Connectivity-based ﬁxel enhancement: Whole-brain statistical analysis
of diffusion MRI measures in the presence of crossing ﬁbres
David A. Raffelt
, J-Donald Tournier
, David N. Vaughan
, Robert Henderson
, Alan Connelly
Florey Institute of Neuroscience and Mental Health, Melbourne, Victoria, Australia
FMRIB Centre, Nufﬁeld Department of Clinical Neurosciences, University of Oxford, Oxford, UK
Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, London, UK
Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, UK.
Centre for the Developing Brain, King's CollegeLondon, London, United Kingdom
Florey Department of Neuroscience and Mental Health, University of Melbourne, Melbourne, Victoria, Australia.
Department of Medicine, Austin Health and Northern Health, University of Melbourne, Melbourne, Victoria, Australia.
The Australian e-Health Research Centre, CSIRO-Digital Productivity Flagship, Royal Brisbane and Women's Hospital, Herston, Australia
Department of Neurology, Royal Brisbane and Women's Hospital, Herston, Australia
Received 27 February 2015
Accepted 15 May 2015
Available online 22 May 2015
In brain regions containing crossing ﬁbre bundles, voxel-average diffusion MRI measures such as fractional an-
isotropy (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 spe-
ciﬁcﬁbre population within a voxel containing crossing ﬁbres (herein we use ﬁxel to refer to a speciﬁcﬁbre 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 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 ﬁxelenhancement (CFE). CFEuses probabilistic tractography
to identify structurally connected ﬁxels that are likely to share underlying anatomy and pathology. Probabilistic
connectivity information is thenused for tract-speciﬁc 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 speciﬁcityusingalargenumberofcombinationsofCFE
enhancement parameters and smoothing extents, using simulated pathology generated with a range of test-
statisticsignal-to-noise ratios in ﬁvedifferent white matter regions(chosen to covera broad range of ﬁbrebundle
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 ﬁbre density between motor neurone disease (MND) patients with control subjects. The MND results
illustrate the beneﬁtofﬁxel-speciﬁc statistical inference in white matter regions that contain crossing ﬁbres.
© 2015 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license
NeuroImage 117 (2015) 40–55
Abbreviations:AFD, apparentﬁbre density;AFROC, alternativefree-response receiver operatorcurve;AUC, area under the curve;CFE, connectivity-based ﬁxel enhancement; CHARMED,
compositehindered and restricted modelof diffusion; CUSP-MFM, cubeand sphere multi-fascicle model; DWI, diffusion-weighted imaging;FA, fractionalanisotropy; Fixel,a speciﬁcﬁbre
population within a voxel; FBA, ﬁxel-based ana lysis; FOD, ﬁbre 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
informedﬁltering oftractograms;SNR, signal to noise;SPM, statistical parametric mapping; TBSS, tract-based spatial statistics; TFCE,threshold-freecluster e nhancement; V BA, voxel-b ased
⁎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@ﬂorey.edu.au (D.A. Raffelt).
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
journal homepage: www.elsevier.com/locate/ynimg
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 speciﬁc 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 ﬁelds 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,
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
One caveat in VBA is the need to account for the large number of
multiple tests during statistical inference. Random ﬁeld 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
apredeﬁned 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 ﬁeld 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.ﬁl.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-speciﬁc 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 ﬁbres, each
belonging to a speciﬁcwhite matter tract with a unique function (a
scenario often referred to as crossing ﬁbres). Recent evidence sug-
gests up to 90% of white matter voxels contain two or more ﬁbre
populations (Jeurissen et al., 2012). Ideally VBA of diffusion MRI
should be able to attribute any signiﬁcant effect to a speciﬁcﬁbre
population in regions with crossing ﬁbres.
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
ﬁbre tract, but not necessarily with all voxel neighbours isotropically
(as is assumed to be the case in grey matter) (see Fig. 1).
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 ﬁbre populations, and ill-deﬁned when adjacent ﬁbre pop-
ulations belong to different ﬁbre 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 ﬁbres.
In recent years, a number of quantitative measures have been pro-
posed that can be assigned to a speciﬁcﬁbre 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: left–right, green: anterior–posterior, blue: inferior–superior). Notall voxels adjacent
to the voxel of interest(yellow voxel withinthe optic radiation)are relevant for smoothing and cluster formation since neighbouring voxels containdifferentﬁbre 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.
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) 40–55
given voxel. Here we coin the term ﬁxel
to refer to a speciﬁcpopulation
of ﬁbres 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 ﬁxel-speciﬁc quantitative measures without making
some assumptions about the diffusion within a single ﬁxel. As a conse-
quence, all ﬁxel-speciﬁc 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 ﬁxel
is estimated by assuming a restricted model of diffusion for each ﬁxel
(Assaf and Basser, 2005). In a similar concept, the apparent ﬁbre 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 Warﬁeld (2012)
use a novel acquisition scheme and ﬁtting procedure (called cube and
sphere multi-fascicle model, CUSP-MFM) to model the intra-axonal dif-
fusion for each ﬁxel with a diffusion tensor. In CUSP-MFM ﬁxel-speciﬁc
volume fractions and diffusivities can be estimated.
All of these ﬁxel-based measures have the potential to give more
speciﬁc information than tensor-derived measures by identifying spe-
ciﬁc white matter tracts that are affected in regions with crossing ﬁbres.
However, due to issues 1 and 2 outlined above, traditional 3D statistical
software packages cannot be applied to perform VBA on these ﬁbre-
In this work we propose a novel statistical framework entitled
connectivity-based ﬁxel enhancement(CFE) for performinggroup com-
parisonsor correlations of ﬁxel-speciﬁc measures within all of the white
matter (i.e. a ﬁxel-based analysis, FBA). We use whole-brain probabilis-
tic tractography on a group average template to deﬁne the connectivity
between each ﬁxel and all other ﬁxels in the brain, and use this ﬁxel-
ﬁxel connectivity information for both smoothing (i.e. ﬁxel-speciﬁc
measures are smoothed only with other ﬁxels that share common
streamlines), and to boost the belief in (enhance) the test-statistic of
each ﬁxel based on information from structurally connected ﬁxels. We
investigate the proposed method using quantitative simulations, and
demonstrate its utility by comparing a cohort of motor neurone disease
patients with healthy controls.
To visually demonstrate the concept of ﬁxel connectivity, consider
the example shown in Fig. 2.Fig. 2a, b shows a group-average template
generated via registration of ﬁbre orientation distribution (FOD) images
(Raffeltetal.,2011). The location and direction of all white matterﬁxels
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/ﬁbre 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 ﬁxels directly, and therefore may not require an explicit
segmentation step). For this example, consider ﬁxel findicated by the
blue arrow in Fig. 2d. Probabilistic streamlines are used to compute
the connectivity to all other white matter ﬁxels (Fig. 2d shows only
those streamlines extracted from the whole-brain tractogram that tra-
verse ﬁxel f). We deﬁne the connectivity from ﬁxel fto ﬁxel i,c
the proportion of the streamlines traversing ﬁxel fthat also traverse
ﬁxel 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.
). In Fig. 2e, each ﬁxel is coloured by c
: this demonstrates how
the use of probabilistic tractography provides a mechanism to quantify
ﬁxel–ﬁxel connectivity based on uncertainty in the estimated ﬁbre ori-
entations, i.e. we are more conﬁdent that ﬁxels with a high density of
the dispersing streamlines are likely to share underlying anatomy
(and therefore be correlated) with ﬁxel f.
When computing the whole-brain ﬁxel–ﬁxel connectivity matrix,
streamlines are assigned to ﬁxels 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
ﬁxel–ﬁxel connectivity values, c
that are less than 0.01. This eliminates
many ﬁxels connected by spurious probabilistically-unlikely stream-
lines, and also increases the sparsity (and therefore decreases the re-
quired memory) of the whole-brain ﬁxel–ﬁxel connectivity matrix.
The ﬁrst application of ﬁxel–ﬁxel connectivity is to weight
neighbourhood ﬁxels 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 ﬁxel–ﬁxel connectivity
weights (Fig. 2e). Connectivity-based smoothing ensures that ﬁxel-
speciﬁc measures are smoothed locally with ﬁxels belonging to the
same ﬁbre tract, and preferentially smooths data with ﬁxels with high
connectivity values, whose ﬁxel data are mostlikely to correlate strong-
ly with that of the ﬁxel of interest. We note that smoothing could be
achieved by using connectivity weights only (Fig. 2e), since values are
larger in local ﬁxels due to probabilistic streamline dispersal. However,
by spatially restricting smoothing with a Gaussian kernel, data are less
likely to be smoothed with remote ﬁxels containing very different
values. This may be an issue for some quantitative measures that vary
along a bundle’s length (e.g measures related to ﬁxel volume fraction
will vary based amount of crossing with other ﬁbres).
Connectivity-based ﬁxel enhancement
The second application of ﬁxel–ﬁxel connectivity is in statistical in-
ference. Here we present a novel approach for ﬁxel-based statistics
called connectivity-based ﬁxel enhancement (CFE).
Conventional cluster-based statistical analysis involves applying a
pre-speciﬁed 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 identiﬁed, 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 ﬁeld 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 scientiﬁcinterpretation.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
Previous publications have used the word ‘ﬁbre’(Assaf and Basser, 2005; Behrens
et al., 2007)(Assaf and Basser, 2005), ‘fascicle’(Scherrer and Warﬁeld, 2012)or‘ﬁbre pop-
ulation’(Behrens et al., 2007; Raffeltet al., 2012b) to referto a speciﬁc populationof ﬁbres
within a single voxel. However, these terms can be ambiguousin certain contexts.For ex-
ample,when attributinga quantitative measure to a ‘ﬁbre’, it may be misinterpreted as be-
longing to the entire ﬁbre bundle. Here, we introduce a new word ‘ﬁxel’to eliminate this
ambiguity when discussing ﬁxel-speciﬁc measures and ﬁxel-based analysis (FBA).
42 D.A. Raffelt et al. / NeuroImage 117 (2015) 40–55
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
. More spe-
ciﬁcally TFCE is deﬁned as:
with default values of constants E= 0.5, H= 2. Note that these defaults
are justiﬁed 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 speciﬁcity (Smith and Nichols, 2009)).
CFE is a TFCE-like approach that exploits connectivity information to
enhance the test-statistic of each ﬁxel based on the support lent to it by
other structurally connected ﬁxels. In the original TFCE paper (Smith
and Nichols, 2009), the cluster extent eis deﬁned as the number of
supra-threshold voxels spatially connected to voxel v. However in CFE,
we redeﬁne eas the weighted sum of ﬁxels structurally connected to
the ﬁxel being enhanced, f.Precisely,CFEisdeﬁned as:
where n(h) is the total number of supra-threshold ﬁxels connected to f,
is the connectivity deﬁned as the proportion of streamlines traversing
ﬁxel fthat also traverse ﬁxel i, and Cis a constant. By weighting each
ﬁxel by c
, highly connected ﬁxels (i.e. those that we are more certain
share many axons) contribute more to the enhancement than ﬁxels
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 ﬁxels
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 ﬁxel may enhance another as long as it is struc-
turally connected, without any requirement that the ﬁxels 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 ﬁxels are likely to
share underlying anatomy and pathology, without any need to assume
that supra-threshold ﬁxels must be spatially contiguous.
Fig. 3 contains an illustrative example of connectivity-based smooth-
ing and CFE enhancement to an artiﬁcially 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 identiﬁed (via streamline visitations) and
assigned a signal value of one (Fig. 3d). All non-arcuate (background)
ﬁxels 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 ‘signal’ﬁxels are separated from
the background ﬁxels, all images in Fig. 3e–h are windowed such that
the colour bar range extends from the 1st to 99th percentile ofthe back-
ground ﬁxel values. Fixels indicated in white are therefore larger than
Fig. 2. Illustration of ﬁxel–ﬁxel connectivity and smoothing. a) A group-average FOD template colour-coded by direction (red: left–right, blue: inferior–superior, green: anterior–posterior).
b) Zoomed in region from a, showing individual FODs within the group-average FOD template. c) The direction and number of ﬁxels in each voxel was computed by segmenting each FOD
in a (coloured by ﬁxel orientation). d) A single exemplar ﬁxel f(blue arrow, belonging to the superior longitudinal fasciculus), with associated probabilistic streamlines. e) Fixels colour-
coded by ‘connectivity’toﬁxel f. The connectivity, c
between exemplar ﬁxel fand ﬁxel iis deﬁned as the proportion of streamlines traversing ﬁxelfthat also traverse ﬁxel i. f) A spatial Gaussian
kernel centred on ﬁxel, f, is multiplied with ﬁxel connectivity in d to estimate the ﬁxel-speciﬁc smoothing neig hbourhood weights shown in f. g) Smoothing neighbourhood weights for ﬁxel, f,
used to smooth ﬁxel data prior to analysis.
43D.A. Raffelt et al. / NeuroImage 117 (2015) 40–55
(separated from) the vast majority of background values. As shown in
Fig. 3f and g, both smoothing alone and CFE alone separate many signal
ﬁxels from the background; however the combination of smoothing
and CFE achieves the best result (Fig. 3h).
Computing a ﬁxel analysis mask and obtaining correspondence across
Whole-brain ﬁxel–ﬁxel connectivity is computed between all ﬁxels
in template space. We deﬁne the location and orientation of all template
ﬁxels using a “ﬁxel 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
In this work (see Section 2.8), we compute the ﬁxel analysis mask by
ﬁrst computing a population-speciﬁc 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 ﬁxel orientations are corrected by reorientation of each
FOD (Raffelt et al., 2012a). The FOD template is computed by averaging
the spherical harmonic coefﬁcients across all registered FOD images. To
identify all ﬁxels 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 ﬁxels from the analysis
mask by thresholding the ﬁxel AFD (as computed by integrating the
FOD amplitude within each FOD lobe (Smith et al., 2013)). We note
that thresholding ﬁxels based on the AFD may undesirably exclude
other ﬁxels in crossing ﬁbre regions that have low AFD (due to partial
volume effects). We therefore compute the ﬁxel analysis mask using a
two-step process. First a relatively high AFD threshold (N0.33) is used
to exclude all unwanted ﬁxels with poor correspondence near the
grey matter interface. From this result we then compute a 3D voxel
mask deﬁning all voxels that contain at least 1 ﬁxel. The AFD threshold
is then relaxed (N0.1) to include ﬁxels with small AFD values (i.e.
those in crossing ﬁbre regions) while excluding all ﬁxels outside the
3D voxel mask.
The beneﬁt of using a study-speciﬁcﬁxel analysismask is that the lo-
cation and orientation of ﬁxels are representative of the population. The
mask is therefore a good candidate for obtaining ﬁxel correspondence
across subjects by matching each template ﬁxel to the nearest ﬁxel in
each of the subject images. Note that if no ﬁxel exists in a subject
image for a given template ﬁxel (with a maximum angular tolerance
of 30°), then it is assigned a quantitative value of zero. If a ﬁxel exists
in the subject that does not map to a template ﬁxel then it is ignored.
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 ﬁxels' test statistics after CFE (i.e. the CFE procedure
is applied to the statistic image for every permutation, effectively
becoming part of the deﬁnition 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 ﬁxel 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 ﬁxel–ﬁxel connectivity for smoothing
and enhancement. Streamlines are coloured by direction (red: left–right, blue: inferior–superior, green: anterior–posterior). b) A tract-of-interest, the arcuate fasciculus, was extracted
from the whole-braintractogram in a (note thatonly streamlinesbelonging to the sliceare shown). c) Individualﬁxels belongingto the arcuate fasciculus were identiﬁed basedon stream-
line visitation. All arcuate ﬁxels wereassigned a ‘signal’of one. d) Zoomedin region of the ‘signalonly’image in c showing the arcuate fasciculus ﬁxelsin white and background(zero) ﬁxels
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 e–f are windowed based on the 1st to 99th percentile of the background ﬁxel values.
44 D.A. Raffelt et al. / NeuroImage 117 (2015) 40–55
45D.A. Raffelt et al. / NeuroImage 117 (2015) 40–55
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 inﬂuence 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
, 2.3 mm. Motion correction,bias ﬁeld
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
(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 ﬁnal 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 ﬁltering of tractograms (SIFT) method to give
aﬁnal count of 3 million streamlines (Fig. 4c) (Smith et al., 2013).
We chose to evaluate CFE by generating a test-statistic signal in ﬁve
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 (ﬁbre bundle length, thickness, curvature and number of
crossings). The arcuate fasciculus has a large proportion of crossing ﬁ-
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 ﬁbres (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/offramps”into 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 ﬁbre 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 ﬁbre ROI (Fig. 4e), streamlines were extracted from
the template-generated tractogram using grey matter include-regions
deﬁned by the SRI24 atlas (Fig. 4d) (Rohlﬁng 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 deﬁned 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 ﬁnal ROIs did not contain regions traversed by
relatively few (probabilistically unlikely) streamlines.
Generating test-statistic images
We computed a white matter ﬁxel mask as described in the section
‘Computing a ﬁxel analysis mask and obtaining correspondence across
subjects’(Fig. 4f). A binary ﬁxel signal image for each ROI (Fig. 4g)
was created by mapping streamlines (Fig. 4e) to associated ﬁxels 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 + noise’images (Fig. 4k). Different SNR levels of the
signal + noise images were created by modifying the signal in the ROI
ﬁxels (SNR = 1, 2, and 3).
Smoothing and enhancement parameters
To test the effect of the proposed connectivity-based smoothing, we
smoothed the ‘noise only’and ‘signal + noise’images 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). Speciﬁcally, 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.
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; 1—speciﬁcity) while a discrimination
threshold is varied. In ﬁxel-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 deﬁning the false-positive rate (FPR) as the fraction of
realisations with any false positive ﬁxels anywhere in the image, while
the true-positive rate (TPR) is computed as the average number of
true-positive ﬁxels across realisations.
Speciﬁcally, 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 only’image and
‘enhanced signal + noise’image (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
ﬁlteredusing SIFT (c). The SRI24 atlas(d) was used to extract tract ROIs(e), which were combinedwith a FOD template-derivedwhite matter ﬁxel-mask (f) to deﬁne ﬁxel ROIs (g). h) For
all maskﬁxels, connectivityto other ﬁxels was computed usingthe tractogram in c. For eachROI, 1000 simulatedtest-statisticimages were createdby adding noise (i) to all ﬁxelsin f and g,
to generate a noise only(j) and signal + noiseimage (k). Fixel imageswere smoothedwith a range of kernelextents (l–n) 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) 40–55
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 ﬁxel-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 identiﬁed
signiﬁcant differences in white matter pathways involved in the
motor system, including the corticospinal tract and corpus callosal ﬁ-
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 deﬁnite MND, as deﬁned by the revised El Escorial
criteria (Brooks et al., 2000). All patients included in this analysis were
classiﬁed 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 ﬁxels 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 1–4 are colouredby streamline direction (red: left–right,blue: inferior–superior, green: anterior–posterior). 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 ﬁbre 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) 40–55
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
), 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 ﬁeld 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
=8(Tournier et al.,
2013). As described in Raffelt et al. (2012b),weusedagroupaveragere-
sponse function to estimate FODs in all subjects.
We compared AFD between the MND and control group over all
white matter ﬁxels. 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
), 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
ﬁxel-speciﬁc measure of AFD by integrating the FOD within each lobe.
As described in Smith et al. (2013), FOD lobes are ﬁrst 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’.AFDdataineachﬁxel were smoothed using the pro-
posed connectivity-based smoothing (10 mm FWHM). The white mat-
ter analysis ﬁxel mask and ﬁxel correspondence was computed as
previously explained in the section ‘Computing a ﬁxel 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. Signiﬁcant ﬁxels (FWE p b0.05) were
displayed using the mrview command in MRtrix 3 (https://github.
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 ﬁt 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/
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 ﬁgures to best illustrate the inﬂuence of each of the tested pa-
rameters (Figs. 6–8). For all Figs. 6–8the heat map plots are coloured by
the area under the curve (AUC) computed on the AFROC plots (FWE-
Fig. 6 demonstrates the inﬂuence 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 inﬂuence of SNR on the optimal ratio of Everses H(with
constant C= 0.5 and smoothing kernel = 10 mm). Fig. 8 demon-
strates the inﬂuence 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
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 inﬂuence of long range ﬁxels
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 inﬂuence 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 signiﬁcant decrease in AFD was observed in
motor neurone disease patients compared to healthycontrols. All signif-
icant ﬁxels in the brain were projected onto a coronal slice, coloured by
ﬁxel orientation (red: left–right, blue: inferior–superior, green: anterior–
posterior) and overlaid on a single coronal slice of the mean AFD template
As expected the affected ﬁxels were restricted to the motor path-
ways, namely the corticospinal tract and the interhemispheric callosal
ﬁbres interconnecting the left and right motor cortex. In addition we ob-
served a signiﬁcant reduction in AFD in the fornix. This is an interesting
ﬁnding 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 signiﬁcant 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 ﬁxels.
48 D.A. Raffelt et al. / NeuroImage 117 (2015) 40–55
Fig. 6. Inﬂuence ofCFE parametersC,Eand Hon simulated pathology in ﬁve 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. Inﬂuence of SNR and CFE parameters (Eand H) on simulated pathology in ﬁve 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) 40–55
Fig. 9b illustrates a single slice of ﬁxels 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 ﬁxels speciﬁc to the corticospinal tract,
while the transpontine ﬁbres are not statistically signiﬁcant.
Tract-based spatial statistic results
Shown in Fig. 10 are the results from the TBSS analysis on the MND
cohort. A signiﬁcant decrease (p b0.05) was detected in FA in MND pa-
tients compared to controls in the corpus callosum motor pathways
(Fig. 10a). No signiﬁcant 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
We have outlined a novel connectivity-based ﬁxel 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
ﬁxels 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 ﬁbre
tracts). In addition to the bundle-speciﬁc smoothing and enhancement,
the primary motivation behind the CFE method is the ability to perform
tract-speciﬁc statistical inference at an individual ﬁxel 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 ﬁxel-
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. 6–8). 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 speciﬁcity”(Smith and Nichols, 2009). However, in
CFE the extent is constrained to anatomically related ﬁxels by
tractography-based connectivity. Therefore at low values of h, unrelated
ﬁbre bundles cannot enhance each other.
Because we weight each ﬁxel's contribution to the enhancement
based on the probabilistic streamline connectivity, c
(Eq. (3)), ﬁxels
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 inﬂuence 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 ‘core’of 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 ﬁxels located outside the ROI. A larger Cvalue still enables
strongly-connected core ﬁxels to contribute to the enhancement, while
decreasing the contribution of more weakly connected ﬁxels.
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. Inﬂuence 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) 40–55
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 ﬁbre 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 ﬁbre 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 beneﬁt 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-speciﬁc 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),
howeverthisistheﬁrst time we have used CFE to study MND (Fig. 9).
The signiﬁcant reduction in AFD of the corticospinal tract of MND pa-
tients corroborates histopathological ﬁndings (Hughes, 1982), and
clearly demonstrates the tract speciﬁcity of the CFE method in the
brain stem region (Fig. 9c). The MND results in Fig. 9asupporttheCFE
simulations with signiﬁcant 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 ﬁnding
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 ﬁxels
The CFE method assumes that group effects in white matter should
be correlated along a ﬁbre 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 signiﬁcant decrease (FWE-corrected p b0.05) in apparent ﬁbre density (AFD) in motor neurone disease (MND) patients compared to
healthy controls. a) Signiﬁcant ﬁxels detected using various combinations of CFE parameters E and H. Fixels are coloured by direction, red: left–right, blue: inferior–superior, green:
anterior–posterior. b) Fixels coloured by FWE-corrected p-value. c) Zoomed in region of the pons. As shown by the many crossing ﬁbres in this region, the proposed CFE-based method
enables ﬁbre tract-speciﬁc analysis by attributing p-values to each ﬁxel in voxels containing multiple ﬁbre populations.
51D.A. Raffelt et al. / NeuroImage 117 (2015) 40–55
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 ﬁbre bundle's length.
By not requiring that ﬁxels are spatially connected by supra-
threshold ﬁxels, a beneﬁt of the CFE method is that two distant regions
of the same ﬁbre bundle may enhance each other even if the
interconnecting ﬁxels 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 ﬁbre crossings) may reduce
the test-statistic of interconnecting ﬁxels that would otherwise prevent
the co-enhancement of distant yet structurally related regions.
Fixel analysis mask construction and ﬁxel 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
ﬁxel-based analysis, not only do we need to identify the voxel locations
to be investigated, but also the number and orientation of ﬁxels within
In this work we compute the ﬁxel analysis mask by segmenting the
study-speciﬁc FOD template, then thresholding the ﬁxel AFD. Previous
work suggests that using an unbiased study-speciﬁctemplatemay
give better sensitivity and speciﬁcity to detect white matter abnormal-
ities (Van Hecke et al., 2011). An additional beneﬁt in the case of ﬁxel-
based analysis is that the ﬁxel 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), ﬁxel orientations may still vary across
subjects. Correspondence is therefore achieved by matching the
study-speciﬁc template ﬁxel orientation to the closest ﬁxel 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
Generation of the ﬁxel mask uses a two-step approach to empirically
select AFD thresholds to ensure that ﬁxels at the grey/white interface
(where the AFD and ﬁxel orientation across subjects is variable due to
imperfect registration and partial volume with grey matter) are exclud-
ed, while ﬁxels within crossing ﬁbre 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 ﬁxel-based anal-
ysis method (Ridgway et al., 2009). However the advantage of white
matter ﬁxel-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 ﬁxels 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 ﬁxel correspondence is obtained.
Analysis of quantitative measures other than AFD
While we have investigated ﬁxel-speciﬁc AFD differences in this
study, the proposed CFE method can be applied to other ﬁxel-speciﬁc
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 Warﬁeld, 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 ﬁxel-based morphometry (FBM). In FBM, the ﬁxel-
speciﬁc measure is based on morphometric differences in ﬁbre-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 ﬁxel-speciﬁc 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 ﬁxels
within that voxel, then using CFE as described in this work. While this is
not optimal since the quantitative measure is not ﬁxel-speciﬁcin
regions with crossing ﬁbres, smoothing and enhancement would still
be more tract-speciﬁc than if performed using traditional 3D
smoothing and clustering, and the estimated p-value of ﬁxels with-
in the same voxel will differ based on the different connectivity-
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
ﬁxel vs. voxel-based measure, sub-optimal tensor b-value (3000 s/mm
in this study), the registration algorithm, tract-speciﬁc 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-ﬁbre version of TBSS approach (Jbabdi et al., 2010).
This would require images to be aligned with the FOD-registration-
derived warps, before projecting ﬁxel-speciﬁcAFDvaluesontotheFA-
skeleton. However, the multi-ﬁbre TBSS method can only analyse a max-
imum of two ﬁxels per voxel. The centrum semiovale (a region containing
signiﬁcant ﬁxels in the MND result) contains many voxels with three
ﬁxels (corticospinal tract, superior longitudinal fasciculus, and corpus
callosum) and therefore it is not possible to correctly convert/map AFD
ﬁxel images to the MF-TBSS two-ﬁxel format. In addition to this issue, a
comprehensive and fair comparison of TBSS and CFE sensitivity and spec-
iﬁcity 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) Signiﬁcant 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 signiﬁcant 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) 40–55
We included an ‘off-the-shelf’TBSS 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 ﬁxel-
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 ﬁbres 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 ﬁxel-level for all major ﬁbre 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-ﬁbre TBSS method (Jbabdi et al.,
2010), high FA voxels are more likely to contain single ﬁbre populations,
and therefore voxels with multiple ﬁxels (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 ﬁxel-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 ﬁxel-speciﬁc 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
ﬁbre populations, and therefore voxels with multiple ﬁxels are less like-
ly to be included in the analysis.
To our knowledge, the only other VBA method to test ﬁbre-speciﬁc 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 ﬁbre orientations due to im-
perfect image registration. In contrast, the proposed CFE method is not
sensitive to small ﬁbre orientation misalignments since we obtain ﬁxel
correspondence using the group-average ﬁxelanalysismaskwithanan-
gular tolerance of 30°. Furthermore, since a single sc alar quantity is t est-
ed per ﬁxel, other ﬁxel-speciﬁcdiffusionMRImeasurescanbe
investigated using CFE (as discussed in Section 4.5).
We implemented the proposed CFE statistical inference method in a
command called ﬁxelcfestats, as part of the freely-available open-source
cross-platform MRtrix software package (https://github.com/MRtrix3).
The ﬁxelcfestats 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 sufﬁcient to achieve precise ﬁxel–ﬁxel connectivity
estimates. In this work we used 30 million streamlines, which were sub-
sequently ﬁltered 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 sufﬁcient. Note that SIFT is an important step to remove tractography
biases (e.g. over seeding in large tracts) and improve ﬁxel–ﬁxel connec-
tivity estimates. Other work conceptually related to SIFT suggests that
weighting streamlines to ﬁt the underlying data may also help to remove
false-positive connections (Daducci et al., 2014).
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 ﬁeld the-
ory cluster-based approaches can fail to control the FWER in such cases.
The random ﬁeld 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
identiﬁed in the simulations should still be appropriate for in vivo
Edden and Jones (2011) identiﬁed an orientational bias in the statis-
tical sensitivity of TBSS method: ﬁbre pathways in the tract-skeleton
that are oblique to the image grid are represented with more voxels
and are more likely to be signiﬁcant than those aligned with the grid.
In CFE there is no tract skeleton, but when computing the ﬁxel–ﬁxel
connectivity, more streamlines are likely to traverse through a voxel
when the ﬁbre is oriented obliquely. It's therefore possible that an
oblique ﬁxel may be structurally connected to more ﬁxels and have a
larger extent, e,comparedtoaﬁxel 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 ﬁxel–ﬁxel connectivity matrix. Certain parameters may inﬂuence
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.
In this work we have introduced a novel approach for whole-brain
statistical analysis of ﬁxel-based measures derived from higher order
53D.A. Raffelt et al. / NeuroImage 117 (2015) 40–55
diffusion MRI models. The CFE method exploits connectivity informa-
tion derived from probabilistic tractography to ensure pre-smoothing
and enhancement is performed using ﬁxels 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-speciﬁc smoothing and enhancement, the
key beneﬁtof the CFE method is to permit ﬁxel-speciﬁc statistical infer-
ence that should yield more interpretable results in white matter re-
gions that contain crossing ﬁbres.
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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