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Brain mapping data have been modeled as Gaussian random fields, and local increases in mean are detected by local maxima of a random field of test statistics derived from these data. Accurate p values for local maxima are readily available for isotropic data based on the expected Euler characteristic of the excursion Set of the test statistic random field. In this article we give a simple method for dealing with nonisotropic data. Our approach has connections to the model of Sampson and Guttorp for nonisotropy in which there exists an unknown mapping of the support of the data to a space in which the random fields are isotropic. Heuristic justification for our approach comes from the Nash embedding theorem. Formally, we show that our method gives consistent unbiased estimators for the true p values based on new results of Taylor and Adler for random fields on manifolds, which replace the Euclidean metric by the variogram. The results are used to detect gender differences in the cortical thickness of the brain and to detect regions of the brain involved in sentence comprehension measured by functional magnetic resonance imaging. [ABSTRACT FROM AUTHOR]

We report new random field theory P values for peaks of canonical correlation SPMs for detecting multiple contrasts in a linear model for multivariate image data. This completes results for all types of univariate and multivariate image data analysis. All other known univariate and multivariate random field theory results are now special cases, so these new results present a true unification of all currently known results. As an illustration, we use these results in a deformation-based morphometry (DBM) analysis to look for regions of the brain where vector deformations of nonmissile trauma patients are related to several verbal memory scores, to detect regions of changes in anatomical effective connectivity between the trauma patients and a group of age- and sex-matched controls, and to look for anatomical connectivity in cortical thickness. [Copyright &y& Elsevier]