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

“For the FC and FDC analysis, we included intracranial volume (as computed using FreeSurfer from T1-weighted images (Dale et al., 1999)) as a nuisance covariate.”

“Furthermore, as in TBSS (Smith et al., 2006), this approach is likely to suffer from inaccurate FA-based projection in regions of crossing fibres (Bach et al., 2014; De Groot et al., 2013; Schwarz et al., 2014), and lack of fibre-specific inference when investigating voxel-wise measures such as FA.”

“By far the most popular approach to VBA of diffusion MRI is the analysis of diffusion tensor-derived fractional anisotropy (FA) (Basser and Pierpaoli, 1996), with voxel- or clusterlevel statistical inference using packages such as SPM (http://www. fil.ion.ucl.ac.uk/spm/) or FSL…”

“Family-wise error corrected p-values were assigned to each fixel using non-parametric permutation testing (Holmes et al., 1996; Winkler et al., 2014) with 5000 permutations.”

“In the context of voxel-averaged DWI measures (e.g. Alexander et al., 2010; Zhang et al., 2012), the ‘density’ of a voxel will also be influenced by partial volume with cerebral spinal fluid.”

“, 2012), individual differences and brain-behaviour correlations (Johansen-Berg, 2010), genetics (Meyer-Lindenberg, 2009), structural plasticity (Scholz et al., 2009), treatment response (Szeszko et al.”

“(Jeurissen et al., 2014)) instead of tissue segmentations from T1-weighted images.”

“However, most white matter voxels contain contributions from multiple fibre populations (often referred to as crossing fibres), and therefore voxel-averaged quantitative measures (e.g. fractional anisotropy) are not fibre-specific and have poor interpretability.”

“…(Johansen-Berg, 2010), genetics (Meyer-Lindenberg, 2009), structural plasticity (Scholz et al., 2009), treatment response (Szeszko et al., 2014) and neuroscientific efforts to relate structural and functional connectivity (Calamante et al., 2013; Stephan et al., 2009; Van Den Heuvel et al., 2009).”

“In recent years, a number of more advanced diffusion MRI models have been proposed that can resolve multiple fibre populations in a single voxel (Tournier et al., 2011).”

“Family-wise error corrected p-values were assigned to each fixel using non-parametric permutation testing (Holmes et al., 1996; Winkler et al., 2014) with 5000 permutations.”

“…known to contain crossing fibres (Jeurissen et al., 2012), and voxel-averaged measures such as FA are not fibre-specific (or even erroneous) in such regions, which confounds interpretation of apparent differences (Douaud et al., 2011; Pierpaoli et al., 2001; Wheeler-Kingshott and Cercignani, 2009).”

“The importance of white matter axons facilitating microsecond communication between different brain regions is evident from the severe brain dysfunction that arises in disconnection syndromes (Catani and Ffytche, 2005).”

“Many DWI models assume that diffusion within axons is restricted in the radial orientation (Alexander, 2008; Assaf and Basser, 2005; Barazany et al., 2009; Jespersen et al., 2007; Lu et al., 2006; Raffelt et al., 2012b; Stanisz et al., 1997; Zhang et al., 2012), and that the exchange of water…”

“…in the radial orientation (Alexander, 2008; Assaf and Basser, 2005; Barazany et al., 2009; Jespersen et al., 2007; Lu et al., 2006; Raffelt et al., 2012b; Stanisz et al., 1997; Zhang et al., 2012), and that the exchange of water between the intra-axonal and extra-axonal space is negligible on the…”

“Briefly, FOD lobes are first segmented based on the peaks and troughs of the FOD, and the apparent FD of each lobe is calculated by nonparametric numerical integration using a dense sampling of the FOD over a hemisphere (Smith et al., 2013).”

“…volume would provide additional information and potentially more biologically meaningful metrics, however current approaches to estimate axon diameters using DWI are not able to assign estimates to individual fixels in crossing fibre regions (Alexander et al., 2010; Assaf et al., 2008).”

“Axon diameter plays a role in the ‘ability to relay information’ via modulating transmission speed, timing and firing rate (Perge et al., 2012; Waxman, 1980).”

“(4) from Alexander et al. (2001): ^′ = ^ ^ ( ) v Jv Jv 1 f f f where v̂f is the unit vector describing the original direction of the fixel, ^′v f is the reoriented direction, and J is the Jacobian matrix that describes the local affine transformation of the non-linear warp, defined as: ⎡ ⎣ ⎢ ⎢ ⎢ ⎢…”

“Many DWI models assume that diffusion within axons is restricted in the radial orientation (Alexander, 2008; Assaf and Basser, 2005; Barazany et al., 2009; Jespersen et al., 2007; Lu et al., 2006; Raffelt et al., 2012b; Stanisz et al., 1997; Zhang et al., 2012), and that the exchange of water between the intra-axonal…”

“, 2006), this approach is likely to suffer from inaccurate FA-based projection in regions of crossing fibres (Bach et al., 2014; De Groot et al., 2013; Schwarz et al., 2014), and lack of fibre-specific inference when investigating voxel-wise measures such as FA.”

“DWI models that estimate parameters related to the volume of intra-axonal restricted water are consequently of biological interest since this volume is influenced by the number of axons.”

“Many DWI models assume that diffusion within axons is restricted in the radial orientation (Alexander, 2008; Assaf and Basser, 2005; Barazany et al., 2009; Jespersen et al., 2007; Lu et al., 2006; Raffelt et al., 2012b; Stanisz et al., 1997; Zhang et al., 2012), and that the exchange of water between the intra-axonal…”

“Many DWI models assume that diffusion within axons is restricted in the radial orientation (Alexander, 2008; Assaf and Basser, 2005; Barazany et al., 2009; Jespersen et al., 2007; Lu et al., 2006; Raffelt et al., 2012b; Stanisz et al., 1997; Zhang et al., 2012), and that the exchange of water between the intra-axonal…”

“Voxel-based analysis (VBA) of diffusion MRI is a common method for studying white matter, providing evidence of altered brain connectivity by detecting differences at a local level (Buchsbaum et al., 1998).”

“Many DWI models assume that diffusion within axons is restricted in the radial orientation (Alexander, 2008; Assaf and Basser, 2005; Barazany et al., 2009; Jespersen et al., 2007; Lu et al., 2006; Raffelt et al., 2012b; Stanisz et al., 1997; Zhang et al., 2012), and that the exchange of water”

“3–5 of Ashburner and Ridgway (2013)).”

“However, most white matter voxels are known to contain crossing fibres (Jeurissen et al., 2012), and voxel-averaged measures such as FA are not fibre-specific (or even erroneous) in such regions, which confounds interpretation of apparent differences (Douaud et al., 2011; Pierpaoli et al., 2001;…”

“Voxel-based analysis (VBA) of diffusion MRI is a common method for studying white matter, providing evidence of altered brain connectivity by detecting differences at a local level (Buchsbaum et al., 1998).”

“…so-called mixture models (Tournier et al., 2011) is that quantitative measures can be associated with a single fibre population within a voxel (Assaf and Basser, 2005; De Santis et al., 2016; Dell’Acqua et al., 2013; Raffelt et al., 2012b, 2014; Scherrer et al., 2016; Scherrer and Warfield, 2012).”

“However, most white matter voxels contain contributions from multiple fibre populations (often referred to as crossing fibres), and therefore voxel-averaged quantitative measures (e.g. fractional anisotropy) are not fibre-specific and have poor interpretability.”

“While FODs benefit from high angular resolution and high b-value DWI data, FOD registration is best performed using a relatively low spherical harmonic degree of 4 (Raffelt et al., 2011).”

“, 2013), partial volume fraction (Jbabdi et al., 2010), fibre density (Alexander et al.”

“, 2012), individual differences and brain-behaviour correlations (Johansen-Berg, 2010), genetics (Meyer-Lindenberg, 2009), structural plasticity (Scholz et al.”

“…Basser, 2005; Barazany et al., 2009; Jespersen et al., 2007; Lu et al., 2006; Raffelt et al., 2012b; Stanisz et al., 1997; Zhang et al., 2012), and that the exchange of water between the intra-axonal and extra-axonal space is negligible on the timescale of a diffusion MRI experiment (Quirk et…”

“…white matter fibre density and morphology using fixel-based analysis David A. Raffelt a,n, J.-Donald Tournier b,c, Robert E. Smith a, David N. Vaughan a,d,e, Graeme Jackson a,d,f, Gerard R. Ridgway g,h, Alan Connelly a,d,e a Florey Institute of Neuroscience and Mental Health, Melbourne,…”

“…(Johansen-Berg, 2010), genetics (Meyer-Lindenberg, 2009), structural plasticity (Scholz et al., 2009), treatment response (Szeszko et al., 2014) and neuroscientific efforts to relate structural and functional connectivity (Calamante et al., 2013; Stephan et al., 2009; Van Den Heuvel et al., 2009).”

“Furthermore, many neurological disorders (including Motor Neurone Disease (Kassubek et al., 2012), Multiple Sclerosis (Haines et al., 2011), Epilepsy (Otte et al., 2012), and Alzheimer's disease (Radanovic et al., 2013)) involve reduction or disruption of brain ‘connectivity’ due to pathological…”

“…correlations (Johansen-Berg, 2010), genetics (Meyer-Lindenberg, 2009), structural plasticity (Scholz et al., 2009), treatment response (Szeszko et al., 2014) and neuroscientific efforts to relate structural and functional connectivity (Calamante et al., 2013; Stephan et al., 2009; Van…”

“It is therefore reasonable to consider that the intra-axonal volume (of axons within a given fixel) is a quantity related to the white matter's local ‘ability to relay information’.”

“While FODs benefit from high angular resolution and high b-value DWI data, FOD registration is best performed using a relatively low spherical harmonic degree of 4 (Raffelt et al., 2011).”

“However, most white matter voxels are known to contain crossing fibres (Jeurissen et al., 2012), and voxel-averaged measures such as FA are not fibre-specific (or even erroneous) in such regions, which confounds interpretation of apparent differences (Douaud et al., 2011; Pierpaoli et al., 2001;…”

“…note that the combined FDC analysis may not always be more sensitive if the effect of interest is predominantly in either FD or FC, since combining FD and FC also combines the variance from each source (see also the argument that modulation in VBM can increase variability, Radua et al. (2014)).”

“…(Mills and Tamnes, 2014), aging (Lebel et al., 2012), individual differences and brain-behaviour correlations (Johansen-Berg, 2010), genetics (Meyer-Lindenberg, 2009), structural plasticity (Scholz et al., 2009), treatment response (Szeszko et al., 2014) and neuroscientific efforts to relate…”

“…Corr Melbou E-m journal homepage: www.elsevier.com/locate/neuroimage Investigating white matter fibre density and morphology using fixel-based analysis David A. Raffelt a,n, J.-Donald Tournier b,c, Robert E. Smith a, David N. Vaughan a,d,e, Graeme Jackson a,d,f, Gerard R. Ridgway g,h, Alan…”

“1 Previous publications have used the word ‘fibre’ (Assaf and Basser, 2005), ‘fascicle’ (Rokem et al., 2015; Scherrer and Warfield, 2012) or ‘fibre population’ (Behrens et al.”

“However, we note that the proposed fixel-based analysis framework can be used to investigate other measures of interest, such as fixel-specific diffusivity measures (Scherrer et al., 2016; Scherrer and Warfield, 2012), or relaxometry (De Santis et al.”

“To investigate white matter morphology, many previous studies have used VBM (Mechelli et al., 2005), which can be thought of as a TBM analysis weighted/masked by the tissue segmentation (note this is only true for modern VBM methods where images are registered as accurately as possible and modulated by the Jacobian de…”

“Contents lists available at ScienceDirect NeuroImage http://d 1053-81 Abbre restricte DWI, di section; populat metry; width a ratio; SP voxel-b n Corr Melbou E-m journal homepage: www.elsevier.com/locate/neuroimage Investigating white matter fibre density and morphology using fixel-based analysis David A. Raffelt a,n,…”

“In related work, Zhang et al. (2010) also proposed a combined analysis of microscopic measures with macroscopic morphology.”

“In vivo methods to quantify white matter changes that alter connectivity are also of interest in relation to psychiatric disorders (Kubicki under the CC BY license (http://creativecommons.org/licenses/by/4.0/). et al., 2007), development (Mills and Tamnes, 2014), aging (Lebel et al., 2012), individual differences and…”

“, 2014) and neuroscientific efforts to relate structural and functional connectivity (Calamante et al., 2013; Stephan et al., 2009; Van Den Heuvel et al., 2009).”

“…2014), apparent fibre density (Dell’acqua et al., 2010; Raffelt et al., 2012b), neurite density (Jespersen et al., 2010; Zhang et al., 2012), intra-axonal volume fraction (Panagiotaki et al., 2012) fibre volume fraction (Cabeen et al., 2015), fascicle fraction of occupancy (Scherrer et al., 2016)).”

“1 Previous publications have used the word ‘fibre’ (Assaf and Basser, 2005), ‘fascicle’ (Rokem et al., 2015; Scherrer and Warfield, 2012) or ‘fibre population’ (Behrens et al., 2007; Raffelt et al., 2012b) to refer to a specific population of fibres within a single voxel.”

“…2005; Barazany et al., 2009; Jespersen et al., 2007; Lu et al., 2006; Raffelt et al., 2012b; Stanisz et al., 1997; Zhang et al., 2012), and that the exchange of water between the intra-axonal and extra-axonal space is negligible on the timescale of a diffusion MRI experiment (Quirk et al., 2003).”

“…known to contain crossing fibres (Jeurissen et al., 2012), and voxel-averaged measures such as FA are not fibre-specific (or even erroneous) in such regions, which confounds interpretation of apparent differences (Douaud et al., 2011; Pierpaoli et al., 2001; Wheeler-Kingshott and Cercignani, 2009).”

“(3) (derived independently in Raffelt et al. (2010)) is mathematically equivalent to the method for computing the change in fibre cross-section in Zhang et al. (2009).”

“…for both microstructural changes in density (with the fibre density metric), and macrostructural, morphometric changes (with the fibre bundle cross-section metric) enables a more comprehensive analysis of total intra-axonal volume changes within a fibre pathway (FDC metric) (Raffelt et al., 2017).”