Keith J. Worsley

A unified statistical approach for determining significant signals in images of cerebral activation

We present a unified statistical theory for assessing the significance of apparent signal observed in noisy difference images. The results are usable in a wide range of applications, including fMRI, but are discussed with particular reference to PET images which represent changes in cerebral blood flow elicited by a specific cognitive or sensorimotor task. Our main result is an estimate of the P‐value for local maxima of Gaussian, t, χ2 and F fields over search regions of any shape or size in any number of dimensions. This unifies the P‐values for large search areas in 2‐D (Friston et al. [1991]: J Cereb Blood Flow Metab 11:690–699) large search regions in 3‐D (Worsley et al. [1992]: J Cereb Blood Flow Metab 12:900–918) and the usual uncorrected P‐value at a single pixel or voxel.

Analysis of fMRI time-series revisited--again.

Friston et al. (1995, NeuroImage 2:45-53) presented a method for detecting activations in fMRI time-series based on the general linear model and a heuristic analysis of the effective degrees of freedom. In this communication we present corrected results that replace those of the previous paper and solve the same problem without recourse to heuristic arguments. Specifically we introduce a proper and unbiased estimator for the error terms and provide a more generally correct expression for the effective degrees of freedom. The previous estimates of error variance were biased and, in some instances, could have led to a 10-20% overestimate of Z values. Although the previous results are almost correct for the random regressors chosen for validation, the present theoretical results are exact for any covariate or waveform. We comment on some aspects of experimental design and data analysis, in the light of the theoretical framework discussed here.

A Three-Dimensional Statistical Analysis for CBF Activation Studies in Human Brain

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. Rather than working with local maxima, our method focuses on the Euler characteristic of the set of voxels with a value larger than a given threshold. The Euler characteristic depends only on the topology of the regions of high activation, irrespective of their shape. For large threshold values this is approximately the same as the number of isolated regions of activation above the threshold. We can thus not only determine if any activation has taken place, but we can also estimate how many isolated regions of activation are present.

Assessing the significance of focal activations using their spatial extent.

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.

A GENERAL STATISTICAL ANALYSIS FOR FMRI DATA

We propose a method for the statistical analysis of fMRI data that seeks a compromise between efficiency, generality, validity, simplicity, and execution speed. The main differences between this analysis and previous ones are: a simple bias reduction and regularization for voxel-wise autoregressive model parameters; the combination of effects and their estimated standard deviations across different runs/sessions/subjects via a hierarchical random effects analysis using the EM algorithm; overcoming the problem of a small number of runs/session/subjects using a regularized variance ratio to increase the degrees of freedom.

Combining Spatial Extent and Peak Intensity to Test for Activations in Functional Imaging

Within the framework of statistical mapping, there are up to now only two tests used to assess the regional significance in functional images. One is based on the magnitude of the foci and tends to detect high intensity signals, while the second is based on the spatial extent of regions defined by a simple thresholding of the statistical map, a test that is more sensitive to extended signals. The aim of this paper is to combine the two tests into a single test that is more sensitive to a wider range of signals. This combined test is based on an analytical approximation of the distribution of these two parameters (size and height) and is applied in the context of statistical maps. The risk of error in noise-only 2D or 3D volumes is assessed under a wide range of experimental conditions obtained by varying both the resolution of the map and the threshold at which clusters are defined. In addition, we have investigated this new test on simulated signals, and applied it to an experimental PET dataset. The experimental risk of error is close to the predicted one, and the overall sensitivity increases when analyzing a volume containing different types of signals.

Unmyelinated tactile afferents signal touch and project to insular cortex.

There is dual tactile innervation of the human hairy skin: in addition to fast-conducting myelinated afferent fibers, there is a system of slow-conducting unmyelinated (C) afferents that respond to light touch. In a unique patient lacking large myelinated afferents, we found that activation of C tactile (CT) afferents produced a faint sensation of pleasant touch. Functional magnetic resonance imaging (fMRI) analysis during CT stimulation showed activation of the insular region, but not of somatosensory areas S1 and S2. These findings identify CT as a system for limbic touch that may underlie emotional, hormonal and affiliative responses to caress-like, skin-to-skin contact between individuals.

Nonstationary cluster-size inference with random field and permutation methods

Because of their increased sensitivity to spatially extended signals, cluster-size tests are widely used to detect changes and activations in brain images. However, when images are nonstationary, the cluster-size distribution varies depending on local smoothness. Clusters tend to be large in smooth regions, resulting in increased false positives, while in rough regions, clusters tend to be small, resulting in decreased sensitivity. Worsley et al. proposed a random field theory (RFT) method that adjusts cluster sizes according to local roughness of images [Worsley, K.J., 2002. Nonstationary FWHM and its effect on statistical inference of fMRI data. Presented at the 8th International Conference on Functional Mapping of the Human Brain, June 2-6, 2002, Sendai, Japan. Available on CD-ROM in NeuroImage 16 (2) 779-780; Hum. Brain Mapp. 8 (1999) 98]. In this paper, we implement this method in a permutation test framework, which requires very few assumptions, is known to be exact [J. Cereb. Blood Flow Metab. 16 (1996) 7] and is robust [NeuroImage 20 (2003) 2343]. We compared our method to stationary permutation, stationary RFT, and nonstationary RFT methods. Using simulated data, we found that our permutation test performs well under any setting examined, whereas the nonstationary RFT test performs well only for smooth images under high df. We also found that the stationary RFT test becomes anticonservative under nonstationarity, while both nonstationary RFT and permutation tests remain valid under nonstationarity. On a real PET data set we found that, though the nonstationary tests have reduced sensitivity due to smoothness estimation variability, these tests have better sensitivity for clusters in rough regions compared to stationary cluster-size tests. We include a detailed and consolidated description of Worsley nonstationary RFT cluster-size test.

Mapping anatomical correlations across cerebral cortex (MACACC) using cortical thickness from MRI

We introduce MACACC-Mapping Anatomical Correlations Across Cerebral Cortex-to study correlated changes within and across different cortical networks. The principal topic of investigation is whether the thickness of one area of the cortex changes in a statistically correlated fashion with changes in thickness of other cortical regions. We further extend these methods by introducing techniques to test whether different population groupings exhibit significantly varying MACACC patterns. The methods are described in detail and applied to a normal childhood development population (n = 292), and show that association cortices have the highest correlation strengths. Taking Brodmann Area (BA) 44 as a seed region revealed MACACC patterns strikingly similar to tractography maps obtained from diffusion tensor imaging. Furthermore, the MACACC map of BA 44 changed with age, older subjects featuring tighter correlations with BA 44 in the anterior portions of the superior temporal gyri. Lastly, IQ-dependent MACACC differences were investigated, revealing steeper correlations between BA 44 and multiple frontal and parietal regions for the higher IQ group, most significantly (t = 4.0) in the anterior cingulate.

Anatomical mapping of functional activation in stereotactic coordinate space

Numerous applications have been reported for the stereotactic mapping of focal changes in cerebral blood flow during sensory and cognitive activation as measured with positron emission tomography (PET) subtraction images. Since these images lack significant anatomical information, analysis of these kinds of data has been restricted to an automated search for peaks in the PET subtraction dataset and localization of the peak coordinates within a standardized stereotactic atlas. This method is designed to identify isolated foci with dimensions smaller than the image resolution. Details of activation patterns that may extend over finite distances, following the underlying anatomical structures, will not be apparent. We describe the combined mapping into stereotactic coordinate space of magnetic resonance imaging (MRI) and PET information from each of a set of subjects such that the major features of the activation pattern, particularly extended tracts of increased blood flow, can be immediately assessed within their true anatomical context as opposed to that presumed using a standard atlas alone. Near areas of high anatomical variability, e.g., central sulcus, or of sharp curvature, e.g., frontal and temporal poles, this information can be essential to the localization of a focus to the correct gyrus or for the rejection of extracerebral peaks. It also allows for the removal from further analysis of data from cognitively-normal subjects with abnormal anatomy such as enlarged ventricles. In patients with neuropathology, e.g., Alzheimers disease, arteriovenous malformation, stroke, or neoplasm, the use of correlated MRI is mandatory for correct localization of functional activation.