Mathematical Modelling and Feature Extraction for Probing Crucial Changes Associated with Alzheimer's Disease

Transverse relaxation time T2 and magnetization transfer ratio MTR are examples of two magnetic resonance imaging parameters that allow for a sensitive characterization of microscopic tissue properties in the brain. Classically, the mean values of these parameters are assessed in a region-of-interest and compared groupwise. In contrast to this, modern voxel-based methods test for localized changes in imaging parameters on a per-voxel basis, by registering the image to an average brain template or atlas. An intermediary method is distributional analysis, where the distribution of an imaging parameter over an anatomical region, identified from a brain atlas, is the main object of interest. This distribution captures local variation and changes in tissue properties and can ideally be described by a parametric mixture model. It can directly be compared across subjects by a distance measure and classification of subjects can be based on features extracted from these distributions of imaging parameters. This approach reduces the high dimensionality of the data and, consequently, the impact of noise and avoids the problem of collinearity. In this article the applicability of these and related methods of feature extraction and discrimination is reviewed in the context of Alzheimer's disease.