Detecting and estimating the regions of activation in 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 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 ∆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.