Conference PaperPDF Available

Toward interrogating relationships between grey and white matter measures using Fixel Track-Weighted Imaging and Fixel-Based Analysis



Neuroimaging studies assessing white and grey matter are most typically performed as independent analyses. The relationships between white and grey matter abnormalities are therefore poorly understood. We present a novel framework for interrogating relationships between quantitative measures derived from grey matter analysis, and diffusion MRI-based, fibre-specific white matter measures.
Toward interrogating relationships between grey and white matter measures using Fixel Track-
Weighted Imaging and Fixel-Based Analysis
Robert E Smith , David Raelt , David N Vaughan , Fernando Calamante , and Alan Connelly
The Florey Institute of Neuroscience and Mental Health, Heidelberg, Australia, Department of Neurology, Austin Health, Melbourne, Australia, Department of
Medicine (AH/NH), The University of Melbourne, Australia
Neuroimaging studies assessing white and grey matter are most typically performed as independent analyses. The relationships between white and grey
matter abnormalities are therefore poorly understood. We present a novel framework for interrogating relationships between quantitative measures
derived from grey matter analysis, and diusion MRI-based, bre-specic white matter measures.
Quantitative measures estimated from neuroimaging typically focus on either grey or white matter. As such, these measures are analysed using
techniques specically tailored for the biological tissue of interest. This however limits the extent to which grey and white matter measures may be
analysed in combination, despite their intrinsic relationship via neuronal connectivity. Here we propose a framework for combining such measures into a
common space, by using updates to the Track-Weighted Imaging (TWI) framework to project grey matter measures into the white matter based on
streamlines tractography, thereby working toward statistical analysis of these data in conjunction with quantitative and bre-specic measures /
methods designed specically for white matter analysis in the presence of crossing bres .
The proposed framework operates as follows (Figure 1):
1. White matter analysis:
1.1. Generate whole-brain tractogram in native subject space (rather than using warped images in template space ).
1.2. Perform image registration to a common template space, ideally based on a higher-order diusion model .
1.3. Dene the target xels (specic bre population elements within voxels) for this analysis in template space.
2. Grey matter analysis:
2.1. For each streamline in the tractogram, sample the grey matter parameter(s) of interest at the two streamline endpoints; either using a native surface
mesh representation, simply sampling at the streamline endpoints e.g. , or 'extending' the streamline endpoints to sample from grey matter e.g. .
2.2. Typically take some statistic of the two endpoint values (e.g. mean) as the 'TWI factor' for that streamline.
2.3. Transform subject tractogram to template space based on the non-linear displacement eld derived during symmetric registration. Unlike FOD-
based spatial normalisation, where modulation of bre density based on bre orientation must be performed explicitly , this approach implicitly
modulates streamlines density appropriately depending on their orientation relative to eld deformations (Figure 2) .
2.4. Perform Fixel Track-Weighted Imaging (TWI), with per-streamline factors dened in step 2.2, and xels dened in group average template space in
step 1.3 acting as the targets for streamlines mapping (common across all subjects).
Demonstration data
Data for 28 healthy controls were acquired on a Siemens 3T Trio system. Image data used included T1-weighted image at 0.9mm isotropic resolution,
DWI (b=3000 , 60 directions, 2.5mm isotropic), and a pair of b=0 images with reversed phase encoding for eld inhomogeneity estimation .
Subject-specic reconstruction included: Cortical thickness estimation using FreeSurfer ; Fibre Orientation Distributions estimated using Multi-Tissue
Constrained Spherical Deconvolution ; tractogram reconstruction using the iFOD2 probabilistic streamlines algorithm and the Anatomically-
Constrained Tractography framework ; quantitative streamline weights derived using the SIFT2 algorithm .
A population-specic Fibre Orientation Distribution (FOD) template image was constructed using previously described methods .
For demonstration purposes, for each streamline, the mean cortical thickness at the streamline endpoints (using only one endpoint if the other did not
terminate at the cortex) was used as the TWI factor for that streamline. During mapping, the mean TWI factor for streamlines traversing a particular xel in
template space was taken as the nal value for that xel.
The white matter quantitative value of interest for this demonstration was the combined measure of Fibre Density and
Cross-sectional area (FDC) throughout the template xel mask.
Figure 3 demonstrates how the proposed framework provides both white and grey matter quantitative measures in a common space: that of xels in a
group average WM template. An example zoomed view of this information is presented in Figure 4.
By drawing grey matter quantitative information directly into the space in which white matter quantitative measures are analysed, the measures become
directly comparable in this higher-dimensional space, without the loss of complex white matter bre crossing information. Although this process may
result in grey matter information that is 'smooth' along the relevant white matter pathway, such smoothness is a preferable trait, and in fact smoothing is
typically applied explicitly .
1 1 1,2 1,3 1,3
1 2 3
[6] [7]
-2 [8]
[10] [11]
[12] [13]
Future developments to the Fixel-Based Analysis (FBA) framework will enable direct multivariate statistical analysis of data such as that shown.
Connectivity-based Fixel Enhancement (CFE) will be used for hypothesis testing in template space, incorporating both grey and white matter
quantitative measures. Combined with the exibility of the Track-Weighted Imaging (TWI) framework (particularly mapping to target xels as presented
here), and the General Linear Model (GLM) with permutation testing , this framework will enable hypothesis formation and testing where (any)
quantitative measures from both white and grey matter are of interest.
Examining relationships between such measures has the potential for improved sensitivity to
neurological diseases, compared to assessing the grey or white matter alone.
We are grateful to the National Health and Medical Research Council (NHMRC) (400121) of Australia and the Victorian Government’s Operational
Infrastructure Support Program for their support.
1. Calamante, F.; Tournier, J.-D.; Smith, R. E. & Connelly, A. A generalised framework for super-resolution track-
weighted imaging. NeuroImage, 2012, 59, 2494-2503
2. Raelt, D. A.; Tournier, J.-D.; Smith, R. E.; Vaughan, D. N.; Jackson, G.; Ridgway, G. R. & Connelly, A. Investigating white matter bre density and
morphology using xel-based analysis. NeuroImage, 2016, j.neuroimage.2016.09.029
3. Christiaens, D.; Dhollander, T.; Maes, F.; Sunaert, S. & Suetens, P. The Eect of Reorientation of the Fibre Orientation Distribution on Fibre Tracking.
Computational Diusion MRI, 2012
4. Raelt, D.; Tournier, J.-D.; Fripp, J.; Crozier, S.; Connelly, A. & Salvado, O. Symmetric dieomorphic registration of bre orientation distributions.
NeuroImage, 2011, 56, 1171-1180
5. Raelt, D. A.; Smith, R. E.; Ridgway, G. R.; Tournier, J.-D.; Vaughan, D. N.; Rose, S.; Henderson, R. & Connelly, A. Connectivity-based xel enhancement:
Whole-brain statistical analysis of diusion MRI measures in the presence of crossing bres. NeuroImage, 2015, 117, 40-55
6. Calamante, F.; Smith, R.E.; Liang, X.; Zalesky, A.; Connelly, A. Track-weighted dynamic functional connectivity (TWdFC): a new method to study dynamic
connectivity. In Proc ISMRM 2016:0308
7. Tozer, D.; Chard, D.; Bodini, B.; Ciccarelli, O.; Miller, D.; Thompson, A. & Wheeler-Kingshott, C. Linking white matter tracts to associated cortical grey
matter: A tract extension methodology. NeuroImage, 2012, 59, 3094-3102
8. Andersson, J. L.; Skare, S. & Ashburner, J. How to correct susceptibility distortions in spin-echo echo-planar images: application to diusion tensor
imaging. NeuroImage, 2003, 20, 870-888
9. Dale, A. M.; Fischl, B. & Sereno, M. I. Cortical Surface-Based Analysis: I. Segmentation and Surface Reconstruction. NeuroImage, 1999, 9, 179-194
10. Dhollander, T.; Connelly, A. A Novel Iterative Approach to Reap the Benets of Multi-Tissue CSD from Just Single-Shell (+b=0) Diusion MRI Data. In
Proc ISMRM, 2016, 3010
11. Tournier, J.-D.; Calamante, F. & Connelly, A. Improved probabilistic streamlines tractography by 2nd order integration over bre orientation
distributions. In proc ISMRM, 2010, 1670
12. Smith, R. E.; Tournier, J.-D.; Calamante, F. & Connelly, A. Anatomically-constrained tractography: Improved diusion MRI streamlines tractography
through eective use of anatomical information. NeuroImage, 2012, 62, 1924-1938
13. Smith, R. E.; Tournier, J.-D.; Calamante, F. & Connelly, A. SIFT2: Enabling dense quantitative assessment of brain white matter connectivity using
streamlines tractography. NeuroImage, 2015, 119, 338-351
14. Winkler, A. M.; Ridgway, G. R.; Webster, M. A.; Smith, S. M. & Nichols, T. E. Permutation inference for the general linear model. NeuroImage, 2014, 92,
Schematic of Fixel TWI operation, including: Registration of subject Fibre Orientation Distribution (FOD) image to template; generation of streamlines
tractogram in subject space; extraction of streamline TWI factors based on grey matter information in subject space; transformation of subject
tractogram to template space; direct mapping of transformed streamlines to xels in template space. The result is an image containing a quantitative
value per xel in template space, which is therefore amenable to comparison with other images dened in the same space.
Demonstration of the benets of applying spatial non-linear transformations directly to streamlines data. In each tracking example (left column), if the
eld compression / expansion is orthogonal to the streamlines direction, then the voxel-wise streamlines density is intrinsically modulated appropriately;
however, if this compression / expansion is along the same direction as the streamlines, then the streamlines lengths are altered, but the voxel-wise
streamlines density is unaected.
Fixel data from the rst four subjects in the group, displayed in template space; axial slice. Fibre Density and Cross-section (FDC; top row) is a white
matter-based measure, whereas the xel Track-Weighted Imaging (TWI) parameter derived here (bottom row) is a grey matter-based measure; but
because the grey matter information is propagated into white matter based on streamlines tractography, both sources of information are available
within the same template space.
Zoomed region of template image showing the data contributed by a single subject. For each individual xel in template space, the subject contributes
one value corresponding to the Fibre Density and Cross-section (FDC) measure, and one value derived from xel Track-Weighted Imaging (TWI), based on
cortical thickness at streamlines endpoints in this particular case. Note that within any particular voxel in template space,not only may there be multiple
xels, but the values of the quantitative measures of interest may vary between those xels.
Proc. Intl. Soc. Mag. Reson. Med. 25 (2017)
... The work presented in this thesis could be extended to a multi-parametric multimodal approach, including quantitative T1 and T2 data, which may be more sensitive to maturation-dependent changes than univariate analysis (Kulikova et al., 2015) and may improve the ability to discriminate between patient and control populations (Dean et al., 2017). Furthermore, while this thesis has focused on WM changes, future studies could combine quantitative measures from GM with WM measures derived from TSA and FBA, as proposed by Smith et al. (2017). Investigating how WM fasciculi influence GM structures, and vice versa, may provide additional insight into developmental changes and injury in the neonatal brain. ...
Full-text available
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.
Conference Paper
Full-text available
Constrained spherical deconvolution (CSD) is a robust approach to resolve the fibre orientation distribution (FOD) from diffusion MRI data. However, the FOD from CSD only aims to represent "pure" white matter (WM) and is inappropriate/distorted in regions of (partial voluming with) grey matter (GM) or cerebrospinal fluid (CSF). Multi-shell multi-tissue CSD was proposed to solve this issue by estimating WM/GM/CSF components, but requires multi-shell data to do so. In this work, we provide the first proof that similar results can also be obtained from only simple single-shell (+b=0) data, and propose a novel specialised optimiser that achieves this goal.
Full-text available
In brain regions containing crossing fibre bundles, voxel-average diffusion MRI measures such as Fractional Anisotropy (FA) are difficult to interpret, and lack within-voxel single fibre population specificity. Recent work has focused on the development of more interpretable quantitative measures that can be associated with a specific fibre population within a voxel containing crossing fibres (herein we use fixel to refer to a specific fibre population within a single voxel). Unfortunately, traditional 3D methods for smoothing and cluster-based statistical inference cannot be used for voxel-based analysis of these measures, since the local neighbourhood for smoothing and cluster formation can be ambiguous when adjacent voxels may have different numbers of fixels, or ill-defined when they belong to different tracts. Here we introduce a novel statistical method to perform whole-brain fixel-based analysis called connectivity-based fixel enhancement (CFE). CFE uses probabilistic tractography to identify structurally connected fixels that are likely to share underlying anatomy and pathology. Probabilistic connectivity information is then used for tract-specific smoothing (prior to the statistical analysis) and enhancement of the statistical map (using a threshold-free cluster enhancement-like approach). To investigate the characteristics of the CFE method, we assessed sensitivity and specificity using a large number of combinations of CFE enhancement parameters and smoothing extents, using simulated pathology generated with a range of test-statistic signal-to-noise ratios in five different white matter regions (chosen to cover a broad range of fibre bundle features). The results suggest that CFE input parameters are relatively insensitive to the characteristics of the simulated pathology. We therefore recommend a single set of CFE parameters that should give near optimal results in future studies where the group effect is unknown. We then demonstrate the proposed method by comparing apparent fibre density between motor neurone disease (MND) patients with control subjects. The MND results illustrate the benefit of fixel-specific statistical inference in white matter regions that contain crossing fibres. Copyright © 2015. Published by Elsevier Inc.
Full-text available
Permutation methods can provide exact control of false positives and allow the use of non-standard statistics, making only weak assumptions about the data. With the availability of fast and inexpensive computing, their main limitation would be some lack of flexibility to work with arbitrary experimental designs. In this paper we report on results on approximate permutation methods that are more flexible with respect to the experimental design and nuisance variables, and conduct detailed simulations to identify the best method for settings that are typical for imaging research scenarios. We present a generic framework for permutation inference for complex general linear models (glms) when the errors are exchangeable and/or have a symmetric distribution, and show that, even in the presence of nuisance effects, these permutation inferences are powerful while providing excellent control of false positives in a wide range of common and relevant imaging research scenarios. We also demonstrate how the inference on glm parameters, originally intended for independent data, can be used in certain special but useful cases in which independence is violated. Detailed examples of common neuroimaging applications are provided, as well as a complete algorithm - the "randomise" algorithm - for permutation inference with the glm.
Conference Paper
Full-text available
Diffusion weighted imaging (DWI) allows to delineate neural fibres, based on local, directional information of the diffusion of water. Due to its directional nature, the local information needs to be reoriented upon image transformation, in order to preserve correspondence to the anatomy. In this work, we show that reorientation of the fODF with preservation of volume fractions (PVF) affects both deterministic and probabilistic fibre tracking. We identify the main causes for this, and validate them on synthetic and real brain DWI data. The problem is not with the PVF reorientation itself, but rather with the fODF reconstruction, its use in fibre tracking, and the influence of the seeds.
Diffusion tensor imaging is often performed by acquiring a series of diffusion-weighted spin-echo echo-planar images with different direction diffusion gradients. A problem of echo-planar images is the geometrical distortions that obtain near junctions between tissues of differing magnetic susceptibility. This results in distorted diffusion-tensor maps. To resolve this we suggest acquiring two images for each diffusion gradient; one with bottom-up and one with top-down traversal of k-space in the phase-encode direction. This achieves the simultaneous goals of providing information on the underlying displacement field and intensity maps with adequate spatial sampling density even in distorted areas. The resulting DT maps exhibit considerably higher geometric fidelity, as assessed by comparison to an image volume acquired using a conventional 3D MR technique.