Book excerpt: Radiotherapy plays an increasingly important role in cancer treatment, and medical imaging plays an increasingly important role in radiotherapy. Magnetic resonance imaging (MRI) is poised to be a major component in the development towards more effective radiotherapy treatments with fewer side effects. This thesis attempts to contribute in realizing this potential. Radiotherapy planning requires simulation of radiation transport. The necessary physical properties are typically derived from CT images, but in some cases only MR images are available. In such a case, a crude but common approach is to approximate all tissue properties as equivalent to those of water. In this thesis we propose two methods to improve upon this approximation. The first uses a machine learning approach to automatically identify bone tissue in MR. The second, which we refer to as atlas-based regression, can be used to generate a realistic, patient-specific, pseudo-CT directly from anatomical MR images. Atlas-based regression uses deformable registration to estimate a pseudo-CT of a new patient based on a database of aligned MR and CT pairs. Cancerous tissue has a different structure from normal tissue. This affects molecular diffusion, which can be measured using MRI. The prototypical diffusion encoding sequence has recently been challenged with the introduction of more general gradient waveforms. One such example is diffusional variance decomposition (DIVIDE), which allows non-invasive mapping of parameters that reflect variable cell eccentricity and density in brain tumors. To take full advantage of such more general gradient waveforms it is, however, imperative to respect the constraints imposed by the hardware while at the same time maximizing the diffusion encoding strength. In this thesis we formulate this as a constrained optimization problem that is easily adaptable to various hardware constraints. We demonstrate that, by using the optimized gradient waveforms, it is technically feasible to perform whole-brain diffusional variance decomposition at clinical MRI systems with varying performance. The last part of the thesis is devoted to estimation of diffusion MRI models from measurements. We show that, by using a machine learning framework called Gaussian processes, it is possible to perform diffusion spectrum imaging using far fewer measurements than ordinarily required. This has the potential of making diffusion spectrum imaging feasible even though the acquisition time is limited. A key property of Gaussian processes, which is a probabilistic model, is that it comes with a rigorous way of reasoning about uncertainty. This is pursued further in the last paper, in which we propose a Bayesian reinterpretation of several of the most popular models for diffusion MRI. Thanks to the Bayesian interpretation it possible to quantify the uncertainty in any property derived from these models. We expect this will be broadly useful, in particular in group analyses and in cases when the uncertainty is large.