should be possible to implement them (and many others) within a unified framework. We present here a general approach that accommodates most forms of experimental layout and ensuing analysis (designed experiments with fixed effects for factors, covariates and interaction of factors). This approach brings together two well established bodies of theory (the general linear model and the theory of Gaussian fields) to provide a complete and simple framework for the analysis of imaging data.The importance of this framework is twofold: (i) Conceptual and mathematical simplicity, in that the same small number of operational equations is used irrespective of the complexity of the experiment or nature of the statistical model and (ii) the generality of the framework provides for great latitude in experimental design and analysis.

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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.

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.

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, chi(2) 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.

Structural maturation of fiber tracts in the human brain, including an increase in the diameter and myelination of axons, may play a role in cognitive development during childhood and adolescence. A computational analysis of structural magnetic resonance images obtained in 111 children and adolescents revealed age-related increases in white matter density in fiber tracts constituting putative corticospinal and frontotemporal pathways. The maturation of the corticospinal tract was bilateral, whereas that of the frontotemporal pathway was found predominantly in the left (speech-dominant) hemisphere. These findings provide evidence for a gradual maturation, during late childhood and adolescence, of fiber pathways presumably supporting motor and speech functions.

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 NRI, 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, x2 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 11590-699) large search regions in 3-D (Worsley et al. [1992]: J Cereb Blood Flow Metab 12:900-918) and the usual uncorrected IJ-value at a single pixel or voxel.

The Wisconsin Card Sorting Task (WCST) has been used to assess dysfunction of the prefrontal cortex and basal ganglia. Previous brain imaging studies have focused on identifying activity related to the set-shifting requirement of the WCST. The present study used event-related functional magnetic resonance imaging (fMRI) to study the pattern of activation during four distinct stages in the performance of this task. Eleven subjects were scanned while performing the WCST and a control task involving matching two identical cards. The results demonstrated specific involvement of different prefrontal areas during different stages of task performance. The mid-dorsolateral prefrontal cortex (area 9/46) increased activity while subjects received either positive or negative feedback, that is at the point when the current information must be related to earlier events stored in working memory. This is consistent with the proposed role of the mid-dorsolateral prefrontal cortex in the monitoring of events in working memory. By contrast, a cortical basal ganglia loop involving the mid-ventrolateral prefrontal cortex (area 47/12), caudate nucleus, and mediodorsal thalamus increased activity specifically during the reception of negative feedback, which signals the need for a mental shift to a new response set. The posterior prefrontal cortex response was less specific; increases in activity occurred during both the reception of feedback and the response period, indicating a role in the association of specific actions to stimuli. The putamen exhibited increased activity while matching after negative feedback but not while matching after positive feedback, implying greater involvement during novel than routine actions.