Manifold Learning Techniques in Image Analysis of High-dimensional Diffusion Tensor Magnetic Resonance Images

Diffusion tensor magnetic resonance imaging (DT-MRI) provides a comprehensive characterization of white matter (WM) in the brain and therefore, plays a crucial role in the investigation of diseases in which WM is suspected to be compromised such as multiple sclerosis and neuropsychiatric disorders like schizophrenia. However changes induced by pathology may be subtle and affected regions of the brain can only be revealed by a group-based analysis of patients in comparison with healthy controls. This in turn requires voxel-based statistical analysis of spatially normalized brain DT images, as in the case of conventional MR images. However this process is rendered extremely challenging in DT-MRI due to the high dimensionality of the data and its inherent non-linearity that causes linear component analysis methods to be inapplicable. We therefore propose a novel framework for the statistical analysis of DT-MRI data using manifold-based techniques such as isomap and kernel PCA that determine the underlying manifold structure of the data, embed it to a manifold and help perform high dimensional statistics on the manifold to determine regions of difference between the groups of patients and controls. The framework has been successfully applied to DT-MRI data from patients with schizophrenia, as well as to study developmental changes in small animals, both of which identify regional changes, indicating the need for manifold-based methods for the statistical analysis of DTI.