High rank tensor and spherical harmonic models for diffusion MRI processing

Diffusion tensor imaging (DTI) is a non-invasive quantitative method of characterizing tissue micro-structure. Diffusion imaging attempts to characterize the manner by which the water molecules within a particular location move within a given amount of time. Measurement of the diffusion tensor (D) within a voxel allows a macroscopic voxel-averaged description of fiber structure, orientation and fully quantitative evaluation of the microstructural features of healthy and diseased tissue.;The rank two tensor model is incapable of resolving multiple fiber orientations within an individual voxel. This shortcoming of single tensor model stems from the fact that the tensor possesses only a single orientational maximum. Several authors reported this non-mono-exponential behavior for the diffusion-induced attenuation in brain tissue in water and N-Acetyl Aspartate (NAA) signals, that is why the Multi-Tensor, Higher Rank Tensor and Orientation Distribution Function (ODF) were introduced.;Using the higher rank tensor, we will propose a scheme for tensor field interpolation which is inspired by subdivision surfaces in computer graphics. The method applies to Cartesian tensors of all ranks and imposes smoothness on the interpolated field by constraining the divergence and curl of the tensor field. Results demonstrate that the subdivision scheme can better preserve anisotropicity and interpolate rotations than some other interpolation methods. As one of the most important applications of DTI, fiber tractography was implemented to study the shape geometry changes. Based on the divergence and curl measurement, we will introduce new scalar measures that are sensitive to behaviors such as fiber bending and fanning.;Based on the ODF analysis, a new anisotropy measure that has the ability to describe multi-fiber heterogeneity while remaining rotationally invariant, will be introduced, which is a problem with many other anisotropy measures defined using the ODF. The performance of this novel measure is demonstrated for data with varying Signal to Noise Ratio (SNR), and different material characteristics