Novel geometry and function based topological data analysis in neuroimaging data

Parkinson's disease (PD) is the most common movement disorder and the second most common neurodegenerative disorder. The diagnosis of PD commonly relies on clinical examination with limited number of non-invasive imaging based methods available for clinical diagnosis. Likewise, preterm birth is a growing global issue with increasing incidence and has been commonly associated with cognitive and functional deficits in later years of life. Non-invasive assessment of morphology change in the brain due to preterm birth can potentially aid proper clinical decision process. As a first step in this direction, this thesis presents novel geometry and function feature based topological data analysis in neuroimaging data. Efficacy of these methods to capture the subtle changes in brain due to nueurological conditions at the beginning and later end of human life cycle show promise in their clinical utility. These topology features are able to discriminate between PD patients and healthy groups and preterm born and term born children. First, we present a novel framework to quantify the brain geometry change with brain abnormalities in an algebraic topology approach to obtain persistent homology features (chapter 3). In chapter 4, we model the whole brain geometrical arrangement of cortical and subcortical structures to obtain topology features and show their potential to discriminate between disease and healthy groups. Subsequently, we study the topology of function indexed on the brain geometry. In chapters 5 & 6 we present a novel surface deformation based surface displacement shape feature to identify change in shape of the subcortical structures due to PD and preterm birth and study the topology of the shape feature in chapter 7. In chapters 8, 9 & 10 we present the study of cortical atrophy in PD, cortical abnormality in preterm born children and the topology of the cortical thickness change in the disease groups. Lastly, in the appendix A we present a library of brain MRI templates with ground truth labels for subcortical structures that was built to obtain accurate segmentation of these structures in pediatric brain MRI images.