Diffusion magnetic resonance imaging (diffusion MRI) is a non-invasive imaging modality which can measure diffusion of water molecules, by making the MRI acquisition sensitive to diffusion. Diffusion MRI provides unique possibilities to study structural connectivity of the human brain, e.g. how the white matter connects different parts of the brain. Diffusion MRI enables a range of tools that permit qualitative and quantitative assessments of many neurological disorders, such as stroke and Parkinson.

This thesis introduces novel methods for diffusion MRI data analysis. Prior to estimating a diffusion model in each location (voxel) of the brain, the diffusion data needs to be preprocessed to correct for geometric distortions and head motion. A deep learning approach to synthesize diffusion scalar maps from a T1-weighted MR image is proposed, and it is shown that the distortion-free synthesized images can be used for distortion correction. An evaluation, involving both simulated data and real data, of six methods for susceptibility distortion correction is also presented in this thesis.

A common problem in diffusion MRI is to estimate the uncertainty of a diffusion model. An empirical evaluation of tractography, a technique that permits reconstruction of white matter pathways in the human brain, is presented in this thesis. The evaluation is based on analyzing 32 diffusion datasets from a single healthy subject, to study how reliable tractography is. In most cases only a single dataset is available for each subject. This thesis presents methods based on frequentistic (bootstrap) as well as Bayesian inference, which can provide uncertainty estimates when only a single dataset is available. These uncertainty measures can then, for example, be used in a group analysis to downweight subjects with a higher uncertainty.

Purpose: Susceptibility distortions impact diffusion MRI data analysis and is typically corrected during preprocessing. Correction strategies involve three classes of methods: registration to a structural image, the use of a fieldmap, or the use of images acquired with opposing phase encoding directions. It has been demonstrated that phase encoding based methods outperform the other two classes, but unfortunately, the choice of which phase encoding based method to use is still an open question due to the absence of any systematic comparisons.

Methods: In this paper we quantitatively evaluated six popular phase encoding based methods for correcting susceptibility distortions in diffusion MRI data. We employed a framework that allows for the simulation of realistic diffusion MRI data with susceptibility distortions. We evaluated the ability for methods to correct distortions by comparing the corrected data with the ground truth. Four diffusion tensor metrics (FA, MD, eigenvalues and eigenvectors) were calculated from the corrected data and compared with the ground truth. We also validated two popular indirect metrics using both simulated data and real data. The two indirect metrics are the difference between the corrected LR and AP data, and the FA standard deviation over the corrected LR, RL, AP, and PA data.

Results: We found that DR-BUDDI and TOPUP offered the most accurate and robust correction compared to the other four methods using both direct and indirect evaluation metrics. EPIC and HySCO performed well in correcting b0 images but produced poor corrections for diffusion weighted volumes, and also they produced large errors for the four diffusion tensor metrics. We also demonstrate that the indirect metric (the difference between corrected LR and AP data) gives a different ordering of correction quality than the direct metric.

Conclusion: We suggest researchers to use DR-BUDDI or TOPUP for susceptibility distortion correction. The two indirect metrics (the difference between corrected LR and AP data, and the FA standard deviation) should be interpreted together as a measure of distortion correction quality. The performance ranking of the various tools inferred from direct and indirect metrics differs slightly. However, across all tools, the results of direct and indirect metrics are highly correlated indicating that the analysis of indirect metrics may provide a good proxy of the performance of a correction tool if assessment using direct metrics is not feasible.

Diffusion magnetic resonance imaging (diffusion MRI) is a non-invasive microstructure assessment technique. Scalar measures, such as FA (fractional anisotropy) and MD (mean diffusivity), quantifying micro-structural tissue properties can be obtained using diffusion models and data processing pipelines. However, it is costly and time consuming to collect high quality diffusion data. Here, we therefore demonstrate how Generative Adversarial Networks (GANs) can be used to generate synthetic diffusion scalar measures from structural T1-weighted images in a single optimized step. Specifically, we train the popular CycleGAN model to learn to map a T1 image to FA or MD, and vice versa. As an application, we show that synthetic FA images can be used as a target for non-linear registration, to correct for geometric distortions common in diffusion MRI.

Purpose: Estimation of uncertainty of MAP-MRI metricsis an important topic, for several reasons. Bootstrap deriveduncertainty, such as the standard deviation, providesvaluable information, and can be incorporated in MAP-MRIstudies to provide more extensive insight.

Methods: In this paper, the uncertainty of different MAPMRImetrics was quantified by estimating the empirical distributionsusing the wild bootstrap. We applied the wildbootstrap to both phantom data and human brain data, andobtain empirical distributions for theMAP-MRImetrics returnto-origin probability (RTOP), non-Gaussianity (NG) and propagatoranisotropy (PA).

Results: We demonstrated the impact of diffusion acquisitionscheme (number of shells and number of measurementsper shell) on the uncertainty of MAP-MRI metrics.We demonstrated how the uncertainty of these metrics canbe used to improve group analyses, and to compare differentpreprocessing pipelines. We demonstrated that withuncertainty considered, the results for a group analysis canbe different.

Conclusion: Bootstrap derived uncertain measures provideadditional information to the MAP-MRI derived metrics, andshould be incorporated in ongoing and future MAP-MRIstudies to provide more extensive insight.

Spatial regularization is a technique that exploits the dependence between nearby regions to locally pool data, with the effect of reducing noise and implicitly smoothing the data. Most of the currently proposed methods are focused on minimizing a cost function, during which the regularization parameter must be tuned in order to find the optimal solution. We propose a fast Markov chain Monte Carlo (MCMC) method for diffusion tensor estimation, for both 2D and 3D priors data. The regularization parameter is jointly with the tensor using MCMC. We compare FA (fractional anisotropy) maps for various b-values using three diffusion tensor estimation methods: least-squares and MCMC with and without spatial priors. Coefficient of variation (CV) is calculated to measure the uncertainty of the FA maps calculated from the MCMC samples, and our results show that the MCMC algorithm with spatial priors provides a denoising effect and reduces the uncertainty of the MCMC samples.

Multi-compartmental models are popular to resolve intra-voxel fiber heterogeneity. One such model is the mixture of central Wishart distributions. In this paper, we use our recently proposed model to estimate the orientations of crossing fibers within a voxel based on mixture of non-central Wishart distributions. We present a thorough comparison of the results from other fiber reconstruction methods with this model. The comparative study includes experiments on a range of separation angles between crossing fibers, with different noise levels, and on real human brain diffusion MRI data. Furthermore, we present multi-fiber visualization results using tractography. Results on synthetic and real data as well as tractography visualization highlight the superior performance of the model specifically for small and middle ranges of separation angles among crossing fibers.

We have investigated the test-retest reliability of diffusion tractography, using 32 diffusion datasets from a single healthy subject. Preprocessing was carried out using functions in FSL (FMRIB Software Library), and tractography was carried out using FSL and Dipy. The tractography was performed in diffusion space, using two seed masks (corticospinal and cingulum gyrus tracts) created from the JHU White-Matter Tractography atlas. The tractography results were then warped into MNI standard space by a linear transformation. The reproducibility of tract metrics was examined using the standard deviation, the coefficient of variation (CV) and the Dice similarity coefficient (DSC), which all indicated a high reproducibility. Our results show that the multi-fiber model in FSL is able to reveal more connections between brain areas, compared to the single fiber model, and that distortion correction increases the reproducibility.