Statistical shape analysis of neuroanatomical structures based on spherical wavelet transformation

Abstract

Evidence suggests that morphological changes of neuroanatomical structures may reflect abnormalities in neurodevelopment, or relate to a variety of disorders, such as schizophrenia and Alzheimer's disease (AD). Advances in high-resolution Magnetic Resonance Imaging (MRI) techniques allow us to study these alterations of brain structures in vivo. Previous work in studying the shape variations of brain structures has provided additional localized information compared with traditional volume-based study. However, challenges remain in finding an accurate shape presentation and conducting shape analysis with sound statistical principles. In this work, we develop methods for automatically extracting localized and multi-scale shape features and conducting statistical shape analysis of neuroanatomical structures obtained from MR images. We first develop a procedure to extract multi-scale shape features of brain structures using biorthogonal spherical wavelets. Using this wavelet-based shape representation, we build multi-scale shape models and study the localized cortical folding variations in a normal population using Principal Component Analysis (PCA). We then build a shape-based classification framework for detecting pathological changes of cortical surfaces using advanced classification methods, such as predictive Automatic Relevance Determination (pred-ARD), and demonstrate promising results in patient/control group comparison studies. Thirdly, we develop a nonlinear temporal model for studying the temporal order and regional difference of cortical folding development based on this shape representation. Furthermore, we develop a shape-guided segmentation method to improve the segmentation of sub-cortical structures, such as hippocampus, by using shape constraints obtained in the wavelet domain.

(cont.) Finally, we improve upon the proposed wavelet-based shape representation by adopting a newly developed over-complete spherical wavelet transformation and demonstrate its utility in improving the accuracy and stability of shape representations. By using these shape representations and statistical analysis methods, we have demonstrated promising results in localizing shape changes of neuroanatomical structures related to aging, neurological diseases, and neurodevelopment at multiple spatial scales. Identification of these shape changes could potentially lead to more accurate diagnoses and improved understanding of neurodevelopment and neurological diseases.