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Cited by 620Advanced Neuroimaging Techniques and ApplicationsFunctional Brain Connectivity StudiesAdvanced MRI Techniques and Applications

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Investigating white matter fibre density and morphology using fixel-based analysis.

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Raffelt, David A., Tournier, J.-Donald, Smith, Robert E., Vaughan, David N., Jackson, Graeme, Ridgway, Gerard R., Connelly, Alan·2017·NeuroImage
DOI 10.1016/j.neuroimage.2016.09.029PMC PMC5182031
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Abstract

Voxel-based analysis of diffusion MRI data is increasingly popular. However, most white matter voxels contain contributions from multiple fibre populations (often referred to as crossing fibres), and therefore voxel-averaged quantitative measures (e.g. fractional anisotropy) are not fibre-specific and have poor interpretability. Using higher-order diffusion models, parameters related to fibre density can be extracted for individual fibre populations within each voxel ('fixels'), and recent advances in statistics enable the multi-subject analysis of such data. However, investigating within-voxel microscopic fibre density alone does not account for macroscopic differences in the white matter morphology (e.g. the calibre of a fibre bundle). In this work, we introduce a novel method to investigate the latter, which we call fixel-based morphometry (FBM). To obtain a more complete measure related to the total number of white matter axons, information from both within-voxel microscopic fibre density and macroscopic morphology must be combined. We therefore present the FBM method as an integral piece within a comprehensive fixel-based analysis framework to investigate measures of fibre density, fibre-bundle morphology (cross-section), and a combined measure of fibre density and cross-section. We performed simulations to demonstrate the proposed measures using various transformations of a numerical fibre bundle phantom. Finally, we provide an example of such an analysis by comparing a clinical patient group to a healthy control group, which demonstrates that all three measures provide distinct and complementary information. By capturing information from both sources, the combined fibre density and cross-section measure is likely to be more sensitive to certain pathologies and more directly interpretable.

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Graphical abstract
Graphical abstract CC BY · PubMed Central
Fig. 1 A schematic representing a fibre bundle cross-section (grey circles represent axons, while the grid represents imaging voxels). A change to the intra-axonal volume (and therefore ‘ability to relay information’) may manifest as: (a) changes in tissue microstructure that result in a change in within-voxel fibre density (b) a macroscopic difference in a fibre bundle's cross-section, or (c) a combination of both fibre density and bundle cross-sectional area.
Fig. 1 A schematic representing a fibre bundle cross-section (grey circles represent axons, while the grid represents imaging voxels). A change to the intra-axonal volume (and therefore ‘ability to relay information’) may manifest as: (a) changes in tissue microstructure that result in a change in within-voxel fibre density (b) a macroscopic difference in a fibre bundle's cross-section, or (c) a combination of both fibre density and bundle cross-sectional area.CC BY · PubMed Central
Fig. 2 Grey matter morphometry vs white matter morphometry. (a) A local group difference in the volume of grey matter might reflect a difference in the number of neurons in that region, and therefore the Jacobian determinant is a relevant measure of interest. (b) When investigating white matter morphology, the fibre orientation must be taken into account. A local difference in the volume along the length of the fibre does not imply a difference in the number of axons. (c) A group difference in volume perpendicular to the fibre orientation (fibre-bundle cross-section) implies a difference in the number of axons and therefore the ‘ability to relay information’.
Fig. 2 Grey matter morphometry vs white matter morphometry. (a) A local group difference in the volume of grey matter might reflect a difference in the number of neurons in that region, and therefore the Jacobian determinant is a relevant measure of interest. (b) When investigating white matter morphology, the fibre orientation must be taken into account. A local difference in the volume along the length of the fibre does not imply a difference in the number of axons. (c) A group difference in volume perpendicular to the fibre orientation (fibre-bundle cross-section) implies a difference in the number of axons and therefore the ‘ability to relay information’.CC BY · PubMed Central
Fig. 3 A comprehensive fixel-based analysis, illustrated for a comparison of a patient group to a control group. (a) Fibre orientation distributions (FOD) were estimated from diffusion MRI data. (b) FOD images were registered towards a study-specific group-average FOD template. (c) Each FOD in the template was segmented into individual fixels, and thresholded based on fibre density to yield a fixel-analysis mask (defining the position and orientation of all fixels-of-interest in the analysis). (d) Warps estimated from registration were used to warp FOD images to template space. (e) Each FOD in the warped images was segmented to estimate a measure of FD per fixel. Angular correspondence between subject and template fixels was obtained. (f) Fibre density was compared between groups, fixel-by-fixel. (g) As per Eq. (3), the change in fibre cross-section (w.r.t. the fixel direction), FC, was estimated from the Jacobian at each voxel in the warp, and compared between groups. (h) Fibre Density was modulated by the change in fibre-bundle cross-section to yield a combined measure of fibre density and cross-section, and compared between groups. Fixel based analysis can be performed on any fixel-based FD measure by replacing steps in red (see Section 5 for more details). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 3 A comprehensive fixel-based analysis, illustrated for a comparison of a patient group to a control group. (a) Fibre orientation distributions (FOD) were estimated from diffusion MRI data. (b) FOD images were registered towards a study-specific group-average FOD template. (c) Each FOD in the template was segmented into individual fixels, and thresholded based on fibre density to yield a fixel-analysis mask (defining the position and orientation of all fixels-of-interest in the analysis). (d) Warps estimated from registration were used to warp FOD images to template space. (e) Each FOD in the warped images was segmented to estimate a measure of FD per fixel. Angular correspondence between subject and template fixels was obtained. (f) Fibre density was compared between groups, fixel-by-fixel. (g) As per Eq. (3), the change in fibre cross-section (w.r.t. the fixel direction), FC, was estimated from the Jacobian at each voxel in the warp, and compared between groups. (h) Fibre Density was modulated by the change in fibre-bundle cross-section to yield a combined measure of fibre density and cross-section, and compared between groups. Fixel based analysis can be performed on any fixel-based FD measure by replacing steps in red (see Section 5 for more details). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)CC BY · PubMed Central
Fig. 4 A method to visualise fixel-based analysis results using streamlines. (a) A 2D slice of fixels rendered as lines along the fibre orientation and coloured by p-value. (b) A fixel significance mask generated by thresholding p-values. (c) Whole-brain tractogram generated using the study-specific template. (d) Streamlines are cropped to display segments that correspond to significant fixels in (b) only. (e) Fixels coloured by effect size. (f) Streamlines cropped by significance and coloured by fixel effect size values in (e). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 4 A method to visualise fixel-based analysis results using streamlines. (a) A 2D slice of fixels rendered as lines along the fibre orientation and coloured by p-value. (b) A fixel significance mask generated by thresholding p-values. (c) Whole-brain tractogram generated using the study-specific template. (d) Streamlines are cropped to display segments that correspond to significant fixels in (b) only. (e) Fixels coloured by effect size. (f) Streamlines cropped by significance and coloured by fixel effect size values in (e). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)CC BY · PubMed Central
Fig. 5 Simulations on a numerical phantom. (a) A simulated fibre bundle oriented along the x-dimension with unit FD. Shown right are cross-sections (purple) that were used to sum the FD across the width of the bundle before transformation. (b) The fibre bundle phantom after a scale, shear and non-linear warp. Fixels are colour coded by FD. (c) Transformed fibre bundles with fixels coloured by FC. (d) Transformed fibre bundles with fixels coloured by FDC. (e) Green lines indicate the cross-sections used to compute the sum of FD and the sum of FDC across the width of each fibre bundle. (f) The sum of the FD and the sum of the FDC across the width of the bundles, plotted as a function of the cross-section position along the fibre's length. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5 Simulations on a numerical phantom. (a) A simulated fibre bundle oriented along the x-dimension with unit FD. Shown right are cross-sections (purple) that were used to sum the FD across the width of the bundle before transformation. (b) The fibre bundle phantom after a scale, shear and non-linear warp. Fixels are colour coded by FD. (c) Transformed fibre bundles with fixels coloured by FC. (d) Transformed fibre bundles with fixels coloured by FDC. (e) Green lines indicate the cross-sections used to compute the sum of FD and the sum of FDC across the width of each fibre bundle. (f) The sum of the FD and the sum of the FDC across the width of the bundles, plotted as a function of the cross-section position along the fibre's length. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)CC BY · PubMed Central
Fig. 6 Fixels with a significant (p<0.05) decrease in fibre density (FD), fibre-bundle cross-section (FC), and fibre density and cross-section (FDC). Fixels are colour-coded by family-wise error (FWE) corrected p-values and overlaid on the total voxel-wise FD map. As shown by the zoomed in region, fixel-based analysis enables fibre tract-specific inference by attributing p-values to each fixel in voxels containing multiple fibre populations. As shown by the FDC result (right column, bottom row), combining FD and FC enabled the localisation of significant differences in additional fixels (belonging to the arcuate fasciculus). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6 Fixels with a significant (p<0.05) decrease in fibre density (FD), fibre-bundle cross-section (FC), and fibre density and cross-section (FDC). Fixels are colour-coded by family-wise error (FWE) corrected p-values and overlaid on the total voxel-wise FD map. As shown by the zoomed in region, fixel-based analysis enables fibre tract-specific inference by attributing p-values to each fixel in voxels containing multiple fibre populations. As shown by the FDC result (right column, bottom row), combining FD and FC enabled the localisation of significant differences in additional fixels (belonging to the arcuate fasciculus). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)CC BY · PubMed Central
Fig. 7 White matter pathways that have a significant decrease in FD, FC, and FDC in TLE patients compared to controls. To enable the visualisation of all significant fixels in 3D (i.e. not just a 2D slice), streamlines from the template-derived whole-brain tractogram were ‘cropped’ to include streamline points that correspond to significant fixels (FWE-corrected p-value <0.05), and coloured by direction (red: left-right, blue: inferior-superior, green: anterior-posterior). While there are significant group differences in both FD and FC, the combined FDC analysis detects a larger spatial extent. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 7 White matter pathways that have a significant decrease in FD, FC, and FDC in TLE patients compared to controls. To enable the visualisation of all significant fixels in 3D (i.e. not just a 2D slice), streamlines from the template-derived whole-brain tractogram were ‘cropped’ to include streamline points that correspond to significant fixels (FWE-corrected p-value <0.05), and coloured by direction (red: left-right, blue: inferior-superior, green: anterior-posterior). While there are significant group differences in both FD and FC, the combined FDC analysis detects a larger spatial extent. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)CC BY · PubMed Central
Fig. 8 Effect sizes expressed as a percentage decrease relative to the control group. To enable a direct comparison of effect sizes across FD, FC, and FDC, streamlines shown correspond to significant fixels from all three analyses combined (i.e. the union of FD, FC, FDC). As shown left, the group differences in FD have a larger effect than FC. In both FD and FC the effect is largest in the temporal lobe. When FD is modulated by FC the effect size is increased in all pathways shown. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Fig. 8 Effect sizes expressed as a percentage decrease relative to the control group. To enable a direct comparison of effect sizes across FD, FC, and FDC, streamlines shown correspond to significant fixels from all three analyses combined (i.e. the union of FD, FC, FDC). As shown left, the group differences in FD have a larger effect than FC. In both FD and FC the effect is largest in the temporal lobe. When FD is modulated by FC the effect size is increased in all pathways shown. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)CC BY · PubMed Central
Fig. 9 Investigating fixel FD and FC in isolation requires careful interpretation. (a) A schematic of a voxel (black square) containing two interdigitating fibre pathways with equal partial volume, crossing at 90°. (b) A scenario where half of the green fibre pathway axons have degenerated, and therefore the FD of the green fibre bundle is reduced. (c) If the remaining white matter tissue becomes atrophic as a consequence of axon loss (as indicated by a 0.75 scale in the left-right direction of the Jacobian matrix, J), then the FD of the remaining tissue now contains an increase in the FD of the unaffected blue pathway, while the FD of the affected green pathway has a smaller effect size. (d) By combining FD and FC, modulation ensures the atrophy is accounted for and the resulting FDC of both pathways have the expected effect size. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 9 Investigating fixel FD and FC in isolation requires careful interpretation. (a) A schematic of a voxel (black square) containing two interdigitating fibre pathways with equal partial volume, crossing at 90°. (b) A scenario where half of the green fibre pathway axons have degenerated, and therefore the FD of the green fibre bundle is reduced. (c) If the remaining white matter tissue becomes atrophic as a consequence of axon loss (as indicated by a 0.75 scale in the left-right direction of the Jacobian matrix, J), then the FD of the remaining tissue now contains an increase in the FD of the unaffected blue pathway, while the FD of the affected green pathway has a smaller effect size. (d) By combining FD and FC, modulation ensures the atrophy is accounted for and the resulting FDC of both pathways have the expected effect size. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)CC BY · PubMed Central

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Citations

Cites

Show all 91 references

Research works printed but not linked: 3

  1. Jackson, 1993, Optimizing the diagnosis of hippocampal sclerosis using MR imaging, Am. J. Neuroradiol., 14, 753
  2. Raffelt, D., Crozier, S., Connelly, A., Salvado, O., Tournier, J.-D., 2010. Apparent fibre density: a new measure for high angular resolution diffusion-weighted image analysis. In: Proceedings of the International Society for Magnetic Resonance in Medicine. Presented at the International Society for Magnetic Resonance in Medicine, Stockholm. Sweden, p. 575.
  3. Tournier, J.-D., Calamante, F., Connelly, A., 2013. A robust spherical deconvolution method for the analysis of low SNR or low angular resolution diffusion data. In: Proceedings of the International Society for Magnetic Resonance in Medicine. Salt Lake City, Utah, USA.

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Metadata

Authors
Raffelt, D. A., Tournier, J.-D., Smith, R. E., Vaughan, D. N., Jackson, G., Ridgway, G. R., & Connelly, A.
Affiliations
  • Florey Institute of Neuroscience and Mental Health (AU)
  • King's College London (GB)
  • The University of Melbourne (AU)
  • Wellcome Centre for Human Neuroimaging (GB)
Corresponding author
Raffelt, David A.
ORCID
Venue
NeuroImage
Publisher
Elsevier BV
Published
2017-01
Volume
144
Issue
Pt A
Pages
58-73
ISSN
1053-8119 (ISSN-L)
DOI
10.1016/j.neuroimage.2016.09.029
PMC
PMC5182031
OpenAlex
W2520744072
Cited by
620
References
91
Citations by year
2026: 74 · 2025: 79 · 2024: 78 · 2023: 76 · 2022: 84 · 2021: 91 · 2020: 71 · 2019: 30 · 2018: 26 · 2017: 9
FWCI
19.39
Type
journal article
Language
en
Open access
Licence
Locations
  • NeuroImage (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • UCL Discovery (University College London) (submittedVersion)
  • Research Portal (King's College London) (submittedVersion, cc-by)
Funders
  • National Health and Medical Research Council (NHMRC)
  • Victorian Government’s Operational Infrastructure
  • UK Medical Research Council (MR/J014257/2)
  • Wellcome Trust (091593/Z/10/Z)
Topics
  • Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced Neuroimaging Techniques and Applications
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
  • Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced MRI Techniques and Applications
Keywords
fixel-based analysis, crossing fibers, axon number
MeSH terms
Humans, Nerve Fibers, Myelinated, Diffusion Magnetic Resonance Imaging, White Matter

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