as “needle in the haystack effect” (Viswanathan et al., 2012). (C) Here, no voxels except the two voxels with the green sphere labeled with “i” carry class information. The information carried by one voxel, however, is sufficiently small so that a searchlight has to include both informative voxels in order to be labeled significant. Hence only the voxels in the middle, where the searchlight contains both informative voxels, are labeled informative, resulting in inaccurate and distorted information maps. effect can also be considered in an image containing only two low-informative voxels. The direct area around each voxel will be mapped uninformative by the searchlight approach, and will thus appear as false negative, while those searchlights that con- tain both informative voxels will be labeled informative (depicted in Figure 5C). Thus a distorted picture of the geometry of infor- mation is provided by SLD. Appropriately, this effect had been given the name “haystack in the needle” (Viswanathan et al., 2012). It is easy to see that the latter effect depends on the search- light diameter, as the number of informative voxels monotonically depends on the diameter of the searchlight. However, the effect also depends on the distribution of information and overall geometry. Lastly, the (multivariate) signal to noise ratio presum- ably also plays an important role. Because one main benefit of ultra-high-field fMRI is that it FIGURE 4 | Precision-sensitivity curves for the three different levels of information distribution of the data simulation. The red dots represent allows the study of activations at fine spatial scales (and so help to the FWM method, and the blue dots the SLD method. (A) Precision- establish structure-function relationships), it thus appears ques- Sensitivity for a fine information spread. The left chart is based on tionable whether the searchlight is the optimal method of choice uncorrected voxel p-values (derived from the permutation distribution), the (Kriegeskorte and Bandettini, 2007). right chart depicts results for the full non-parametric multiple comparison The results of our case study and simulations fully supported correction (B) Precision-Sensitivity for an intermediate distribution of information. The left and right charts are as above. (C) Precision-Sensitivity the above considerations with regard to exaggeration of spatial curve for a coarse information spread. The left and right charts are as above. extent and other spatial inaccuracies. The searchlight method indeed yielded inflated estimates of information distribution in both the simulated and ultra-high-field fMRI data set. SLD searchlight information maps may be spatially exaggerated and labeled a high fraction of voxels as informative outside gray distorted. matter areas, obscuring the actual distribution of information Let us consider for example an image containing no signal in the cortex (Figure 2A). This issue becomes especially pre- except one center voxel containing a large amount of class infor- dominant for larger searchlight radii, such as five and seven mation. The resulting searchlight information map (depicted in millimeters (Figures 2B,C). It should be noted that searchlights Figures 5A,B) will label every searchlight location which con- of such dimensions are common practice, or even exceeding tains this center voxel as “informative,” effectively grossly inflating seven millimeters (Soon et al., 2008; Stelzer et al., 2013). The the actual informative regions—thus giving many false positive simulations reflected the same spatial inaccuracies of the search- attributions. In a recent study, this effect has been termed a “nee- light method as found previously in our fMRI data. In here, dle in the haystack effect” (Viswanathan et al., 2012). Another we were able to modify the underlying spatial geometry of the Frontiers in Neuroscience | Brain Imaging Methods April 2014 | Volume 8 | Article 66 | 6 Stelzer et al. Multivariate feature weight mapping true information distribution. We found that the spatial inac- statistical analysis. Ultimately this allows computation of fea- curacies of the resulting information maps were especially vis- ture importance and includes multiple comparison correction. ible in areas of information distributed on small spatial scales The FWM method is tailored for the analysis of extremely high- (Figure 3B). dimensional data such as that produced by high-field fMRI while The effect was especially pronounced in cases where adja- yielding spatially precise information maps. cent informative regions were separated by a small uninformative We found that FWM consistently yielded fine-structured information maps. In 7T fMRI data FWM revealed informative layer (middle column of Figure 3B). Here, the searchlight method labeled the uninformative border region as highly informative. regions precisely within the thickness of the cortex. Compared The issue of exaggeration of spatial extent (“inflation”) may be to SLD, FWM labeled uninformative regions (e.g., within white mitigated by limiting the searchlight only to gray matter voxels matter) much less often as significant. or even directly applying it on the cortical surface (Chen et al., In simulations, it delineated the informative regions precisely. 2011). However, for the surface-based methods, inflation is only Precision and sensitivity curves were generally better for FWM reduced in one of three spatial dimensions; while the spatial accu- than for SLD, when the spatial distribution of information was racy in the direction normal to the cortical surface is improved, within the fine and intermediate information spread range. For the two in-plane dimensions (along the cortical sheet) remain any given value of sensitivity (detected informative volume), inflated and distorted. FWM was more precise than SLD (less false positivity). In the Another issue that needs to be addressed is the claim that the simulations, FWM never reached the highest sensitivity levels searchlight method is only sensitive to local patterns, because (>90%), which were accompanied by an extreme loss in spatial it analyzes only a small neighborhood of voxels at a time. The precision in the SLD method. searchlight method is often considered advantageous when it Another advantage of FWM over SLD is the sign of the comes to fine-grained local representations, where the infor- mapping, which reveals the particular class to which the voxel mation is contained in a small region including only few influences the classifier. For instance, if a voxel activates con- voxels. While this argument may hold for a single search- sistently when in class A but does not activate when in class light location in isolation, the argument does not necessarily B, the resulting weight component would be positive. On the carry over to a searchlight map consisting of many search- other hand, if the voxel activates consistently when in class A but light locations. Due to the inflationary nature of the search- does not activate when in class B, the weight component would light’s information maps, small informative regions will be be determined negative. Hence, the individual weight mapping contained in many searchlight locations. Ultimately, the rep- reveals how the corresponding voxel influences the classification resentation of the information content is hence inflated to a decision depending on the level of activation found in the fea- degree where small representations either fall under the statisti- ture. In an area with positive weights, a high activity level would cal threshold (when including a whole-brain correction) or are influence the classifier to decide on class A, while a low level of grossly overestimated in their spatial extent (see Figures 1, 4). activity would indicate class B. For negative weights, an analogous Furthermore, the intrinsic “smoothing” effect of the search- argument can be made: Here a high level of activity would influ- light method may be severely exacerbated by the inclusion of ence the classifier to decide on class B and a low level of activity spatial smoothing as a post-processing step (e.g., group-level would indicate class A. In contrast, the SLD method is unable to comparisons). deliver such information about the direction of influence for any From a conceptual point of view it can be argued that the given features, as it only determines whether class information is searchlight’s exclusive sensitivity to local patterns may provoke an present or not. unrealistic impression of brain function, given that the brain is In contrast to SLD, FWM is a truly global multivariate a large and massively interconnected network. It is most likely approach, that is, it considers all voxels simultaneously. Since the that the fingerprint of distinct brain states does not solely exist classification has to be computed only once on a relatively small at small spatial scales. Instead, the brain processes information data set (for each permutation), the computational resources nec- on larger spatial dimensions across wide-spread networks. For essary for the non-parametric statistical framework are drastically instance, remote brain areas have been observed to jointly exhibit lower compared to those needed for SLD. Depending on the size patterns of activation governed by long-range neural communica- of the data set in terms of voxels (resolution) and experimental tion (e.g., Laughlin, 2003). Evidently, such large-scale interactions trials, we found that the computation of the permutations in the cannot be captured by the searchlight method. Although some- FWM method was between 5,000 and 30,000 times faster than the times a strictly local investigation at small spatial scales is desired, SLD method. for example in (Diedrichsen et al., 2013), it is not clear that Because the potential for Type I and Type II errors is vastly the searchlight method is even suitable for such studies, given reduced, the interpretability of FWM-generated information its potential for false positive and false negative attributions of maps is much improved as compared with SLD. With FWM, the informative voxels. influence attributed to a given voxel is solely its influence on the classification of that particular voxel. FEATURE WEIGHT MAPPING Contrastingly, in the SLD method the accuracy at a voxel char- The FWM method is a global multivariate information mapping acterizes the aggregate decodability of a neighborhood of voxels technique based on dimensionality reduction, which comprises a around it. 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Diffusion- R (2014) Prioritizing spatial accuracy in high-resolution fMRI data using multivariate based spatial priors for functional magnetic resonance images. Neuroimage 41, feature weight mapping. Front. Neurosci. 8:66. doi: 10.3389/fnins.2014.00066 408–423. doi: 10.1016/j.neuroimage.2008.02.005 This article was submitted to Brain Imaging Methods, a section of the journal Frontiers Heidemann, R. M., Anwander, A., Feiweier, T., Knösche, T. R., and Turner, R. in Neuroscience. (2012). k-space and q-space: combining ultra-high spatial and angular reso- Copyright © 2014 Stelzer, Buschmann, Lohmann, Margulies, Trampel and Turner. lution in diffusion imaging using ZOOPPA at 7T. Curr. Opin. Neurobiol. 60, This is an open-access article distributed under the terms of the Creative Commons 967–978. doi: 10.1016/j.neuroimage.2011.12.081 Attribution License (CC BY). The use, distribution or reproduction in other forums is Kriegeskorte, N., and Bandettini, P. (2007). Analyzing for information, not permitted, provided the original author(s) or licensor are credited and that the original activation, to exploit high-resolution fMRI. Neuroimage 38, 649–662. doi: publication in this journal is cited, in accordance with accepted academic practice. No 10.1016/j.neuroimage.2007.02.022 use, distribution or reproduction is permitted which does not comply with these terms. Frontiers in Neuroscience | Brain Imaging Methods April 2014 | Volume 8 | Article 66 | 8

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