John Martin, Alex Pentland, and Ron Kikinis
Various neurological disorders affect the gross anatomical shape of different brain structures. Hydrocephalus, for example, affects the morphology of the ventricular system. These changes have been studied for several decades, using both postmortem and in vivo methods. Recent advances in the contrast and resolution of magnetic resonance (MR) scanners now make it possible to study these shape effects in vivo and noninvasively, with the potential for better diagnosis and treatment. Our aim is to quantitatively describe these pathological shape deformations. Because of both genetic and environmental factors, however, biological structures have a large normal range of variation. The onset of a disease introduces further changes in morphology, with each particular disease causing its own type of shape changes and range of variation in these changes. Therefore to properly study the pathological deformations, we must first account for the large normal variation in biological shape. For structures inside the cranium, part of this normal shape variability is due to the different head shapes seen across individuals. These macroscopic shape effects interfere with the analysis of local shape deformations caused.by disease. What is needed then is a method that separates out these two types of deformations, allowing just the disease deformations to be analyzed. In this paper we create a mathematical framework that (1) separates out disease deformation from head shape deformation, and (2) allows us to represent the deformations caused disease in an intuitive manner. This is accomplished by USl~ng the finitelement method (FEM) to create a physical model that describes the macroscopic effects caused by different head shapes. After elastically warping the cranial contents according to this physical model, we are left with residual shape differences across patients that are largely independent of head shape. Because detailed physical models of neurological diseases do not exist, we turn to statistical techniques to examine this data.