Statistical shape analysis of hippocampus for Alzheimer's disease

Abstract

The population suffering from the neurodegenerative diseases, for instance the Alzheimer's disease, is large. Such diseases are usually fatal and difficult for diagnosis, because they may begin long before the patient experiences any symptoms. However, shape changes may have already occurred at certain brain structures under the damage of the disease. At least this is the case for hippocampus under the influence of the Alzheimer's disease. Consequently, these shape changes are of great research and clinic interest. Once identified, they may serve as the biomarkers for the early stage diagnosis of the disease. The advances in medical imaging techniques make it possible to study in vivo the relationship between the shape of a brain structure and a particular mental disorder. As the most important means to conduct this study, statistical shape analysis becomes a very active field in neuro-imaging research. In this thesis, we aim to develop a set of statistical shape analysis methods that can be applied to the study of hippocampal shapes with respect to the Alzheimer's disease, and improve the general process of shape analysis as well. This thesis has discussed some basic problems in the statistical shape analysis, including shape alignment, hypothesis test, localization of shape difference and feature selection for better classification. Three novel algorithms are proposed, which push forward the state-of-the-art work in statistical shape analysis. They include i) an efficient permutation test generalized to multivariate shape descriptors. This is a fast, accurate method, being able to detect the subtle shape differences between classes. As a data-driven method, it is especially useful when the distribution assumption is uncertain for the input data; ii) a reliable method to localize the shape differences captured by kernel classifiers. This approach manages to convert the shape class differences detected in the feature space of kernel methods to anatomical interpretations in the shape descriptor space. Realizing that the shape descriptors usually reside on a sub-dimensional manifold in the input space, this approach significantly improves the fidelity of the interpretations of the shape class differences; iii) a redundancy constrained feature selection method on top of the class separability measure. This method outperforms some commonly used feature selection methods that cannot effectively select discriminative and mutually independent features, for instance the prevailing SVM-RFE used in hippocampus feature selection. The redundancy constraints are carefully generated in our method in order to satisfy the totally unimodular condition, which guarantees a globally optimal solution for our optimization problem. In addition to the three proposed algorithms, an investigation is also conducted in this thesis to compare different distance functions in hippocampal shape alignment. The properties of all the proposed algorithms are theoretically analyzed in detail. Their performances are fully demonstrated by the experiments on both the benchmark data and the hippocampus data at the end of each chapter. In addition to proposing new algorithms, systematically conducting experiments of shape analysis on large scale hippocampus data sets is another contribution of this thesis. Our findings confirm the documented observations of shape difference between either the sex groups or the groups of the Alzheimer's disease and the normal control.