This thesis examines the advantages to nonlinear least-squares (NLS) fitting of diffusion-weighted MRI data over the commonly used linear least-squares (LLS) approach. A modified fitting algorithm is proposed which accounts for the positive bias experienced in magnitude images at low SNR. For b-values in the clinical range (~1000 s/mm2), the increase in precision of FA and fibre orientation estimates is almost negligible, except at very high anisotropy. The optimal b-value for estimating tensor parameters was slightly higher for NLS. The primary advantage to NLS was improved performance at high b-values, for which complex fibre architectures were more easily resolved. This was demonstrated using a model-selection classifier based on higher-order diffusion models. Using a b-value of 3000 s/mm2 and magnitude-corrected NLS fitting, at least 10% of voxels in the brain exhibited diffusion profiles which could not be represented by the tensor model.

This thesis examines the advantages to nonlinear least-squares (NLS) fitting of diffusion-weighted MRI data over the commonly used linear least-squares (LLS) approach. A modified fitting algorithm is proposed which accounts for the positive bias experienced in magnitude images at low SNR. For b-values in the clinical range (~1000 s/mm2), the increase in precision of FA and fibre orientation estimates is almost negligible, except at very high anisotropy. The optimal b-value for estimating tensor parameters was slightly higher for NLS. The primary advantage to NLS was improved performance at high b-values, for which complex fibre architectures were more easily resolved. This was demonstrated using a model-selection classifier based on higher-order diffusion models. Using a b-value of 3000 s/mm2 and magnitude-corrected NLS fitting, at least 10% of voxels in the brain exhibited diffusion profiles which could not be represented by the tensor model.