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.

/pdf/nonparametric-permutation-tests-for-functional-neuroimaging-2tnaunteli.pdf

Nonparametric permutation tests for functional neuroimaging: A primer with examples

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.

https://science.sciencemag.org/content/sci/280/5364/747.full.pdf

Anterior cingulate cortex, error detection, and the online monitoring of performance

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.

https://science.sciencemag.org/content/sci/302/5643/290.full.pdf

Does Rejection Hurt? An fMRI Study of Social Exclusion

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.

https://www.pnas.org/content/pnas/113/28/7900.full.pdf

Cluster failure: Why fMRI inferences for spatial extent have inflated false-positive rates

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.

Medial prefrontal cortex and self-referential mental activity: Relation to a default mode of brain function

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.

Improved assessment of significant activation in functional magnetic resonance imaging (fMRI) : use of a cluster-size threshold

This paper presents a technique for performing two-dimensional rigid-body image registration for functional magnetic resonance images (fMRI). The method provides accurate motion correction without local distortion. The approach is to perform the translation and rotation in the Fourier domain. For images sampled on a grid, such as in echo-planar imaging (EPI), one potential stumbling block to this approach is the computational burden of reconstruction, since the rotated image will no longer be on the Cartesian grid. A method of approximating rotations via local translations (shearing) is presented, which keeps the data on the Cartesian grid. This can provide quite accurate approximations with only a moderate amount of computation. A mean squared error (MSE) criterion is used for determining the registration parameters. This method is tested on several sets of simulated images and shown to have an accuracy ranging from 0.02 to 0.3 pixels for images with SNRs ranging from 100 to 10, respectively. These techniques have been tested on several sets of images. They are shown to work well on real subjects, for both echo-planar and spiral data acquisition schemes. The techniques are used in an activation study in which the subject moved his head during image collection. After use of this registration technique, the activation is easily detected.

Improved image registration by using Fourier interpolation.

Magnetic resonance imaging (MRI) is a modern technique for producing pictures of the internals of the human body. An MR scanner subjects its contents to carefully modulated electro-magnetic fields and records the resulting radio signal. The radio signal is the Fourier transform of the density of (for example) hydrogen atoms. Computing the inverse Fourier transform of the digitized signal reveals an image of the (hydrogen density of the) contents of the scanner. Functional MRI (fMRI) is a very recent development in which MRI is used to produce images of the human brain which show regions of activation reflecting the functioning of the brain.

Functional Imaging Analysis Software — Computational Olio

Functional magnetic resonance imaging of the human brain in action presents large statistical and computational challenges. Here we describe those challenges and provide references to a number of other papers where detailed methods developed to meet them are reported. The first seven sections of this paper were written in 1995 when our work was in its infancy. The last four sections were written more recently, to update the earlier sections and to show the directions we have gone and the directions we intend to go.

/pdf/the-challenge-of-functional-magnetic-resonance-imaging-48ws99xm00.pdf

The Challenge of Functional Magnetic Resonance Imaging

Bayesian reliability demonstration test plans are developed for binomial and exponential sampling distributions using mixtures of beta and inverse gamma prior distributions, respectively. Both types of plans consider a single specified target reliability and rectify an important drawback of an existing well-known classical single-level test planning procedure. The plans are developed in such a way that they attain a specified probability of passing the test when the target reliability has been met as well as provide desired confidence that the target reliability has been met given that the test has been passed.

Mark Fitzgerald

Papers

Improved assessment of significant activation in functional magnetic resonance imaging (fMRI) : use of a cluster-size threshold

Improved image registration by using Fourier interpolation.

Functional Imaging Analysis Software — Computational Olio

The Challenge of Functional Magnetic Resonance Imaging

Bayesian single-level binomial and exponential reliability demonstration test plans