Abstract
Many studies of brain function with positron emission tomography (PET) involve the interpretation of a subtracted PET image, usually the difference between two images of cerebral blood flow (CBF) under baseline and activation conditions. In many cognitive studies, the activation is so slight (4-8%) that the experiment must be repeated on several subjects. The images are then mapped into a standardised coordinate space to account for differences in brain size and orientation, and the subtracted images averaged to improve the signal to noise ratio. The averaged Delta CBF image is then normalised to have unit variance and the resulting t-statistic image is searched for local maxima. If the between-subject variance is not demonstrably (significantly) different across all voxels then the normalisation can be based on a pooled estimate of the between subjects variance. If this is not so then a voxel-based normalisation must be used. We describe a method for determining if the population standard deviation image has regions of high or low values. If these are detected then we give an approximate P-value for the global maximum of the voxel-based t-statistic. We propose an estimator of the number of regions of high or low standard deviation, and the number of regions of activation in the voxel-based t-statistic image. The method uses the Euler characteristic, a concept borrowed from topology. We can thus determine not only if any activation has taken place, but also how many isolated regions of activation are present.