Abstract
We present a framework for analyzing the shape deformation 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. Using our technique, the total shape deformation is decomposed into analytic modes of variation obtained from finite element modeling, and statistical modes of variation obtained from sample data. Our method is general, and can be applied to many problems where the goal is to separate out important from unimportant shape variation across a class of objects. In this paper, we focus on the analysis of diseases that affect the shape of brain structures. Because the shape of these structures 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 shape variation. This allows us to experimentally characterize modes of variation that are indicative of disease processes. We apply our technique to magnetic resonance images of the brains of individuals with schizophrenia, Alzheimer's disease, and normal-pressure hydrocephalus, as well as to healthy volunteers. Classification results are presented.
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