The goal of this paper is to increase the statistical power of crossing-fiber statistics in voxelwise analyses of diffusion-weighted magnetic resonance imaging (DW-MRI) data. In the proposed framework, a fiber orientation atlas and a model complexity atlas were used to fit the ball-and-sticks model to diffusion-weighted images of subjects in a prospective population-based cohort study. Reproducibility and sensitivity of the partial volume fractions in the ball-and-sticks model were analyzed using TBSS (tract-based spatial statistics) and compared to a reference framework. The reproducibility was investigated on two scans of 30 subjects acquired with an interval of approximately three weeks by studying the intraclass correlation coefficient (ICC). The sensitivity to true biological effects was evaluated by studying the regression with age on 500 subjects from 65 to 90 years old. Compared to the reference framework, the ICC improved significantly when using the proposed framework. Higher t-statistics indicated that regression coefficients with age could be determined more precisely with the proposed framework and more voxels correlated significantly with age. The application of a fiber orientation atlas and a model complexity atlas can significantly improve the reproducibility and sensitivity of crossing-fiber statistics in TBSS.

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The brain’s white matter mainly consists of (myelinated) axons that connect different parts of the brain. Diffusion-weighted MRI (DW-MRI) is a technique that is particularly suited to image this white matter. The MRI signal in DW-MRI is sensitized to diffusion of water in the microstructure by introducing strong bipolar gradients in the MRI pulse sequence. By measuring the diffusion in different directions, the local diffusion profile of water molecules is obtained which reflects microstructural characteristics of the white matter. The focus of this thesis is on the analysis of conventional DW-MRI data acquired in the context of the Rotterdam Scan Study. This is a prospective population-based cohort study with more than 10.000 participants to investigate causes of neurological disease in elderly people. Conventional DW-MRI is defined as diffusion data acquired with a single diffusion-weighting factor and a small number of diffusion-sensitizing gradient orientations. The objectives of this thesis are (1) to enhance our insight in the relation between tissue structure and the DW-MRI signal from conventional DW-MRI sequences, and (2) to develop methods to quantify diffusion properties in the brain as accurately and precisely as possible based on conventional DW-MRI data. To gain insight into the relation between tissue structure and the DW-MRI signal, simulated DW-MRI signals based on Monte Carlo simulations of spins between randomly packed cylinders are compared to experimentally acquired data from a hardware phantom. The hardware phantom consists of solid fibers and acts as a model for the extra-axonal diffusion. The simulated DW-MRI signal is in good agreement with the experimentally acquired data. Furthermore, simulations show that the DW-MRI signal from spins between randomly packed cylinders is relatively independent of the cylinder diameter for b-values up to 1500 s/mm2. For b-values higher than 1500 s/mm2, substrates with a smaller cylinder diameter yield a larger attenuation of the diffusion-weighted signal (chapter 2). Conventional DW-MRI data is commonly analyzed with a technique known as diffusion tensor imaging. Here, thewater diffusion profile is modelled by a 3D Gaussian diffusion profile. However, in white matter structures in close proximity to the cerebrospinal fluid (CSF) the use of the single diffusion tensor model is inappropriate. A novel framework is introduced to analyze white matter structures adjacent to the CSF. In this framework a constrained two-compartment diffusion model is fit to the data in which the CSF is explicitly modeled with a free water diffusion compartment. The proposed diffusion statistics are shown to be relatively independent of partial volume effects with CSF and are applied to study ageing in the fornix, a small white matter structure bordering the CSF (chapter 3). A significant part of the white matter constitutes of ‘crossing fibers’, whereby two or more white matter tracts contribute to the DW-MRI signal in a voxel. The single diffusion tensor model cannot adequately describe the data in such voxels. To solve this issue a fiber orientation atlas and a model complexity atlas were used to analyze conventional DW-MRI data with a simple crossing fibers model, namely the ball-and-sticks model. It is shown that the application of a fiber orientation atlas and a model complexity atlas can significantly improve the reproducibility and sensitivity of diffusion statistics in a voxel-based analysis (chapter 4). Finally, a framework is proposed that aims to specifically improve the analysis of longitudinal DW-MRI data. In this framework the ball-and-sticks model is fit simultaneously to multiple scans of the same subject. The orientations of the sticks are constrained to be the same over different scans, while all other parameters are estimated separately for each scan. The use of this framework is shown to increase the precision of estimated ball-and-sticks model parameters in longitudinal DW-MRI studies (chapter 5). In conclusion, this thesis describes frameworks to enhance the accuracy or precision of estimated diffusion properties of the white matter by applying sophisticated diffusion models to conventional DW-MRI data. We anticipate that many diffusion MRI studies may benefit from the work described in this thesis.@en

Fiber tractography aims to reconstruct white matter (WM) connections in the brain. Challenges in these reconstructions include estimation of the fiber orientations in regions with multiple fiber populations, and the uncertainty in the fiber orientations as a result of noise. In this work, we use a range of multi-tensor models to cope with crossing fibers. The uncertainty in fiber orientation is captured using the Cramér-Rao lower bound. Furthermore, model selection is performed based on model complexity and goodness of fit. The performance of the framework on the fibercup phantom and human data was compared to the open source diffusion MRI toolkit Camino for a range of SNRs. Performance was quantified by using the Tractometer measures in the fibercup phantom and by comparing streamline counts of lateral projections of the corpus callosum (CC) in the human data. On the phantom data, the comparison showed that our method performs similar to Camino in crossing fiber regions, whilst performing better in a region with kissing fibers (median angular error of 0.73∘ vs 2.7∘, valid connections of 57% vs 21% when seed is in the corresponding region of interest). Furthermore, the amount of counts in the lateral projections was found to be higher using our method (19–89% increase depending on a subject). Altogether, our method outperforms the reference method on both phantom and human data allowing for in-vivo probabilistic multi fiber tractography with an objective model selection procedure.@en

The goal of this paper is to develop a method for assessment of microstructural properties of the fornix in conventional (low resolution, single non-zero b-value) diffusion-weighted magnetic resonance imaging (DW-MRI) data. For this purpose, a bi-tensor model, comprising of an isotropic and an anisotropic diffusion compartment, was fitted to the diffusion-weighted images. Two subject-specific constraints were studied to solve the ill-posedness of the parameter estimation at a single (non-zero) b-value, namely by fixating the mean diffusivity (MD) or the axial diffusivity (AxD) of the anisotropic compartment. The bi-tensor statistics were compared to conventional diffusion statistics using simulated fiber bundles with different diameters and using fornix segmentations of 577 elderly subjects. Based on simulated fiber bundles, the anisotropy (FA) estimated by the bi-tensor model did not become biased with decreasing fiber bundle diameter, unlike conventional diffusion statistics such as FA and MD estimated by the single tensor model. In the population-based study, the bi-tensor tissue fraction decreased significantly with age, suggesting an increase of free water. The FA estimated by the bi-tensor model decreased with age, but this relation was not significant when the subject-specific values to which MD or AxD were constrained were added as covariates in the regression analysis. The distinction of an isotropic and an anisotropic diffusion compartment may allow a more sophisticated analysis of the fornix based on conventional DW-MRI data.@en

Purpose: To increase the sensitivity in longitudinal analysis of DW-MRI data with the ball-and-sticks model.

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