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Connectivity-Based Fixel Enhancement: Whole-Brain Statistical Analysis of Diffusion MRI Measures in the Presence of Crossing Fibres

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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.
Content may be subject to copyright.
Connectivity-based xel enhancement: Whole-brain statistical analysis
of diffusion MRI measures in the presence of crossing bres
David A. Raffelt
a,
,RobertE.Smith
a
,GerardR.Ridgway
b,c
, J-Donald Tournier
d,e
, David N. Vaughan
a,f,g
,
Stephen Rose
h
, Robert Henderson
i
, Alan Connelly
a,f,g
a
Florey Institute of Neuroscience and Mental Health, Melbourne, Victoria, Australia
b
FMRIB Centre, Nufeld Department of Clinical Neurosciences, University of Oxford, Oxford, UK
c
Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, London, UK
d
Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, UK.
e
Centre for the Developing Brain, King's CollegeLondon, London, United Kingdom
f
Florey Department of Neuroscience and Mental Health, University of Melbourne, Melbourne, Victoria, Australia.
g
Department of Medicine, Austin Health and Northern Health, University of Melbourne, Melbourne, Victoria, Australia.
h
The Australian e-Health Research Centre, CSIRO-Digital Productivity Flagship, Royal Brisbane and Women's Hospital, Herston, Australia
i
Department of Neurology, Royal Brisbane and Women's Hospital, Herston, Australia
abstractarticle info
Article history:
Received 27 February 2015
Accepted 15 May 2015
Available online 22 May 2015
Keywords:
Diffusion
MRI
Statistics
Fixel
Connectivity
Analysis
In brain regions containing crossing bre bundles, voxel-average diffusion MRI measures such as fractional an-
isotropy (FA) are difcult to interpret, and lack within-voxel single bre population specicity. Recent work
has focused on the development of more interpretable quantitative measures that can be associated with a spe-
cicbre population within a voxel containing crossing bres (herein we use xel to refer to a specicbre pop-
ulation 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 smooth-
ing and cluster formation can be ambiguous when adjacent voxels may have different numbers of xels, or ill-
dened when they belong to different tracts. Here we introduce a novel statistical method to perform whole-
brain xel-based analysis called connectivity-based xelenhancement (CFE). CFEuses probabilistic tractography
to identify structurally connected xels that are likely to share underlying anatomy and pathology. Probabilistic
connectivity information is thenused for tract-specic smoothing (prior to the statistical analysis) and enhance-
ment of the statisticalmap (using a threshold-free cluster enhancement-like approach). To investigate the char-
acteristics of the CFE method, weassessed sensitivity and specicityusingalargenumberofcombinationsofCFE
enhancement parameters and smoothing extents, using simulated pathology generated with a range of test-
statisticsignal-to-noise ratios in vedifferent white matter regions(chosen to covera broad range of brebundle
features). The resultssuggest that CFE input parameters are relatively insensitive to the characteristics of the sim-
ulated 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 bre density between motor neurone disease (MND) patients with control subjects. The MND results
illustrate the benetofxel-specic statistical inference in white matter regions that contain crossing bres.
© 2015 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).
NeuroImage 117 (2015) 4055
Abbreviations:AFD, apparentbre density;AFROC, alternativefree-response receiver operatorcurve;AUC, area under the curve;CFE, connectivity-based xel enhancement; CHARMED,
compositehindered and restricted modelof diffusion; CUSP-MFM, cubeand sphere multi-fascicle model; DWI, diffusion-weighted imaging;FA, fractionalanisotropy; Fixel,a specicbre
population within a voxel; FBA, xel-based ana lysis; FOD, bre orientation distribution;FWE, family-wiseerror; FWHM, fullwidth at half maximum; HMOA, hindrancemodulated orienta-
tionalanisotropy;MD, mean diffusivity;MND, motorneurone disease;MRI, magneticresonance imaging;ROC, receiveroperatorcurve; ROI, regionof interest; SIFT,spherical deconvolution
informedltering oftractograms;SNR, signal to noise;SPM, statistical parametric mapping; TBSS, tract-based spatial statistics; TFCE,threshold-freecluster e nhancement; V BA, voxel-b ased
analysis.
Corresponding author at: Florey Institute of Neuroscience and Mental Health, Melbourne Brain Centre, 245 Burgundy Street, Heidelberg, Victoria 3084, Australia.
E-mail address: david.raffelt@orey.edu.au (D.A. Raffelt).
http://dx.doi.org/10.1016/j.neuroimage.2015.05.039
1053-8119/© 2015 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Contents lists available at ScienceDirect
NeuroImage
journal homepage: www.elsevier.com/locate/ynimg
Introduction
Voxel-based analysis (VBA) is an image analysis technique for
performing whole-brain voxel-wise statistical tests across and within
groups of subjects, originally introduced in the form of statistical para-
metric mapping (SPM; Friston et al., 1991). A particular strength of
the VBA approach is that, in addition to enabling specic hypotheses
to be tested, it has the ability to localise group differences or correlations
without any prior spatial hypothesis. Over the last two decades, VBA has
been applied in many elds of neuroimaging to investigate quantitative
information derived from image intensity (e.g. positron emission tomog-
raphy (Worsley et al., 1992) and functional MRI (Friston et al., 1995)) and
image morphology (e.g. voxel-based morphometry (Ashburner and
Friston, 2000) and tensor-based morphometry (Ashburner, 2000; Gee,
1999)).
VBA commonly involves four key steps:
1. Obtain anatomical correspondence by transforming all subject im-
ages to a common template using an image registration algorithm.
2. Smooth images to boost the signal-to-noise ratio, alleviate registra-
tion misalignments, and improve the normality of residuals when
performing parametric statistical analysis.
3. Perform a statistical test at each voxel resulting in a test-statistic
image (also known as a statistical parametric map).
4. Statistical inference (assign p-values to voxels, peaks or clusters of
voxels).
One caveat in VBA is the need to account for the large number of
multiple tests during statistical inference. Random eld theory (RFT)
(Worsley et al., 1992) and non-parametric permutation testing
(Nichols and Holmes, 2002) are two commonly used methods to com-
pute family-wise error (FWE) corrected p-values. While these methods
can be used to make voxel-level inferences, they can also be applied to
derive FWE-corrected p-values for clusters of contiguous voxels above
apredened threshold (Friston et al., 1994; Poline and Mazoyer,
1993). Cluster-level inference can be more sensitive than voxel-level in-
ference by exploiting spatial correlations in voxel intensities due to
shared underlying anatomy and pathology (Friston et al., 1996).
In the eld of diffusion-weighted imaging (DWI), VBA is being used
increasingly to study white matter development, aging and pathology.
The vast majority of these studies have involved quantitative measures
derived from the diffusion tensor model, such as mean diffusivity (MD)
and fractional anisotropy (FA) (Basser and Pierpaoli, 1996). Since these
tensor-derived measures are scalar quantities, traditional VBA software
packages (such as SPM (www.l.ion.ucl.ac.uk/spm/) and FSL (www.
fmrib.ox.ac.uk/fsl)) can be used to analyse the resultant 3D images.
More recently, several diffusion-specic VBA approaches have been
proposed that perform statistics on a tract skeleton (Smith et al.,
2006) or surface (Maddah et al., 2011; Yushkevich et al., 2008; Zhang
et al., 2010). By projecting local quantitative measures onto a tract skel-
eton or 2D surface, these methods aim to reduce the impact of imperfect
image registration on anatomical correspondence. However, not all
white matter tracts can be modelled by a skeleton or surface, and there-
fore these methods suffer from other problems related to inaccurate
tract representation and projection (Bach et al., 2014).
Two issues relevant to VBA of white matter that have been largely
neglected to date are as follows:
1. A white matter voxel can contain multiple populations of bres, each
belonging to a specicwhite matter tract with a unique function (a
scenario often referred to as crossing bres). Recent evidence sug-
gests up to 90% of white matter voxels contain two or more bre
populations (Jeurissen et al., 2012). Ideally VBA of diffusion MRI
should be able to attribute any signicant effect to a specicbre
population in regions with crossing bres.
2. White matter contains anatomical structures that are oriented and can
span many voxels in the image. Spatially distant voxels can share the
same underlying anatomy, yet adjacent voxels may share no anatomy
(e.g. at a bundle interface). It is therefore reasonable to assume that
correlations in quantitative measures can occur anywhere along a
bre tract, but not necessarily with all voxel neighbours isotropically
(as is assumed to be the case in grey matter) (see Fig. 1).
1
This is
based on the assumption that axons are likely to be affected by devel-
opment, pathology or aging along their entire length.
Both issues 1 and 2 are problematic for appropriate smoothing and
cluster-based statistical inference. A neighbourhood for traditional isotro-
pic smoothing and cluster formation is ambiguous when adjacent voxels
have multiple bre populations, and ill-dened when adjacent bre pop-
ulations belong to different bre tracts. Note that in the aforementioned
surface- and tract-skeleton-based methods (Maddah et al., 2011; Smith
et al., 2006; Yushkevich et al., 2008; Zhang et al., 2010), parameterisation
of the tract enables smoothing and clustering with a more appropriate
neighbourhood. However, 2D surfaces or 3D skeletons cannot appropri-
ately represent all white matter tracts (e.g. fanning of the corpus
callosum), and current methods do not account for crossing bres.
In recent years, a number of quantitative measures have been pro-
posed that can be assigned to a specicbre population within a
Fig. 1. a)In grey matter, it is reasonable to assumeimage intensitiesare spatially correlated with neighbours isotropically for the purposesof smoothing andcluster formation.Illustrated in
yellow is a voxelof interest with neighbouring voxels coloured red.b) White matter anatomyis oriented and extended in nature, therefore an isotopicneighbourhood is notappropriate.
Shown isa fractionalanisotropy mapcoloured by the direction of the primarytensor eigenvector (red: leftright, green: anteriorposterior, blue: inferiorsuperior). Notall voxels adjacent
to the voxel of interest(yellow voxel withinthe optic radiation)are relevant for smoothing and cluster formation since neighbouring voxels containdifferentbre tracts (e.g.tapetum of
corpus callosum and arcuate fasciculus). In this example only the voxels anterior and posterior (shown in red) should be considered as neighbours for clustering and smoothing.
1
Note that thismay not be true for lesions in diseases such as Stroke and MultipleScle-
rosis. However, these lesions tend to be spatially heterogeneous and therefore less suited
to multi-subject VBA.
41D.A. Raffelt et al. / NeuroImage 117 (2015) 4055
given voxel. Here we coin the term xel
2
to refer to a specicpopulation
of bres within a single voxel. We note that while voxel-average summa-
ry statistics such as generalized fractional anisotropy (Tuch, 2004)can
be used to characterise model-free data derived via Diffusion Spectrum
Imaging (Wedeen et al., 2005) or Q-Ball imaging (Tuch, 2004), it is im-
possible to derive xel-specic quantitative measures without making
some assumptions about the diffusion within a single xel. As a conse-
quence, all xel-specic quantitative measures to date are based on
mixture models. For example, in the composite hindered and restricted
model of diffusion(CHARMED) model, the volume fraction of each xel
is estimated by assuming a restricted model of diffusion for each xel
(Assaf and Basser, 2005). In a similar concept, the apparent bre density
(AFD) and hindrance modulated orientational anisotropy (HMOA) are
measures also related to the volume of the intra-axonal restricted com-
partment (Dell'Acqua et al., 2013; Raffelt et al., 2012b). The motivation
behind these measures is that the intra-axonal restricted compartment
should be sensitive to various white matter pathologies that affect the
number of axons. In more recent work, Scherrer and Wareld (2012)
use a novel acquisition scheme and tting procedure (called cube and
sphere multi-fascicle model, CUSP-MFM) to model the intra-axonal dif-
fusion for each xel with a diffusion tensor. In CUSP-MFM xel-specic
volume fractions and diffusivities can be estimated.
All of these xel-based measures have the potential to give more
specic information than tensor-derived measures by identifying spe-
cic white matter tracts that are affected in regions with crossing bres.
However, due to issues 1 and 2 outlined above, traditional 3D statistical
software packages cannot be applied to perform VBA on these bre-
specic measures.
In this work we propose a novel statistical framework entitled
connectivity-based xel enhancement(CFE) for performinggroup com-
parisonsor correlations of xel-specic measures within all of the white
matter (i.e. a xel-based analysis, FBA). We use whole-brain probabilis-
tic tractography on a group average template to dene the connectivity
between each xel and all other xels in the brain, and use this xel-
xel connectivity information for both smoothing (i.e. xel-specic
measures are smoothed only with other xels that share common
streamlines), and to boost the belief in (enhance) the test-statistic of
each xel based on information from structurally connected xels. We
investigate the proposed method using quantitative simulations, and
demonstrate its utility by comparing a cohort of motor neurone disease
patients with healthy controls.
Methods
Fixelxel connectivity
To visually demonstrate the concept of xel connectivity, consider
the example shown in Fig. 2.Fig. 2a, b shows a group-average template
generated via registration of bre orientation distribution (FOD) images
(Raffeltetal.,2011). The location and direction of all white matterxels
can be computed via segmentation of each FOD lobe in the group-
average template (Fig. 2c). FOD segmentation was performed using
the method outlined in Smith et al. (2013), which involves segmenting
each lobe/bre using zero crossings of the FOD and their directions
based on peak amplitude (note that while we use the spherical
deconvolution model in this example, some diffusion MRI models com-
pute xels directly, and therefore may not require an explicit
segmentation step). For this example, consider xel findicated by the
blue arrow in Fig. 2d. Probabilistic streamlines are used to compute
the connectivity to all other white matter xels (Fig. 2d shows only
those streamlines extracted from the whole-brain tractogram that tra-
verse xel f). We dene the connectivity from xel fto xel i,c
,as
the proportion of the streamlines traversing xel fthat also traverse
xel i. Note that since c
is the number of shared streamlines relative
to all streamlines associated with f, this measure is not symmetric, (i.e.
c
c
if
). In Fig. 2e, each xel is coloured by c
: this demonstrates how
the use of probabilistic tractography provides a mechanism to quantify
xelxel connectivity based on uncertainty in the estimated bre ori-
entations, i.e. we are more condent that xels with a high density of
the dispersing streamlines are likely to share underlying anatomy
(and therefore be correlated) with xel f.
When computing the whole-brain xelxel connectivity matrix,
streamlines are assigned to xels in the template based on the local
streamline tangent. The streamline tangent is computed by the entry
and exit point through the voxel. For practical reasons, we remove all
xelxel connectivity values, c
i,
that are less than 0.01. This eliminates
many xels connected by spurious probabilistically-unlikely stream-
lines, and also increases the sparsity (and therefore decreases the re-
quired memory) of the whole-brain xelxel connectivity matrix.
Connectivity-based smoothing
The rst application of xelxel connectivity is to weight
neighbourhood xels for the purposes of pre-smoothing data. In 3D
voxel-based analysis data is typically smoothed with a local isotropic
neighbourhood using a Gaussian kernel. In this work we als o smooth lo-
cally, however we compute smoothing weights (Fig. 2g) by multiplying
Gaussian kernel weights (Fig. 2f) with the xelxel connectivity
weights (Fig. 2e). Connectivity-based smoothing ensures that xel-
specic measures are smoothed locally with xels belonging to the
same bre tract, and preferentially smooths data with xels with high
connectivity values, whose xel data are mostlikely to correlate strong-
ly with that of the xel of interest. We note that smoothing could be
achieved by using connectivity weights only (Fig. 2e), since values are
larger in local xels due to probabilistic streamline dispersal. However,
by spatially restricting smoothing with a Gaussian kernel, data are less
likely to be smoothed with remote xels containing very different
values. This may be an issue for some quantitative measures that vary
along a bundles length (e.g measures related to xel volume fraction
will vary based amount of crossing with other bres).
Connectivity-based xel enhancement
The second application of xelxel connectivity is in statistical in-
ference. Here we present a novel approach for xel-based statistics
called connectivity-based xel enhancement (CFE).
Conventional cluster-based statistical analysis involves applying a
pre-specied threshold to the test-statistic image to identify co-
located (clustered) voxels. The motivation behind cluster-based analy-
sis is to identify extended areas of group differences that are more
spatially extended than would be expected due to the noise coherence
alone. Once clusters of voxels have been identied, the likelihood
(p-value) that each cluster (of a certain size) has occurred due to
chance can be computed by comparing the cluster size to the null distri-
bution of cluster sizes (estimated via Gaussian random eld theory
(Worsley et al., 1992) or permutation testing (Holmes et al., 1996)).
One dilemma in any method for cluster-based inference is the choice
of an arbitrary threshold. While the choiceof threshold does not impact
on the validity of the results, it can greatly affect the outcome and
therefore complicate scienticinterpretation.Smith and Nichols
(2009) proposed an alternative to threshold-based cluster analysis
called threshold-free cluster enhancement(TFCE). In the Smith and
Nichols (2009) 3D TFCE implementation, the enhanced test-statistic at
2
Previous publications have used the word bre(Assaf and Basser, 2005; Behrens
et al., 2007)(Assaf and Basser, 2005), fascicle(Scherrer and Wareld, 2012)orbre pop-
ulation(Behrens et al., 2007; Raffeltet al., 2012b) to referto a specic populationof bres
within a single voxel. However, these terms can be ambiguousin certain contexts.For ex-
ample,when attributinga quantitative measure to a bre, it may be misinterpreted as be-
longing to the entire bre bundle. Here, we introduce a new word xelto eliminate this
ambiguity when discussing xel-specic measures and xel-based analysis (FBA).
42 D.A. Raffelt et al. / NeuroImage 117 (2015) 4055
voxel v, is equal to the sum of the cluster extents, e, as the statistic image
is thresholded at various heights, h, up to the height of v,h
v
. More spe-
cically TFCE is dened as:
TFCE vðÞ¼
Zhv
0
ehðÞ
EhHdh ð1Þ
with default values of constants E= 0.5, H= 2. Note that these defaults
are justied by theory and empirical results in Smith et al. (9). Bysetting
Hto more than 1 the TFCE output gives more weight to extents (clus-
ters) at larger levels of h, while setting Eto less than 1 ensures the
TFCE output scales less than linearly with cluster size (something that
is desirable at low thresholds when clusters are large and do not provide
useful spatial specicity (Smith and Nichols, 2009)).
CFE is a TFCE-like approach that exploits connectivity information to
enhance the test-statistic of each xel based on the support lent to it by
other structurally connected xels. In the original TFCE paper (Smith
and Nichols, 2009), the cluster extent eis dened as the number of
supra-threshold voxels spatially connected to voxel v. However in CFE,
we redene eas the weighted sum of xels structurally connected to
the xel being enhanced, f.Precisely,CFEisdened as:
CFE fðÞ¼hf
0ef;hðÞ
EhHdh ð2Þ
ef;hðÞ¼nhðÞ
i¼1cfiCð3Þ
where n(h) is the total number of supra-threshold xels connected to f,
c
is the connectivity dened as the proportion of streamlines traversing
xel fthat also traverse xel i, and Cis a constant. By weighting each
xel by c
, highly connected xels (i.e. those that we are more certain
share many axons) contribute more to the enhancement than xels
with low connectivity. Furthermore, c
is raised to the power C, which
enables the option to modulate thestrength of this connectivity depen-
dent enhancement. For example when C= 0 all connected xels
contribute evenly to the enhancement, whereas when C= 1 they con-
tribute with a weight proportional to their measured connectivity.
It is worth emphasising that in the original TFCE method, a voxel
may contribute to the enhancement of another only if they are spatially
connected by coexisting within a supra-threshold cluster. However in
CFE, a supra-threshold xel may enhance another as long as it is struc-
turally connected, without any requirement that the xels are spatially
connected within a suprathreshold cluster. This distinction arises from
the fact that in CFE, we have additional information provided by
tractography. This enables us to determine whether xels are likely to
share underlying anatomy and pathology, without any need to assume
that supra-threshold xels must be spatially contiguous.
Illustrative example
Fig. 3 contains an illustrative example of connectivity-based smooth-
ing and CFE enhancement to an articially generated signal + noise
image. A tract-of-interest (the arcuate fasciculus, Fig. 3b) was extracted
from the whole-brain tractogram (Fig. 3a) computed on the FOD tem-
plate (Fig. 2a, b) (see the following section for details). Fixels belonging
to the arcuate fasciculus were identied (via streamline visitations) and
assigned a signal value of one (Fig. 3d). All non-arcuate (background)
xels were assigned a value of zero. A signal + noise image was created
by adding random Gaussian noise with a standard deviation of 0.5, cor-
responding to a signal-to-noise ratio of 2 (Fig. 3e). We then applied the
following enhancements to separate the signal from the noise:
Connectivity-based smoothing only, FWHM = 10 mm (Fig. 3f);
CFE only (no smoothing), E=1,H=2,C=0.5(Fig. 3g);
Connectivity-based smoothing then CFE, FWHM = 10 m, E=1,H=
2, C = 0.5 (Fig. 3h).
To best visualise that the arcuate signalxels are separated from
the background xels, all images in Fig. 3eh are windowed such that
the colour bar range extends from the 1st to 99th percentile ofthe back-
ground xel values. Fixels indicated in white are therefore larger than
Fig. 2. Illustration of xelxel connectivity and smoothing. a) A group-average FOD template colour-coded by direction (red: leftright, blue: inferiorsuperior, green: anteriorposterior).
b) Zoomed in region from a, showing individual FODs within the group-average FOD template. c) The direction and number of xels in each voxel was computed by segmenting each FOD
in a (coloured by xel orientation). d) A single exemplar xel f(blue arrow, belonging to the superior longitudinal fasciculus), with associated probabilistic streamlines. e) Fixels colour-
coded by connectivitytoxel f. The connectivity, c
,
between exemplar xel fand xel iis dened as the proportion of streamlines traversing xelfthat also traverse xel i. f) A spatial Gaussian
kernel centred on xel, f, is multiplied with xel connectivity in d to estimate the xel-specic smoothing neig hbourhood weights shown in f. g) Smoothing neighbourhood weights for xel, f,
used to smooth xel data prior to analysis.
43D.A. Raffelt et al. / NeuroImage 117 (2015) 4055
(separated from) the vast majority of background values. As shown in
Fig. 3f and g, both smoothing alone and CFE alone separate many signal
xels from the background; however the combination of smoothing
and CFE achieves the best result (Fig. 3h).
Computing a xel analysis mask and obtaining correspondence across
subjects
Whole-brain xelxel connectivity is computed between all xels
in template space. We dene the location and orientation of all template
xels using a xel analysis mask. The approach used to generate this
mask may differ depending on the diffusion model being analysed;
however, ideally it should be representative of the population under
investigation.
In this work (see Section 2.8), we compute the xel analysis mask by
rst computing a population-specic FOD template using an iterative
update approach (Raffelt et al., 2011). Accurate alignment of white mat-
ter is achieved by using FOD images to drive registration (Raffelt et al.,
2011), and xel orientations are corrected by reorientation of each
FOD (Raffelt et al., 2012a). The FOD template is computed by averaging
the spherical harmonic coefcients across all registered FOD images. To
identify all xels in the FOD template, we segment each FOD lobe using
the method outlined in Smith et al. (2013). When correspondence and
FOD alignment is poor across subjects (for example at the grey/white
matter interface where inter-subject variation is greatest and registra-
tion is imperfect), the FOD lobes will not average constructively and
their size will be small. We exclude these xels from the analysis
mask by thresholding the xel AFD (as computed by integrating the
FOD amplitude within each FOD lobe (Smith et al., 2013)). We note
that thresholding xels based on the AFD may undesirably exclude
other xels in crossing bre regions that have low AFD (due to partial
volume effects). We therefore compute the xel analysis mask using a
two-step process. First a relatively high AFD threshold (N0.33) is used
to exclude all unwanted xels with poor correspondence near the
grey matter interface. From this result we then compute a 3D voxel
mask dening all voxels that contain at least 1 xel. The AFD threshold
is then relaxed (N0.1) to include xels with small AFD values (i.e.
those in crossing bre regions) while excluding all xels outside the
3D voxel mask.
The benet of using a study-specicxel analysismask is that the lo-
cation and orientation of xels are representative of the population. The
mask is therefore a good candidate for obtaining xel correspondence
across subjects by matching each template xel to the nearest xel in
each of the subject images. Note that if no xel exists in a subject
image for a given template xel (with a maximum angular tolerance
of 30°), then it is assigned a quantitative value of zero. If a xel exists
in the subject that does not map to a template xel then it is ignored.
Statistical inference
In multiple testingproblems, a family-wise error (FWE) refers to one
or more false positives among the set of tests; such an error occursif and
only if the maximum over the set exceeds the decision threshold, imply-
ing that a suitable threshold to control the FWE rate (or equivalently,
FWE-corrected p-values) can be obtained from the null distribution of
the maximum-statistic (Nichols and Hayasaka, 2003). Permutation test-
ing provides a non-parametric empirical null-distribution by recording
the maximum-statistic computed for multiple permuted versions of
the data, resting on the assumption of exchangeability under the null
hypothesis (Holmes et al., 1996; Nichols and Holmes, 2002). For a gen-
eral linear model, under the assumption that the (unobservable) errors
are exchangeable, permutation of appropriate statistical residuals pro-
vides an approximate test that performs well in practice (Winkler
et al., 2014). Here, complete images are permuted as a whole, preserv-
ing the complicated dependence structure, and the maximum is
computed over all xels' test statistics after CFE (i.e. the CFE procedure
is applied to the statistic image for every permutation, effectively
becoming part of the denition of the test statistic, as for TFCE or for
the smoothed-variance t-map described by Nichols and Holmes,
2002). P-values are then assigned to each xel by computing the pro-
portion of the maximal CFE statistic distribution that is as-or-more ex-
treme than the CFE value estimated using the original labelling of the
Fig. 3. Illustrativeexample. a) Whole-brain probabilistic tractogram computed on the group-averageFOD template. Streamlines were usedto derive xelxel connectivity for smoothing
and enhancement. Streamlines are coloured by direction (red: leftright, blue: inferiorsuperior, green: anteriorposterior). b) A tract-of-interest, the arcuate fasciculus, was extracted
from the whole-braintractogram in a (note thatonly streamlinesbelonging to the sliceare shown). c) Individualxels belongingto the arcuate fasciculus were identied basedon stream-
line visitation. All arcuate xels wereassigned a signalof one. d) Zoomedin region of the signalonlyimage in c showing the arcuate fasciculus xelsin white and background(zero) xels
in black. e) Signal + noise image afteradding Gaussian noise (signal-to-noise of 2) to the signal only image in d. f) Connectivity-based smoothing of e. g) CFE of e. h) Both connectivity-
based smoothing and CFE of e. To best visualise the separation of signalfrom background, allimages ef are windowed based on the 1st to 99th percentile of the background xel values.
44 D.A. Raffelt et al. / NeuroImage 117 (2015) 4055
45D.A. Raffelt et al. / NeuroImage 117 (2015) 4055
data. For example, if 1000 permutations are performed (including the
original labelling), and the original maximum is the 5th largest of
these 1000, then its corrected p-value is 5/1000.
Quantitative evaluation of CFE
We assessed the performance of CFE by generating a series of test
statistic signals within an in vivo population-average template image.
We explored the inuence of CFE parameters E, H and Cwhile varying
the test statistic signal region-of-interest (ROI), signal-to-noise ratio
(SNR) and smoothing spatial extent. Performance was assessed using
a receiver-operator characteristic (ROC)-based evaluation.
In vivo data and pre-processing
Diffusion-weighted images were acquired from 80 healthy control
subjects on a 3 T Siemens TIM Trio system (Erlangen, Germany), 60 dif-
fusion directions,b = 3000 s/mm
2
, 2.3 mm. Motion correction,bias eld
correction and intensity normalisation were performed as described in
Raffelt et al. (2012b). Fibre orientation distributions (FODs) were com-
puted using robust constrained spherical deconvolution at l
max
=8
(Tournier et al., 2013).
Group-average FOD template and tractography
All FOD images were registered to a group-average template using a
FOD-based symmetric diffeomorphic registration algorithm (Raffelt
et al., 2011)(Fig. 4a). During registration and the nal spatial transfor-
mation, FODs were reoriented using apodised point spread functions
(Raffelt et al., 2012a). Whole-brain probabilistic tractography was per-
formed on the FOD template image to generate 30 million streamlines
(Fig. 4b). This was performed using the iFOD2 tractography algorithm
(Tournier et al., 2010), as part of the MRtrix software package
(Tournier et al., 2012)(https://github.com/MRtrix3) (parameters: step
size 0.625, angle 22.5, max length 250 mm, min length 10, power 0.5).
To reduce tractography reconstruction biases we applied the spherical
deconvolution informed ltering of tractograms (SIFT) method to give
anal count of 3 million streamlines (Fig. 4c) (Smith et al., 2013).
Regions-of-interest
We chose to evaluate CFE by generating a test-statistic signal in ve
different regions-of-interest (ROI) (Fig. 5). ROIs selected were the arcu-
ate fasciculus, corticospinal tract, cingulum, posterior cingulum, and an
Alzheimer's-likepathology. ROIs were selected to cover a broad range of
properties (bre bundle length, thickness, curvature and number of
crossings). The arcuate fasciculus has a large proportion of crossing -
bres with high posterior curvature (Fig. 5, top row). The corticospinal
tract is a relatively large bundle that contains some crossings and a
high degree of fanning (Fig. 5, 2nd row). The cingulum bundle is long
and thin with a low proportion of crossing bres (Fig. 5, middle row).
The posterior cingulum was selected to test small and focal pathology
(Fig. 5, 4th row). While it is our assumption that white matter patholo-
gy/maldevelopment generally should occur along the entire length of a
bundle, the cingulum bundle contains many on/offrampsinto the cin-
gulate cortex, and therefore it is feasible that only a portion of the cingu-
lum may be affected. The last ROI tested was an Alzheimer's-like
pathology, chosen to represent diseases that affect several white matter
bundles (Fig. 5, bottom row). Alzheimer's-like bre bundles included
the left arcuate fasciculus (yellow), cingulum (dark blue), anterior com-
missure (pink), uncinate fasciculus (green), anterior corpus callosum
(red), and posterior corpus callosum connecting the left and right
precuneus (light blue).
To identify each bre ROI (Fig. 4e), streamlines were extracted from
the template-generated tractogram using grey matter include-regions
dened by the SRI24 atlas (Fig. 4d) (Rohlng et al., 2010). The SRI24
atlas was co-registered to the group-average template using fractional
anisotropy and mean diffusivity maps simultaneously (using the ANTS
software package; http://picsl.upenn.edu/software/ants/). Spurious
streamlines were removed with exclude-regions dened by a neurolo-
gist. In addition we cropped streamlines in regions where the stream-
line density was less than 2% of the maximum density within that
tract. This ensured that nal ROIs did not contain regions traversed by
relatively few (probabilistically unlikely) streamlines.
Generating test-statistic images
We computed a white matter xel mask as described in the section
Computing a xel analysis mask and obtaining correspondence across
subjects(Fig. 4f). A binary xel signal image for each ROI (Fig. 4g)
was created by mapping streamlines (Fig. 4e) to associated xels in
thetemplatemask(Fig. 4f). We then generated 1000 instances of ran-
dom Gaussian noise (N(0,1)) (Fig. 4i) to give 1000 noise only(Fig. 4j)
and 1000 signal + noiseimages (Fig. 4k). Different SNR levels of the
signal + noise images were created by modifying the signal in the ROI
xels (SNR = 1, 2, and 3).
Smoothing and enhancement parameters
To test the effect of the proposed connectivity-based smoothing, we
smoothed the noise onlyand signal + noiseimages with kernels of 0,
5, 10, and 20 mm full width half maximum (FWHM) (Fig. 4l). The
smoothed data (Fig. 4m, n) was renormalised so that the noise standard
deviation was equal to 1. Variance renormalisation ensures that
smoothing of the simulated test statistic image is equivalent to smooth-
ing of the original data (as performed in a typical VBA) (Smith and
Nichols, 2009). We tested CFE performance with various combinations
of parameters E,Hand C (Fig. 4o). Specically, we selected E=0.5,1,
2, 3, 4, 5, 6, H=0.5,1,2,3,4,5,6,andC= 0, 0.25, 0.5, 0.75, 1.0.
ROC-based evaluation
We assessed the performance of CFE using a receiver operator curve
(ROC)-based approach. ROC curves are typically used to evaluate a sin-
gle inference by plotting the true-positive rate (TPR; sensitivity) verses
the false-positive rate (FPR; 1specicity) while a discrimination
threshold is varied. In xel-based analysis, we are interested in the per-
formance of many inferences, while controlling for the family-wise error
rate. To account for these multiple comparisons we assessed CFE perfor-
mance using the Alternative Free-response ROC (AFROC) method
(Chakraborty and Winter, 1990) (as also performed in Smith and
Nichols (2009)). The AFROC method controls the family-wise error
rate (FWER) by dening the false-positive rate (FPR) as the fraction of
realisations with any false positive xels anywhere in the image, while
the true-positive rate (TPR) is computed as the average number of
true-positive xels across realisations.
Specically, the ROC curves (Fig. 4r) were computed by varying a
threshold applied to the enhanced statistic images (Fig. 4p, q). The
same thresholds were applied to the enhanced noisy onlyimage and
enhanced signal + noiseimage (between zero and the maximum en-
hanced signal + noise value).
To quantitatively assess each ROC curve we computed the area
under the curve (AUC). As per Smith and Nichols (2009) we limit the
AUC calculation to FPR values less than 0.05 (since we are not interested
in FWER over 0.05) and divide the AUC by 0.05 so that it ranges from 0
Fig. 4. Schematic of the quantitativeCFE evaluations performed using simulated test-statisticimages. A FOD template(a) was used to generatea whole-brain tractogram (b) that was then
lteredusing SIFT (c). The SRI24 atlas(d) was used to extract tract ROIs(e), which were combinedwith a FOD template-derivedwhite matter xel-mask (f) to dene xel ROIs (g). h) For
all maskxels, connectivityto other xels was computed usingthe tractogram in c. For eachROI, 1000 simulatedtest-statisticimages were createdby adding noise (i) to all xelsin f and g,
to generate a noise only(j) and signal + noiseimage (k). Fixel imageswere smoothedwith a range of kernelextents (ln) and CFEenhanced (o) usinga range of values forparameters E,H
and C. Enhanced images (p and q) were evaluated by computing the area-under the curve (AUC) (s) of an AFROC curve (r).
46 D.A. Raffelt et al. / NeuroImage 117 (2015) 4055
to 1 (Fig. 4s). We visualised the AUC results using heat maps generated
with the ggplot2 R software package (Core R Team, 2013)
Application to motor neurone disease
To illustrate an in vivo application of the proposed CFE statistical in-
ference method, we performed anAFD xel-based analysis comparing a
group of motor neurone disease (MND) patients with healthy controls.
MND is characterised by progressive degeneration of motor neurons
resulting in clinical symptoms that include muscular atrophy, muscular
paralysis, and spasticity. Previous diffusion MRI studies have identied
signicant differences in white matter pathways involved in the
motor system, including the corticospinal tract and corpus callosal -
bres associated with the primary motor cortex. For a recent review of
MND diffusion MRI studies see Foerster et al. (2012, 2013).
Participants, data and pre-processing
Participants included in this study were recruited as part of a MND
study described in our previous work (Raffeltetal.,2012b). For a com-
prehensive description of participant details, acquisition protocols, and
pre-processing methods the reader is referred to Raffelt et al. (2012b).
However, for completeness we have included a brief summary of
these details below.
We acquired data from 24 healthy control subjects and 24 patients
with probable or denite MND, as dened by the revised El Escorial
criteria (Brooks et al., 2000). All patients included in this analysis were
classied as having upper motor neurone disease (Primary Lateral Scle-
rosis). Twenty-four healthy control participants were also recruited
who had no history of hypertension or cerebrovascular disease and
were not on any medications. All of the subjects gave their informed
written consent, in line with the Declaration of Helsinki, and as ap-
proved by the local Human Research Ethics Committee.
Fig. 5. Fibre tractography regions-of-interest used to identify xels with a test-statistic signal. All tracts were extracted from a whole-brain tractogram (Fig. 4c) using the SRI24 atlas
(Fig. 4d) and editedby a neurologist. All tracts in rows 14 are colouredby streamline direction (red: leftright,blue: inferiorsuperior, green: anteriorposterior). The bottom row illus-
trates tracts that would be affected in an Alzheimer's-like pathology, chosen to simulate diseases that have a more global pathology. Alzheimer's-like bre tracts include the left arcuate
fasciculus(yellow), cingulum(dark blue), anterior commissure (pink), uncinate fasciculus(green), anteriorcorpus callosum (red), and posterior corpuscallosum connecting the left and
right precuneus (light blue).
47D.A. Raffelt et al. / NeuroImage 117 (2015) 4055
MRI data were acquired using a 3 T Siemens Tim Trio (Siemens,
Erlangen, Germany) and with a 12 channel head coil. The diffusion im-
aging parameters were: 60 axial slices, TR/TE 9200/112 ms, 2.5 mm slice
thickness, 2.3 mm in plane image resolution, and an acceleration factor
of 2. Sixty-four diffusion-weighted images (b = 3000 s/mm
2
), and one
b = 0 image were acquired using echo planar imaging. Gradient
encodingvectors were uniformly distributed in space using electrostatic
repulsion (Jones et al., 1999). The acquisition time for the diffusion
dataset was 9:40 min.
Pre-processing of diffusion MRIs included EPI correction (Jenkinson,
2003), motion correction (Raffelt et al., 2012c), bias eld correction
based on the b = 0 image (Tustison et al., 2010), and up-sampling by
a factor of 2 using b-spline interpolation (Raffelt et al., 2012b). Diffusion
MR images were intensity normalised across subjects based on the me-
dian b = 0 intensity within a white matter mask. Note that the
corticospinal tract and mid body of the corpus callosum were manually
excluded from the normalisation white matter mask since T2 hyper-
intensities are observed in MND. FODs were computed using robust
constrained spherical deconvolution at l
max
=8(Tournier et al.,
2013). As described in Raffelt et al. (2012b),weusedagroupaveragere-
sponse function to estimate FODs in all subjects.
Fixel-based analysis
We compared AFD between the MND and control group over all
white matter xels. AFD is a quantitative measure derived from the
FOD (Raffelt et al., 2012b). At typical diffusion gradient pulse durations
(~30 ms) and high b-values (b = 3000 s/mm
2
), the FOD amplitude (i.e.
the AFD) along a given direction is proportional to the intra-axonal vol-
ume of axons aligned with that direction. In this work we compute a
xel-specic measure of AFD by integrating the FOD within each lobe.
As described in Smith et al. (2013), FOD lobes are rst segmented
based on FOD amplitude zero crossings, and the AFD of each lobe is in-
tegrated using a non-parametric numerical integration using a dense
sampling of the FOD over a hemisphere.
Spatial normalisation of subjects and template-based tractography
were performed as previously described in the section Quantitative
evaluation of CFE.AFDdataineachxel were smoothed using the pro-
posed connectivity-based smoothing (10 mm FWHM). The white mat-
ter analysis xel mask and xel correspondence was computed as
previously explained in the section Computing a xel analysis mask
and obtaining correspondence across subjects.
To illustrate the effect of different CFE parameters on in vivo data, we
performed several statistical tests. We chose a range of CFE parameters
(E=0.5,2,4,H= 0.5, 3, 6 and C= 0.5) based on the AUC results from
the quantitative evaluations. Statistical inference was performed using a
general linear model (GLM) and non-parametric permutation testing
(Freedman and Lane, 1983; Nichols and Holmes, 2002; Winkler et al.,
2014), with 5000 permutations. Signicant xels (FWE p b0.05) were
displayed using the mrview command in MRtrix 3 (https://github.
com/MRtrix3).
Analysis using tract-based spatial statistics
Tract-based spatial statistics (TBSS) is currently the most commonly
used method for VBA of white matter using diffusion MRI (Smith et al.,
2006). Numerous clinical studies have used the tools available as part of
the FSL software package to investigate population differences in
tensor-derived indices. We therefore included an additional analysis
to investigate the TBSS results using the MND cohort. All pre-
processing steps were performed as described above. Fractional anisot-
ropy images were computed with a non-linear tensor t using MRtrix3
(https://github.com/MRtrix3). The default TBSS pipeline was used by
performing registration, skeletonisation and statistical analysis as
per the TBSS user guide (http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/TBSS/
UserGuide).
Results
Quantitative evaluation of CFE
We evaluated CFE performancewith every combination of ROI, SNR,
smoothing extent, and CFE parameters C,Eand Hshown by the orange
boxes in Fig. 4. After careful investigation of all combinations, we includ-
ed three gures to best illustrate the inuence of each of the tested pa-
rameters (Figs. 68). For all Figs. 68the heat map plots are coloured by
the area under the curve (AUC) computed on the AFROC plots (FWE-
FPR b0.05).
Fig. 6 demonstrates the inuence of CFE parameters C,Eand Hon
a simulated test-statistic in 5 regions-of-interest (with a constant
SNR = 1 and smoothing kernel = 10 mm FWHM). Fig. 7 demon-
strates the inuence of SNR on the optimal ratio of Everses H(with
constant C= 0.5 and smoothing kernel = 10 mm). Fig. 8 demon-
strates the inuence of smoothing spatial extent with different effect
sizes (with constant C= 0.5 and arcuate fasciculus ROI).
Based on these results a number of interesting observations were
made:
1. Despite the fact that the ROIs have a broad range of properties (spa-
tial extent, curvature and crossings), the optimal H,Eand Care not
heavily ROI-dependent (Fig. 6). As indicated by the red squares,
values H=3,E=2,C= 0.5 achieves good results for all ROIs tested.
2. As Cincreases, the optimal ratio of Eand Hshifts towards a larger E
(Fig. 6). This effect can be explained by the fact that a larger Cvalue
reduces the contribution of spatial extent to the enhancement rela-
tive to the height (by reducing the inuence of long range xels
with lower connectivity).
3. The optimal Cvalue is somewhat ROI dependent (Fig.6). For example
in the arcuate, corticospinal and Alzheimer's like ROIs, higher C
values have reduced AUC values. However in both cingulum bundle
ROIs lower Cvalues perform poorly.
4. At a higher SNR, better AUC values are obtained over a wider range of
EandHvalues (Fig. 7). Values H=3,E= 2 give good results for all
SNRs (as indicated by the red squares).
5. As shown in Fig. 8, connectivity-based smoothing improves the AUC
results, but only up to a smoothing extent of 10 mm FWHM. There is
no change in AUC when increasing the smoothing extent from 10 to
20 mm. Fig. 8 demonstrates the inuence of smoothing only on the
arcuate fasciculus ROI; however this trend was observed for all
ROIs tested (data not shown).
Motor neurone disease results
Fixel-based analysis results
As shown in Fig. 9, a signicant decrease in AFD was observed in
motor neurone disease patients compared to healthycontrols. All signif-
icant xels in the brain were projected onto a coronal slice, coloured by
xel orientation (red: leftright, blue: inferiorsuperior, green: anterior
posterior) and overlaid on a single coronal slice of the mean AFD template
image.
As expected the affected xels were restricted to the motor path-
ways, namely the corticospinal tract and the interhemispheric callosal
bres interconnecting the left and right motor cortex. In addition we ob-
served a signicant reduction in AFD in the fornix. This is an interesting
nding since many studies have linked MND with frontotemporal
dementia, a disease that affects episodic memory and the fornix
(Hornberger et al., 2012).
As demonstrated by the spatial extent of the signicant region, the
sensitivity of different CFE parameter combinations matches the trend
observed in the simulation results shown in Fig. 6. We note that CFE
values of H=3,E= 2 and C= 0.5 (those that give consistently good
results in the simulations) result in a large spatial extent, including
many fornix xels.
48 D.A. Raffelt et al. / NeuroImage 117 (2015) 4055
Fig. 6. Inuence ofCFE parametersC,Eand Hon simulated pathology in ve regions-of-interest.Plots are colour-coded by AFROC area underthe curve (AUC).All plots were generated with
SNR = 1 and a connectivity-based smoothing kernel of 10 mm FWHM. As indicated by the red squares, values H=3,E=2,C= 0.5 achieve good results for all regions-of-interest.
Fig. 7. Inuence of SNR and CFE parameters (Eand H) on simulated pathology in ve regions-of-interest. Plots are colour-coded by AFROC area under the curve (AUC). All plots weregen-
erated with C= 0.5 and a connectivity-based smoothing kernel of 10 mm FWHM. Red squares indicate recommended values (H=3,E=2).
49D.A. Raffelt et al. / NeuroImage 117 (2015) 4055
Fig. 9b illustrates a single slice of xels colour-coded by p-value. As
shown by the zoomed in region of the pons (Fig. 9c), the CFE method
detects a group difference in xels specic to the corticospinal tract,
while the transpontine bres are not statistically signicant.
Tract-based spatial statistic results
Shown in Fig. 10 are the results from the TBSS analysis on the MND
cohort. A signicant decrease (p b0.05) was detected in FA in MND pa-
tients compared to controls in the corpus callosum motor pathways
(Fig. 10a). No signicant differences were detected in the corticospinal
tract. Supra-threshold voxels could be observed in the corticospinal
tract by relaxing the p-value threshold to p b0.2 (Fig. 10b); however,
as might be expected at such a lenient threshold, many voxels are also
then supra-threshold in regions that are not typically associated with
MND.
Discussion
We have outlined a novel connectivity-based xel enhancement
method for multi-subject whole-brain analysis of quantitative measures
derived from higher-order diffusion MRI models. The CFE approach uses
tractography-derived information to smooth and enhance between
xels that are structurally connected (and therefore likely share underly-
ing anatomy and pathology). This is in contrast to 3D cluster-based
methods (including TFCE), where a voxel may contribute to the en-
hancement of another if they are spatially connected by coexisting with-
in a supra-threshold cluster (even if both voxels belong to different bre
tracts). In addition to the bundle-specic smoothing and enhancement,
the primary motivation behind the CFE method is the ability to perform
tract-specic statistical inference at an individual xel level.
Quantitative evaluation of CFE
Using in vivo data with a simulated test-statistic signal, we have
demonstrated that the optimal CFE parameters are relatively insensitive
to the signal ROI and SNR (Fig. 7). This is encouraging for future xel-
based analyses since close to maximum sensitivity should be obtained
for most studies with H=3,E= 2 and C= 0.5.
In all simulations larger AUC values were obtained with EN1, which
causes the enhancement to increase more than linearly with extent size
(Figs. 68). This is in contrast to the original TFCE method (Smith and
Nichols, 2009), where the recommended E= 0.5 causes enhancement
to be scaled less than linearly with extent size. In 3D VBA of grey matter
Eb1is desirable because at the lowest values of h the sections (clusters)
can become very large, but these large low areas of support are not provid-
ing very useful spatial specicity(Smith and Nichols, 2009). However, in
CFE the extent is constrained to anatomically related xels by
tractography-based connectivity. Therefore at low values of h, unrelated
bre bundles cannot enhance each other.
Because we weight each xel's contribution to the enhancement
based on the probabilistic streamline connectivity, c
(Eq. (3)), xels
with larger connectivity values (i.e. those that we are more certain
share underlying anatomy) contribute more to the enhancement. In addi-
tion we raise c
to the power of Cto tune the inuence of connectivity; for
example when Cb1 the contribution from lower connectivities (e.g. over
long ranges) is increased. As shown by Fig. 6,C= 0.5 gives good results
for all ROIs. When CN0.5 the arcuate, corticospinal, and Alzheimer's-
like ROIs have a reduced AUC, while the two cingulum ROIs have a re-
duced AUC when Cb0.5. A possible explanation for the different behav-
iour observed in the cingulum ROIs is the mismatch between our
simulated signal and the cingulum tractography. The signal was simulat-
ed in only the coreof the cingulum bundle (Fig. 5), however the
tractography streamlines branch frequently along the entire length into
the cingulate cortex (as they do in reality), which results in many weakly
connected xels located outside the ROI. A larger Cvalue still enables
strongly-connected core xels to contribute to the enhancement, while
decreasing the contribution of more weakly connected xels.
As shown by the simulation results in Fig. 8, connectivity-based
smoothing improved AUC values up to a smoothing kernel of 10 mm
FWHM. We note that a FWHM = 10 mm kernel is relatively large
Fig. 8. Inuence of connectivity-based smoothingkernel size with different SNR andCFE parameters (Eand H).Plots are colour-coded by AFROCarea under the curve(AUC). All plots were
generated by simulatinga test-statistic signal in the arcuate fasciculus, and enhancing with C= 0.5. Red squares indicate recommended values (H=3,E=2).
50 D.A. Raffelt et al. / NeuroImage 117 (2015) 4055
compared to the sigma = 1.5 mm (FWHM = 3.5 mm) suggested in
TFCE (Smith and Nichols, 2009), however connectivity-based smooth-
ing ensures minimal blurring occurs across unrelated bre tracts, as
discussed earlier in relation to the E parameter.
The simulations included an Alzheimer's-like ROI to investigate CFE
performance with a widespread pathology containing several bre bun-
dles. As shown in Figs. 6 and 7, the Alzheimer's-like ROI gives a similar
relationship between Eand Hto the other ROIs tested. This is in contrast
to what would be expected in TFCE, where an extensive pathology is
likely to benet from a larger E/H ratio. The relative insensitivity of
CFE input parameters to small vs. extensive multi-bundle pathology is
likely another consequence of the tract-specic enhancement.
Motor neurone disease
The proposed CFE method has been recently applied in preliminary
analyses of Alzheimer's disease (Raffeltetal.,2013), temporal lobe epi-
lepsy (Raffelt et al., 2014c), adolescents born preterm (Raffelt et al.,
2014a), grey matter heterotopia (Farquharson et al., 2014), Dravet syn-
drome (Raffelt et al., 2014b), and glaucoma (Raffelt et al., 2015),
howeverthisistherst time we have used CFE to study MND (Fig. 9).
The signicant reduction in AFD of the corticospinal tract of MND pa-
tients corroborates histopathological ndings (Hughes, 1982), and
clearly demonstrates the tract specicity of the CFE method in the
brain stem region (Fig. 9c). The MND results in Fig. 9asupporttheCFE
simulations with signicant group differences being widespread with
H=3,E=2,andC= 0.5. We note that in these results the group effect
is more extensive in the right corticospinal tract (left side of the image)
compared to the left corticospinal tract. This is an encouraging nding
given that most patients in this MND cohort reported a left-sided
onset of disease (15 left, 5 bilateral, 9 right).
Inter-dependence of structurally connected xels
The CFE method assumes that group effects in white matter should
be correlated along a bre bundle since the underlying axonsshould ex-
perience similar pathology along their entire length. While this assump-
tion is sound for most developmental and neurodegenerative diseases,
it may not hold for focal lesions found in diseases such as multiple scle-
rosis, stroke or traumatic brain injury. However, we point out that these
Fig. 9. Fixel-based analysis results demonstrating a signicant decrease (FWE-corrected p b0.05) in apparent bre density (AFD) in motor neurone disease (MND) patients compared to
healthy controls. a) Signicant xels detected using various combinations of CFE parameters E and H. Fixels are coloured by direction, red: leftright, blue: inferiorsuperior, green:
anteriorposterior. b) Fixels coloured by FWE-corrected p-value. c) Zoomed in region of the pons. As shown by the many crossing bres in this region, the proposed CFE-based method
enables bre tract-specic analysis by attributing p-values to each xel in voxels containing multiple bre populations.
51D.A. Raffelt et al. / NeuroImage 117 (2015) 4055
diseasestend to be less suitedfor all VBA methods due to the spatial het-
erogeneity of the lesions across subjects. We also note that axon degen-
eration secondary to the site of the lesion is often of more interest,
which is likely to be correlated along a bre bundle's length.
By not requiring that xels are spatially connected by supra-
threshold xels, a benet of the CFE method is that two distant regions
of the same bre bundle may enhance each other even if the
interconnecting xels are sub-threshold. While this is unlikely to
occur if axons are affected along their entire length, it is feasible that
non-stationary variance (for example at bre crossings) may reduce
the test-statistic of interconnecting xels that would otherwise prevent
the co-enhancement of distant yet structurally related regions.
Fixel analysis mask construction and xel correspondence
When performing a traditional 3D voxel-based analysis, a mask is
often used to restrict the analysis to voxels of interest. In the case of a
xel-based analysis, not only do we need to identify the voxel locations
to be investigated, but also the number and orientation of xels within
the voxels.
In this work we compute the xel analysis mask by segmenting the
study-specic FOD template, then thresholding the xel AFD. Previous
work suggests that using an unbiased study-specictemplatemay
give better sensitivity and specicity to detect white matter abnormal-
ities (Van Hecke et al., 2011). An additional benet in the case of xel-
based analysis is that the xel orientations computed from the FOD
template will also be representative (an average) of the population.
We note that even with a robust neighbourhood-based FOD estimation
(Tournier et al., 2013), combined with FOD registration and reorienta-
tion (Raffelt et al., 2011, 2012a), xel orientations may still vary across
subjects. Correspondence is therefore achieved by matching the
study-specic template xel orientation to the closest xel in all sub-
jects (using a maximum angular tolerance of 30 degrees). This can be
thought of as a projection step in the angular domain (akin to a TBSS
spatial projection).
Generation of the xel mask uses a two-step approach to empirically
select AFD thresholds to ensure that xels at the grey/white interface
(where the AFD and xel orientation across subjects is variable due to
imperfect registration and partial volume with grey matter) are exclud-
ed, while xels within crossing bre regions in deep white matter are
included. It is worth emphasising that the issue of choosing the optimal
analysis mask threshold is not unique to the proposed xel-based anal-
ysis method (Ridgway et al., 2009). However the advantage of white
matter xel-based analysis (e.g. compared to grey matter voxel-based
analysis) is that white matter axons are extended in nature, and there-
fore while false-negative xels may arise from increased variance at the
periphery or an inappropriate mask threshold, group differences are
still likely to be detected in more central (connected) regions where
good registration and xel correspondence is obtained.
Analysis of quantitative measures other than AFD
While we have investigated xel-specic AFD differences in this
study, the proposed CFE method can be applied to other xel-specic
quantitative measures derived from the composite hindered and re-
stricted model of diffusion(CHARMED) model (Assaf and Basser,
2005) and the cube and sphere multi-fascicle model (CUSP-MFM)
(Scherrer and Wareld, 2012). In other preliminary work (Raffelt
et al., 2014c), we used the proposed CFE method to investigate popula-
tion differences in white matter morphometry, using in a novel
technique called xel-based morphometry (FBM). In FBM, the xel-
specic measure is based on morphometric differences in bre-bundle
cross-sectional area derived entirely from the non-linear transforma-
tions of each subject to the template.
We also note that while the proposed method was designed to in-
vestigate xel-specic measures, the CFE method could also be used
to investigate voxel-average quantities (e.g. myelin water fractions).
This would be achieved by mapping the value at each voxel to all xels
within that voxel, then using CFE as described in this work. While this is
not optimal since the quantitative measure is not xel-specicin
regions with crossing bres, smoothing and enhancement would still
be more tract-specic than if performed using traditional 3D
smoothing and clustering, and the estimated p-value of xels with-
in the same voxel will differ based on the different connectivity-
derived neighbourhoods.
Contrast to previous methods
The reduced sensitivity in the TBSS result (Fig. 10 vs. Fig. 9)maybe
due to differences in the quantitative measure (FA vs AFD), the use of a
xel vs. voxel-based measure, sub-optimal tensor b-value (3000 s/mm
2
in this study), the registration algorithm, tract-specic vs isotropic
smoothing, or the statistical method (projection vs whole-brain, spatial
vs connectivity enhancement). To eliminate most of these confounds
and compare the smoothing and statistical method only, one could com-
pare CFE to the multi-bre version of TBSS approach (Jbabdi et al., 2010).
This would require images to be aligned with the FOD-registration-
derived warps, before projecting xel-specicAFDvaluesontotheFA-
skeleton. However, the multi-bre TBSS method can only analyse a max-
imum of two xels per voxel. The centrum semiovale (a region containing
signicant xels in the MND result) contains many voxels with three
xels (corticospinal tract, superior longitudinal fasciculus, and corpus
callosum) and therefore it is not possible to correctly convert/map AFD
xel images to the MF-TBSS two-xel format. In addition to this issue, a
comprehensive and fair comparison of TBSS and CFE sensitivity and spec-
icity should ideally be performed using ground truth simulated patholo-
gy (in several white matter regions) and is therefore beyond the scope of
this current work.
Fig. 10.Tract-based spatialstatistic (TBSS)results demonstrating a reduction in fractionalanisotropy in the MNDpopulation comparedto controls. a) Signicant voxels(p b0.05) a re over-
laid on the template FA skeleton. Differences were observed in the corpus callosum region associated with the motor cortex, with no voxels being signicant in the corticospinal tract.
b) When the p-value threshold is relaxed to 0.2, supra-threshold voxels are observed in the corticospinal tract; however at this threshold other regions not typically associated with
MND are also supra-threshold. For both images the orientation shown is coronal (top left), sagittal (top right) and axial (bottom left).
52 D.A. Raffelt et al. / NeuroImage 117 (2015) 4055
We included an off-the-shelfTBSS analysis in this paper since TBSS
is the mostcommonly used method for voxel-based analysis in diffusion
MRI. However, TBSS is very different in kind to the whole-brain xel-
based analysis presented in this work. TBSS is often cited as a whole-
brain voxel-based method; however only a very small percentage of
the white matter is investigated since the skeletonisation and projection
step is based on regions with high FA (and therefore the majority of
white matter voxels with crossing bres and low FA are excluded
from analysis). Part of the motivation behind the projection step in
TBSS is to improve alignments in FA-based registration. However, recent
work suggests that using more advanced DTI registration improves
white matter alignment, while the TBSS projection stepactually reduces
detection accuracy and produces less biologically plausible results
in vivo compared to a whole-brain VBA (Bach et al., 2014; De Groot
et al., 2013; Schwarz et al., 2014). In this present work, we perform reg-
istration using FODimages that contain high contrast within white mat-
ter (Raffeltetal.,2011), and therefore good correspondence is achieved
across subjects at the xel-level for all major bre tracts. Furthermore,
the TBSS projection step may also fail to capture group differences in pa-
thology (where the FA is low), since the projection step is based on high
FA voxels. In the context of the multi-bre TBSS method (Jbabdi et al.,
2010), high FA voxels are more likely to contain single bre populations,
and therefore voxels with multiple xels (that typically have low FA)
are also less likely to be included in the analysis.
Tract-based spatial statistics (TBSS) is the most commonly used
method for VBA of white matter using diffusion MRI (Smith et al.,
2006). Furthermore, TBSS is insensitive to cases where pathology may
affect a low FA subset of axons belonging to a bundle (since the projec-
tion step preferentially selects high FA voxels). The xel-based analysis
method proposed in this work tests all white matter regions and there-
fore does not suffer from this limitation.
More recent work has extended the TBSS framework to investigate
higher order models with multiple xel-specic quantitative measures
per voxel (Jbabdi et al., 2010). However this approach still relies on
tract skeleton projection and therefore only tests a relatively small frac-
tion of whitematter. Moreover, the tract skeletonisation and projection
procedure rely on high FA voxels that are more likely to contain single
bre populations, and therefore voxels with multiple xels are less like-
ly to be included in the analysis.
To our knowledge, the only other VBA method to test bre-specic in-
formation from higher order diffusion MRI models was presented in our
previous work (Raffeltetal.,2012b). This approach enabled group com-
parisons of AFD that was derived by sampling the FOD uniformly over
many directions within each voxel. That method is therefore limited to
quantitative measures derived from continuous spherical functions, and
is very sensitive to subtle miss alignments in bre orientations due to im-
perfect image registration. In contrast, the proposed CFE method is not
sensitive to small bre orientation misalignments since we obtain xel
correspondence using the group-average xelanalysismaskwithanan-
gular tolerance of 30°. Furthermore, since a single sc alar quantity is t est-
ed per xel, other xel-specicdiffusionMRImeasurescanbe
investigated using CFE (as discussed in Section 4.5).
Implementation considerations
We implemented the proposed CFE statistical inference method in a
command called xelcfestats, as part of the freely-available open-source
cross-platform MRtrix software package (https://github.com/MRtrix3).
The xelcfestats command is multi-threaded and therefore computation
time decreases linearly with the number of CPU cores. At typical DWI
resolution (2.5 mm), 5000 permutations can be completed in several
hours on a standard desktop PC. On high resolution data (1.25 mm)
5000 permutations can be completed overnight, however more memo-
ry is required (N64 GB).
When computing the whole-brain tractogram the total number of
streamlines should be sufcient to achieve precise xelxel connectivity
estimates. In this work we used 30 million streamlines, which were sub-
sequently ltered with SIFT to a total 3 million streamlines (Smith et al.,
2013). We chose 3 million since this was the maximum possible given
memory limitations, however in practise 2 million streamlines should
be sufcient. Note that SIFT is an important step to remove tractography
biases (e.g. over seeding in large tracts) and improve xelxel connec-
tivity estimates. Other work conceptually related to SIFT suggests that
weighting streamlines to t the underlying data may also help to remove
false-positive connections (Daducci et al., 2014).
Limitations
In a similar approach to Smith and Nichols (2009), we assessed CFE
performance using a test-statistic image generated by adding stationary
Gaussian noise to a fake signal, and smoothing with a stationary kernel.
However in vivo generated test-statistic images are inherently nonsta-
tionary due to spatial variations in scanner SNR and anatomical variabil-
ity. Nonstationary smoothness is problematic because larger clusters
are expected in smoother areas by chance. Stationary random eld the-
ory cluster-based approaches can fail to control the FWER in such cases.
The random eld theory approach has been adapted for non-stationary
smoothness (Worsley et al., 1999), but has been found to work well
only for high degrees of freedom and high smoothness (Hayasaka
et al., 2004). Importantly, permutation-based approaches control
FWER in all cases, though versions wrongly assuming stationarity will
exhibit non-stationary sensitivity, motivating non-stationary versions.
Hayasaka et al. (2004) evaluated a permutation approach that used
the estimated local smoothness, while Salimi-Khorshidi et al. (2011)ad-
just cluster sizes using a resampling-based estimate of nonstationarity.
The latter approach can be employed to adjust both cluster sizes and
TFCE (or CFE) output. It is important to note that while cluster-extent
is strongly affected by non-stationary smoothness, methods that com-
bine extent and height, such as cluster-mass and TFCE, are expected to
be more robust to non-stationary smoothness, since the larger clusters
in smoother areas will tend to have reducedheights. This was supported
by experimental results for TFCE by Salimi-Khorshidi et al. (2011),and
is likely to hold for CFE as well. Nevertheless, the lack of non-
stationary effects in our simulations must be acknowledged as a limita-
tion, and we planto investigate approaches like that of Salimi-Khorshidi
et al. (2011) in future work. Our results on real (presumably non-
stationary) MND data provide reassurance that the optimal parameters
identied in the simulations should still be appropriate for in vivo
studies.
Edden and Jones (2011) identied an orientational bias in the statis-
tical sensitivity of TBSS method: bre pathways in the tract-skeleton
that are oblique to the image grid are represented with more voxels
and are more likely to be signicant than those aligned with the grid.
In CFE there is no tract skeleton, but when computing the xelxel
connectivity, more streamlines are likely to traverse through a voxel
when the bre is oriented obliquely. It's therefore possible that an
oblique xel may be structurally connected to more xels and have a
larger extent, e,comparedtoaxel aligned with the image axis. Future
experiments will investigate this, alongside potential adjustments like
that of Salimi-Khorshidi et al. (2011).
Our simulations encompassed 50,700 combinations of ROI, effect
size, smoothing and CFE parameters. However, we did not explore the
effect of different tractography algorithms and parameters on the com-
puted xelxel connectivity matrix. Certain parameters may inuence
the tractography output (e.g. probabilistic spread) and therefore the ac-
curacy and sparsity of the connectivity matrix. Further investigation on
this is warranted but is beyond the scope of this work.
Conclusion
In this work we have introduced a novel approach for whole-brain
statistical analysis of xel-based measures derived from higher order
53D.A. Raffelt et al. / NeuroImage 117 (2015) 4055
diffusion MRI models. The CFE method exploits connectivity informa-
tion derived from probabilistic tractography to ensure pre-smoothing
and enhancement is performed using xels that are likely to share un-
derlying anatomy and pathology. Simulations suggest that enhance-
ment parameters are relatively insensitive to the simulated pathology
ROI and SNR, and therefore we can recommend a single set of parame-
ters (H=3,E=2,C= 0.5) that should give near optimal results in fu-
ture studies where the group effect is unknown. We demonstrated the
proposed method by comparinga group of MND patients to control sub-
jects and achieve good results with the simulation-derived parameters.
In addition to providing tract-specic smoothing and enhancement, the
key benetof the CFE method is to permit xel-specic statistical infer-
ence that should yield more interpretable results in white matter re-
gions that contain crossing bres.
Acknowledgments
We are grateful to the National Health and Medical Research Council
(NHMRC) of Australia and the Victorian Government's Operational In-
frastructure Support Program for their support. GRR is supported by
the UK Medical Research Council (grant number MR/J014257/1). The
Wellcome Trust Centre for Neuroimaging is supported by core funding
from the Wellcome Trust (grant number 091593/Z/10/Z).
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55D.A. Raffelt et al. / NeuroImage 117 (2015) 4055
... We employ MRtrix3's fixel-based diffusion imaging pipeline, which has not previously been used to analyze white matter correlates of OCS. This recently developed DWI analysis approach [26,27] represents an advance on traditional tensor model-derived diffusion metrics in that it estimates whitematter properties for individual fiber bundle populations within voxels that contain complex crossing architecture; fixel-based analysis has been shown to better capture anatomicallyestablished ground truth than tensor-based analysis [28]. Our primary focus here is on the fixel-based analyses, which have the potential to allow greater insight into the nature of white-matter abnormalities than fractional anisotropy (FA), an older measure. ...
... A pair of DWI scans were obtained using a twice-refocused spin-echo SS EPI sequence, with a total of 64 directions with b = 1000 and 7 unweighted (b = 0) scans; voxel size 1.875 × 1.875 × 1.875, PE direction = AP, TR/TE = 8100/81. Full acquisition details are described in [26,36]. ...
... All participants' data were subjected to visual inspection by an experienced analyst (RGG) prior to inclusion in the analysis pipeline; 90 participants were excluded based on the presence of visually apparent MR artifacts (venetian blinding artifacts, FOV errors, and cerebellar hyperintensities). Fixel-based processing steps were conducted using MRtrix3 software suite (version RC3), according to the procedures outlined in the MRtrix3 documentation [26]). Full details of the analytic workflow can be found in Supplementary Materials. ...
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Obsessive-compulsive symptoms (OCS) are common in school-aged children and predict the development of obsessive compulsive disorder (OCD). White-matter abnormalities have been described in OCD, but the white matter correlates of OCS in the developing brain are unclear. Some correlates of OCS (or a diagnosis of OCD) may reflect correlates of a transdiagnostic or even general psychopathology factor. We examined these questions in a large sample of typically developing youth (N = 1208), using a hierarchical analysis of fixel-based white matter measures in relation to OCS and general psychopathology. General psychopathology was associated with abnormalities in the posterior corpus callosum and forceps major in an age-dependent manner, suggesting altered maturation (specifically, hypermaturation in younger subjects). A unidimensional measure of OCS did not associate with any white-matter abnormalities, but analysis of separate OCS dimensions (derived from factor analysis within this sample) revealed the ‘Bad Thoughts’ dimension to associate with white-matter abnormalities in dorsal parietal white-matter and descending corticospinal tracts, and the ‘Symmetry’ dimension to associate with abnormalities in the anterior corpus callosum. Repetition/checking and Symmetry OCS were additionally associated with posterior abnormalities overlapping with the correlates of general psychopathology. Contamination symptoms had no white-matter correlates. Secondary analysis of fractional anisotropy (FA) revealed distinct white-matter abnormalities, suggesting that fixel-based and FA analyses identify distinct features of white matter relevant to psychopathology. These findings suggest that OCS dimensions correlate with dissociable abnormalities in white matter, implicating separable networks. Future studies should examine these white-matter signatures in a longitudinal framework.
... However, DTI cannot effectively model two or more crossing fibers within a given voxel; crossing fibers are thought to comprise up to ~90% of white matter (WM) voxels (Jeurissen et al., 2013;Schilling et al., 2018;Yeh et al., 2013). One method for addressing crossing fibers that is increasingly ascendant is fixel-based analysis (FBA; Raffelt et al., 2015Raffelt et al., , 2017. A fixel refers to a specific fiber population in a voxel; with FBA, multiple distinct fiber populations can be estimated within a voxel and multiple fiber-specific properties can be quantified (Raffelt et al., 2015(Raffelt et al., , 2017. ...
... One method for addressing crossing fibers that is increasingly ascendant is fixel-based analysis (FBA; Raffelt et al., 2015Raffelt et al., , 2017. A fixel refers to a specific fiber population in a voxel; with FBA, multiple distinct fiber populations can be estimated within a voxel and multiple fiber-specific properties can be quantified (Raffelt et al., 2015(Raffelt et al., , 2017. The FBA pipeline typically includes two parts. ...
... However, current tools have two limitations. First, CFE has high memory demands, which may scale by image resolution and sample size (Raffelt et al., 2015). This impedes the application of FBA in large-scale dMRI data resources that include thousands of participants; e.g., the Philadelphia Neurodevelopmental Cohort (PNC; Satterthwaite et al., 2014), the Human reduce the dimensionality of the data and use regional summary measures, even if it is not scientifically optimal. ...
Preprint
Diffusion MRI is the dominant non-invasive imaging method used to characterize white matter organization in health and disease. Increasingly, fiber-specific properties within a voxel are analyzed using fixels. While tools for conducting statistical analyses of fixel data exist, currently available tools are memory intensive, difficult to scale to large datasets, and support only a limited number of statistical models. Here we introduce ModelArray, a memory-efficient R package for mass-univariate statistical analysis of fixel data. With only several lines of code, even large fixel datasets can be analyzed using a standard personal computer. At present, ModelArray supports linear models as well as generalized additive models (GAMs), which are particularly useful for studying nonlinear effects in lifespan data. Detailed memory profiling revealed that ModelArray required only limited memory even for large datasets. As an example, we applied ModelArray to fixel data derived from diffusion images acquired as part of the Philadelphia Neurodevelopmental Cohort (n=938). ModelArray required far less memory than existing tools and revealed anticipated nonlinear developmental effects in white matter. Moving forward, ModelArray is supported by an open-source software development model that can incorporate additional statistical models and other imaging data types. Taken together, ModelArray provides an efficient and flexible platform for statistical analysis of fixel data. HIGHLIGHTS ModelArray is an R package for mass-univariate statistical analysis of fixel data ModelArray is memory-efficient even for large-scale datasets ModelArray supports linear and nonlinear modeling and is extensible to more models ModelArray facilitates easy statistical analysis of large-scale fixel data Graphical abstract
... Fixel-based analysis (FBA) We analyzed individual fiber-specific properties in the presence of crossing fiber populations ('fixels') (Raffelt et al., 2015), following the steps described in (Raffelt et al., 2017), using the tools available in MRtrix3 . A WM mask was computed for each subject, followed by global signal intensity normalization of the DWI, which was performed across subjects by dividing all volumes by the median b = 0 s/mm2 intensity. ...
... Next, the SIFT algorithm (Smith et al., 2013) was used to select a subset of streamlines (n=2 million) that best fit the diffusion signal and therefore reduce tractography biases. Based on the probabilistic tractography, the structural connectivity metric between fixels was obtained by performing the Connectivity-based fixel enhancement (CFE) tool (Raffelt et al., 2015). ...
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We determined the intersubject association between rhythmic entrainment abilities of human subjects during a synchronization continuation tapping task (SCT) and the macro and microstructural properties of their superficial (SWM) and deep (dWM) white matter. Diffusion-weighted images were obtained from 32 subjects who also performed the SCT with auditory or visual metronomes and five tempos ranging from 550 to 950 ms. We developed a method to determine the fiber density of U-fibers running tangentially to the cortex. Notably, the right audiomotor system showed individual differences in the density of U-fibers that were correlated with the degree of predictive entrainment across subjects. These correlations were selective for the synchronization epoch with auditory metronomes and were specific for tempos around 1.5 Hz. In addition, there was a significant association between predictive rhythmic entrainment and the density and bundle diameter of the corpus callosum (CC), forming a chronotopic map where behavioural correlations of short and long intervals were found with the anterior and posterior portions of the CC. Finally, the fiber bundle cross-section of the arcuate fasciculus, the CC, and the Superior Longitudinal Fasciculus showed a significant correlation with the mean asynchronies of the auditory SCT. These findings suggest that the structural properties of the SWM and dWM in the audiomotor system support the predictive abilities of subjects during rhythmic tapping, where the density of cortical U-fibers are linked to the preferred tapping tempo, while the bundle properties of CC define an interval selective topography that has an anterior posterior gradient.
... Recently emerged high-order dMRI models provide novel estimates to assess specific microstructural features of WM and cGM using high angular resolution diffusion imaging (HARDI) data. For instance, the fixel-based analysis (FBA) ( Raffelt et al., 2015( Raffelt et al., , 2017 method could disentangle crossing fibers within a voxel to characterize individual fiber components, such as the fiber density (FD) and fiber cross-section (FC); and neurite orientation dispersion and density imaging (NODDI) ( Zhang et al., 2012 ) decomposed brain tissue to intraand extra-neurite compartments and offers intracellular volume fraction (ICV) and orientation dispersion index (ODI) measurements. These advanced dMRI measurements have been used to study WM and cGM in neonates and children ( Karmacharya et al., 2018 ;Kelly et al., 2020 ;Pannek et al., 2018 ). ...
... FBA ( Raffelt et al., 2015( Raffelt et al., , 2017 was performed using the MRtrix3 MSMT-CSD pipeline ( Jeurissen et al., 2014 ). Participants were categorized into 3 groups based on PMA, including TEA-1 month, 1-3 months, and 3-5 months groups. ...
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Association fibers connect the cortical regions and experience rapid development involving myelination and axonal growth during infancy. Yet, the spatiotemporal patterns of microstructural changes along these tracts, as well as the developmental interaction between the white matter (WM) tracts and the cortical gray matter (cGM) connected to them, are mostly unknown during infancy. In this study, we performed a diffusion MRI-based tractography and microstructure study in a cohort of 89 healthy preterm-born infants with gestational age at birth between 28.1∼36.4 weeks and postmenstrual age at scan between 39.9∼59.9 weeks. Results revealed that several C-shaped fibers, such as the arcuate fasciculus, cingulum, and uncinate fasciculus, demonstrated symmetrical along-tract profiles; and the horizontally oriented running fibers, including the inferior fronto-occipital fasciculus and the inferior longitudinal fasciculus, demonstrated an anterior-posterior developmental gradient. This study characterized the along-tract profiles using fixel-based analysis and revealed that the fiber cross-section (FC) of all five association fibers demonstrated a fluctuating increase with age, while the fiber density (FD) monotonically increase with age. NODDI was utilized to analyze the microstructural development of cGM and indicated cGM connected to the anterior end of the association fibers developed faster than that of the posterior end during 0-5 months. Notably, a mediation analysis was used to explore the relation between the development of WM and associated cGM, and demonstrated a partial mediation effect of FD in WM on the development of intracellular volume (ICV) in cGM and a full mediation effect of ICV on the growth of FD in most fibers, suggesting a predominant mediation of cGM on the WM development. Furthermore, for assessing whether those results were biased by prematurity, we compared preterm- and term-born neonates with matched scan age, gender, and multiple births from the developing human connectome project (dHCP) dataset to assess the effect of preterm-birth, and the results indicated a similar developmental pattern of the association fibers and their attached cGM. These findings presented a comprehensive picture of the major association fibers during early infancy and deciphered the developmental interaction between WM and cGM in this period.
... Neural group differences. Whole-brain FBA metrics (FDC, FD, and log-FC) were compared between groups using non-parametric permutation testing (5000 permutations) with connectivity-based fixel enhancement (Raffelt et al., 2015) to derive family-wise error (FWE) corrected fixel-wise p-values. Age, sex, and scanner were included as covariates of no interest. ...
Article
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Tuberous sclerosis complex is a rare genetic multisystem condition that is associated with a high prevalence of neurodevelopmental disorders such as autism and attention-deficit/hyperactivity disorder. The underlying neural mechanisms of the emergence of these symptom domains in tuberous sclerosis complex remain unclear. Here, we use fixel-based analysis of diffusion-weighted imaging, which allows for the differentiation between multiple fibre populations within a voxel, to compare white matter properties in 16 participants with tuberous sclerosis complex (aged 11-19) and 12 age and sex matched control participants. We further tested associations between white matter alterations and autism and inattention symptoms as well as cognitive ability in participants with tuberous sclerosis complex. Compared to controls, participants with tuberous sclerosis complex showed reduced fibre density cross-section (FDC) in the dorsal branch of right superior longitudinal fasciculus and bilateral inferior longitudinal fasciculus, reduced fibre density (FD) in bilateral tapetum, and reduced fibre cross-section (FC) in the ventral branch of right superior longitudinal fasciculus. In participants with tuberous sclerosis complex, the extent of FDC reductions in right superior longitudinal fasciculus was significantly associated with autism traits (social communication difficulties and restricted, repetitive behaviours), whereas FDC reductions in right inferior longitudinal fasciculus were associated with inattention. The observed white matter alterations were unrelated to cognitive ability. Our findings shed light on the fibre-specific biophysical properties of white matter alterations in tuberous sclerosis complex and suggest that these regional changes are selectively associated with the severity of neurodevelopmental symptoms.
... 20 The FD for the fiber population within a single voxel was calculated using a fixel-based approach. 40 We identified WM microstructural changes in the COV+ group: a reduction in FD in several bundles, such as the arcuate fasciculus, cingulum, fornix, inferior fronto-occipital fasciculus, inferior longitudinal fasciculus, superior longitudinal fasciculus, uncinate fasciculus, corona radiata, corticospinal tract, and corpus callosum, in comparison to the COV-group. Reduced FD suggests that intra-axonal volume reduction of specific fiber populations (e.g., axonal loss) might be a contributing factor to the pathological substrate for post-COVID symptoms and deserves further exploration. ...
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Background Fatigue and cognitive complaints are the most frequent persistent symptoms in patients after severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection. This study aimed to assess fatigue and neuropsychological performance and investigate changes in the thickness and volume of gray matter (GM) and microstructural abnormalities in the white matter (WM) in a group of patients with mild-to-moderate coronavirus disease 2019 (COVID-19). Methods We studied 56 COVID-19 patients and 37 matched controls using magnetic resonance imaging (MRI). Cognition was assessed using Montreal Cognitive Assessment and Cambridge Neuropsychological Test Automated Battery, and fatigue was assessed using Chalder Fatigue Scale (CFQ-11). T1-weighted MRI was used to assess GM thickness and volume. Fiber-specific apparent fiber density (FD), free water index, and diffusion tensor imaging data were extracted using diffusion-weighted MRI (d-MRI). d-MRI data were correlated with clinical and cognitive measures using partial correlations and general linear modeling. Results COVID-19 patients had mild-to-moderate acute illness (95% non-hospitalized). The average period between real-time quantitative reverse transcription polymerase chain reaction-based diagnosis and clinical/MRI assessments was 93.3 (±26.4) days. The COVID-19 group had higher CFQ-11 scores than the control group (p < 0.001). There were no differences in neuropsychological performance between groups. The COVID-19 group had lower FD in the association, projection, and commissural tracts, but no change in GM. The corona radiata, corticospinal tract, corpus callosum, arcuate fasciculus, cingulate, fornix, inferior fronto-occipital fasciculus, inferior longitudinal fasciculus, superior longitudinal fasciculus, and uncinate fasciculus were involved. CFQ-11 scores correlated with microstructural changes in patients with COVID-19. Conclusions Quantitative d-MRI detected changes in the WM microstructure of patients recovering from COVID-19. This study suggests a possible brain substrate underlying the symptoms caused by SARS-CoV-2 during medium- to long-term recovery.
... The significance threshold was P < 0.05 (TFCE and FWE corrected). Whole brain fiber density and fiberbundle cross-section area were also compared between the patients and NCs, with significant differences estimated with 5000 permutations using non-parametric permutation testing and FWE corrected p value 54 . To explore whether WM functional signals could predict subject's behavior, multiple stepwise linear regression analyses were employed to examine the relation of WM functional signals to clinical variables (UMSARS-I, UMSARS-II, and SARA) in the patient group. ...
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Advances in fMRI of brain white matter (WM) have established the feasibility of understanding how functional signals of WM evolve with brain diseases. By combining functional signals with structural features of WM, the current study characterizes functional and structural impairments of WM in cerebelar type multiple system atrophy, with the goal to derive new mechanistic insights into the pathological progression of this disease. Our analysis of 30 well-diagnosed patients revealed pronounced decreases in functional connectivity in WM bundles of the cerebellum and brainstem, and concomitant local structural alterations that depended on the disease stage. The novel findings implicate a critical time point in the pathological evolution of the disease, which could guide optimal therapeutic interventions. Furthermore, fMRI signals of impaired WM bundles exhibited superior sensitivity in differentiating initial disease development, which demonstrates great potential of using these signals to inform disease management.
... Age and intracranial volume were included as nuisance covariates. Connectivity-based smoothing and statistical inference were performed using connectivity-based fixel enhancement (CFE), using 2 million streamlines from the template tractogram and default smoothing parameters (smoothing = 10 mm full-width half-maximum) 61 . Family-wise error (FWE)-corrected p-values were assigned to each fixel using non-parametric permutation testing over 5000 permutations 62 . ...
Article
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Sports-related concussion, a form of mild traumatic brain injury, is characterised by transient disturbances of brain function. There is increasing evidence that functional brain changes may be driven by subtle abnormalities in white matter microstructure, and diffusion MRI has been instrumental in demonstrating these white matter abnormalities in vivo. However, the reported location and direction of the observed white matter changes in mild traumatic brain injury are variable, likely attributable to the inherent limitations of the white matter models used. This cross-sectional study applies an advanced and robust technique known as fixel-based analysis to investigate fibre tract-specific abnormalities in professional Australian Football League players with a recent mild traumatic brain injury. We used the fixel-based analysis framework to identify common abnormalities found in specific fibre tracts in participants with an acute injury (≤ 12 days after injury; n = 14). We then assessed whether similar changes exist in subacute injury (> 12 days and < 3 months after injury; n = 15). The control group was 29 neurologically healthy control participants. We assessed microstructural differences in fibre density and fibre bundle morphology and performed whole-brain fixel-based analysis to compare groups. Subsequent tract-of-interest analyses were performed within five selected white matter tracts to investigate the relationship between the observed tract-specific abnormalities and days since injury and the relationship between these tract-specific changes with cognitive abnormalities. Our whole-brain analyses revealed significant increases in fibre density and bundle cross-section in the acute mild traumatic brain injury group when compared to controls. The acute mild traumatic brain injury group showed even more extensive differences when compared to the subacute injury group than to controls. The fibre structures affected in acute concussion included the corpus callosum, left prefrontal and left parahippocampal white matter. The fibre density and cross-sectional increases were independent of time since injury in the acute injury group, and were not associated with cognitive deficits. Overall, this study demonstrates that acute mild traumatic brain injury is characterised by specific white matter abnormalities, which are compatible with tract-specific cytotoxic oedema. These potential oedematous changes were absent in our subacute mild traumatic brain injury participants, suggesting that they may normalise within 12 days after injury, although subtle abnormalities may persist in the subacute stage. Future longitudinal studies are needed to elucidate individualised recovery after brain injury.
Article
Purpose The goal of this study is to validate the muscle architecture derived from both ex vivo and in vivo diffusion-weighted magnetic resonance imaging (dMRI) of the human tongue with histology of an ex vivo tongue. Method dMRI was acquired with a 200-direction high angular resolution diffusion imaging (HARDI) diffusion scheme for both a postmortem head (imaged within 48 hr after death) and a healthy volunteer. After MRI, the postmortem head was fixed and the tongue excised for hematoxylin and eosin (H&E) staining and histology imaging. Structure tensor images were generated from the stained images to better demonstrate muscle fiber orientations. The tongue muscle fiber orientations, estimated from dMRI, were visualized using the tractogram, a novel representation of crossing fiber orientations, and compared against the histology images of the ex vivo tongue. Results Muscle fibers identified in the tractograms showed good correspondence with those appearing in the histology images. We further demonstrated tongue muscle architecture in in vivo tractograms for the entire tongue. Conclusion The study demonstrates that dMRI can accurately reveal the complex muscle architecture of the human tongue and may potentially benefit planning and evaluation of oral surgery and research on speech and swallowing.
Article
Background: Diffusion MRI (dMRI) is known to be sensitive to hypoxic-ischemic encephalopathy (HIE). However, existing dMRI studies used simple diffusion tensor metrics and focused only on a few selected cerebral regions, which cannot provide a comprehensive picture of microstructural injury. Purpose: To systematically characterize the microstructural alterations in mild, moderate, and severe HIE neonates compared to healthy neonates with advanced dMRI using region of interest (ROI), tract, and fixel-based analyses. Study type: Prospective. Population: A total of 42 neonates (24 males and 18 females). Field strength/sequence: 3-T, diffusion-weighted echo-planar imaging. Assessment: Fractional anisotropy (FA), mean diffusivity (MD), radial diffusivity (RD), axial diffusivity (AD), fiber density (FD), fiber cross-section (FC), and fiber density and cross-section (FDC) were calculated in 40 ROIs and 6 tracts. Fixel-based analysis was performed to assess group differences in individual fiber components within a voxel (fixel). Statistical tests: One-way analysis of covariance (ANCOVA) to compare dMRI metrics among severe/moderate/mild HIE and control groups and general linear model for fixel-wise group differences (age, sex, and body weight as covariates). Adjusted P value < 0.05 was considered statistically significant. Results: For severe HIE, ROI-based analysis revealed widespread regions, including the deep nuclei and white matter with reduced FA, while in moderate injury, only FC was decreased around the posterior watershed zones. Tract-based analysis demonstrated significantly reduced FA, FD, and FC in the right inferior fronto-occipital fasciculus (IFOF), right inferior longitudinal fasciculus (ILF), and splenium of corpus callosum (SCC) in moderate HIE, and in right IFOF and left anterior thalamic radiation (ATR) in mild HIE. Correspondingly, we found altered fixels in the right middle-posterior IFOF and ILF, and in the central-to-right part of SCC in moderate HIE. Data conclusion: For severe HIE, extensive microstructural injury was identified. For moderate-mild HIE, association fiber injury in posterior watershed area with a rightward lateralization was found. Evidence level: 1 TECHNICAL EFFICACY: Stage 3.