Geometric Alignment of Functional and Diffusion Data from Magnetic Resonance Imaging
- Author(s): Lee, David
- Advisor(s): Joshi, Shantanu
- Hsu, William
- et al.
The advancement of various modalities within magnetic resonance imaging (MRI) techniques has generated a wealth of data with rich and complex information. We adopt a geometric perspective for analyzing these data. Particularly we treat such data as functions and apply tools from differential geometry to exploit the underlying shape information present in time-series from functional MRI (fMRI) and tractography profiles from diffusion-weighted MRI (DWI). The shape information is harmonized or registered using an elastic alignment, which serves as a unified framework for analyzing the amplitude and phase variability in the data. This is achieved by simultaneously performing matching and encoding the differences in shapes embedded in the functional signals by doing registration via reparameterization. For task-based fMRI, we demonstrate potential improvement in statistical power, by matching the brain activity signals in response to shared tasks. In resting-state fMRI, elastic alignment offers improved identification of shared intrinsic response of the brain at rest, and therefore, improved identification of the functional networks. In DWI, we align scalar diffusion properties along the models of white matter fiber tracts. We also propose a geometric approach for complex and multi-feature tabular type data representation and alignment. We construct a kernel density distribution of mean values over salient regions of interest in the brain using structural or diffusional measures, such as cortical thickness or fractional anisotropy. These ideas are also demonstrated by way of high-dimensional network representations of multimodal features in the brain.