Brain shaving: adaptive detection for brain PET data.

The intricacy of brain biology is such that the variation of imaging end-points in health and disease exhibits an unpredictable range of spatial distributions from the extremely localized to the very diffuse. This represents a challenge for the two standard approaches to analysis, the mass univariate and the multivariate that exhibit either strong specificity but not as good sensitivity (the former) or poor specificity and comparatively better sensitivity (the latter). In this work, we develop an analytical methodology for positron emission tomography that operates an extraction ('shaving') of coherent patterns of signal variation while maintaining control of the type I error. The methodology operates two rotations on the image data, one local using the wavelet transform and one global using the singular value decomposition. The control of specificity is obtained by using the gap statistic that selects, within each eigenvector, a subset of significantly coherent elements. Face-validity of the algorithm is demonstrated using a paradigmatic data-set with two radiotracers, [(11)C]-raclopride and [(11)C]-(R)-PK11195, measured on the same Huntington's disease patients, a disorder with a genetic based diagnosis. The algorithm is able to detect the two well-known separate but connected processes of dopamine neuronal loss (localized in the basal ganglia) and neuroinflammation (diffusive around the whole brain). These processes are at the two extremes of the distributional envelope, one being very sparse and the latter being perfectly Gaussian and they are not adequately detected by the univariate and the multivariate approaches.