Alzheimer's disease (AD) is associated with progressive cognitive decline leading to dementia. The atrophy/loss of brain structure as seen on Magnetic Resonance Imaging (MRI) is strongly correlated with the severity of the cognitive impairment in AD. In this paper, we set out to find associations between predefined regions of the brain (regions of interest; ROIs) and the severity of the disease. Specifically, we use these associations to address two important issues in AD: (i) typical versus atypical atrophy patterns and (ii) the origin and direction of progression of atrophy, which is currently under debate. We observed that each AD-related ROI is associated with a wide range of severity and that the difference between ROIs is merely a difference in severity distribution. To model differences between the severity distribution of a subpopulation (with significant atrophy in certain ROIs) and the severity distribution of the entire population, we developed the concept of Distributional Association Rules. Using the Distributional Association Rules, we clustered ROIs into disease subsystems. We define a disease subsystem as a contiguous set of ROIs that are collectively implicated in AD. AD is known to be heterogeneous in the sense that multiple sets of ROIs may be related to the disease in a population. We proposed an enhancement to the association rule mining where the algorithm only discovers association rules with ROIs that form an approximately contiguous volume. Next, we applied these association rules to infer the direction of disease progression based on the support measures of the association rules. We also developed a novel statistical test to determine the statistical significance of the discovered direction. We evaluated the proposed method on the Mayo Clinic Alzheimer's Disease Research Center (ADRC) prospective patient cohorts. The key achievements of the methodology is that it accurately identified larger disease subsystems implicated in typical and atypical AD and it successfully mapped the directions of disease progression. The wealth of data available in Radiology gives rise to opportunities for applying this methodology to map out the trajectory of several other diseases, e.g. other neurodegenerative diseases and cancers, most notably, breast cancer. The applicability of this method is not limited to image data, as associating predictors with severity provides valuable information in most areas of medicine as well as other industries.