Synopsis
We conduct model comparison experiments on the widely available HCP dataset to assess the importance of fibre-dispersion when modelling the brain’s tissue-microstructure from diffusion MRI (dMRI). Although many fibre dispersion configurations have been identified in the brain, most dMRI methods only model parallel or crossing fibres. To highlight the importance of dispersion, we design k-fold cross-validation experiments, on two HCP subjects, and compare ten compartment-based models using three metrics. We find that up to 50% of the brain-voxels, including white matter regions, support dispersion models over crossing models. Hence we conclude that it is important to model dispersion in dMRI.Purpose
To assess the importance of fibre-dispersion in modelling the brain’s tissue-microstructure from diffusion MRI (dMRI).
Introduction
At the typical dMRI acquisition-resolution of ~2mm
3 the fibres in cerebral tissue can adopt a wide range of complex configurations. Models that consider only parallel fibres are over-simplistic in most of the brain. Recent studies indicate up to 90% of voxels in the white matter have complex multiple-fibre orientation distributions
1. That complexity may arise from crossings, i.e. a multi-modal orientation distribution arising from interdigitating or interfacing fibres with distinct orientation, and/or dispersion, i.e. unimodal distribution with significant variance arising from e.g. fanning, bending or undulating fibres. However, the distinction between these different types of complex configurations is rarely considered. For example, Jeurissen et al
1. do not consider dispersion. Hence, we attempt to map the relative importance of crossing and dispersion in dMRI datasets over the brain.
Methods
We conduct model comparison experiments in a comprehensive data driven framework and examine how the dMRI data supports distinct models of fibre crossing and dispersion. Previous studies2,3 make similar comparisons in isolated voxels or regions. Here, we use the widely available, high-quality HCP dataset4 and consider a number of slices that contain various types of fibre configurations to map their relative importance over entire brain regions for the first time.
We construct ten compartment models2 that represent different configurations. These include five single-fibre (parallel) models: Stick-Ball (FSL5), Stick-CSF, Stick-Zeppelin, Tensor-CSF and Stick-Tensor-CSF; three crossing models: Stick-Stick-Ball (FSL6), Stick-Stick-CSF and Stick-Stick-Stick-CSF; and two dispersion models: NODDI-Watson7 and NODDI-Bingham8.
We design k-fold cross-validation (CV) experiments as follows. The HCP dataset contains 3 b-shells with 90 directions each. We divide each shell into six subsets of 15 isotropically distributed directions using Camino9. Then we create new protocols removing one subset of 15 gradients from each shell. From the possible 216 protocols, we randomly select 50 for our experiments.
We fit the ten tissue-models to each CV fold voxel-by-voxel over the brain-slices using maximum likelihood estimation accounting for Rician noise7. We compare each model’s ability to explain the data using three metrics: AIC and BIC, which trade-off goodness of fit with model complexity10, and CV, which assesses generalisation to unseen data. We compute the average metrics over all the trials, rank the models in each voxel according to each criterion, and select the model with the highest average rank to create one map for each metric visualising the most likely model in each voxel.
Results
Figure 1 presents the colour-coded maps in an axial slice from one HCP subject. The results, which are consistent over the three metrics, indicate that a large portion of the slice -- up to 50% of the voxels -- strongly support dispersion models. In particular, the NODDI-Bingham model is substantially favoured by the dMRI data -- even within white matter areas. This is also seen in the corpus callosum (CC), which is in agreement with the literature3. Known fibre-crossing regions, e.g. where the corticospinal tract (CST) crosses the CC, favour crossing models as expected. The ventricles and boundary regions favour single-fibre models because these are the simplest models that contain a CSF compartment. The results from a different subject (figure 2) confirm these findings. Again dispersion is highly favoured and crossing-regions between the superior longitudinal fasciculus (SLF), CC and CST favour crossing models.
Figure 3 shows the frequency with which each model is selected in each of the two HCP subjects. These quantitative results show that ~50% of the voxels support dispersion, about 10-20% support crossings and 30-40% support single-fibres (which also include CSF voxels). The statistics, especially for dispersion configurations and the NODDI-Bingham model, are remarkably consistent for all three metrics, in all the slices and in both subjects.
Discussion
Our results strongly support the inclusion of fibre dispersion in dMRI models, even in white matter regions. Although this is not a pure white matter study, the results challenge the high percentage of crossing voxels previously reported in the literature
1. Here we consider only two subjects with two slices each -- one coronal and one axial. Current work is extending the analysis to more slices of more subjects, although we emphasise that processing one subject is equivalent to fitting a single model over all 500 HCP subjects -- 50 trials with 10 models. The current results are consistent over all four slices and we expect the trend to extend over the broader cohort. Future work will also look into a wider range of models, for example capturing subtler distinctions between macroscopic and microscopic (undulation) dispersion.
Acknowledgements
The authors were supported by the EPSRC grant: EP/L022680/1. Data were provided by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University.References
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