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Metrics that Matter: Improved statistical power to detect differences in tissue microstructure through dimensionality reduction
Maxime Chamberland1, Erika Raven1, Sila Genc1,2,3, Kate Duffy1, Greg Parker1, Chantal M.W. Tax1, Maxime Descoteaux4, and Derek K. Jones1,5

1School of Psychology, Cardiff University Brain Research Imaging Centre, Cardiff, United Kingdom, 2Department of Paediatrics, The University of Melbourne, Parkville, Australia, 3Developmental Imaging, Murdoch Childrens Research Institute, Parkville, Australia, 4Computer Science, University of Sherbrooke, Sherbrooke, QC, Canada, 5School of Psychology, Australian Catholic University, Victoria, Australia

Synopsis

Various diffusion metrics have been proposed for characterising tissue microstructure. However, it is unclear which metric best captures individual microstructural differences. One possible approach is to explore all available metrics. However, this increases the chance of Type I error and makes interpretation difficult. Using data-reduction approaches, we identified two principal components that capture 85% of the variance in diffusion measurements. The first captures properties related to hindrance, while the second reflects tissue complexity. We demonstrate the utility of this approach by showing significant correlations with age of these new metrics, whereas little to no effects were observed with any individual metric.

Introduction

Profiling diffusion MRI metrics along brain pathways allows for a comprehensive assessment of white matter microstructure1-4. However, many of these metrics share overlapping information which may cause redundancies in data analysis and ultimately decrease statistical power. To avoid this, we propose a data reduction framework to explore redundant covariance using various diffusion MRI metrics. We hypothesize that this process will 1) provide better insight into patterns of associations between the different metrics and 2) show increased sensitivity to individual differences in tissue microstructure. We demonstrate the utility of this approach by applying our method to study age-related differences in tissue microstructure in healthy children and adolescents.

Methods

Acquisition: Data from 37 young healthy volunteers (age 8-18) were acquired using a CHARMED5 protocol on a Siemens 3T Connectom system with 14 b0 images, 30 directions at b = 500,1200 s/mm², 60 directions at b = 2400, 4000, 6000 s/mm² and 2×2×2 mm³ voxels (TE/TR: 59/3000 ms, δ/Δ: 7.0/23.3 ms).

Preprocessing: Data were denoised6, corrected for signal drift7, motion8, distortion9, gradient non-linearities10 and Gibbs ringing11.

Processing: Multi-shell multi-tissue constrained spherical deconvolution12 (MSMT-CSD) was applied to generate fiber Orientation Distribution Functions (fODFs, lmax = 8) using 3-tissue group-averaged response functions, followed by image intensity normalisation MRtrix13. For each subject, whole-brain tractography and manual extraction of 22 bundles was done using FiberNavigator14 (1.8M seeds, fODF peaks > 0.1). For each bundle, along-tract profiling was performed along 20 sections using the Python toolbox developed by Cousineau et al.4, where streamlines points are assigned to a representative core version of the bundle. The following metrics (Fig. 1) were then averaged per sections of the core, based on their weighted distance assignments: Fractional Anisotropy (FA), Axial Diffusivity (AD), Radial Diffusivity (RD), Mean Diffusivity (MD), Geodesic Anisotropy15 (GA), Tensor Mode16, Apparent Fiber Density17 (AFD, fiber-specific), AFDtot (l = 0), Number of Fiber Orientations18 (NuFO) and Restricted fraction5 (FR).

Statistical analysis: A principal component analysis (PCA) was applied to analyse the contribution of each metric (variables) by concatenating the entire set of profiles (z-transformed) across subjects and bundles. Metrics showing shared variance or failing the Kaiser-Meyer-Olkin test for sampling adequacy (KMO < 0.5) were discarded to balance stability and the PCA was re-computed. PC maps were then derived using a linear combination of the z-transformed metrics (weighted by their contribution to each PC). Finally, age relationships were investigated for each bundle using a conservative Bonferroni multiple comparisons correction (0.05 / (M maps × N bundles)), whereby statistical significance was defined as: pPCs < 1.1e-3, and pmetrics < 2.2e-4.

Results

Fig. 1 illustrates the various input metrics mapped along the corticospinal tract (CST) of a representative subject. Clear dissociation between those metrics is observed in Fig. 2 after the removal of redundant ones (i.e., GA, AFD, Mode and MD). The first two PCs account for 85% of the variability in the data (KMOtot: 0.70). The PC that explains the largest part of the variability comprises FA, RD, AFDtot and FR. (Fig. 3, PC1). The second PC is mostly driven by dispersion and complexity-sensitive measurements (NuFO, AD). Fig. 4 shows how different bundles project and cluster in the new reference frame (bundle averages). Fig. 5 shows that PC1 and PC2 have a stronger relationship with age in the CST when compared to the individual metrics forming those same PCs. Age relationships were also observed in other developmental-sensitive tracts19, 20 (e.g., arcuate fasciculus, cingulum and genu of the corpus callosum).

Discussion

Metrics accounting for the largest percent of variance in the data (PC1) are those known to be most sensitive to hindrance or restriction in the signal, including FA, FR and AFD. In contrast, PC2 features metrics that are sensitive to complexity in the signal, such as NuFO and AD. Our results highlight the sensitivity of PC1 and PC2 as a composite measure by 1) showing significant correlation with age in regions where other metrics did not, and 2) reflecting effects captured by the other metrics.

Conclusion

Our results support the use of data reduction to detect along tract differences in tissue microstructure. Specifically, the curse of dimensionality and redundancies in statistical analyses were considerably mitigated by the extracting components sensitive to the properties of hindrance/restriction and dispersion/complexity. Future work will involve non-linear dimensionality reduction techniques (e.g., manifold learning) to fully disentangle the metric space. The proposed framework may open new avenues for examining brain microstructure in general.

Acknowledgements

MC is supported by the Postdoctoral Fellowships Program from the Natural Sciences and Engineering Research Council of Canada (NSERC) and a Wellcome Trust New Investigator Award (to DKJ). CMWT is supported by a Rubicon grant from the NWO. This work was also funded by a Wellcome Trust Strategic Award and a Wellcome Trust New Investigator Award.

References

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[11] Kellner, Elias, et al. "Gibbs‐ringing artifact removal based on local subvoxel‐shifts." Magnetic resonance in medicine 76.5 (2016): 1574-1581.

[12] Jeurissen, Ben, et al. "Multi-tissue constrained spherical deconvolution for improved analysis of multi-shell diffusion MRI data." NeuroImage 103 (2014): 411-426.

[13] Tournier, J‐Donald, Fernando Calamante, and Alan Connelly. "MRtrix: diffusion tractography in crossing fiber regions." International Journal of Imaging Systems and Technology 22.1 (2012): 53-66.

[14] Chamberland, Maxime, et al. "Real-time multi-peak tractography for instantaneous connectivity display." Frontiers in neuroinformatics 8 (2014): 59.

[15] Fletcher, P. Thomas, Stephen M. Pizer, and Sarang Joshi. Statistical variability in nonlinear spaces: Application to shape analysis and DT-MRI. University of North Carolina at Chapel Hill, 2004.

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[18] Dell'Acqua, Flavio, et al. "Can spherical deconvolution provide more information than fiber orientations? Hindrance modulated orientational anisotropy, a true‐tract specific index to characterize white matter diffusion." Human brain mapping34.10 (2013): 2464-2483.

[19] Lebel, Catherine, Sarah Treit, and Christian Beaulieu. "A review of diffusion MRI of typical white matter development from early childhood to young adulthood." NMR in Biomedicine (2017): e3778.

[20] Genc, Sila, et al. "Development of white matter fibre density and morphology over childhood: A longitudinal fixel-based analysis." NeuroImage 183 (2018): 666-676.

Figures

Fig. 1: Overview of the input metrics overlaid (non-scaled colorbar) on the CST. Whole-brain tractograms (top-left) were manually dissected into the following 22 bundles: Anterior Commissure (AC), Corpus Callosum body (CC), Genu, Splenium, inferior Fronto-Occipital Fasciculus (iFOF), Inferior Longitudinal Fasciculus (ILF), Arcuate Fasciculus (AF), Superior Longitudinal Fasciculus (SLF), Optic Radiation (OR), Frontal Aslant Tract (FAT), Corticospinal Tract (CST), Cingulum, Uncinate Fasciculus (UF).

Fig. 2: PCA results pre- (left) and post- (right) clean-up for redundancies. MD was removed after failing the sampling test (KMO = 0.37). To improve stability around PC1, FA was kept over GA and AFD because of its greater contribution to that PC (although a choice could be made here with AFD being fiber-specific). Tensor mode was also discarded based on its collinearity with axial diffusivity (R² = 0.74). One can observe separation between the various metrics, generating a hindrance/restricted component (PC1) and a dispersion/complexity component (PC2).

Fig. 3: Principal Components illustrated for the CST (using the z-transformed version of each metric). The first PC captures most of the hindrance/restriction related metrics (FA, RD, AFD, FR). The second PC mostly represents complexity/dispersion properties (NuFO, AD). Cumulative proportion of the variance explained by the various PCs is shown on the left.

Fig. 4: Bundle clustering based on PC1 and PC2. The horizontal axis shows increasing restriction or hindrance perpendicular to the main axis of the bundles. On the right-most part of this axis are located densely-packed bundles such as the CST (green), genu (blue) and splenium (pink). The vertical axis represents the complexity degree of bundles (based on NuFO). On top of this axis are the arcuate fasciculus (orange) and superior longitudinal fasciculus (purple), two pathways which are known to have many crossing regions. Each point represents one subject. Concentration ellipsoids cover 95% confidence around the mean.

Fig. 5: Age relationships captured by PC1 and PC2. PC scores are mapped on the left CST of a representative subject. Highlighted sections indicate areas where PC1 and PC2 showed significant linear correlation with age. PC1 shows significant changes in hindrance/restriction of the signal in the body of the CST (R²: 0.35, p < 2.2e-4) but not FA and RD. PC2 and NuFO shows significant age-effect related to dispersion/complexity near the cortex (R²: 0.43 and 0.56 respectively), but not AD. The bottom graphs show the full correlation profiles along the bundle for the metrics contributing the most to each PC (-log(p)).

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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