Abstract

Positron emission tomography (PET) produces images of blood flow that can be used to find the regions of the brain that are activated by a linguistic task or a sensory stimulus. Several images are obtained on each subject in a randomised block design, and the first step is to test if any change in mean or `activation' has occurred. We first treat the images as repeated measures in space and propose an ANOVA-like quadratic test statistic for testing whether any activation has taken place. We show that it has some optimality properties for detecting a single peak of increased mean activation at an unknown location in the image. We also investigate a statistic that is used in the medical literature which is based on the proportion of the image that exceeds a fixed threshold value. For both test statistics we provide a simple approximate null distribution in which the effective degrees of freedom, or effective number of independent observations in the image, depends on the volume of the brain multiplied by a known measure of the resolution of the PET camera. Once activation is detected, we propose a Stein-type shrinkage estimator for the mean change that has lower mean squared error than the usual sample average. The methods are illustrated on a set of cerebral blood flow images from an experiment in pain perception.

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