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NeuroImage 241 (2021) 118417
Contents lists available at ScienceDirect
NeuroImage
journal homepage: www.elsevier.com/locate/neuroimage
Fixel-based Analysis of Diusion MRI: Methods, Applications, Challenges
and Opportunities
Thijs Dhollander
a
,
∗
, Adam Clemente
b
,
†
, Mervyn Singh
c
,
†
, Frederique Boonstra
d
, Oren Civier
e
,
Juan Dominguez Duque
c
, Natalia Egorova
f , g
, Peter Enticott
c
, Ian Fuelscher
c
, Sanuji Gajamange
h
,
Sila Genc
a , i
, Elie Gottlieb
g
, Christian Hyde
c
, Phoebe Imms
b
, Claire Kelly
a , j
, Melissa Kirkovski
c
,
Scott Kolbe
d
, Xiaoyun Liang
b , g , j
, Atul Malhotra
k , l , m
, Remika Mito
g
, Govinda Poudel
b
,
Tim J. Silk
a , c , n
, David N. Vaughan
g , o
, Julien Zanin
p
, David Raelt
g
, Karen Caeyenberghs
c
a
Developmental Imaging, Murdoch Children’s Research Institute, Melbourne, Victoria, Australia
b
Mary MacKillop Institute for Health Research, Faculty of Health Sciences, Australian Catholic University, Melbourne, Victoria, Australia
c
Cognitive Neuroscience Unit, School of Psychology, Deakin University, Geelong, Victoria, Australia
d
Department of Neuroscience, Central Clinical School, Monash University, Prahran, Victoria, Australia
e
Swinburne Neuroimaging, Swinburne University of Technology, Melbourne, Victoria, Australia
f
Melbourne School of Psychological Sciences, University of Melbourne, Melbourne, Victoria, Australia
g
Florey Institute of Neuroscience and Mental Health, University of Melbourne, Melbourne, Victoria, Australia
h
The Walter and Eliza Hall Institute of Medical Research, Melbourne, Victoria, Australia
i
Cardiff University Brain Research Imaging Centre (CUBRIC), School of Psychology, Cardiff University, Wales, United Kingdom
j
Victorian Infant Brain Studies (VIBeS), Murdoch Children’s Research Institute, Melbourne, Victoria, Australia
k
Department of Paediatrics, Monash University, Melbourne, Victoria, Australia
l
Monash Newborn, Monash Children’s Hospital, Melbourne, Victoria, Australia
m
The Ritchie Centre, Hudson Institute of Medical Research, Melbourne, Victoria, Australia
n
Department of Paediatrics, University of Melbourne, Melbourne, Victoria, Australia
o
Department of Neurology, Austin Health, Melbourne, Victoria, Australia
p
Department of Audiology and Speech Pathology, University of Melbourne, Melbourne, Victoria, Australia
Keywords:
Fixel-Based Analysis
Diusion MRI
Fixel
White matter
Microstructure
Fibre density
Fibre-bundle cross-section
Statistical analysis
Diusion MRI has provided the neuroimaging community with a powerful tool to acquire in-vivo data sensitive
to microstructural features of white matter, up to 3 orders of magnitude smaller than typical voxel sizes. The key
to extracting such valuable information lies in complex modelling techniques, which form the link between the
rich diusion MRI data and various metrics related to the microstructural organization. Over time, increasingly
advanced techniques have been developed, up to the point where some diusion MRI models can now provide
access to properties specic to individual bre populations in each voxel in the presence of multiple “crossing ”
bre pathways. While highly valuable, such bre-specic information poses unique challenges for typical image
processing pipelines and statistical analysis. In this work, we review the “Fixel-Based Analysis ”( FBA ) framework,
which implements bespoke solutions to this end. It has recently seen a stark increase in adoption for studies
of both typical (healthy) populations as well as a wide range of clinical populations. We describe the main
Abbreviations: AFD, apparent bre density; BEDPOSTX, Bayesian estimation of diusion parameters obtained using sampling techniques with modelling of crossing
bres; CFE, connectivity-based xel enhancement; CHARMED, composite hindered and restricted model of diusion; CSD, constrained spherical deconvolution; CSF,
cerebrospinal uid; dMRI, diusion magnetic resonance imaging; DTI, diusion tensor imaging; EPI, echo-planar imaging; FA, fractional anisotropy; FC, bre-bundle
cross-section; FD, bre density; FDC, bre density and cross-section; Fixel, a specic bre population within a voxel; FBA, xel-based analysis; FBM, xel-based
morphometry; FLAIR, uid-attenuated inversion recovery; FOD, bre orientation distribution; FWE, family-wise error; FWHM, full width at half maximum; GM, grey
matter; HARDI, high angular resolution diusion imaging; MD, mean diusivity; MRI, magnetic resonance imaging; MSMT-CSD, multi-shell multi-tissue constrained
spherical deconvolution; NODDI, neurite orientation dispersion and density imaging; ROI, region-of-interest; SNR, signal-to-noise ratio; SS3T-CSD, single-shell 3-tissue
constrained spherical deconvolution; SWI, susceptibility-weighted imaging; TBM, tensor-based morphometry; TBSS, tract-based spatial statistics; TFCE, threshold-free
cluster enhancement; VBA, voxel-based analysis; VBM, voxel-based morphometry; WM, white matter.
∗ Corresponding author: Murdoch Children’s Research Institute, Royal Children’s Hospital, 50 Flemington Road, Parkville, VIC 3052, Australia
E-mail addresses: thijs.dhollander@mcri.edu.au , thijs.dhollander@gmail.com (T. Dhollander).
† Adam Clemente and Mervyn Singh contributed equally to this work.
https://doi.org/10.1016/j.neuroimage.2021.118417 .
Received 22 November 2020; Received in revised form 11 July 2021; Accepted 20 July 2021
Available online 21 July 2021.
1053-8119/© 2021 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )
T. Dhollander, A. Clemente, M. Singh et al. NeuroImage 241 (2021) 118417
concepts related to Fixel-Based Analyses, as well as the methods and specic steps involved in a state-of-the-art
FBA pipeline, with a focus on providing researchers with practical advice on how to interpret results. We also
include an overview of the scope of all current FBA studies, categorized across a broad range of neuro-scientic
domains, listing key design choices and summarizing their main results and conclusions. Finally, we critically
discuss several aspects and challenges involved with the FBA framework, and outline some directions and future
opportunities.
Introduction
Diusion MRI (dMRI) has revolutionized our capabilities to study
white matter (WM) microstructure and organization in healthy and dis-
eased populations ( Jones, 2010 ; Johansen-Berg & Behrens, 2013 ): it
enables us to visualize WM bre bundles and measure properties of
their microstructure non-invasively, in-vivo and without relying on ion-
izing radiation. Over more than 2 decades, numerous dMRI guided stud-
ies have demonstrated that clinical populations present with altered
WM organization in various specic WM bre tracts (see reviews: e.g.,
Deprez et al., 2013 ; Hulkower et al., 2013 ; Pasternak et al., 2018 ). These
studies have also generally reported signicant, moderate-to-high cor-
relations between disease symptoms and dMRI derived metrics sensitive
to WM microstructure, with more severe changes in WM microstructure
typically relating to more pronounced symptoms.
The key factor enabling such studies to assess this valuable in-
formation lies in complex modelling techniques, which form the link
between the rich diusion MRI data and various metrics related to
the microstructural aspects of interest ( Novikov, Kiselev, & Jespersen,
2018 ). These include a range of biophysical models, such as the com-
posite hindered and restricted model of diusion (CHARMED) ( Assaf &
Basser, 2005 ) or the neurite orientation dispersion and density imag-
ing (NODDI) ( Zhang et al., 2012 ) model, which aim to model the dif-
fusion signal as distinct microstructural compartments with biophysi-
cal parameters; as well as more generalized representations of the dif-
fusion signal, including diusion tensor imaging (DTI) ( Basser & Pier-
paoli, 1996 ), diusion kurtosis imaging (DKI) ( Jensen et al., 2005 ) and
diusion spectrum imaging (DSI) ( Wedeen et al., 2008 ). Some of the
most commonly used approaches to date for studies of WM microstruc-
ture have been based on DTI, which provides general information on
the local orientation of white matter bres as well as metrics describ-
ing the fractional anisotropy (FA) and mean diusivity (MD). Prepro-
cessing, various tting strategies, and post-processing for DTI are well-
documented ( Van Hecke et al., 2015 ; Mori & Tournier, 2014 ). Statis-
tical analyses are often performed using region-of-interest (ROI) ap-
proaches, or voxel-based analysis (VBA) with statistical enhancement
mechanisms such as threshold-free cluster enhancement (TFCE) ( Smith
& Nichols, 2009 ), but bespoke frameworks such as tract-based spatial
statistics (TBSS) ( Smith et al., 2006 ) have also been proposed to ad-
dress specic challenges with registration and smoothing. However, DTI
(as well as several other commonly used models or signal representa-
tions) is unable to correctly represent complex geometrical WM bre
congurations generally referred to as “crossing bres ”, leading to prob-
lems with interpretation and limited biological specicity of associated
metrics, as well as various detrimental eects on processing techniques
such as streamline tractography ( Farquharson et al., 2013 ; Jones, 2010 ;
Jones et al., 2013 ). The aforementioned statistical analysis approaches
also lack mechanisms to leverage information from multiple distinct -
bre populations within voxels.
To address these challenges, a statistical analysis framework named
“Fixel-Based Analysis ”( FBA ) was proposed ( Raelt et al., 2015 , 2017 ).
In this context, a “fixel ”refers to an individual fibre population within
a vo xel , allowing for fibre-specific metrics to quantify WM properties
and changes. Unlike voxels, xels relate directly to the underlying WM
anatomy itself. In a typical FBA, xels are derived from WM bre ori-
entation distributions (FODs) as computed by constrained spherical de-
convolution (CSD) techniques ( Tournier et al., 2007 ; Jeurissen et al.,
2014 ; Dhollander & Connelly, 2016 ). A corresponding fixel-wise mea-
sure of apparent fibre density ( Raelt et al., 2012b ), more broadly re-
ferred to as “fibre density ”(FD) , can be computed directly from the FODs
themselves as well ( Raelt et al., 2015 ). Apparent FD is a measure of
white matter microstructure : its value is approximately proportional to
total intra-axonal volume under certain conditions ( Raelt et al., 2012b ;
Genc et al., 2020a ). Interestingly, macroscopic dierences of fibre-bundle
cross-section (FC) ( Raelt et al., 2017 ) can also be measured on a xel-
wise level by leveraging information from individual subject warps to
a common template space, eectively resulting in the xel-wise equiv-
alent of the traditional tensor-based morphometry (TBM) ( Ashburner &
Friston, 2000 ) approach. Finally, the xel-wise analysis of a combined
fibre density and cross-section (FDC) ( Raelt et al., 2017 ) measure leads
to an approach very similar to the well-known voxel-based morphome-
try (VBM) ( Ashburner & Friston, 2000 ) method. Using this entire range
of techniques to its full potential for the rst time, an example FBA
study was presented in Raelt et al. 2017 , comparing a clinical group of
patients with temporal lobe epilepsy to healthy controls. This revealed
statistically signicant reductions in both apparent FD and FC in bre
pathways of the aected temporal lobe in patients as compared to con-
trols. Furthermore, the combined FDC measure enabled a more sensitive
assessment of xel-wise eects, with greater eect sizes detected than
when testing apparent FD or FC alone. The core tools to implement such
FBA studies ( Raelt et al., 2015 , 2017 ) have been made available as part
of the MRtrix3 software package ( Tournier et al., 2019 ). Since the orig-
inal description of the FBA framework, several FBA studies have been
undertaken, with a particular surge in published studies in the most re-
cent years (as can be appreciated in Fig. 1 ). Despite this quickly emerg-
ing base of recent empirical work, the scope and methodological aspects
of the FBA framework have not been critically reviewed yet.
In this work, we review the FBA framework. We (1) provide an
overview of the main concepts related to the FBA framework and de-
scribe the methods and specic steps involved in modern FBA pipelines,
(2) include an overview of the scope of all current FBA studies, cate-
gorised across a broad range of neuro-scientic domains and (3) criti-
cally discuss a range of aspects and challenges involved with the FBA
framework and its various applications.
Fixel-based Analysis (FBA): Concepts and Methods
In this section, we provide an overview of the main concepts and
methods of the FBA framework, and specic steps involved in a state-of-
the-art xel-based analysis (FBA) pipeline. While the FBA framework is
unique in that it allows researchers to investigate fibre-specific properties
extracted from diusion MRI (dMRI) data, the pipeline otherwise rela-
tively closely reects the structure of a “traditional ” voxel-based analysis
(VBA) pipeline. Conceptually, the core dierence lies in the introduc-
tion of a new type of grid element, the “fixel ”, which refers to a specic
individual bre population within a voxel. While this may seem like a
relatively simple and straightforward adaptation of VBA at rst sight,
working with fixels (and bre orientation distributions, from which x-
els are typically derived) rather than voxels poses various unique chal-
lenges for some of the key steps of a typical standard VBA pipeline. A
range of works have proposed and implemented specic solutions to ad-
dress these challenges ( Raelt et al., 2011 , 2012a , 2012b , 2015 , 2017 ),
which has resulted in the current FBA framework.
2
T. Dhollander, A. Clemente, M. Singh et al. NeuroImage 241 (2021) 118417
Fig. 1. Number of xel-based analysis (FBA)
studies per year. When both a preprint as well
as a subsequent peer reviewed publication ex-
ist for a given study, this was only counted once
(towards the year of publication of the peer re-
viewed work). Incomplete data for 2021 are not
included in this plot. However, we found an ad-
ditional 17 FBA studies in the rst two months
of 2021, resulting in a total of 75 published FBA
studies (see Supplementary Document 2 ).
From voxels to fixels
In a VBA approach, image values are analyzed on a voxel-wise ba-
sis. To this end, individual subject images are spatially registered and
warped to a common template space. Because the voxel grid for which
the original image values are sampled is a discrete regular lattice, warp-
ing images to a template space requires regridding of the images to a
new (common) voxel grid. This is however trivially enabled by various
interpolation methods, which allow to sample the original image val-
ues for any set of 3D spatial coordinates. This then establishes spatial
correspondence between voxels across all subject images after warping to
and regridding in template space, allowing for direct comparison and
statistical analysis at a voxel-specic level without requiring any spatial
hypothesis a priori. Region-of-interest (ROI) type of analyses can bene-
t from this approach as well, as ROIs can be dened just once on the
template for areas where image registration has aligned all images with
sucient accuracy.
The FBA framework is centered around the concept of a fixel , a spe-
cic bre population within a voxel ( Raelt et al., 2015 ), enabling anal-
ysis of individual fibre-specific properties in the presence of crossing bre
populations. In addition to a 3D position in the spatial domain, xels
also have a (2D) orientation in the angular domain. While xels are an
adequate choice of grid element for the purpose of mapping bre-specic
metrics, they are fundamentally dierent from voxels in the context of
image processing: the xel “grid ”is derived directly from modelling of
the dMRI data themselves in each voxel ( Raelt et al., 2015 ). This has
several notable implications ( Raelt et al., 2015 , 2017 ):
1 Unlike voxels —which cover the entire spatial domain at regular po-
sitions independently of what is represented in the image data —the
fixels’ presence and orientation is directly tied to white matter (WM)
anatomy , as shown in Fig. 2 . In the angular domain, xels can have
any orientation. In the spatial domain, xel positions are still limited
to the discrete positions of an underlying voxel grid. However, x-
els do not exist everywhere in space: some voxels contain no xels.
On the other hand, some xels share the same space: some voxels
contain multiple xels.
2 Because xel orientations are linked to the WM anatomy and ob-
tained from the image data themselves, spatial transformations of
fixel-wise image data require corresponding reorientations of the fixels ,
i.e., spatial transformations imply angular transformations. For non-
rigid transformations, these reorientations can dier for xels in dif-
ferent voxels and even for individual xels contained in the same
voxel: the angles between xels in the same voxel can change. On
the upside, because xels can have any orientation, no regridding is
required in the angular domain: the local (forward) angular trans-
formation can be applied directly to the xel orientation.
3 Even though the spatial positions of xels are still restricted to those
of an underlying voxel grid, the spatial regridding required for image
transformation cannot be trivially overcome by interpolation methods in
the same way as for voxel-wise image data: there is no implied no-
tion of which xels in neighbouring voxels “belong together ”. This is
made even more clear (and challenging) by the fact that neighbour-
ing voxels can contain dierent numbers of xels, and some voxels
contain no xels at all. Put dierently, the xel grid does not exist
consistently throughout the spatial domain.
4 Even if the spatial regridding problem would be overcome (and
proper xel reorientation be applied) to map individual subject xel
images to a common template space, this still does not establish fixel-
wise correspondence across all subject images. Even though the im-
ages should align up to the accuracy of image registration and the
voxel grid is shared, the xel grids’ local presence and orientations
still relate to the individual subjects’ anatomy. Establishing a common
fixel grid is a unique challenge in and of itself.
5 Finally, for the purpose of statistics, VBA typically relies on spatial
smoothing (e.g., to boost signal-to-noise ratio and increase normality
of residuals) and statistical cluster enhancement (to improve sensi-
tivity). Both of these require a notion of local voxel neighbourhoods .
While dening an equivalent concept for xels poses yet another
challenge, this also provides a unique opportunity: a cluster of fixels
in a local part of a given WM tract could be in a neighbourhood entirely
separated from the fixels of another crossing tract , even when these
tracts overlap spatially (i.e., share voxels).
Overall, while a fixel grid is a logical and sensible extension of a voxel
grid, it is clearly not a trivial one. The FBA framework provides solutions
to the above challenges. All FBA studies to date have relied on WM
bre orientation distributions (FODs) from which both xels and xel-
wise metrics are derived ( Raelt et al., 2015 ). In this context, an FBA
pipeline “circumvents ”the challenges related to points 1 and 3 above
by delaying the computation of xels from (voxel-wise) FODs until after
the registration, warping and regridding of subject FOD images to the
3
T. Dhollander, A. Clemente, M. Singh et al. NeuroImage 241 (2021) 118417
Fig. 2. Derivation of a xel “grid ”and xel-wise apparent bre density (FD). Left : voxel-wise WM FODs (here obtained from 3-tissue CSD) serve as the source from
which both the xel grid and xel-wise apparent FD metric are computed. In this image, WM FODs in a coronal slice are overlaid on an FOD-based directionally-
encoded colour map ( Dhollander et al., 2015 ) ( red = mediolateral, green = anteroposterior, blue = superoinferior ). Middle : the xels are obtained by segmenting the
FODs into their individual “peaks ”. Unlike the regular lattice structure of the underlying voxel grid, the xel grid’s presence and orientations are tied to the WM
anatomy itself. Right : apparent bre density (FD), a fixel-wise metric, is computed as the integral of each FOD lobe ( hot colour scale ). The underlying voxel intensities
show the total voxel-wise apparent FD ( grey colour scale ). Both xel-wise and voxel-wise apparent bre densities are expressed in arbitrary units .
common template space ( Raelt et al., 2011 , 2012a , 2015 ). While point
2 (reorientation) conceptually goes hand in hand with point 3 (spatial
regridding), it is then in practice separated and performed after xels
are derived in template space ( Raelt et al., 2017 ). Finally, for points
4 and 5, unique strategies are implemented ( Raelt et al., 2015 ). A com-
mon xel grid is derived from an average FOD template and angular
correspondence of subject xels to the common xel grid is established
by identifying subject xels within a certain angular threshold. Fixel
neighbourhoods are locally derived by computing connectivity between
xels, informed by template-based streamline tractography. All these
steps and solutions are evident in the structure of the state-of-the-art
FBA pipeline as described below.
Fixel-wise metrics and apparent fibre density
In voxel-wise MRI data, the measurement(s) for each voxel relate to
underlying properties of tissue within the volume of the voxel . The same
holds for xel-wise data. However, the presence of multiple xels in a
voxel allows an individual specic xel-wise metric to relate to only
part of the contents of the voxel. The specic location of these xel-
wise compartments within the voxel is typically not known, due to the
partial volume eect. Rather, xel-wise metrics relate to properties of
the population of bres along or close to the orientation of the fixel . WM
axons of dierent crossing bre populations might for instance even
interdigitate within the voxel.
Fixel-wise metrics can be obtained from advanced dMRI mod-
els. Some dMRI models or signal representations only estimate voxel-
averaged properties: e.g., the tensor from DTI allows for the extraction
of a single principal orientation of diusion, and voxel-wise metrics such
as FA and MD can be calculated ( Basser & Pierpaoli, 1996 ). Other (typi-
cally multi-compartment) models represent xels explicitly, along with
corresponding xel-wise metrics: e.g., the CHARMED model includes
separate compartments for individual bre populations and estimates a
signal fraction for each of these ( Assaf & Basser, 2005 ). Note that not all
multi-compartment models are necessarily multi-bre models: e.g., the
NODDI model has a single intra- and extra-cellular compartment (both
relating to only a single bre population), as well as an isotropic free-
water compartment, and yields voxel-averaged measures of neurite den-
sity and orientational dispersion ( Zhang et al., 2012 ).
All FBA studies to date have relied on CSD techniques
( Tournier et al., 2007 ; Jeurissen et al., 2014 ; Dhollander & Con-
nelly, 2016 ); these estimate a WM FOD in each voxel, and some
additionally estimate separate grey matter (GM) and cerebrospinal
uid (CSF) signal compartments. The WM FOD as obtained from these
techniques is a free-form continuous angular function, i.e., it does
not explicitly represent xels and xel-wise metrics. However, the
FOD typically shows an angular contrast with several “peaks ” clearly
relating to individual bre populations. In a quantitative context, the
amplitude of the WM FOD is referred to as the apparent bre density
(AFD) ( Raelt et al., 2012b ). The AFD along a given orientation of the
WM FOD is mostly proportional to the dMRI signal perpendicular to
it. Hence, the AFD is approximately proportional to the total amount of
intra-cellular volume of axons along this orientation under certain con-
ditions, including a suciently long diusion gradient pulse duration
(e.g., ≥ 30 ms), a relatively high b-value (e.g., ≥ 3000 s/mm
2
) and
for a certain scale of microstructural features (e.g., axon diameters ≤
6 𝜇m) ( Raelt et al., 2012b ). Recent ndings have demonstrated that
the accuracy and specicity of AFD can be improved by using higher
b-values and single-shell data (as opposed to multi-shell data, which
includes lower b-values), as these choices help to suppress extra-axonal
signal ( Genc et al., 2020a ) (see also the later section on “Requirements
and effects of acquisition parameters ”for an in-depth discussion on
this topic).
In the FBA framework, xels are derived directly from the WM
FODs themselves by segmenting each FOD “lobe ” (this refers to the
shape of the FOD peaks when visualised by radial scaling of amplitudes)
( Raelt et al., 2015 ), as shown in Fig. 2 . The xel-wise total AFD is ob-
tained by integrating the AFD values across the corresponding lobe. The
nal xel-wise metric is often referred to more broadly as “fibre density ”
(FD) ( Raelt et al., 2017 ). Because the apparent FD is approximately
proportional to the total intra-cellular volume of axons within the voxel
(and along the xel), it can not distinguish between effects specific to axon
4
T. Dhollander, A. Clemente, M. Singh et al. NeuroImage 241 (2021) 118417
count or axon diameter(s): both factor into the apparent FD metric . Also note
that apparent FD is largely not sensitive to myelin , as myelin-associated
water has a very short T2 relaxation time and therefore contributes lit-
tle to the dMRI signal ( Raelt et al., 2012b ). Finally, signal related to
other non-WM tissues, cells and uids can be teased out from the WM
FOD to render the apparent FD more specic to WM only, by using
3-tissue CSD techniques such as multi-shell multi-tissue CSD (MSMT-
CSD) ( Jeurissen et al., 2014 ) and single-shell 3-tissue CSD (SS3T-CSD)
( Dhollander & Connelly, 2016 ).
While apparent FD is approximately (linearly) proportional to intra-
axonal volume, it doesn’t provide a direct absolute or standardized vol-
ume measurement of it. CSD techniques in this context are applied to
the dMRI signal without voxel-wise normalisation by the b = 0 image
( Raelt et al., 2012b ), unlike most other dMRI modelling techniques.
Not only is apparent FD expressed in arbitrary units , it also requires cor-
rection for spatial intensity inhomogeneities (bias elds) of the dMRI
data as well as some form of global intensity normalization to render
it comparable between dierent subjects within a study ( Raelt et al.,
2012b , 2017 ; Dhollander et al., 2021 ). This is in addition to using the
same acquisition hardware and parameters throughout any given study,
as well as using a single common study-specic response function (per
tissue) with the CSD method for all subjects to be compared (as reected
in relevant steps of the pipeline; see also Fig. 3 ).
Fixel-based Analysis pipeline
Even though the basic components enabling the FBA framework
were fully established earlier ( Raelt et al., 2015 , 2017 ), the implemen-
tation of various FBA studies has since been improved due to the introduc-
tion of new techniques related to preprocessing and dMRI signal modelling .
Of particular note in this context is the introduction of 3-tissue CSD tech-
niques, which can estimate GM and CSF signal compartments in addition
to the WM FOD ( Jeurissen et al., 2014 ; Dhollander & Connelly, 2016 ).
Other than an increased specicity of the WM FOD, it also enables a
more robust approach to global intensity normalization and bias eld
correction. The latter is then informed by and performed on the 3-tissue
CSD derived signal compartments themselves ( Dhollander et al., 2021 ),
rather than as a “preprocessing ”step on the original dMRI data. This
practice and the accompanying structure of the (preprocessing) pipeline
have been adopted across recent FBA studies, as 3-tissue CSD process-
ing has become possible for both multi-shell as well as single-shell dMRI
data since the introduction of the SS3T-CSD method ( Dhollander & Con-
nelly, 2016 ).
As mentioned, the FBA pipeline otherwise closely reects the over-
all structure of a “traditional ” VBA pipeline. Compared to VBA, most
additional steps relate to either dMRI-specic preprocessing earlier on
in the pipeline, and specic solutions to deal with the challenges of x-
els and xel-wise metrics later in the pipeline. The information of local
deformations obtained from the spatial warps of subject images to tem-
plate space can be used in a xel-wise fashion as well. This yields the
xel-based equivalents of tensor-based morphometry (TBM) via compu-
tation of the xel-wise “fibre-bundle cross-section ”(FC) , and voxel-based
morphometry (VBM) ( Ashburner & Friston, 2000 ) by combining FD
and FC into “fibre density and cross-section ”(FDC) ( Raelt et al., 2017 ).
The core tools to run the FBA pipeline ( Raelt et al., 2017 ) have been
made available as part of the MRtrix3 software package ( Tournier et al.,
2019 ; https://www.mrtrix.org ); and are often complemented with other
tools, e.g., for motion and distortion corrections ( Jenkinson et al., 2012 ;
https://fsl.fmrib.ox.ac.uk/fsl/ ) or SS3T-CSD ( https://3tissue.github.io ).
A schematic overview of all steps, their relationships and the overall
ow of the pipeline is provided in Fig. 3 . In Supplementary Document
1 , we describe each step with a focus on its purpose, interpretation, and
practical aspects for consideration by researchers, and we list additional
software resources.
Ultimately, the FBA pipeline yields fixel-wise statistical results and a
specic p-value is assigned to each individual xel (even in the presence
of multiple dierent xels in the same voxel). Fig. 4 shows a typical re-
sult using some of the most common visualization techniques typically
relied upon in published FBA studies. Notably, all these visualizations
present the exact same xel-wise result. While the cropped streamlines
tractogram visualization is more convenient to observe and explore the
result as a whole, it otherwise still only shows those areas where indi-
vidual xels eectively reached a threshold for statistical signicance.
However, it’s not surprising that FBA results often feature some anatom-
ical “continuity ”or a pattern of “clusteredness ”. On the one hand, for a
range of biological mechanisms it makes sense that larger parts of WM
tracts would be involved or aected, but on the other hand this is also
promoted inherently in the FBA framework itself, e.g., by connectivity-
based xel-wise smoothing and the connectivity-based xel enhance-
ment (CFE) mechanism ( Raelt et al., 2015 ).
FBA studies: Applications
We have performed a systematic search to retrieve all currently pub-
lished FBA application studies, as dened and detailed in Supplemen-
tary Document 2 . Note we also included research preprints with the
intention of more exhaustively sampling the current scope of applica-
tions. Since the introduction of the FBA framework, 75 FBA studies (66
peer-reviewed, 9 preprints) have been published. The adoption of the
FBA framework has seen a stark increase over time ( Fig. 1 ).
For convenience, we categorized all 75 FBA studies as follows:
healthy ageing and healthy adults ( Adab et al., 2020 ; Choy et al., 2020 ;
Honnedevasthana Arun et al., 2021 ; Kelley et al., 2019 ; Kelley et al.,
2021 ; Mizuguchi et al., 2019 ; Park et al., 2021 ; Radhakrishnan et al.,
2020 ; Verhelst et al., 2021 ), typical and atypical childhood develop-
ment ( Barendse et al., 2020 ; Bleker et al., 2019 ; Bleker et al., 2020 ;
Blommaert et al., 2020 ; Burley et al., 2021 ; Chahal et al., 2021a ;
Chahal et al., 2021b ; Dimond et al., 2019 ; Dimond et al., 2020 ;
Fuelscher et al., 2021 ; Genc et al., 2017 ; Genc et al., 2018 ; Genc et al.,
2020a ; Genc et al., 2020b ; Grazioplene et al., 2020 ; Hyde et al., 2021 ;
Kirkovski et al., 2020 ; Lugo-Candelas et al., 2020 ), fetal and neonatal
development ( Kelly et al., 2018 ; Kelly et al., 2020 ; Malhotra et al., 2019 ;
Pannek et al., 2018 ; Pannek et al., 2020 ; Pecheva et al., 2019 ; Wu et al.,
2020 ), psychiatric disorders ( Grazioplene et al., 2018 ; Lyon et al., 2019 ),
neurodegenerative and demyelinating disorders ( Adanyeguh et al., 2018 ;
Adanyeguh et al., 2021 ; Al-Amin et al., 2020 ; Boonstra et al., 2020 ;
Carandini et al., 2021 ; Gajamange et al., 2018 ; Janssen et al., 2020 ;
Li et al., 2020 ; Luo et al., 2020 ; Mito et al., 2018 ; Palmer et al., 2021 ;
Park et al., 2020 ; Raelt et al., 2015 ; Rau et al., 2019 ; Sakamoto et al.,
2020 ; Sanchez et al., 2020 ; Savard et al., 2020 ; Storelli et al., 2020 ;
Wang et al., 2020 ; Xiao et al., 2021 ; Zarkali et al., 2020 ; Zarkali et al.,
2021 ; Zeun et al., 2021 ), brain injury and insult ( Egorova et al., 2020 ;
Fekonja et al., 2021 ; Friedman et al., 2019 ; Gottlieb et al., 2020 ;
Verhelst et al., 2019 ; Wallace et al., 2020 ; Zamani et al., 2021 ), epilepsy
( Bauer et al., 2020 ; Raelt et al., 2017 ; Vaughan et al., 2017 ), and other
disorders ( Bishop et al., 2018 ; Haykal et al., 2019 ; Haykal et al., 2020 ;
Mu et al., 2018 ; Sleurs et al., 2018 ; Zanin et al., 2020 ).
We summarized the main results and conclusions of each study in
Supplementary Document 3 . Finally, we also documented all key
study parameters and outcomes in a comprehensive overview in Sup-
plementary Document 4 .
Discussion: Challenges and Opportunities
FBA and other dMRI analysis strategies
FBA is one amongst a range of techniques which have been used
to assess and analyse white matter microstructure. Diusion MRI data
is also commonly analysed using voxel-based analysis (VBA) of various
metrics derived from dierent diusion and microstructure models. An-
other popular analysis framework developed specically for dMRI data
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T. Dhollander, A. Clemente, M. Singh et al. NeuroImage 241 (2021) 118417
Fig. 3. The FBA pipeline reects the general structure of a VBA pipeline, but with many additional steps to appropriately process dMRI data (red boxes), FOD
images (blue boxes) and fixel-wise image data (gold boxes) . The left column shows the main flow of the pipeline. The FBA framework avoids problems related to spatial
interpolation of xel-wise image data by warping FOD images to template space instead, and delaying denition of xels to a later stage in the pipeline. In the
right columns , each box names a processing step and its resulting output. Subject-level steps are performed once per individual subject image in the study, whereas
study-level steps are computed only once for the entire study. All steps are described in detail in Supplementary Document 1 . Apart from the introduction of 3-tissue
CSD techniques and log-domain intensity normalisation, this pipeline matches all steps described originally ( Raelt et al., 2017 ). It is also broadly in line with the
online documentation provided with the MRtrix3 software ( Tournier et al., 2019 ).
is tract-based spatial statistics (TBSS) (
Smith et al., 2006 ). The major-
ity of studies applying either VBA or TBSS on dMRI data have focused
on metrics derived from diusion tensor imaging (DTI) ( Basser & Pier-
paoli, 1996 ), or more recently the neurite orientation dispersion and
density imaging (NODDI) microstructure model ( Zhang et al 2012 ).
Of note is that several FBA studies themselves have also additionally
included results based on DTI-derived metrics, e.g., fractional anisotropy
(FA): of all 75 FBA studies we included for this review, 33 studies (44%)
included additional DTI-based results via either VBA, TBSS and/or re-
gion of interest based analyses. Given limitations of the DTI model and
problems with interpretation of derived metrics ( Fig. 5 ), it is somewhat
surprising to see such results are still included quite often. One expla-
nation might be the desire to more directly relate ndings to previous
studies in the same application area (e.g., similar clinical groups), where
their conclusions typically did rely solely on DTI-based ndings. In some
cases, these studies combined and directly compared FBA and DTI nd-
ings, for instance exhibiting larger eect sizes using the FBA framework
compared to analyses based on DTI results ( Adanyeguh et al., 2018 ).
Others reported lower sensitivity of voxel-wise DTI metrics in detecting
group-wise dierences when compared to bre-specic FBA results, par-
ticularly in crossing-bre regions ( Raelt et al., 2015 ; Gajamange et al.,
2018 ; Mito et al., 2018 ; Zarkali et al., 2020 ). In another study, almost no
overlap between signicant voxel-wise DTI and xel-wise FBA ndings
was found ( Lyon et al., 2019 ), which is quite remarkable. Understanding
these discrepancies remains an ongoing challenge. Their impact is rele-
vant, as it confounds which WM structures are reported to be associated
to specic conditions in the literature over time.
FBA oers two key advantages over alternative dMRI analysis tech-
niques: sensitization to microstructure-specic properties independent
of local bre geometry, and specicity of the analysis and results with
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T. Dhollander, A. Clemente, M. Singh et al. NeuroImage 241 (2021) 118417
Fig. 4. Common visualisations of FBA results
(these all depict the same result from one of the
analyses in Mito et al. (2018) , whereby a co-
hort of Alzheimer’s disease patients was tested
for FDC decreases compared to healthy control
subjects). Panel A : direct visualization of the
xel-wise statistical results by colouring each
xel according to its p-value. Due to the partic-
ular choice of the ( hot colour ) scale bar limits,
xels with p < 0.05 are highlighted, whereas
others are black. Panel B : the same result is
visualized by cropping a whole-brain stream-
lines tractogram. Parts of streamlines are only
shown when they intersect voxels containing
xels with p < 0.05 , while running along an
orientation close to those xels. Coloring here
was chosen similar to Panel A to highlight
that this is merely a dierent visualization of
the same result. Panel C : the benet of the
streamlines visualization of an FBA result is
that it more easily allows to identify larger
continuous patterns in the result, e.g., relat-
ing to known anatomy of WM tracts. Here, the
cropped streamlines visualization is shown in
3D for the whole brain (augmented by a glass
brain volume). The researchers have addition-
ally labeled the streamlines via targeted trac-
tography approaches based on prior knowledge
of WM tract anatomy.
respect to individual be-specic eects. While DTI metrics have proven
to be sensitive to certain changes of white matter microstructural prop-
erties, they are inherently non-specific to axonal properties, and con-
ated by extra-axonal signal contamination as well as various aspects
of bre geometry (e.g., crossing bres, dispersion, etc.), rendering bio-
physical interpretations challenging, non-intuitive or even misleading
( Jones et al. 2013 ; Bach et al. 2014 ; Beaulieu 2009 ). The example
in Fig. 5 illustrates how a genuine decrease of fibre density (FD) in
presence of crossing bre populations might for instance result in an
increase of FA as derived from DTI. Typical studies of, e.g., neuro-
degeneration, based on DTI might not even recover such regions as only
decreases of FA would often be hypothesised and tested for. But even
when tested and recovered, such an eect would be counter-intuitive.
Some FBA studies have incorporated DTI analyses to highlight these
issues in areas with crossing bres. Grazioplene et al. (2018) demon-
strated in a schizophrenia cohort that signicant group dierences
of FA substantially overlapped with regions containing complex -
bre architecture: they conclude that DTI ndings could be lacking in
specicity due to macro-structural complexity and thus may not nec-
essarily reect group dierences in microstructural properties. Mito
et al. (2018) recovered regions of increased FA in crossing bre re-
gions in Alzheimer’s disease patients, and explicitly demonstrated these
to be misleading ndings reecting inherent issues of voxel-wise FA
values.
Alternative multi-compartment methods, such as neurite orienta-
tion dispersion and density imaging (NODDI) ( Zhang et al., 2012 ) have
been proposed to quantify white matter microstructural properties with
greater specicity to intra-cellular properties, and separate these from
eects due to geometry. For example, NODDI incorporates a separate
parameter for orientational dispersion of the neurite distribution, inde-
pendently of (the magnitude of) neurite density. In DTI, on the other
hand, both such eects are “entangled ”in the FA metric, leading to
the aforementioned problems. However, another distinct advantage of
FBA is its ability to analyse individual bre-specic properties separately ,
whereas VBA approaches are inherently unable to assign signicant ef-
fects to specic bre populations due to partial voluming. Even when
models (such as NODDI) do address and disentangle certain bre geom-
etry confounds, they do not per se model individual bre populations.
For example, while NODDI does account for dispersion, it does not de-
ne this for separate bre populations within a voxel. Hence, genuine
bre crossing congurations are tted as a single population with a large
amount of dispersion, and neurite density is not separately quantied for
crossing neurite populations.
Some researchers might be interested in comparing results directly
between or across different analysis frameworks and dMRI models. While
the improved specicity of FBA relative to other voxel-based analysis ap-
proaches has been well documented, it is typically dicult to relate the
nature of the eects of the various other voxel-wise diusion metrics to
a given bre-specic eect. Individual studies relying on dierent clini-
cal populations, acquisition parameters, and image processing steps only
add further to the complexity of such direct comparisons. Therefore we
would generally caution users against attempting to infer intuitive or
even complex relationships between results, as the lack of specicity of
voxel-based approaches and models renders this theoretically impossi-
ble without strong assumptions.
The aforementioned tract-based spatial statistics (TBSS) framework
( Smith et al., 2006 ) constitutes another popular approach to analyze
voxel-wise metrics (e.g., derived from DTI or NODDI). In the context
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T. Dhollander, A. Clemente, M. Singh et al. NeuroImage 241 (2021) 118417
Fig. 5. A fibre-specific decrease of apparent FD resulting in a DTI-based increase of FA , in a voxel containing crossing bres (adapted with permission from Mito
et al., 2018 ). The example depicts a voxel in the centrum semiovale, where the corticospinal tract, (lateral projections of) the corpus callosum and the superior
longitudinal fasciculus (SLF) cross. Patients show a xel-specic decrease of apparent FD in the SLF, with both other tracts unaected. DTI-based analysis will yield a
counterintuitive result in this scenario, whereby the FA is increased in such voxels. Such a change might go undetected (when increases of FA are not tested for), could
be misinterpreted (as if a certain aspect of WM microstructure has “improved ”), and cannot be attributed to any specic individual bre population or combinations
thereof due to lack of bre-specicity. Finally, note this change has even impacted on the diusion tensor’s main orientation, whereas no individual WM tract
orientations had in reality been aected.
Table 1
Comparison of key dening aspects of voxel-based analysis (VBA), tract-based spatial statistics (TBSS) and xel-based analysis (FBA). Note that tensor-
based morphometry (TBM) and voxel-based morphometry (VBM) are regarded as a type of VBA in this context.
Voxel-based analysis (VBA) Tract-based spatial statistics (TBSS) Fixel-based analysis (FBA)
Domain of analysis Entire voxel grid within the brain. Only voxels on a mean (template) FA
“skeleton ”.
Entire xel grid: mostly WM, some
(sub)cortical GM.
Specicity Voxel-level (spatial) specicity. Voxel-level specicity; limited to the
mean FA skeleton.
Fixel-level specicity for individual
xels in a voxel.
Alignment & correspondence Image registration to a common
template space and spatial
interpolation.
Image registration to a common
template space.
Thinning of FA template to obtain a
mean FA skeleton.
Project maximum subject FA value
perpendicular to mean FA skeleton
onto the skeleton voxels.
FOD-based image registration to a
common FOD template.
Segmentation of template
xels and
subject xels.
Bespoke xel correspondence criteria
to assign reoriented subject xels to
template xels.
Statistics Correction for a large number of
comparisons.
Spatial smoothing and threshold-free
cluster enhancement (TFCE).
Correction for a reduced number of
comparisons (less voxels on the FA
skeleton).
Correction for a very large number of
comparisons (typically more xels
than voxels).
Connectivity-based xel-wise
smoothing and connectivity-based
xel enhancement (CFE).
of this review and the topic of xel-specicity, to avoid confusion on
the TBSS naming (in particular the term “tract-based ”): this is eec-
tively a voxel-based technique. The problems with VBA that TBSS aims
to address are of an entirely dierent nature: they relate to challenges
with alignment of subject images (due to limited precision and accu-
racy of image registration techniques) as well as the dependence of VBA
on an arbitrary amount of smoothing (which does impact strongly on
the result) ( Smith et al., 2006 ). To put it dierently: TBSS mostly ad-
dresses existing problems of VBA related to establishing voxel-wise corre-
spondence between images . While FBA also implements a bespoke strategy
towards establishing correspondence between subject data, this is rather
to tackle new challenges introduced by the nature of fixels (see also the
earlier section “From voxels to fixels ”). Interestingly, the challenges
addressed by TBSS do remain largely present for FBA in principle. How-
ever, due to the incorporation of FOD-based population template con-
struction and registration in the pipeline, image alignment is expected
to be more accurate in the rst place ( Raelt et al., 2011 , 2012a ). We
provide a general overview comparing the key dening aspects of the
VBA (also covering TBM and VBM), TBSS and FBA approaches towards
analysis in Table 1 . For specic details on TBSS, we refer the reader to
Smith et al. (2006) and Smith et al. (2007) . All relevant details on the
FBA framework are provided in the earlier section “Fixel-based Anal-
ysis pipeline ”and Supplementary Document 1 .
Finally, as mentioned in the earlier section “Fixel-wise metrics and
apparent fibre density ”, other diusion modelling and parameter es-
timation techniques can also yield fixel-wise measures. The CHARMED
model estimates signal fractions for individual bre populations in a
voxel ( Assaf & Basser, 2005 ). Another example is the “Bayesian estima-
tion of diusion parameters obtained using sampling techniques with
modelling of crossing bres ”(BEDPOSTX) technique ( Behrens et al.,
2007 ; Jbabdi et al., 2012 ), which similarly estimates xel-wise param-
eters. The key dierence with CSD techniques is that the aforemen-
tioned methods compute xel-wise metrics directly from the dMRI data,
whereas CSD techniques yield a free-form continuous FOD rst, from
which xels are obtained later on in the FBA pipeline (see Fig. 2 for
an illustration of xel derivation from FODs, and Fig. 3 for the order of
these steps in the pipeline). This eectively makes it possible to analyse
bre-specic parameters obtained from other estimation strategies such
as CHARMED or BEDPOSTX using the FBA framework . However, since the
CSD-based FBA pipeline implements the transition from subject space
to template space by warping FOD images to avoid the problems asso-
ciated with spatial interpolation of xel-wise data, a few adjustments
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T. Dhollander, A. Clemente, M. Singh et al. NeuroImage 241 (2021) 118417
have to be made to achieve this ( Raelt et al., 2017 ). Such a pipeline
should warp the (preprocessed) dMRI data themselves directly to template
space (without reorientation). Obtaining the xels and their orienta-
tions as well as the xel-wise parameters (e.g., applying CHARMED or
BEDPOSTX) should then be performed in template space , after which x-
els can be reoriented similarly to the original pipeline ( Fig. 3 ). A solu-
tion would also have to be implemented for deriving a common xel
analysis mask. Note that for this purpose, FODs obtained from a CSD
technique could still be relied upon to build a study-specic FOD tem-
plate from which a xel analysis mask can be derived. However, the
nal xel-wise statistics would be performed directly on the parameters
derived from the other dMRI modelling technique (e.g., CHARMED or
BEDPOSTX).
Requirements and effects of acquisition parameters
Since the main goal of FBA is to investigate bre-specic eects, re-
solving individual crossing bres in the rst place is of course essential.
In this context, so-called “high angular resolution diusion imaging ”
(HARDI) gradient schemes are commonly employed to collect dMRI data
( Tuch et al., 2002 ). As the name suggests, HARDI schemes are designed
to acquire images for a large number of diusion gradient directions,
uniformly distributed over the angular domain, and typically at a con-
stant amount of diusion-weighting (i.e., a specic b-value, referred to
as a “shell ”). Hence, with the capacity to resolve crossing bres in mind,
two key parameters are to be considered: the number of diffusion gradient
directions and the b-value .
Tournier et al. (2013) have systematically investigated the re-
quired number of gradient directions to capture the angular contrast
of dMRI data for a range of b-values, up to b = 5000 s/mm
2
. Gener-
ally, while the signal (and thus also the signal-to-noise ratio (SNR)) of
dMRI data decreases for higher b-values, the angular contrast increases
with b-value . However, higher angular contrast implies higher angu-
lar frequencies of the signal, thus also increasing the required num-
ber of gradient directions to capture all features of this signal well.
Tournier et al. (2013) conrmed this by investigating the angular fre-
quency content of the signal via a spherical harmonics (SH) representa-
tion (the angular equivalent of a Fourier basis). Specically, they found
that terms beyond an SH order of 8 were negligible for all b-values up
to b = 5000 s/mm
2
. In their b-value sampling range, the trend of re-
quiring higher SH orders also levelled o around b = 3000 s/mm
2
.
The mathematical equivalent to sample an order 8 SH signal equals
45 diffusion gradient directions . What these results thus suggest is that
45 directions constitutes a sufficient HARDI sampling to capture all fea-
tures in the signal, and that those features themselves don’t manifest
much stronger beyond b = 3000 s/mm
2 (at least in the range up to
b = 5000 s/mm
2
).
However, in practice it might still be desirable to acquire data for
more than 45 gradient directions: SNR at high b-values is typically very
low, and hence more data points are useful for a robust t of various
models. On the other hand —and often overlooked —when resolving the
WM FOD using a CSD method, the non-negativity constraint on the
FOD amplitude also “injects ” information into the model tting process,
an inherent eect referred to as “super-resolved ”CSD ( Tournier et al.,
2007 ). This eect is substantial for most FODs throughout the WM, as
these are typically very sparse in the angular domain (i.e., large parts of
the angular domain have zero FOD amplitude). In practice, this means
reasonable quality WM FODs can be resolved with even less than 45 gra-
dient directions sampled. How far this can be stretched reliably is hard
to determine though, and the exact extent of it would also depend on the
local bre conguration (i.e., the sparsity of the FOD). In light of this
and the aforementioned contribution of more images to the overall SNR,
45 gradient directions can still reasonably be argued to be a good (minimum)
target to aim for when designing a HARDI protocol for the purpose of FBA .
Of the 75 FBA studies we included, 66 studies (88%) used data with 45
gradient or more gradient directions (for the highest b-value), whereas
6 studies (8%) still managed to run FBA with 30 or less gradient direc-
tions (for the highest b-value). Overall, HARDI gradient schemes appear
to be well adopted in practice.
While both the number of diusion gradient directions and the b-
value thus have an impact on the overall qualitative aspects of the WM
FODs, several FBA studies using a low number of gradient directions
and/or low b-values have still yielded fairly encouraging results, which
demonstrates that FBA is eectively feasible for such data as well as sen-
sitive to signicant eects. FBA is certainly technically compatible with
a range of angular resolutions and b-values, as these parameters do not
preclude any preprocessing steps, 3-tissue CSD reconstruction (using ei-
ther MSMT-CSD or SS3T-CSD), intensity normalization, template con-
struction, xel segmentation and reorientation, or any other steps in a
state-of-the-art FBA pipeline (see also the earlier section “Fixel-based
Analysis pipeline ”and Supplementary Document 1 ).
However, the main caveat lies in the interpretation of the apparent FD
metric (see also the earlier section “Fixel-wise metrics and apparent
fibre density ”). At a suciently high b-value, e.g., b = 3000 s/mm
2
or similar, increased specicity to the intra-axonal water signal results
in more accurate measures of apparent bre density that are approxi-
mately proportional to the total amount of intra-cellular volume of axons
under certain conditions ( Raelt et al., 2012b ; Genc et al., 2020a ). This
is achieved due to the strong attenuation of extra-axonal water signals at
such high b-values. At lower b-values, such as those commonly acquired
for DTI processing (e.g., b = 1000 s/mm
2
or similar), signals from the
extra-cellular space outside the axons will contribute to the apparent
FD metric, undermining the intended denition of the latter and thus
rendering biological interpretation challenging and fundamentally lim-
ited. For example, a clinical patient group may experience substantial
changes to the extra-cellular architecture, which would be articially
reected as a (group) dierence in apparent FD. Furthermore, eective
dierences in apparent FD due to actual changes of intra-axonal vol-
ume are likely to induce concomitant changes to the extra-cellular vol-
ume and architecture. Hence, most measured apparent FD eects will
eectively be biased at low b-values. For example, a decrease of intra-
axonal volume should result in a decrease of apparent FD reecting it;
but if this leads to a corresponding increase of the volume of the extra-
cellular space, the signal from the latter at a low b-value would also
increase and thus counteract the expected decrease in apparent FD. In
such a scenario, apparent FD eect sizes are diminished and sensitiv-
ity of the FBA to apparent FD is negatively impacted. Interestingly, this
also challenges the use of multi-shell data for the purposes of quanti-
fying apparent FD, as this introduces lower b-values as well. While it
might be intuitively appealing to use all (or generally “more ”) data to
compute the WM FOD, this is not necessarily compatible with the very
assumptions on which apparent FD relies ( Genc et al., 2020a ). Indeed,
the MSMT-CSD equations ( Jeurissen et al., 2014 ) apply to each b-value
shell in the data, and thus lower b-values will weigh in, again introduc-
ing undesirable extra-cellular signal contributions into the apparent FD
metric. Genc et al. (2020a) demonstrate this via simulations as well as
in-vivo data in a relevant FBA scenario. Their results revealed that (1)
apparent FD was estimated less accurately when lower b-value or multi-
shell data were used and showed a larger dependency on extra-cellular
signal, as compared to single-shell high b-value data and (2) using lower
b-value or multi-shell data also led to reduced sensitivity (in an exper-
iment involving age-related patterns of development). Of all 75 studies
sampled in this review, 44 studies (59%) were limited to data with b ≤
2500 s/mm
2
. Of these, 20 studies were even limited to b ≤ 1000 s/mm
2
data. While the remaining 31 studies (41%) did work with datasets with
a maximal b > 2500 s/mm
2
, 12 of those relied on multi-shell data and
included lower b-value shells to resolve the WM FOD from which the
apparent FD metric was estimated. Dimond et al. (2020) did have multi-
shell data available, but for the reasons described above they chose to
only use the highest b-value shell ( + b = 0) with SS3T-CSD to compute ap-
parent FD for FBA (and lower b-value data was used only for a separate
analysis of DTI-derived metrics). Overall, we note that —in contrast to
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T. Dhollander, A. Clemente, M. Singh et al. NeuroImage 241 (2021) 118417
HARDI gradient schemes —higher b-values are still relatively less well
adopted.
In conclusion, on the one hand, it is technically entirely feasible
to run a state-of-the-art 3-tissue CSD based FBA pipeline even on data
limited to, e.g., only 30 gradient directions and/or b-values as low as
b = 1000 s/mm
2
. This opens up possibilities for revealing xel-specic
eects in many existing older datasets, or for long-running studies that
have already “locked in ”their dMRI protocols. However, further work
may be required to assess the reliability of specic conclusions drawn
from data including low b-values. On the other hand, for new studies it
is highly advisable to collect HARDI data with, e.g., ≥ 45 gradient direc-
tions and b ≥ 3000 s/mm
2
, so as to ensure both good WM FOD quality
(which promotes robust processing) and specicity to intra-axonal sig-
nals, enabling proper quantitative interpretation of the apparent FD metric
at the core of a typical FBA.
Challenges with interpretation of FD and FC
Beyond the eects of acquisition parameters, which can complicate
or limit interpretation of apparent FD eects as explained above (e.g.,
due to partial sensitisation to extra-axonal signals at limited b-values),
other challenges with and limitations of the apparent FD metric exist. As
mentioned in the earlier section on “Fixel-wise metrics and apparent
fibre density ”, apparent FD does not tease apart eects of axon count
and axon diameters. This is an important consideration when interpret-
ing apparent FD changes, as without a proper context, e.g., thinking
of decreases in apparent FD strictly as a loss of individual axons could
constitute a critical misinterpretation of ndings. Moreover, apparent
FD is largely not sensitive to myelin ( Raelt et al., 2012b ), and thus de-
creases in apparent FD do not necessarily reveal demyelination (nor do
apparent FD increases imply myelinogenesis), even though they might
accompany or eventually follow it in a number of (biologically) realis-
tic scenarios. Note that, while dMRI signal in general is not sensitized
to myelin, it is still a popular choice to study myelin ( Mancini et al.,
2020 ). This is possible due to myelin changes indirectly aecting the
geometrical architecture of the extra-axonal space, which in turn inu-
ences parameters of certain dMRI models. However, such parameters are
also aected by a range of other eects, so they cannot be specically
interpreted as myelin ( Mancini et al., 2020 ).
Apart from the aforementioned notes on the specic sensitization of
apparent FD, another challenge is involved with its interpretation: the
mere fact that it represents a local (apparent) density metric has surpris-
ingly complex implications, which could easily be overlooked or mis-
understood. The local FD of axons provides us with a measure approxi-
mately proportional to the amount of “axonal matter ” present per unit of
volume, i.e., within a voxel (and along the xel orientation). Hence, this
depends not only on those axons themselves, but also on all the other
(non-axonal) space or volume in between . For example, a decrease in FD
could result from vasogenic edema (as might occur, e.g., after traumatic
brain injury), whereby an excess of uid accumulates in the interstitial
matrix and causes it to expand: this might simply move the axons further
apart without otherwise aecting their individual size (i.e., diameter).
Interestingly, note that several other multi-compartment dMRI models
also involve local (voxel-wise or xel-wise) density metrics: for example,
the NODDI model yields a neurite density measure ( Zhang et al., 2012 ).
As such, considerations related to interpreting a density metric are sim-
ilarly relevant.
In the vasogenic edema example, the FD metric is sensitive to the
decrease of the number of axons within a given voxel , even though no
actual axons were lost: some were merely displaced outside the voxel,
into other voxels. Macroscopically, a swelling of the tract might thus
be observed (which “compensates ”for the decreased FD). In the FBA
framework, the latter macroscopic piece of the puzzle can be assessed
by computing the fibre-bundle cross-section (FC) metric, which expresses
this property for dierent subject images relative to a common template.
This is obtained from the warps mapping each subject to the template
space, and thus relies on accurate image registration (see the section
“Fibre-bundle cross-section (FC) computation ”in Supplementary
Document 1 ). This information can then be combined with the FD metric
in a strategy akin to VBM ( Ashburner & Friston, 2000 ), resulting in the
fibre density and cross-section (FDC) metric ( Raelt et al., 2017 ). In our
edema example, the FD decrease would be offset by a similar FC increase
(i.e., the swelling), resulting in an unchanged FDC . The latter would then
ultimately reect the fact that no actual axons were lost in the overall bun-
dle. However, FDC would indeed not be sensitive to the vasogenic edema
eect, even though it might still be of critical biological relevance. Ul-
timately, the complete picture is only provided by assessing FD, FC and
FDC and jointly considering their individual decreases or increases. This
leads to many dierent possible combinations of eects, of which we
have provided a range of basic examples and more complex scenarios in
the “Combined fibre density and cross-section (FDC) computation ”
section in Supplementary Document 1 . Yet another more complex ex-
ample involving crossing bre tracts is presented in Fig. 6 . The latter
illustrates that eects within one bundle can result in (surprising) con-
comitant eects in another crossing bundle. We should note, however,
that these examples do not demonstrate any technical limitations of the
framework. Rather, they illustrate that reasoning about density and/or
cross-sectional eects is not as straightforward as it might seem at rst
sight, and interpreting such results requires careful consideration of any
possible underlying scenario that might explain these.
Finally, even the specicity in separating FD and FC eects is not
entirely clear-cut in practice: it is limited by the accuracy and preci-
sion with which image registration is able to map subject images to
the common template space and as such establish spatial (or xel-wise)
correspondence between them. The eects of registration on density
and volume assessments have been known and well described since the
introduction of VBM ( Ashburner & Friston, 2000 ), but are sometimes
overlooked in practice. In the context of FBA, these imply that part of
what “should have been ”an FC eect can be underestimated and par-
tially transfer into an FD eect instead when image registration does
not entirely bridge the spatial gap between images. This will for cer-
tain anatomical structures always be the case up to an extent, because
non-rigid registration algorithms rely on spatial regularization to ro-
bustly produce a suciently smooth mapping between images. More-
over, the amount of “transfer ”of such FC eects to FD will depend on
the size of the anatomy, and generally be more pronounced for thinner
structures (in particular those approaching the acquisition voxel size)
( Raelt et al., 2017 ). The opposite is possible as well, when strong in-
tensity dierences due to pronounced FD eects might induce a non-
linear deformation (and thus FC eect), especially when using a sum of
squared dierences metric to drive registration. Because the specicity
to distinguish FD and FC eects thus depends on spatial resolution, sizes
of dierent anatomical structures and a range of image registration pa-
rameters (e.g., regularization or smoothness of the warp) which are un-
der arbitrary control of researchers, FD and FC eect sizes can not be
meaningfully directly compared.
FD is often said to relate to microstructural eects, while FC reects
macro-structural eects. This is a useful intuition to introduce and ex-
plain complex combinations of FD, FC and FDC eects and motivate
researchers to carefully consider various biological scenarios that might
explain their results. However, we conclude that caution is advised, as
the “separation ” between FD and FC is less clear-cut due to practical
limitations of methods.
Multimodal studies
Combining complementary information from different (MRI) con-
trasts or modalities may allow for more comprehensive and insightful
conclusions than reporting FBA (or other dMRI analysis) results in iso-
lation (for reviews, see Damoiseaux and Greicius, 2009 ; Straathof et al.,
2019 ; Suárez et al., 2020 ). This is particularly important when studying
brain injured patients whereby white matter damage is not occurring
10
T. Dhollander, A. Clemente, M. Singh et al. NeuroImage 241 (2021) 118417
Fig. 6. Complex pitfalls when interpreting xel-specic FD and FC changes (example similar to Raelt et al., 2017 ; but with critical corrections to the number
of axons in the illustrated voxel). This example demonstrates how changes in one bundle of axons can explain concomitant changes in another crossing bundle. A
bundle of crossing orange ( vertical ) and blue ( perpendicular to this page ) axons are shown, and measured in the ( black ) voxel. The orange tract suers microscopic axon
loss, followed by a macroscopic collapse (atrophy) of the tissue. The blue tract features no actual axon loss, but merely “joins in ”the collapse of tissue due to the
available space. Upon initial axon loss, all results are intuitive: only FD of the orange bre population is decreased (and this is also reected in its FDC), while all
other properties ( orange FC; blue FD and FC) are unaected. However, when the tissue collapses (atrophy), a set of complex eects plays out across FD and FC values
of both orange and blue bundles . The FD of both bundles increases (!), whereas FC jointly decreases. Compared to the original “healthy ” setting, the eect size of FD
alone underrepresents the impact to the orange tract, but also describes an increase (!) for the blue tract. Arguably, FDC is “easier ”to interpret (only showing impact
on the orange bundle, with the blue bundle unaected throughout); but in turn it is not sensitized to the atrophy, which might itself indicate a biologically relevant
stage or transition in a complex disease process.
in isolation from other brain alterations, such as GM atrophy, changes
in functional connectivity, and neuro-inammation. Of the 75 stud-
ies sampled in this review, 22 employed multimodal data and analy-
sis techniques in combination with FBA of dMRI data. However, only
9 of these multimodal MRI studies quantied the relationship between
xel-wise metrics and other (e.g., structural or functional) MRI met-
rics ( Adanyeguh et al., 2018 ; Boonstra et al., 2020 ; Gajamange et al.,
2018 ; Luo et al., 2020 ; Mizuguchi et al., 2019 ; Park et al., 2021 ;
Sanchez et al., 2020 ; Savard et al., 2020 ; Vaughan et al., 2017 ). For
example, Luo et al. (2020) reported that apparent FD of the fornix col-
umn and body, and FC of ventral cingulum correlated with composite
amyloid and tau levels in Alzheimer’s disease patients. As another ex-
ample, Savard et al. (2020) observed that the amount of grey matter
atrophy was strongly related to reduced apparent FD and FC in patients
with fronto-temporal dementia. Multimodal studies can also improve in-
terpretation of ndings with regards to structure-function relationships,
e.g., progression of disease with reference to cognition and behavior.
Savard et al. (2020) were able to dissociate the contribution of apparent
FD, FC and GM volume to semantic symptoms and executive dysfunction
in fronto-temporal dementia, adding to our understanding of diering
pathophysiological paths to both types of impairment and suggesting
targets for therapy.
Despite encouraging ndings, some multimodal MRI studies combin-
ing FBA results with other modalities show a number of common limita-
tions. In many of these studies, the reported correlations between xel-
wise metrics and other measures were still just weak to moderate. Also,
appropriate correction for multiple comparisons was not always per-
formed. Sometimes uncorrected thresholds and trends were reported for
correlation analyses between xel-wise and other metrics. Such issues
are not specic to FBA studies or underlying methodology though: these
are very common among multimodal studies in general, and this prob-
lem has only recently started to attract more attention ( Alberton et al.,
2020 ). Generally, studies should aim to employ p-values adjusted for
multiple comparisons; not only for the number of xels, but also for the
testing of multiple contrasts (within FBA) as well as for multiple experi-
ments involving (combinations of) dierent modalities ( Alberton et al.,
2020 ). While this would better ensure the validity of statistical results,
trends can still be reported to help motivate future (multimodal) imag-
ing studies. Unambiguous documentation of which results are supported
by what kind of correction(s) is key, and the choice of words and lan-
guage used in results, discussion and conclusion sections should be care-
fully considered accordingly.
Not all studies have found signicant relationships be-
tween xel-wise metrics and other measures. For example,
Adanyeguh et al. (2018) reported no signicant correlations be-
tween xel-wise metrics and atrophy scores in patients with cerebellar
ataxia. Failure to detect signicant correlations could be explained by a
more complex, non-linear relationship between both metrics. However,
not all intuitively formulated hypotheses of this nature are necessarily
valid in the rst place (i.e., a correlation might genuinely not exist
even when two eects are independently observed or described in a
particular cohort). Regardlessly, studies would generally benet from
more advanced statistical analyses to reveal potentially non-linear
relationships between xel-wise and other brain metrics. Due to the
magnitude and nature of FD and FC metrics (respectively volumetric
and related to surface area), various non-linear transformations (e.g., a
logarithm) arguably present as sensible candidates.
Researchers have also explored associations between various brain
measurements and xel-wise metrics, aording researchers greater
freedom to pinpoint eect locations across the brain with increased
specicity. Mizuguchi et al. (2019) reported that resting state func-
tional connectivity between right lateral prefrontal cortex and left stria-
tum was positively correlated with FC in the right anterior corona
radiata. Boonstra et al. (2020) found that cerebellar decrease of
FDC in multiple sclerosis (MS) patients was associated with cerebel-
lar white matter atrophy and lesion load. Savard et al. (2020) ob-
served in fronto-temporal dementia patients that reductions of appar-
ent FD and FC in tracts of a fronto-temporal network were strongly
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T. Dhollander, A. Clemente, M. Singh et al. NeuroImage 241 (2021) 118417
linked to the amount of GM atrophy of peak nodes within this
network.
Behavioral relevance of FBA results
Several FBA studies have investigated associations between xel-
wise metrics and behavioural scores as a secondary aim, e.g.,
Adab et al. (2020) studied bimanual coordination performance, and
Verhelst et al. (2019) looked at verbal working memory. Others in-
corporated clinical outcomes, e.g., via Mini-Mental State Examina-
tion ( Luo et al., 2020 ). These studies often examined such asso-
ciations using correlation analyses between xel-wise metrics and
the relevant outcomes of interest across populations. For example,
Choy et al. (2020) found signicant negative correlations between age
and xel-wise metrics across multiple tracts in healthy adults, while
Pannek et al. (2020) observed developmental improvements in cogni-
tive and motor performance to be positively associated with xel-wise
metrics in infants. It should be noted that the majority of correlation
coecients of xel-wise metrics with behavioural outcomes were often
weak to moderate in strength across those studies implementing such
analyses. Remarkably, Verhelst et al. (2019) found correlations between
traditional DTI metrics and verbal working memory which were not
present for the xel-wise metrics. As mentioned in previous sections, in-
terpreting disparate results between FBA and analysis of voxel-wise DTI
metrics remains an ongoing challenge, due to the non-specic nature of
DTI and its derived metrics (see also the earlier section “FBA and other
dMRI analysis strategies ”).
Whilst correlational analyses are important to understand brain-
behavior relationships, some studies have employed other advanced an-
alytical approaches, including multivariate prole analysis ( Genc et al.,
2018 ) and mediation analyses ( Adab et al., 2020 ). For example, the me-
diation analyses performed by Adab et al. (2020) revealed that FDC
partially mediates the relationship between age and bimanual coordi-
nation in the splenium and genu of the corpus callosum. Similar to the
challenges of multimodal studies (see the earlier section “Multimodal
studies ”), it might be relevant to also explore non-linear relationships
between xel-wise metrics and behavioral metrics.
With increasing numbers of xel-wise metrics and behavioral mea-
sures, the number of combinations and thus statistical tests (or “con-
trasts ”) can easily grow. Without careful consideration, this can increase
the prevalence of type 1 errors ( Alberton et al., 2020 ). However, prop-
erly correcting for these will then impact on the overall statistical power
of studies. In this context, FBA in particular already faces a challenge due
to the large numbers of individual xels that are often analyzed; even
though it implements the connectivity-based xel enhancement (CFE)
mechanism to partially address this (see also the earlier section “FBA
and other dMRI analysis strategies ”). Other strategies include using
fixel regions of interest , either obtained from signicant results of a prior
FBA contrast (e.g., Mito et al., 2018 ) or by dening tracts of interest
using an a priori anatomical hypothesis (e.g., Adab et al., 2020 ).
Longitudinal FBA studies
The majority of FBA studies thus far have primarily focused on re-
vealing cross-sectional group dierences of xel-wise metrics. How-
ever, it is often of clinical interest to examine longitudinal changes
in brain microstructure, particularly in response to development, ag-
ing, disease, or training interventions. Of the 75 studies reviewed, we
identied 14 that have investigated changes in xel-wise metrics over
time. On the one hand, these changes were often assessed within one
specic group of participants, and statistical analyses were performed
comparing metrics between dierent time points (e.g., Mizuguchi et al.,
2019 ; Verhelst et al., 2019 ; Rau et al., 2019 ). On the other hand, e.g.,
Genc et al. (2018 ) and Kelly et al. (2020) directly analysed the changes
in xel-wise metrics over the time period that each subject was studied,
and assessed the relationship between such changes and developmental
factors. This was in practice achieved by pre-computing the dierence in
xel-wise metrics between dierent time points for each participant, re-
ecting a measure of change over time. Those were then analyzed in turn
via a whole-brain FBA, either cross-sectionally to determine whether
the change over time was dierent between groups, or to test whether
changes over time were associated with phenotypic and clinical charac-
teristics.
An important consideration for researchers relates to the denition
and pre-computation of changes in xel-wise metrics over time. In cer-
tain studies, the actual time dierence between “time points ”might vary
to a certain extent across subjects due to how these “time points ”are de-
ned or when data could be acquired from the subjects. In these cases,
it might be sensible to quantify change per unit of time , i.e., by normaliz-
ing the pre-computed change in xel-wise metric by the time dierence.
Whether this is desirable or not, however, depends on the kind of change
that is studied (or hypothesized). In this context, selecting time points
for acquisition of data and modelling changes of FD and FC over time
can prove highly challenging and involves a priori assumptions on the
biological and biophysical processes. Note for example the surprisingly
complex eects of atrophy (see the section “Combined Fibre Density
and Cross-section (FDC) computation ”in Supplementary Document
1 ) or vasogenic edema (see the earlier section “Challenges with inter-
pretation of FD and FC ”) on the FD and FC metrics, whereby they might
(non-monotonically) go up and down over time. Being able to measure
this, critically depends on sampling particular time points in the rst
place.
Another challenge many longitudinal studies are facing, involves
missing data for some time point(s) of certain subjects. These scenar-
ios call for statistical analyses which can more appropriately deal with
this, such as mixed eects modelling. Some FBA studies have computed
(average) xel-wise metrics in a range of white matter pathways, in or-
der to accurately model mixed eects due to missing data at the tract
level rather than xel level ( Dimond et al., 2020 ; Genc et al., 2020b ).
More generally, for particularly complex statistical challenges it might
be useful to extract tract-wise or xel ROI-wise metrics and process these
in dedicated advanced statistical software packages. The results of such
advanced statistical analyses can often also be visualized in bespoke
ways (using specialized plots), which might otherwise not be possible
for many individual xels (or it would at least defeat the purpose of
a clear and thus useful visualization). Similarly, it might help to avoid
over-interpretation of complex results.
Finally, another methodological aspect that is frequently brought up
when implementing longitudinal FBA studies relates to the construction
of the study-specic (FOD) template. Generally, the considerations in
this context are not dierent to those for cross-sectional analyses, or non-
FBA (e.g., VBA or VBM) studies (see the section on “Study-specific FOD
template construction ”in Supplementary Document 1 ). The FOD
template serves as a common reference point for the study: for example,
while the FC metric values are locally expressed relative to the template
(by virtue of being calculated from the subject-to-template warps), they
scale to it equally across all images of subjects and time points. Hence,
relative FC eects between subjects or time points are not aected by
the choice of a (common) template, even though the actual FC values
themselves are ( Raelt et al., 2017 ).
Dealing with WM lesions in FBA studies
Many clinical populations, such as patients with traumatic brain in-
jury (TBI), stroke, multiple sclerosis (MS), dementias, stroke and other
neurodegenerative diseases are clinically heterogeneous due to the pres-
ence of lesions in variable (and often widespread) locations and of dif-
ferent types and sizes. These include large focal lesions, diuse axonal
injuries, white matter (T2) hyperintensities (WMHs), inammation, and
edema. Even in healthy elderly subjects, lesions can present in a simi-
larly challenging fashion. The specic eects lesions have on FBA —both
processing steps and results —is relatively unexplored in the literature.
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T. Dhollander, A. Clemente, M. Singh et al. NeuroImage 241 (2021) 118417
Due to the complex nature of the FBA pipeline and its many dier-
ent interacting steps (see also the earlier section “Fixel-based Analysis
pipeline ”and Supplementary Document 1 ), rigorous quality assess-
ments are highly recommended at most stages of the pipeline (including
preprocessing steps to deal with artefacts and motion, brain mask esti-
mation, response function estimation, 3-tissue CSD, etc.) towards the
estimation of the relevant xel-wise metrics, especially in populations
where large focal lesions, inammation and edema are present. The rea-
sons for this stem mostly from the fact that lesions can severely alter im-
age intensities, but also geometry. For example, such lesions could aect
the accuracy and precision of image registration and even the construc-
tion of a study FOD template itself. Several aspects of lesions and how
they impact on 3-tissue modelling and metrics have been studied outside
of the FBA framework, e.g., by Mito et al. (2020) and Khan et al. (2020 ,
2021) . Generally, it is important for FBA studies to take an appropriately
cautious approach when lesioned subject populations are included.
One typical practice for studies is to actively exclude participants
with such extensive amounts of lesioned tissue that it would otherwise
lead to specic problems with the processing or statistical analysis. For
example, Verhelst et al. (2019) chose to only examine TBI patients with
diffuse axonal injuries and excluded those with larger focal lesions . While
on the one hand it makes sense to specically study a TBI subpopula-
tion with a focus on decits more likely caused by white-matter discon-
nections, on the other hand being restricted to such an approach has
inherent limitations in other scenarios. Consistently excluding partici-
pants might sometimes result in non-representative samples across the
literature describing particular populations. One avenue to address this
challenge was recently suggested: to enable more specic insights into
rare or heterogeneous populations, a shift from group studies to single-
case approaches could be considered ( Attye et al., 2021 ; Chamberland
et al., 2020 ). Dening robust pipelines for single-case FBA inspired ap-
proaches could be an interesting direction for future research. In this
context, to the best of our knowledge, only Fekonja et al. (2021) im-
plemented a modest initial attempt at subject-specic analysis of two
randomly selected cases from their study on corticospinal tract impair-
ment in patients with tumours.
Some studies have attempted to address challenges due to lesions
by performing analyses within subdivisions of cohorts, e.g., based on
shared lesion characteristics, which can as such limit the amount of
heterogeneity. Wallace et al. (2020) performed an FBA that combined
a largely heterogeneous sample of mild, moderate, and severe TBI pa-
tients. While descriptions of exclusion criteria were not provided, they
performed subgroup analyses separately for mild TBI and moderate-
severe TBI participants. As another example, Egorova et al. (2020) per-
formed a whole-sample FBA of a cohort of stroke patients, but addition-
ally also analyzed right hemisphere stroke and left hemisphere stroke
patients separately (all three analyses as a cross-sectional comparison
with healthy controls). Note the latter example showcases an aspect that
is relevant beyond lesions specically: lateralized pathologies. These are
particularly challenging to study, as xel-wise apparent FD, FC and FDC
show widespread and non-trivial laterality even in the healthy brain
( Honnedevasthana Arun et al., 2021 ; Verhelst et al., 2021 ). Notably,
Verhelst et al. (2021) urged caution with the typical approach of ip-
ping brain images that is sometimes relied upon for studying lateral-
ized pathology, as this might lead to false positive ndings unrelated
to the eect of interest. They formulated a range of caveats and ad-
vice in this context, concluding that it might often be preferable to
avoid the brain ipping strategy altogether for this purpose and ana-
lyze the (dierently lateralized) patient groups separately , as was done
in Egorova et al. (2020) . More broadly, pathological tissue might af-
fect nearby (or more remote) WM structure and function dierentially,
depending on its specic location.
Some FBA studies have assessed lesion load or volume measure-
ments, as derived from other MRI modalities such as uid-attenuated in-
version recovery (FLAIR) or susceptibility-weighted imaging (SWI) data
( Boonstra et al., 2020 ; Egorova et al., 2020 ; Gottlieb et al., 2020 ). In
these studies, lesion volumes have typically not been integrated in the
FBA itself, e.g., as a covariate of non-interest or variable of interest.
Instead, they were reported or analyzed separately. Some studies, e.g.,
Boonstra et al. (2020) , have furthermore (visually) inspected the lesion
segmentations and nearby regions for the purposes of quality assessment
of certain steps, e.g., image registration.
Finally, particular studies in MS ( Gajamange et al. 2018 ), stroke
( Egorova et al., 2020 ; Gottlieb et al., 2020 ), and mild cognitive impair-
ment and Alzheimer’s disease ( Mito et al., 2018 ) have computed WM
FODs using SS3T-CSD. By including additional isotropic signal compart-
ments for other tissues and uid in the model, 3-tissue CSD techniques
resolve WM FODs that are more specically sensitized to the anisotropic
signal from axons. Critically, this allows for resolving and preserving the
angular contrast of the WM FODs in presence of inltrating pathology
( Aerts et al., 2019 ). Preservation of the aforementioned angular contrast
of WM FODs in turn enables FOD-guided population template construc-
tion and registration of subject FOD images to this template to result
in better spatial alignment (similar to how 3-tissue CSD techniques in-
crease the same contrast for axonal projections into the cortical GM).
Furthermore, accurate xel segmentation is then also possible in le-
sioned regions or those inltrated by pathological tissue. Ultimately,
it also enables more accurate and specic apparent FD measures by re-
moving signal contributions unrelated to the intra-axonal space. How-
ever, note that the use of high b-values is additionally recommended to
further suppress extra-axonal signal contributions ( Raelt et al., 2012b ;
Genc et al., 2020a ) (see also the earlier sections on “Fixel-wise met-
rics and apparent fibre density ”and “Requirements and effects of
acquisition parameters ”).
Limitations and future challenges
The FBA framework has introduced a unique capability, where the
partial volume eect between dierent crossing bre populations has
been largely tackled. Yet this still does not represent the “ultimate ”
specicity to disentangle eects for all relevant distinct bre popula-
tions. Several WM bundles in the brain “funnel ”together along substan-
tial portions of their length. This can not be overcome by modelling
at the local voxel-level or even xel-level alone: it is eectively an in-
herent limitation to the dMRI measurements in isolated voxels . This also
causes major problems, e.g., for bre tractography and might even be
the most important reason it is challenged by large amounts of false
positive connections ( Maier-Hein et al., 2017 ). For FBA, this becomes
a challenge when interpreting results in terms of known anatomy. The
increased bre-specicity might even impose a false sense of condence
in labelling those results, with a bias towards larger or more commonly
known bundles (with a further risk of relating these to the wrong corti-
cal regions or even functions). An opportunity exists to develop objective
labelling strategies , based on carefully curated prior knowledge.
Another challenge lies in the obvious complexity of the FBA frame-
work (e.g., see Figure 3 ). Compared to VBA, many additional steps are
necessary to appropriately address the unique nature of dMRI data, FOD
images and xel-wise image data. While several of these steps are rela-
tively straightforward for researchers, in the sense that they are largely
automated, others do introduce new user-defined parameters or choices
and a need for specialized quality assessments at various stages in the
pipeline. With so many complex interactions between steps, it can be
hard to anticipate how certain choices early on in the pipeline might
ultimately impact on the nal result. For some of the bespoke mech-
anisms, default parameters do exist: e.g., Raelt et al. (2015) deter-
mined reasonable choices for the smoothing extent and CFE parame-
ters. However, it is unknown to what extent these generalize beyond
those initial experimental ndings. Similarly, the practice of spatial up-
sampling has been adopted for its benets towards improving image
contrast (with further downstream benets for other pipeline steps, e.g.,
image registration), but a systematic investigation of up-sampling reso-
lutions and their eect on FBA study results has not been performed to
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T. Dhollander, A. Clemente, M. Singh et al. NeuroImage 241 (2021) 118417
date. Yet other user-dened choices exist, e.g., in determining appropri-
ate thresholds or criteria to derive the common xel analysis mask and
its spatial (xel) extent. Most current FBA studies have adopted exist-
ing parameters and choices without further questioning whether these
could be improved or tailored to t their research questions better. This
might be addressed in the future by more systematic investigations of the
eects of certain FBA pipeline parameters and choices. Reproducibility
studies could play another key role in increasing our understanding of
the strengths of the framework, but might also reveal possible pitfalls
for researchers undertaking FBA studies. While there exists some evi-
dence on good test-retest reliability and long term stability of 3-tissue
CSD methods ( Newman et al., 2020 ), the same has not been pursued yet
for derived xel-wise FD, FC or FDC values (note that this additionally
depends on registration steps, xel denition, and xel correspondence
computation). Furthermore, beyond the preprocessing and complexities
involved with computing these metrics, the FBA framework as a whole
includes many other steps. Future studies should look into the test-retest
reliability of the more nal steps and outputs of the FBA pipeline. Repro-
ducing entire FBA study outcomes, either using the same data, newly
acquired data of the same subjects, or an entirely new sample of sub-
jects, would also help to further establish the robustness of the frame-
work. Finally, more tools and guidance to assist researchers in assessing
the quality of FBA results could prove to be of added value. We have
provided recommendations and state-of-the-art best practices in Sup-
plementary Document 1 for all individual steps of the FBA pipeline.
These should help to ensure high quality accurate FBA results by allow-
ing researchers to perform diligent quality checks at each stage of the
pipeline. However, assessing the quality of the nal result remains a
dicult challenge.
While analyzing bre density and bre-bundle cross-section using
the FBA framework provides more (bre) specic white matter assess-
ments, relating these to the real underlying biophysical and biological
mechanisms is also still challenging. More studies and validation are
essential to provide further insights and validate specic FBA results
against gold standard histological measurements, in order to better un-
derstand the cellular mechanisms underlying xel-wise eects in white
matter ( Al-Amin et al., 2020 ; Malhotra et al., 2019 ; Wu et al., 2020 ). De-
spite some FBA studies eectively incorporating other multimodal MRI
data and analysis strategies (e.g., Adanyeguh et al., 2018 ; Boonstra et al.,
2020 ; Luo et al., 2020 ; Mizuguchi et al., 2019 ; Vaughan et al., 2017 ),
there still exists scope for improved integration of information derived from
different modalities (when available) with FBA results. Specically, in or-
der to extract relevant information from various brain measurements,
it has been suggested to validate these against dierent parameters of
another framework, such as connectome embedding ( Rosenthal et al.,
2018 ). Of particular interest might be other modalities sensitized to
myelin, especially given that apparent FD itself is not (directly) sensitive
to myelin. A good candidate might for instance be relaxo-metry, from
which a myelin water fraction can be obtained that correlates relatively
well with histology ( Mancini et al., 2020 ). An interesting opportunity in
this context relates to a technique developed by De Santis et al. (2016) ,
which combines dMRI and relaxo-metry to resolve bre-specic values
for the longitudinal relaxation time (T1). Such bre-specic measure-
ments could be analyzed directly with the FBA framework, either to
compare or relate to apparent FD, or to augment it.
Most current FBA studies performed group-based analyses, which
may prove insucient to further our understanding of the pathophys-
iology and management of rare conditions. Group analyses are unable
to reect individual dierences between patients and cannot entirely
account for between-subject heterogeneity, e.g., in lesion topography
( Attye et al., 2021 ; Chamberland et al., 2020 ). Given this, there is a
relevant need for a paradigm shift from groupwise comparisons (e.g.,
a group of patients, compared to a group of controls) to more individu-
alized profiling (i.e., a single patient, compared to a group of reference
controls) of xel-wise and other metrics, which would aid in concep-
tualizing both microstructural and macro-structural changes in white
matter across rare or clinically heterogeneous populations. Continued
work in this area will hopefully allow xel-wise metrics to be used as
diagnostic or prognostic biomarkers ( Atkinson et al., 2001 ), providing
new and increased value for both researchers and clinicians alike.
Conclusion
We reviewed the FBA framework for the analysis of whole-brain
bre-specic properties of white matter micro- and macrostructure, as
typically derived from diusion MRI data. Similar to voxel-based analy-
sis, FBA enables analysis of the whole brain without a priori hypothesis
as to which parts or structures of the brain might show (signicant) ef-
fects of interest. However, it allows for this in a truly bre-specic man-
ner where eects can manifest individually even for dierent bre pop-
ulations within a single voxel. This brings a range of unique challenges,
for which the framework implements bespoke solutions. Since its orig-
inal development, the framework has seen a stark increase in adoption
across diverse application areas, yielding unique and valuable insights
into various clinical populations as well as healthy subjects. However,
limitations and challenges remain, in particular related to validation and
translation. Interpretation of results —while greatly improved over other
approaches due to bre-specicity —should still be performed cautiously
and is not always trivial due to the complex nature of and interactions
between microstructural properties of WM tissue.
Data and Code Availability Statement
There are no relevant data related to this review paper, apart from
the parameters and details sourced directly from the 75 FBA studies.
These are all included in the table in Supplementary Document 4 .
Acknowledgements
TD, SiG, CK, XL and TS acknowledge the support of the Murdoch
Children’s Research Institute, the Royal Children’s Hospital Foundation,
Department of Paediatrics at The University of Melbourne and the Vic-
torian Government’s Operational Infrastructure Support Program. OC
acknowledges the facilities and scientic and technical assistance of
the National Imaging Facility, a National Collaborative Research In-
frastructure Strategy (NCRIS) capability, at Swinburne Neuroimaging,
Swinburne University of Technology. NE is supported by the Discovery
Early Career Researcher Award Fellowship from the Australian Research
Council (DE180100893). PE is supported by a Future Fellowship from
the Australian Research Council (FT160100077). XL and GP are funded
by an Australian Catholic University Research Funding (ACURF) Pro-
gram Grant. RM and DV acknowledge the facilities and scientic and
technical assistance of the National Imaging Facility, a National Col-
laborative Research Infrastructure Strategy (NCRIS) capability, at the
Florey Institute of Neuroscience and Mental Health. KC is supported by
a National Health and Medical Research Council Career Development
Fellowship (APP1143816). We thank Honey Baseri for assistance with
the compilation of reference lists, and John Engel and Laura Dal Pozzo
for help with gure construction.
Supplementary materials
Supplementary material associated with this article can be found, in
the online version, at doi:10.1016/j.neuroimage.2021.118417 .
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