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Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on many factors such as the number of coils and the methodology used to combine multichannel MRI signals. Indeed, the two prevailing methods for multichannel signal combination lead to noise patterns better described by Rician and noncentral Chi distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in human brain data.

The cerebellum is the region most commonly used as a reference when normalizing the intensity of perfusion images acquired using magnetic resonance imaging (MRI) in Alzheimer's disease (AD) studies. In addition, the cerebellum provides unbiased estimations with nuclear medicine techniques. However, no reports confirm the cerebellum as an optimal reference region in MRI studies or evaluate the consequences of using different normalization regions. In this study, we address the effect of using the cerebellum, whole-brain white matter, and whole-brain cortical gray matter in the normalization of cerebral blood flow (CBF) parametric maps by comparing patients with stable mild cognitive impairment (MCI), patients with AD and healthy controls. According to our results, normalization by whole-brain cortical gray matter enables more sensitive detection of perfusion abnormalities in AD patients and reveals a larger number of affected regions than data normalized by the cerebellum or whole-brain white matter. Therefore, the cerebellum is not the most valid reference region in MRI studies for early stages of AD. After normalization by whole-brain cortical gray matter, we found a significant decrease in CBF in both parietal lobes and an increase in CBF in the right medial temporal lobe. We found no differences in perfusion between patients with stable MCI and healthy controls either before or after normalization.