Improved assessment of significant activation in functional magnetic resonance imaging (fMRI) : use of a cluster-size threshold
TL;DR: In this article, an alternative approach, which relies on the assumption that areas of true neural activity will tend to stimulate signal changes over contiguous pixels, is presented, which can improve statistical power by as much as fivefold over techniques that rely solely on adjusting per pixel false positive probabilities.
Abstract: The typical functional magnetic resonance (fMRI) study presents a formidable problem of multiple statistical comparisons (i.e., > 10,000 in a 128 x 128 image). To protect against false positives, investigators have typically relied on decreasing the per pixel false positive probability. This approach incurs an inevitable loss of power to detect statistically significant activity. An alternative approach, which relies on the assumption that areas of true neural activity will tend to stimulate signal changes over contiguous pixels, is presented. If one knows the probability distribution of such cluster sizes as a function of per pixel false positive probability, one can use cluster-size thresholds independently to reject false positives. Both Monte Carlo simulations and fMRI studies of human subjects have been used to verify that this approach can improve statistical power by as much as fivefold over techniques that rely solely on adjusting per pixel false positive probabilities.
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TL;DR: The standard nonparametric randomization and permutation testing ideas are developed at an accessible level, using practical examples from functional neuroimaging, and the extensions for multiple comparisons described.
Abstract: Requiring only minimal assumptions for validity, nonparametric permutation testing provides a flexible and intuitive methodology for the statistical analysis of data from functional neuroimaging experiments, at some computational expense. Introduced into the functional neuroimaging literature by Holmes et al. ([1996]: J Cereb Blood Flow Metab 16:7-22), the permutation approach readily accounts for the multiple comparisons problem implicit in the standard voxel-by-voxel hypothesis testing framework. When the appropriate assumptions hold, the nonparametric permutation approach gives results similar to those obtained from a comparable Statistical Parametric Mapping approach using a general linear model with multiple comparisons corrections derived from random field theory. For analyses with low degrees of freedom, such as single subject PET/SPECT experiments or multi-subject PET/SPECT or fMRI designs assessed for population effects, the nonparametric approach employing a locally pooled (smoothed) variance estimate can outperform the comparable Statistical Parametric Mapping approach. Thus, these nonparametric techniques can be used to verify the validity of less computationally expensive parametric approaches. Although the theory and relative advantages of permutation approaches have been discussed by various authors, there has been no accessible explication of the method, and no freely distributed software implementing it. Consequently, there have been few practical applications of the technique. This article, and the accompanying MATLAB software, attempts to address these issues. The standard nonparametric randomization and permutation testing ideas are developed at an accessible level, using practical examples from functional neuroimaging, and the extensions for multiple comparisons described. Three worked examples from PET and fMRI are presented, with discussion, and comparisons with standard parametric approaches made where appropriate. Practical considerations are given throughout, and relevant statistical concepts are expounded in appendices.
5,777 citations
TL;DR: Results confirm that this region shows activity during erroneous responses, but activity was also observed in the same region during correct responses under conditions of increased response competition, which suggests that the ACC detects conditions under which errors are likely to occur rather than errors themselves.
Abstract: An unresolved question in neuroscience and psychology is how the brain monitors performance to regulate behavior. It has been proposed that the anterior cingulate cortex (ACC), on the medial surface of the frontal lobe, contributes to performance monitoring by detecting errors. In this study, event-related functional magnetic resonance imaging was used to examine ACC function. Results confirm that this region shows activity during erroneous responses. However, activity was also observed in the same region during correct responses under conditions of increased response competition. This suggests that the ACC detects conditions under which errors are likely to occur rather than errors themselves.
3,236 citations
TL;DR: A neuroimaging study examined the neural correlates of social exclusion and tested the hypothesis that the brain bases of social pain are similar to those of physical pain, suggesting that RVPFC regulates the distress of socialclusion by disrupting ACC activity.
Abstract: A neuroimaging study examined the neural correlates of social exclusion and tested the hypothesis that the brain bases of social pain are similar to those of physical pain. Participants were scanned while playing a virtual ball-tossing game in which they were ultimately excluded. Paralleling results from physical pain studies, the anterior cingulate cortex (ACC) was more active during exclusion than during inclusion and correlated positively with self-reported distress. Right ventral prefrontal cortex (RVPFC) was active during exclusion and correlated negatively with self-reported distress. ACC changes mediated the RVPFC-distress correlation, suggesting that RVPFC regulates the distress of social exclusion by disrupting ACC activity.
3,188 citations
TL;DR: It is found that the most common software packages for fMRI analysis (SPM, FSL, AFNI) can result in false-positive rates of up to 70%.
Abstract: The most widely used task functional magnetic resonance imaging (fMRI) analyses use parametric statistical methods that depend on a variety of assumptions. In this work, we use real resting-state data and a total of 3 million random task group analyses to compute empirical familywise error rates for the fMRI software packages SPM, FSL, and AFNI, as well as a nonparametric permutation method. For a nominal familywise error rate of 5%, the parametric statistical methods are shown to be conservative for voxelwise inference and invalid for clusterwise inference. Our results suggest that the principal cause of the invalid cluster inferences is spatial autocorrelation functions that do not follow the assumed Gaussian shape. By comparison, the nonparametric permutation test is found to produce nominal results for voxelwise as well as clusterwise inference. These findings speak to the need of validating the statistical methods being used in the field of neuroimaging.
2,946 citations
TL;DR: The presence of self-referential mental activity appears to be associated with increases from the baseline in dorsal MPFC, and reductions in ventral MPFC occurred consistent with the fact that attention-demanding tasks attenuate emotional processing.
Abstract: Medial prefrontal cortex (MPFC) is among those brain regions having the highest baseline metabolic activity at rest and one that exhibits decreases from this baseline across a wide variety of goal-directed behaviors in functional imaging studies. This high metabolic rate and this behavior suggest the existence of an organized mode of default brain function, elements of which may be either attenuated or enhanced. Extant data suggest that these MPFC regions may contribute to the neural instantiation of aspects of the multifaceted “self.” We explore this important concept by targeting and manipulating elements of MPFC default state activity. In this functional magnetic resonance imaging (fMRI) study, subjects made two judgments, one self-referential, the other not, in response to affectively normed pictures: pleasant vs. unpleasant (an internally cued condition, ICC) and indoors vs. outdoors (an externally cued condition, ECC). The ICC was preferentially associated with activity increases along the dorsal MPFC. These increases were accompanied by decreases in both active task conditions in ventral MPFC. These results support the view that dorsal and ventral MPFC are differentially influenced by attentiondemanding tasks and explicitly self-referential tasks. The presence of self-referential mental activity appears to be associated with increases from the baseline in dorsal MPFC. Reductions in ventral MPFC occurred consistent with the fact that attention-demanding tasks attenuate emotional processing. We posit that both self-referential mental activity and emotional processing represent elements of the default state as represented by activity in MPFC. We suggest that a useful way to explore the neurobiology of the self is to explore the nature of default state activity.
2,844 citations
References
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31 Jan 1986TL;DR: Numerical Recipes: The Art of Scientific Computing as discussed by the authors is a complete text and reference book on scientific computing with over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, with many new topics presented at the same accessible level.
Abstract: From the Publisher:
This is the revised and greatly expanded Second Edition of the hugely popular Numerical Recipes: The Art of Scientific Computing. The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. With over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, this book is more than ever the most practical, comprehensive handbook of scientific computing available today. The book retains the informal, easy-to-read style that made the first edition so popular, with many new topics presented at the same accessible level. In addition, some sections of more advanced material have been introduced, set off in small type from the main body of the text. Numerical Recipes is an ideal textbook for scientists and engineers and an indispensable reference for anyone who works in scientific computing. Highlights of the new material include a new chapter on integral equations and inverse methods; multigrid methods for solving partial differential equations; improved random number routines; wavelet transforms; the statistical bootstrap method; a new chapter on "less-numerical" algorithms including compression coding and arbitrary precision arithmetic; band diagonal linear systems; linear algebra on sparse matrices; Cholesky and QR decomposition; calculation of numerical derivatives; Pade approximants, and rational Chebyshev approximation; new special functions; Monte Carlo integration in high-dimensional spaces; globally convergent methods for sets of nonlinear equations; an expanded chapter on fast Fourier methods; spectral analysis on unevenly sampled data; Savitzky-Golay smoothing filters; and two-dimensional Kolmogorov-Smirnoff tests. All this is in addition to material on such basic top
12,662 citations
TL;DR: The results mean that detecting significant activations no longer depends on a fixed threshold, but can be effected at any (lower) threshold, in terms of the spatial extent of the activated region.
Abstract: Current approaches to detecting significantly activated regions of cerebral tissue use statistical parametric maps, which are thresholded to render the probability of one or more activated regions of one voxel, or larger, suitably small (e. g., 0.05). We present an approximate analysis giving the probability that one or more activated regions of a specified volume, or larger, could have occurred by chance. These results mean that detecting significant activations no longer depends on a fixed (and high) threshold, but can be effected at any (lower) threshold, in terms of the spatial extent of the activated region. The substantial improvement in sensitivity that ensues is illustrated using a power analysis and a simulated phantom activation study. © 1994 Wiley-Liss, Inc.
1,936 citations
TL;DR: A simple method for determining an approximate p value for the global maximum based on the theory of Gaussian random fields is described, which focuses on the Euler characteristic of the set of voxels with a value larger than a given threshold.
Abstract: Many studies of brain function with positron emission tomography (PET) involve the interpretation of a subtracted PET image, usually the difference between two images under baseline and stimulation conditions. The purpose of these studies is to see which areas of the brain are activated by the stimulation condition. In many cognitive studies, the activation is so slight that the experiment must be repeated on several subjects and the subtracted images are averaged to improve the signal-to-noise ratio. The averaged image is then standardized to have unit variance and then searched for local maxima. The main problem facing investigators is which of these local maxima are statistically significant. We describe a simple method for determining an approximate p value for the global maximum based on the theory of Gaussian random fields. The p value is proportional to the volume searched divided by the product of the full widths at half-maximum of the image reconstruction process or number of resolution elements....
1,918 citations
TL;DR: Modifications to this method that allow for cross-modality registration of MRI and PET brain images obtained from a single subject are described and validated quantitatively using data from patients with stereotaxic fiducial markers rigidly fixed in the skull.
Abstract: ObjectiveWe have previously reported an automated method for within-modality (e.g., PET-to-PET) image alignment. We now describe modifications to this method that allow for cross-modality registration of MRI and PET brain images obtained from a single subject.MethodsThis method does not require fidu
1,759 citations
TL;DR: In this paper, a distinction is made between using statistical parametric maps (SPMs) as images of change significance and using them to identify foci of significant change, where the SPM can be reported nonselectively as a single mathematical object with its omnibus significance.
Abstract: Statistical parametric maps (SPMs) are potentially powerful ways of localizing differences in regional cerebral activity. This potential is limited by uncertainties in assessing the significance of these maps. In this report, we describe an approach that may partially resolve this issue. A distinction is made between using SPMs as images of change significance and using them to identify foci of significant change. In the first case, the SPM can be reported nonselectively as a single mathematical object with its omnibus significance. Alternatively, the SPM constitutes a large number of repeated measures over the brain. To reject the null hypothesis, that no change has occurred at a specific location, a threshold adjustment must be made that accounts for the large number of comparisons made. This adjustment is shown to depend on the SPM's smoothness. Smoothness can be determined empirically and be used to calculate a threshold required to identify significant foci. The approach models the SPM as a stationary stochastic process. The theory and applications are illustrated using uniform phantom images and data from a verbal fluency activation study of four normal subjects.
1,658 citations