Synopsis
Diffusion MRI (dMRI) is unique in its ability to probe tissue microstructure, and is clearly relevant in many neuroscientific investigations. Group studies are particularly powerful here given the typically small effect sizes. However, dMRI data come in various forms, leading to a multitude of different approaches for group studies, ranging from relatively traditional voxel-based analyses of microstructural features through to graph-theoretical analyses of connectomics, with many different variations in between, each requiring bespoke statistical handling to make the most of the data. In this talk, we will review the most common approaches used for group studies.
Introduction
Diffusion MRI (dMRI) provides a unique probe into tissue microstructure, and has been used to provide a wide array of different metrics and other outputs in various forms: voxel-wise quantitative measures such as mean diffusivity, fractional anisotropy, and other metrics derived from more complex models; orientation-specific metrics such as the apparent fibre density or volume fraction; tractography outputs in the form of streamlines; estimates of structural connectivity between specific regions; and full matrices of connectivity between all brain regions [1]. These reflect different aspects of brain microstructure and/or large-scale organisation, and may be affected differently in pathology, with different conditions, or by normal development [2]–[4].
There is clearly a wealth of information to be extracted from these types of data, but effect sizes are typically small and too subtle to observe at the single-subject level. Group studies are therefore critically important in such neuroscientific investigations to ascertain the relationship between dMRI-derived measures and the specific pathology or process of interest.
However, these measures all differ markedly in interpretation and structure, and often require bespoke statistical handling to make the most of the data. Here, we go through the various types of data that can be produced in dMRI, and how these can be used in group studies. Voxel-based analysis
Where dMRI is used to generate voxel-wise quantitative metrics, these can be used directly within a relatively standard voxel-based analysis (VBA) framework [5]. Suitable metrics include mean diffusivity (MD), fractional anisotropy (FA), or other metrics derived from more complex models (e.g. Neurite Density, Orientation dispersion or isotropic fraction from NODDI [6], mean kurtosis from diffusion kurtosis imaging [7] etc). These approaches typically rely on image registration to bring the data from all subjects into the same standard ‘template’ space, followed by statistical inference based on the model of interest.
Since the statistical tests are performed independently across all voxels, proper consideration of multiple comparisons is required to ensure the family-wise error (FWE) rate is as expected (typically set to α=0.05). There are various approaches for this, with the most common methods relying on cluster-based inference with permutation testing. Skeleton or tract-based analysis
An alternative approach to VBA involves defining a smaller domain over which to perform statistical testing, such as the set of streamlines identified as belonging to a specific tract of interest (as produced using tractography or related approaches [8]–[10]) or the white matter skeleton as defined by the high FA regions of the white matter. The latter is the approach used in the popular tract-based spatial statistics (TBSS) technique [11]. These approaches provide two main advantages over ‘standard’ VBA: (i) higher statistical power by vastly reducing the number of multiple comparisons to correct for, and (ii) the potential to better deal with any misalignment due to imperfect registration (though these issues are much less problematic nowadays using modern registration techniques [12]). Structural connectivity analysis
Tractography techniques provide a means of delineating the path of white matter tracts, and these can be used in several ways: (i) to define a region or tract of interest, which can then be used to define the locations where statistical testing is to be performed (as above); (ii) to obtain geometric summary measures describing the path of the tract [13]; or (iii) to estimate a measure of the connectivity between different regions of the brain [14]. The latter two can be used as features in follow-on statistical comparisons across groups; for example, to investigate any potential difference in the structural connectivity of the motor tracts in pathologies such as motor neurone disease or following stroke.
While various measures of connectivity have been proposed, care must be taken to minimise any biases in these estimates that might be introduced in various ways by the tractography algorithms employed [15], [16]. An advantage of these approaches is that the metrics will often reduce to a single parameter per subject, which can then be fed into relatively standard statistical analyses that don’t require bespoke solutions to control for multiple comparisons. Connectomic analysis
These types of analysis are the natural extension of the previous single-tract connectivity analyses, and rely on the availability of a parcellation of the brain gray matter into anatomically distinct regions [17]. The structural connectivity between each pair of regions is then estimated using extensive whole-brain tractography approaches, and these estimates can then be stored in a matrix of region-region connectivity values, often referred to as the connectome matrix. These connectomes can be thought of as descriptions of networks, and are often analysed using approaches based on graph theory [18]. For this reason, the gray matter regions and the white matter connections between them are often referred to as nodes and edges respectively, following the terminology widely employed in the graph theory literature. There are many ways to analyse these types of data, ranging from comparisons of summary measures such as density, modularity or average shortest path length, some of which are estimated per connectome, others per node. These metrics can then be compared across groups using relatively standard statistical approaches.
Alternatively, the connectomes themselves can be used to identify networks of nodes & edges that may differ between groups or be implicated in the biological process of interest, using approaches such as network-based statistics [19]. Fixel-based analysis
It is now possible to derive a number of orientation-specific metrics to characterise the properties of individual bundles of fibres even within the same voxel [20]. The term ‘fixel’ was coined to denote an individual fibre element within a voxel. The idea behind fixel-based analysis is to extend the familiar concept of voxel-based analysis so that comparisons can be made between the different pixels present within each voxel across subjects (e.g. compare the estimated fibre density for the fibre population oriented anterior-posterior within a voxel in the centrum semiovale). The potential presence of multiple values within any given voxel complicates the analysis and exacerbates the multiple comparisons problem, and requires bespoke handling. On the other hand, it also provides opportunities for statistical enhancement by exploiting the expectation that changes should apply along the affected tracts, leaving fixels attributed to different tracts unaffected [21]. Statistical considerations
A common concern with all of these approaches is the need for an appropriate statistical model, combined with appropriate correction for multiple comparisons to effectively control the FWE without losing too much statistical power. Most studies rely on the general linear model (GLM) due to its simplicity and applicability to most conditions under investigations, where the effect size is small and non-linear effects can therefore be considered negligible. The correction for multiple comparisons on the other hand is a complex problem, and depends intimately on the nature of the data, its expected noise distribution, and the expected structure of correlations between tests that may be leveraged to boost statistical power. Non-parametric permutation testing is nowadays widely employed due to its robustness to non-Gaussian data and compatibility with a wide range of metrics and correction methods.Conclusion
Diffusion MRI can be used to produce a vast array of outputs of different types, each with different properties and interpretations. These can be used to address many neuroscientific questions when applied to a cohort of subjects, but the exact nature of the analysis in such group studies depends intimately on the characteristics of the data to be investigated. Acknowledgements
This work was supported by core funding from the Wellcome/EPSRC
Centre for Medical Engineering (WT 203148/Z/16/Z), MRC strategic grant
(MR/K006355/1), Medical Research Council Centre grant (MR/N026063/1), and by
the National Institute for Health Research (NIHR) Biomedical Research Centre
based at Guy’s and St Thomas’ NHS Foundation Trust and Kings College London.
The views expressed are those of the author(s) and not necessarily those of the
NHS, the NIHR or the Department of Health and social care. References
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