Shape analysis of brain structures using physical and experimental modes

We present a framework for analyzing the shape of structures within the human brain. A mathematical model is developed describing the deformation of any brain structure whose shape is affected by both gross and detailed physical processes. The total shape deformation is decomposed into physical modes of variation obtained from finite element analysis, and experimental modes of variation obtained from sample data using principal component analysis. This mathematical model is used to classify diseases that affect the shape of the ventricular system of the brain. Because ventricular shape is affected not only by pathology but also by overall brain shape, disease discrimination is difficult. By modeling the brain´s elastic properties, we are able to compensate for some of the nonpathological modes of ventricular shape variation. This allows us to experimentally characterize modes of variation that are indicative of disease processes