Four-dimensional flow (4D Flow) CMR affords comprehensive 3D maps of advanced hemodynamics parameters such as wall shear stress (WSS). However, the evaluation of these data is often restricted to spatial averages in large regions of interests, such as the ascending aorta. Recent studies have explored ways of analyzing local intercohort WSS differences by using basic statistical tests with a p-value of 0.05 for determining significance, thus not accounting for the large number of comparisons made when exploring differences for multiple locations across the ascending aorta surface.

Permutation tests, frequently used in brain MRI, permit statistical analysis on a local level while controlling for the family-wise error rate by constructing the null hypothesis distribution based on the maximum statistic over the voxels at each permutation. We sought to use permutation tests to identify local regions of abnormal WSS in the ascending aorta in patients with aortic dilation.

The incessant, random motion of water molecules within biological tissues reveals unique information about the tissues’ structural and functional characteristics. Diffusion magnetic resonance imaging is sensitive to this random motion, and since the mid-1990s it has been extensively employed for studying the human brain. Most notably, measurements of water diffusion allow for the early detection of ischaemic stroke and for the unveiling of the brain’s wiring via reconstruction of the neuronal connections. Ultimately, the goal is to employ this imaging technique to perform non-invasive, in vivo virtual histology to directly characterise both healthy and diseased tissue. 

Recent developments in the field have introduced new ways to measure the diffusion process in clinically feasible settings. These new measurements, performed by employing generalised magnetic field gradient waveforms, grant access to specific features of the cellular composition and structural organisation of the tissue. Methods based on them have already proven beneficial for the assessment of different brain diseases, sparking interest in translating such techniques into clinical practice. This thesis focuses on improving the methods currently employed for the analysis of such diffusion MRI data, with the aim of facilitating their clinical adoption. 

The first two publications introduce constrained frameworks for the estimation of parameters from diffusion MRI data acquired with generalised gradient waveforms. The constraints are dictated by mathematical and physical properties of a multi-compartment model used to represent the brain tissue, and can be efficiently enforced by employing a relatively new optimisation scheme called semidefinite programming. The developed routines are demonstrated to improve robustness to noise and imperfect data collection. Moreover, constraining the fit is shown to relax the requirements on the number of points needed for the estimation, thus allowing for faster data acquisition. 

In the third paper, the developed frameworks are employed to study the brain’s white matter in patients previously hospitalised for COVID-19 and who still suffer from neurological symptoms months after discharge. The results show widespread alterations to the structural integrity of their brain, with the metrics available through the advanced diffusion measurements providing new insights into the damage to the white matter. 

The fourth paper revisits the modelling paradigm currently adopted for the analysis of diffusion MRI data acquired with generalised gradient waveforms. Hitherto, the assumption of free diffusion has been employed to represent each domain in a multi-compartmental picture of the brain tissue. In this work, a model for restricted diffusion is considered instead to alleviate the paradoxical assumption of free but compartmentalised diffusion. The model is shown to perfectly capture restricted diffusion as measured with the generalised diffusion gradient waveforms, thus endorsing its use for representing each domain in the multi-compartmental model of the tissue. 

Q-space trajectory imaging (QTI) allows non-invasive estimation of microstructural features of heterogeneous porous media via diffusion magnetic resonance imaging performed with generalised gradient waveforms. A recently proposed constrained estimation framework, called QTI+, improved QTI’s resilience to noise and data sparsity, thus increasing the reliability of the method by enforcing relevant positivity constraints. In this work we consider expanding the set of constraints to be applied during the fitting of the QTI model. We show that the additional conditions, which introduce an upper bound on the diffusivity values, further improve the retrieved parameters on a publicly available human brain dataset as well as on data acquired from healthy volunteers using a scanner-ready protocol.

There is mounting evidence of the long-term effects of COVID-19 on the central nervous system, with patients experiencing diverse symptoms, often suggesting brain involvement. Conventional brain MRI of these patients shows unspecific patterns, with no clear connection of the symptomatology to brain tissue abnormalities, whereas diffusion tensor studies and volumetric analyses detect measurable changes in the brain after COVID-19. Diffusion MRI exploits the random motion of water molecules to achieve unique sensitivity to structures at the microscopic level, and new sequences employing generalized diffusion encoding provide structural information which are sensitive to intravoxel features. In this observational study, a total of 32 persons were investigated: 16 patients previously hospitalized for COVID-19 with persisting symptoms of post-COVID condition (mean age 60 years: range 41–79, all male) at 7-month follow-up and 16 matched controls, not previously hospitalized for COVID-19, with no post-COVID symptoms (mean age 58 years, range 46–69, 11 males). Standard MRI and generalized diffusion encoding MRI were employed to examine the brain white matter of the subjects. To detect possible group differences, several tissue microstructure descriptors obtainable with the employed diffusion sequence, the fractional anisotropy, mean diffusivity, axial diffusivity, radial diffusivity, microscopic anisotropy, orientational coherence (Cc) and variance in compartment’s size (CMD) were analysed using the tract-based spatial statistics framework. The tract-based spatial statistics analysis showed widespread statistically significant differences (P < 0.05, corrected for multiple comparisons using the familywise error rate) in all the considered metrics in the white matter of the patients compared to the controls. Fractional anisotropy, microscopic anisotropy and Cc were lower in the patient group, while axial diffusivity, radial diffusivity, mean diffusivity and CMD were higher. Significant changes in fractional anisotropy, microscopic anisotropy and CMD affected approximately half of the analysed white matter voxels located across all brain lobes, while changes in Cc were mainly found in the occipital parts of the brain. Given the predominant alteration in microscopic anisotropy compared to Cc, the observed changes in diffusion anisotropy are mostly due to loss of local anisotropy, possibly connected to axonal damage, rather than white matter fibre coherence disruption. The increase in radial diffusivity is indicative of demyelination, while the changes in mean diffusivity and CMD are compatible with vasogenic oedema. In summary, these widespread alterations of white matter microstructure are indicative of vasogenic oedema, demyelination and axonal damage. These changes might be a contributing factor to the diversity of central nervous system symptoms that many patients experience after COVID-19.