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Inherent spatial structure in myelin water fraction maps
Journal Pre-proof Inherent spatial structure in myelin water fraction maps
Tobias R. Baumeister, Shannon H. Kolind, Alex L. MacKay, Martin J. McKeown PII:
S0730-725X(19)30340-6
DOI:
https://doi.org/10.1016/j.mri.2019.09.012
Reference:
MRI 9323
To appear in:
Magnetic Resonance Imaging
Received date:
29 May 2019
Revised date:
23 August 2019
Accepted date:
27 September 2019
Please cite this article as: T.R. Baumeister, S.H. Kolind, A.L. MacKay, et al., Inherent spatial structure in myelin water fraction maps, Magnetic Resonance Imaging(2019), https://doi.org/10.1016/j.mri.2019.09.012
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier.
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Inherent spatial structure in Myelin Water Fraction maps Tobias R. Baumeistera, Shannon H. Kolindb,c,d, Alex L. MacKayc,d, Martin J. McKeownb a
School of Biomedical Engineering, The University of British Columbia Faculty of Medicine, Division of Neurology, The University of British Columbia c Department of Radiology, The University of British Columbia d Department of Physics & Astronomy, The University of British Columbia
Abstract
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Corresponding Author: Martin J. McKeown M33, Purdy Pavilion University Hospital, UBC Site 2221 Wesbrook Mall Vancouver, British Columbia V6T 2B5 Canada Tel. (604) 822-7516 Fax. (604) 822-7866 [email protected]
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Myelin water fraction (MWF) images in brain tend to be spatially noisy with unknown or no apparent spatial patterns structure, so values are therefore typically averaged over large white matter (WM) volumes. We investigated the existence of an inherent spatial structure in MWF maps and explored the benefits of examining MWF values along diffusion tensor imaging (DTI)derived white matter tracts. We compared spatial anisotropy between MWF and the more widely-used fractional anisotropy (FA) measure. Sixteen major white matter fibre bundles were extracted based on DTI data from 41 healthy subjects. MWF coefficients of variation (CoV) were computed in sub-segments along each fibre tract and compared to MWF CoVs from the
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surrounding “tubes” – i.e. voxels just exterior to the tract -- of each segment. We further assessed the consistency of the MWF along fibre bundles across subjects and investigated the benefit of examining MWF values in sections along each fibre bundle rather than integrating over the whole tract. CoVs of MWF and FA were lower in fibre bundles compared to their enclosing tubes in all investigated tracts. Both measures possessed a spatial gradient of CoV that was smaller aligned along, compared to perpendicular to, the fibre bundles. All WM tracts showed
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MWF profiles along their trajectory that were consistent across subjects and were more accurate
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than the mean overall fibre MWF value in estimating ages of the subjects. We conclude that,
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although less obvious visually, the spatial MWF distribution in white matter consistently follows
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a distinct pattern along underlying fibre bundles across subjects. Assessing MWF in sections along white matter tracts may provide a sensitive and robust way to assess myelin across
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subjects.
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Keywords:
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Myelin Water Imaging, Brain, Spatial Pattern
Highlights
The coefficient of variation gradient of Myelin Water Fraction values is minimal along white matter tracts
Myelin Water Fraction maps possess spatial structure and characteristic pattern along each major white matter fibre bundle
Utilizing these patterns results in more accurate age estimation and sex differentiation in healthy controls
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Graphical Abstract
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Major white matter tracts display a characteristic pattern of myelin water fraction values along their trajectories.
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1. Introduction The ability to assess myelin integrity with MRI in vivo holds great promise for characterising normal brain function as well as for identifying changes associated with disease or injury. The fatty myelin bilayers that make up myelin surrounding the majority of axons in the central nervous system are indispensable for efficient signal transmission, as they enable saltatory
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conduction that greatly increases the propagation velocity of action potentials along nerve fibers.
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A compromised myelin structure leads to detrimental brain function including impaired motor
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performance, worsening cognitive abilities, and loss of vision [1]. The importance of myelin is highlighted by the multitude of neurological and neurodegenerative diseases it has been
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implicated in such as multiple sclerosis (MS) [2,3], schizophrenia [4], and even diseases
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previously not thought to involve myelin, such as Parkinson’s disease [5]. Although much
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research has focused on assessing myelin at specific loci, such as lesions seen in multiple sclerosis [2,6], often more diffuse changes in normal-appearing or diffusely affected tissue are of
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interest. In such cases, myelin features are commonly assessed in large volumes of interest, such
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as white matter (WM) across the entire brain or whole fibre bundles [3]. However, myelin changes during development [7] aging [8–10], neurodegeneration [11], disease processes [11], and even sex differences [12] lead to spatial variability in myelin content, that may obscure findings if myelin content is integrated over too large a volume. Myelin water imaging is a quantitative MRI technique that can be used to calculate the myelin water fraction (MWF), a measure that has been validated as being directly correlated with myelin content [13], [14]. This technique uses a multi-echo T2 relaxation sequence to sample a large range of echo times, enabling the decomposition of the measured decay curve into constituent T2
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times. Myelin water is represented by short T2 times between 15-40ms. The MWF is then defined as the fraction of myelin water-related T2 amplitudes compared to the total water. A nonnegative least squares (NNLS) algorithm is typically used to fit the multi-echo T2 decay curve with a set of exponential basis functions [15]. However, such an approach is potentially illposed due to the non-orthogonality of the different exponential basis functions and may lack robustness in the presence of noise [16]. Thus, both biological and numerical processing factors
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may lead to visually noisy spatial maps with little apparent spatial structure apart from discerning
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white matter from grey matter.
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Diffusion Tensor Imaging (DTI) studies provide complementary information about WM
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integrity. DTI metrics such as fractional anisotropy (FA) display consistent patterns along
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specific WM fibre bundles [17] that are sensitive to pathology [18,19] and age [20]. While DTI studies are somewhat quantitative and provide insight into general WM microstructure, they do
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not easily correspond to known biological quantities such as myelin [21,22] or iron content [23]
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that can be measured during pathological examination. In contrast, MWF shows a strong
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correlation with myelin in histopathological studies [14]. DTI measures and MWF have been shown to correlate to some degree [24], with both measures being confounded to varying degrees by other WM microstructural factors such as crossing fibres [25] and axonal packing [26] for DTI, and high SNR sensitivity [16] and potential exchange effects [27] for MWF. However, almost all MWF reconstruction algorithms lead to maps that appear spatially “noisier” compared to DTI (e.g. FA) maps. Changes in myelin along tracts would be consistent with a large body of animal literature. Studies in mice have shown a complex pattern of myelin ensheathment that varies in length and
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thickness along axons relative to its location in the brain [28,29]. These differences in myelination along individual axons may be related to another critical role of overall myelination -- the maintenance of synchronous firing of connected neurons. Maintaining synchronicity in timings of signals arriving at a given brain area but originating from different areas with differing lengths of axons could be another important aspect of brain signalling in order to elicit a neural response at the target brain area [30–32]. This phenomenon has been observed in neural
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input originating from different thalamic regions and ending in the somatosensory cortex and is
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believed to be due to the differing myelination of these axonal populations [31,33]. While these
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studies report findings on individual axons utilizing mouse models and electron microscopy, the
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effect of differently myelinated axons would conceivably be seen on a larger macroscale with MWI. Thus, investigating a spatial pattern of myelination along major fibre bundles could
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provide further evidence of distinct myelination along trajectories supporting synchronicity in
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the brain on the macroscale.
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A number of studies have started to examine imaging changes within WM tracts. De Santis et al. [34] created a MRI atlas of white matter microstructure in healthy subjects by comparing means
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and standard deviations in different ROIs of several measures calculated using DTI and mcDESPOT. mcDESPOT can be used to calculate MWF, although the acquisition and analysis procedures differ from the multi-echo T2 relaxation approach used here, and MWF values differ between these two approaches. They investigated seven WM tracts and subsampled each measure along each tract where they found a left/right hemisphere asymmetry pattern with varying degree of asymmetry between measures. Compared to typical DTI measures, MWF calculated based on mcDESPOT generally showed more asymmetry. Furthermore, when taking the average of each tract, in five out of the seven WM tracts investigated, the mcDESPOT MWF
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required a larger sample size than FA to reach significant results. While their work was aimed at disentangling the interrelations between different measures of white matter integrity in several ROIs, they only examined variations in measures along fibre tracts for their asymmetry analysis between hemispheres. Another study investigated MWF and radial diffusivity (RD) along a selection of fibre tracts in both MS and healthy subjects and could pinpoint differences along
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tract profiles that coincided with lesion locations [35]. In this work, we aimed to characterise the basic spatial structure of MWF maps with respect to
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white matter structural organisation and relate the spatial structure of MWF maps to that of FA
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maps. To this end, we examined whether the MWF variance within major WM fibre bundles is
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less than in regions immediately surrounding the fibre bundle. Additionally, we explored if
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MWF maps follow a tight spatial pattern that follows the underlying fibre organisation, and therefore the MWF variance gradient along fibre bundles should be smaller compared to an
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orthogonal direction. Furthermore, we investigated if different major white matter tracts have a
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characteristic pattern of MWF values along their trajectories allowing for the identification of local changes that may be of diagnostic value and related this to structure and patterns in FA
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maps. Finally, to determine if there was biological significance to the characteristic pattern along the fibre bundles we investigated the capabilities of tract MWF profiles versus tract MWF averages to estimate subjects age and differentiate between sex.
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2. Materials and Methods All subjects provided written, informed consent. We acquired data from a total of 41 healthy subjects (18 M and 23 F), with median age of 28 years with a total age range of 32 years from 20 to 52 years. All subjects had no known history of neurological disease. All data were acquired on a Philips (Netherlands) Achieva 3T MRI scanner with an 8 channel head coil. We acquired a full brain 3DT1-weighted scan for structural references with an MPRAGE sequence TI=808ms,
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TR=1800ms and an isotropic voxel size of 1mm3. T2 relaxation data were collected using a
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modified GRASE sequence with 32 echoes with 10ms echo spacing and TR=1000ms. Twenty
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slices were acquired at 5mm slice thickness and reconstructed to 40 slices at 2.5mm [15]. The in-
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plane voxel size was 1x1mm. Twenty subjects (mean age 26.8 5.4 years, 9 females) had DTI
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data sets with TE=69ms, TR=6179ms, with 32 gradient orientations, a b value of 700 s/mm2 and one b0 volume. The remaining 21 subjects (mean age 35.6 9.9 years, 14 females) had diffusion
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tensor imaging data sets acquired with TE=75ms, TR=7465ms, 16 directions, with a b value of
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900 s/mm2 and one b0 volume. Both DTI sequences were acquired at a 2.2 x 2.2mm in-plane
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resolution and reconstructed to 0.8 x 0.8mm in-plane resolution with a 2.2mm slice thickness.. The multi-echo GRASE sequence was analysed using in-house written MATLAB (Natick, MA, USA) code which uses an NNLS fitting method to approximate the multi-exponential decay curve with a number of basis functions, including corrections for stimulated echoes as well as a regularizer to make the fit more robust against noise in the time domain [36], resulting in one MWF map per subject. DTI data were corrected for geometric distortions and subject motions using FSL’s DTIFIT [37] prior to fitting the tensors and performing whole brain deterministic tractography using
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mrDiffusion, part of vistasoft (http://white.stanford.edu/software/). Sixteen major white matter tracts were segmented in both hemispheres with the AFQ toolbox [17]. Briefly, AFQ uses whole brain fibres and segments major fibre bundles based on predefined waypoint region-of-interest (ROIs), after which it compares the selected fibre bundles to a probabilistic atlas to remove potential outliers. Once the fibre tracts have been segmented, they are clipped to contain the fibres in between two defining waypoints per tract, as the intersubject variability beyond those
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endpoints was too large to robustly segment the tracts, precluding any quantitative attempt for
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characterization.
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In order to apply the fibre bundle masks to the MWF maps, for each subject the first echo of the
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GRASE data was registered to the non-diffusion weighted scan from the DTI acquisition (b = 0
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s/mm2 or b0) and the resulting transformation matrix was then applied to each MWF map. Registrations were done with FLIRT [37]. A white matter mask was generated using FSL’s
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FAST [37] on the high resolution and skull-stripped 3DT1-weighted images and registered to the
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b0 image using a transformation matrix generated by registering the 3DT1-weighted image to the b0 image. All registrations were visually checked for accuracy and, if needed, performed again
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with tweaked parameters in order to obtain well aligned images. In order to compare the spatial smoothness of MWF and FA maps, we first computed the local coefficients of variation (CoV) in a 9x9 voxel neighbourhood, on axial slices, across all white matter. The coefficient of variation was selected for a fair comparison to compensate the different plausible numerical ranges between the MWF and FA maps that will be accounted for in the CoV. Note that this comparison was done on a MWF map that went through a coregistration process to DTI space, so that the spatial resolutions are the same, and thus some
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degree of smoothing occurs during this procedure. Nevertheless, this should only impact the result slightly, and if anything, increase the spatial smoothness of MWF maps. Following this, we compared the variances of MWF and FA values in WM fibre bundles to their respective “tubes” – i.e. one-voxel layer of WM voxels surrounding each tract. To account for possible partial volume effects, imperfect fibre tracking, and registration misalignments between
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the b0 and myelin data, we introduced a gap of one voxel between the fibre bundles and their enclosing tubes (see Figure 1 for a schematic illustration). To further limit the influence of
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potential partial volume effects, we masked the generated tubes with the individuals WM mask
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to ensure that only WM voxels were being considered. The WM masks were based on the
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probabilistic output from FAST and only voxels with a probability of 95% or greater were
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retained. Note that this may lead to incompletely closed tubes in some fibre bundles that were close to the grey/white matter interface but allows for a fairer comparison between tracts and
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their enclosing tubes since only WM voxels are being examined.
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We further tested if the gradients of MWF and FA CoVs along adjacent segments of fibre
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bundles differed compared to perpendicular directions. More specifically, we calculated the differences of CoV between two adjacent segments along each tract and compared this gradient to the differences between a fibre segment and its immediate tube-segment neighbour (voxels enclosing the fibre bundle voxels, in perpendicular direction to the main fibre bundle direction). We divided each fibre bundle into 15 equidistant sub-regions and extracted the averages and CoVs of MWF and FA values in each segment. We used fibre bundles to create a weighted mask to subsequently interrogate MWF and FA values.
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Finally, we determined the biological significance of sampling MWF values along fibre bundles in two ways: 1) we examined if the age of a subject could be better estimated by average MWF in segments along a fibre bundle compared to the average MWF of the whole bundle and 2) we investigated if a classification by sex was more accurate with tract profiles than with tract averages.
2.1 Statistical Tests
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All statistical tests were performed using MATLAB v2015a (Natick, MA, USA). Results were
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deemed statistically significant at p<0.05 without correction for multiple comparisons in this
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exploratory analysis. A two sample t-test was used to compare the local, slice-by-slice computed
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CoVs between one representative MWF and FA map. Differences in variance of the WM tracts, and tubes were assessed with a two-sample t-test. A multiple linear regression model was used to
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examine the relation between age and the 15 segments per tract where all segments per tract
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served as predictors. In the case of the average MWF per fibre bundle, a simple linear regression was performed with the average MWF per tract as predictor and age as the outcome variable. A
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Linear Discriminant Analysis (LDA) was performed with the goal to differentiate males and
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females based on their MWF. Two LDAs per tract, with either its segments or whole average as features, and with subjects as observations were performed. LDA maximises the ratio of between-class variance to within-class variance, thus finding the most discriminative projections of data features so that the projected data is well distinguished between classes. We compared the accuracy of sex classification between tract profiles and tract averages as well as computing the Akaike Information Criterion (AIC) for both, the regression and LDA in order to test whether the models utilizing tract profiles were more appropriate. Statistical significance is marked with
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black stars in all figures. The significance level was set to p<0.05 without correction for multiple
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comparisons in this exploratory analysis.
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3. Results Despite the differences in DTI acquisition parameters in the two cohorts, the extracted fibre bundles were visually comparable across subjects. An individual analysis of MWF variances in fibre bundles and tubes in both cohorts demonstrated similar behaviour, so that the results shown here are from the combined cohort. Individual plots of the main findings can be seen in the
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supplementary material.
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Figure 2 shows the histograms of accumulated local CoVs for both maps, normalized to
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probabilities, in WM voxels only. It is apparent that MWF maps have higher CoV than FA maps,
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consistent with the empirical observation that the maps appear less spatially smooth.
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All extracted major white matter fibre bundles from one representative subject can be seen in Figure 3.
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Comparing the CoV of MWF values between fibre bundles and their respective tubes revealed
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that the CoV of tubes was higher in all WM tracts except the callosum forceps minor, but only
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the left/right thalamic radiation, left/right corticospinal tract, callsoum forceps major, right ILF, left/right SLF, as well as left/right arcuate showed significance (p<0.05), see Figure 4a. A comparison of FA CoV between fibre bundles and their respective tubes revealed that all tubes show higher CoV than major WM tracts (p<0.001 for all comparisons), Figure 4b. Comparing the CoV gradient along WM fibre bundles to the perpendicular direction revealed a consistently lower variance gradient between adjacent fibre segments than between fibre segments and tubes (Figure 5). While this was true for both MWF and FA, the MWF maps displayed slightly larger CoV gradients in most WM tracts. CoV gradients in MWF maps were significantly lower along fibre bundles than in perpendicular directions in all examined WM
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tracts except in the cingulum cingulate and callosum forceps minor where some pairs of segment-to-segment and segment-to-tube gradients did not display significant differences. The CoV gradients in FA maps exhibited a very similar behaviour in all tracts where the CoV gradient was lower between segments than between segments and tubes. The across-subject averages of MWF and FA along major fibre bundles are displayed in Figure
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6. Note a characteristic pattern along major fibre bundles. Some tracts such as the callosum forceps minor and major as well as the inferior fronto-occipital fasciculus were very consistent
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across subjects as indicated by low standard errors. This qualitative comparison held true for
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both MWF and FA patterns along the WM tracts. Further, some fibre bundles show a similar
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behaviour for both MWF and FA such as the callosum forceps major or the inferior longitudinal
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fasciculus (ILF). Others, such as the thalamic radiation or inferior fronto-occipital fasciculus (IFOF), show only some commonalities between MWF and FA patterns. In the case of the
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thalamic radiation, both show an increase of MWF and FA until roughly to the middle of tract
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decreases and increases.
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where the FA pattern shows a monotone decrease while the MWF pattern shows more complex
Note all Figures displaying either the CoV gradients or the averages of segments along each fibre bundle are showing results from the left hemisphere WM tracts. Please refer to supplementary Figures S1-S4 for results of right hemisphere tracts. To determine if there was biological significance to the characteristic pattern along the fibre bundles, we performed a multiple linear regression in an effort to estimate the subjects’ age, as this is known to robustly influence myelin [8–10] and compared the performance between including the individual averages of all segments per tract or the average of all segments per tract
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as predictors. We found that using fibre segment averages was more predictive of age than a single average per tract. We found that the callosum forceps major (R2adj=0.41, p=0.012), left IFOF (R2adj=0.36, p=0.035), and left arcuate (R2adj=0.54, p=0.003) could significantly estimate age (Figure 7). To ensure that the improved estimations were not only due to the increased number of predictors,
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outperformed the model using only the average (Figure 7).
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we compared the AIC between the two models and found that the model including the segments
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Additionally, we compared the tracts in which MWF values could estimate age with the corresponding FA tract profiles in order to identify regional differences. Figure 8 illustrates the
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MWF profiles (green) and FA profiles (orange) in the three tracts. Stars indicate significant
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segments in the multiple linear regression estimating age using MWF values. The MWF profiles demonstrated mostly adjacent segments that were significant predictors, except in the left IFOF.
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their general trend.
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Furthermore, significant segments can be observed where the MWF and FA profiles differ in
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The results from the LDA are shown in Figure 9a, where the accuracy of differentiating males from females was higher for tract profiles in each tract. The lower AIC as seen in Figure 9b indicates a superior model for the tract profiles as well. Figure 10 displays the receiver operator curves (ROC) for each LDA performed using either the tract profiles (blue) or whole tract (red). LDA models performed on the tract profiles consistently outperformed the models utilizing only the tract averages. The average area under the curve (AUC) for tract profiles was 0.87 while the average AUC for the whole tracts was 0.69 (p<0.0001). A table with individual sensitivity and specificity values can be found in the supplementary information (Supplementary Table T1).
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4. Discussion We have shown that MWF maps, despite their spatially unsmooth appearance, possess a spatial structure that substantially follows tracts derived from DTI. This draws into question how informative simply averaging MWF values over broad volumes really is. We have demonstrated MWF values are more consistent along a fibre bundle compared to “tubes” surrounding the fibre
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bundles, although MWF values are still more variable than FA values. Furthermore, we report that the variances of MWF as well as FA values exhibit a spatial gradient in major white matter
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(WM) fibre bundles that is lower along fibre tracts compared to perpendicular directions. This
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lower gradient along axonal pathways indicates a central role of MRI-derived major white matter
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tracts in the overall microstructural organisation of the cerebral WM and that indices of WM
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integrity should be evaluated with care to the underlying microstructure.
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While MWF CoVs were typically less in fibre bundles than their surrounding tubes, only 10 out of the total 16 fibre bundles exhibited significant differences. In contrast, FA CoVs displayed
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significant differences in all fibre bundles, making them appear to be a more stable measure of
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characterising WM microstructural integrity, albeit less biologically specific. However, it should be noted that the extraction of fibre bundles is directly biased towards FA values in terms of selecting voxels to fibre tracking as well as indirectly when tracing each fibre. Additionally, the left/right IFOF are one of the longest bundles and tend to be more difficult to track from occipital to frontal areas. In conjunction with the generally observed pattern of higher MWF values in posterior regions compared to anterior regions, these fibre bundles cover a wide range of MWF values.
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The lower CoV gradients along fibre tracts suggest evidence of MWF values following a pattern of microstructural WM organisation, highlighting the importance of WM fibre bundles. Both MWF and FA followed the same trend, in that the CoV gradient was lower between fibre bundle segments than in perpendicular directions with the difference being usually more pronounced in FA maps indicative of a steeper change of FA values from within fibres to its surroundings.
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We have demonstrated that each major fibre bundle has its own specific pattern of myelination, which is relatively consistent across subjects, with a general observation of higher to lower
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MWF values when one moves from posterior to anterior. Some structures such as the callosum
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forceps major/minor have quite intricate spatial patterns, which are completely lost when simply
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averaging over the entire tract. Thus, studies investigating age effects on myelination or inferring
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disease progression based on tract informed analysis may potentially more sensitive to subtle local changes in MWF. While it might be apparent that including more information about MWF
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values would increase predictability of a clinical index such as age, the key point is that the
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enhanced predictability implies consistency across subjects of MWF segments within a fibre bundle. It should be noted that MWF tract profiles has been computed before, with the focus
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there on four fibre bundles of the right hemisphere that were relevant to their specific MS cohort at hand [35]. In this work, we focused on characterising 16 major fibre bundles in a healthy cohort in order to outline the majority of healthy WM. We note that the overlapping investigated fibre bundles show qualitative similarities. The MWF tract profiles were able to significantly estimate age in three fibre tracts, the callosum forceps major, left IFOF and left arcuate. The most important segments in the left arcuate were segments exhibiting a steady decline in MWF profiles but showed a large variability in FA profiles. Similarly, the important segment in the left IFOF marked the point of a steep increase in
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the FA profile while in the MWF profile it was the start of a plateau. In case of the callosum forceps major, both profiles showed a similar behaviour, however the steep increase and decrease around the midline in the MWF profile seems to have profound effects in age estimation. Further, the MWF tract profiles could consistently better separate male and female sex when
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compared to using the tract average MWF and could present a method to gain more detailed insight into WM microstructural differences based on sex. While sex differences in MWF of the
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corpus callosum have been previously reported [12], other human adult studies of sex differences
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in MWF are scarce, potentially due to the limitation of commonplace ROI/tract average
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measures used in statistical analysis. Additionally, since LDA estimates a projection which
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maximises within to between class variance, it may be able to detect subtle sex differences more robustly than more traditional methods such as simple t-tests or logistic regression.
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We recognize that the true biological origin of the tract profiles cannot be fully determined in
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this study. The tract profiles could stem from differing myelination patterns along the axons that
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in sum produce a characteristic pattern of MWF values along each tract, in line with the synchronicity theory. Another explanation for the tract profiles we observed could be due to different fibre bundles crossing and merging into each other creating a heterogeneous microstructure which may not be resolved with the current MWF maps. The MWF profile of the callosum forceps minor/major, fibre bundles with little crossing or merging fibres, however do suggest a distinct myelination pattern. Further studies with higher spatial resolution in both MWI and DTI as well as more DTI gradient directions are needed to obtain a more detailed description of the trajectories myelination patterns of WM fibre bundles.
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We note that there are a number of limitations to this study. We had a rather narrow age range that may have limited the capacity of the regression analysis to predict age in some WM tracts. The use of two different DTI data sets with different acquisition parameters may introduce some confounding factors, namely in the accuracy of fibre tracking. However, examining these two
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sub-data sets separately did not reveal striking differences (see Supplementary Material) except possibly the thalamic radiation. A possible explanation could be imperfect fibre tracking
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in the thalamus, which is known to be a mixture of white- and grey matter tissue and thus finding
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a principal diffusion direction is always challenging and directly relates to the number of
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diffusion gradient used during data acquisition (16 vs 32 directions in our cohorts). Since our
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main focus was to establish a biological significance of the tract profiles, this difference does not appear to affect our conclusions. Future studies may use diffusion spectrum imaging (DSI) in
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order to mitigate the effects of crossing fibres and thus getting more accurate fibre tracking and
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consequently more robust measures. This could then be used to look further into the differences between the MWF and FA profiles as an area with crossing fibres should influence FA more than
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MWF and thus provide information whether or not crossing fibres are a dominant factor in the discrepancies between MWF and FA tract profiles. It should be noted that due to the healthy cohort, age and sex were the only available demographic variables to test usefulness of the tract profiles. This can easily be extended to a patient population with various clinical and behavioural data in order to pinpoint specific segments most associated with aberrant behaviour. Regarding the contribution of individual segments of the left IFOF in the estimation of age, the only segment significantly contributing may be influenced by partial volume effects as this part of the
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tract is running through the external capsule, a very thin WM structure that may not be purely WM with a 5 mm slice thickness. In summary, our results suggest that there is a deterministic spatial pattern in MWF despite the apparent unsmooth appearance of MWF maps. Our results indicate that when performing an ROI based analysis, one should be aware to the underlying white matter microstructure when
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investigating large ROIs containing multiple fibre tracts. When investigating whole fibre tracts, it may be inadvisable to integrate the MWF over the entire tract length rather than looking at
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smaller segments within each tract. The number of sections to divide each fibre bundle that we
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chose is somewhat arbitrary; further work will be required to determine the optimal number of
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segments.
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Acknowledgements: We are grateful to Saurabh Garg for the meaningful discussions during the
acquiring the data.
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course of this study. We thankfully acknowledge the help of all the MR technologists for
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Conflict of interest: None
Grant support: This work was partially supported by a Multiple Sclerosis of Canada Operating grant awarded to Professors McKeown and MacKay. MJM was supported by the PPRI/UBC Chair in Parkinson’s Research. Dr. Kolind has received research support from Roche, Genzyme, the MS Society of Canada, NSERC, VCHRI, MSFHR and Milan & Maureen Ilich Foundation, and consultancy fees for Acorda, Genzyme.
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Figure Captions
Figure 1: Schematic illustration explaining the subdivision of a fibre bundle (blue) into segments as well as the "tubes" (red), i.e. voxels enclosing the fibre bundle with a one voxel gap (grey) in between.
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Figure 2: Histogram of local CoV in a 9x9 voxel rectangle comparing MWF and FA maps. Significantly lower variances can be observed in FA maps, indicating an overall smoother spatial appearance.
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Figure 3: Rendering of the extracted major fibre bundles. a) blue: callosum forceps minor/major, red: thalamic radiation, green: cingulum cingulate, orange: superior longitudinal fasciculus (SLF). b) blue: inferior fronto-occipital fasciculus (IFOF), red: corticospinal tract, green: inferior longitudinal fasciculus (ILF), orange: arcuate
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Figure 4: Coefficient of Variation (CoV) of whole tracts and tubes in a) MWF and b) FA.
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Figure 5: CoV gradients between adjacent fibre segments (blue) and between fibre segments and tube segments perpendicular to fibre tract orientation (red). MWF CoV shown in a) and FA CoV shown in b). In both cases the majority of segment-to-segment and segment-to-tube pairs show significant differences. Errorbars depict standard errors across subjects. Shown are tracts from the left hemisphere.
Figure 6: Tract profiles of MWF and FA measures. a) average MWF and b) average FA in segments along each tract. Segments are shown along the x-axis indicating relative directions in the brain (A=anterior, P=posterior, L=left, R=right, I=inferior, S=superior). Errorbars show standard errors across subjects. Shown are tract profiles of left hemisphere tracts.
Figure 7: Age estimations based on multiple linear regression using tract profiles as predictors (blue) versus using only the tract average as a predictor (red). Shown are the significant
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estimation based on segments. The AICs for each model are listed below and showing lower values for the tract profile models, indicating favorable models.
Figure 8: MWF (green) and FA (orange) tract profiles of tracts able to significantly estimate age based on MWF predictors. Stars indicate significant segments in the model along the MWF profile
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Figure 9: Linear Discriminant Analysis (LDA) results for differentiating sex based on MWF. a) shows the accuracy of LDA when using the MWF tract profile (blue) or MWF tract average (red). Higher accuracy can be seen for all tract profiles. b) AIC per tract model, the model utilizing the tract profiles show a smaller AIC and are thus preferred.
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Figure 10: ROC plots for each LDA. Light blue and light red show the ROCs for each LDA per tract, thicker lines show the average. Mean AUC for tract profiles: 0.87, mean AUC for whole tracts: 0.69
Tobias R. Baumeister, Shannon H. Kolind, Alex L. MacKay, Martin J. McKeown PII:
S0730-725X(19)30340-6
DOI:
https://doi.org/10.1016/j.mri.2019.09.012
Reference:
MRI 9323
To appear in:
Magnetic Resonance Imaging
Received date:
29 May 2019
Revised date:
23 August 2019
Accepted date:
27 September 2019
Please cite this article as: T.R. Baumeister, S.H. Kolind, A.L. MacKay, et al., Inherent spatial structure in myelin water fraction maps, Magnetic Resonance Imaging(2019), https://doi.org/10.1016/j.mri.2019.09.012
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier.
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Inherent spatial structure in Myelin Water Fraction maps Tobias R. Baumeistera, Shannon H. Kolindb,c,d, Alex L. MacKayc,d, Martin J. McKeownb a
School of Biomedical Engineering, The University of British Columbia Faculty of Medicine, Division of Neurology, The University of British Columbia c Department of Radiology, The University of British Columbia d Department of Physics & Astronomy, The University of British Columbia
Abstract
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Corresponding Author: Martin J. McKeown M33, Purdy Pavilion University Hospital, UBC Site 2221 Wesbrook Mall Vancouver, British Columbia V6T 2B5 Canada Tel. (604) 822-7516 Fax. (604) 822-7866 [email protected]
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Myelin water fraction (MWF) images in brain tend to be spatially noisy with unknown or no apparent spatial patterns structure, so values are therefore typically averaged over large white matter (WM) volumes. We investigated the existence of an inherent spatial structure in MWF maps and explored the benefits of examining MWF values along diffusion tensor imaging (DTI)derived white matter tracts. We compared spatial anisotropy between MWF and the more widely-used fractional anisotropy (FA) measure. Sixteen major white matter fibre bundles were extracted based on DTI data from 41 healthy subjects. MWF coefficients of variation (CoV) were computed in sub-segments along each fibre tract and compared to MWF CoVs from the
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surrounding “tubes” – i.e. voxels just exterior to the tract -- of each segment. We further assessed the consistency of the MWF along fibre bundles across subjects and investigated the benefit of examining MWF values in sections along each fibre bundle rather than integrating over the whole tract. CoVs of MWF and FA were lower in fibre bundles compared to their enclosing tubes in all investigated tracts. Both measures possessed a spatial gradient of CoV that was smaller aligned along, compared to perpendicular to, the fibre bundles. All WM tracts showed
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MWF profiles along their trajectory that were consistent across subjects and were more accurate
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than the mean overall fibre MWF value in estimating ages of the subjects. We conclude that,
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although less obvious visually, the spatial MWF distribution in white matter consistently follows
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a distinct pattern along underlying fibre bundles across subjects. Assessing MWF in sections along white matter tracts may provide a sensitive and robust way to assess myelin across
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subjects.
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Keywords:
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Myelin Water Imaging, Brain, Spatial Pattern
Highlights
The coefficient of variation gradient of Myelin Water Fraction values is minimal along white matter tracts
Myelin Water Fraction maps possess spatial structure and characteristic pattern along each major white matter fibre bundle
Utilizing these patterns results in more accurate age estimation and sex differentiation in healthy controls
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Graphical Abstract
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Major white matter tracts display a characteristic pattern of myelin water fraction values along their trajectories.
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1. Introduction The ability to assess myelin integrity with MRI in vivo holds great promise for characterising normal brain function as well as for identifying changes associated with disease or injury. The fatty myelin bilayers that make up myelin surrounding the majority of axons in the central nervous system are indispensable for efficient signal transmission, as they enable saltatory
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conduction that greatly increases the propagation velocity of action potentials along nerve fibers.
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A compromised myelin structure leads to detrimental brain function including impaired motor
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performance, worsening cognitive abilities, and loss of vision [1]. The importance of myelin is highlighted by the multitude of neurological and neurodegenerative diseases it has been
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implicated in such as multiple sclerosis (MS) [2,3], schizophrenia [4], and even diseases
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previously not thought to involve myelin, such as Parkinson’s disease [5]. Although much
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research has focused on assessing myelin at specific loci, such as lesions seen in multiple sclerosis [2,6], often more diffuse changes in normal-appearing or diffusely affected tissue are of
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interest. In such cases, myelin features are commonly assessed in large volumes of interest, such
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as white matter (WM) across the entire brain or whole fibre bundles [3]. However, myelin changes during development [7] aging [8–10], neurodegeneration [11], disease processes [11], and even sex differences [12] lead to spatial variability in myelin content, that may obscure findings if myelin content is integrated over too large a volume. Myelin water imaging is a quantitative MRI technique that can be used to calculate the myelin water fraction (MWF), a measure that has been validated as being directly correlated with myelin content [13], [14]. This technique uses a multi-echo T2 relaxation sequence to sample a large range of echo times, enabling the decomposition of the measured decay curve into constituent T2
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times. Myelin water is represented by short T2 times between 15-40ms. The MWF is then defined as the fraction of myelin water-related T2 amplitudes compared to the total water. A nonnegative least squares (NNLS) algorithm is typically used to fit the multi-echo T2 decay curve with a set of exponential basis functions [15]. However, such an approach is potentially illposed due to the non-orthogonality of the different exponential basis functions and may lack robustness in the presence of noise [16]. Thus, both biological and numerical processing factors
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may lead to visually noisy spatial maps with little apparent spatial structure apart from discerning
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white matter from grey matter.
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Diffusion Tensor Imaging (DTI) studies provide complementary information about WM
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integrity. DTI metrics such as fractional anisotropy (FA) display consistent patterns along
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specific WM fibre bundles [17] that are sensitive to pathology [18,19] and age [20]. While DTI studies are somewhat quantitative and provide insight into general WM microstructure, they do
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not easily correspond to known biological quantities such as myelin [21,22] or iron content [23]
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that can be measured during pathological examination. In contrast, MWF shows a strong
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correlation with myelin in histopathological studies [14]. DTI measures and MWF have been shown to correlate to some degree [24], with both measures being confounded to varying degrees by other WM microstructural factors such as crossing fibres [25] and axonal packing [26] for DTI, and high SNR sensitivity [16] and potential exchange effects [27] for MWF. However, almost all MWF reconstruction algorithms lead to maps that appear spatially “noisier” compared to DTI (e.g. FA) maps. Changes in myelin along tracts would be consistent with a large body of animal literature. Studies in mice have shown a complex pattern of myelin ensheathment that varies in length and
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thickness along axons relative to its location in the brain [28,29]. These differences in myelination along individual axons may be related to another critical role of overall myelination -- the maintenance of synchronous firing of connected neurons. Maintaining synchronicity in timings of signals arriving at a given brain area but originating from different areas with differing lengths of axons could be another important aspect of brain signalling in order to elicit a neural response at the target brain area [30–32]. This phenomenon has been observed in neural
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input originating from different thalamic regions and ending in the somatosensory cortex and is
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believed to be due to the differing myelination of these axonal populations [31,33]. While these
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studies report findings on individual axons utilizing mouse models and electron microscopy, the
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effect of differently myelinated axons would conceivably be seen on a larger macroscale with MWI. Thus, investigating a spatial pattern of myelination along major fibre bundles could
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provide further evidence of distinct myelination along trajectories supporting synchronicity in
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the brain on the macroscale.
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A number of studies have started to examine imaging changes within WM tracts. De Santis et al. [34] created a MRI atlas of white matter microstructure in healthy subjects by comparing means
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and standard deviations in different ROIs of several measures calculated using DTI and mcDESPOT. mcDESPOT can be used to calculate MWF, although the acquisition and analysis procedures differ from the multi-echo T2 relaxation approach used here, and MWF values differ between these two approaches. They investigated seven WM tracts and subsampled each measure along each tract where they found a left/right hemisphere asymmetry pattern with varying degree of asymmetry between measures. Compared to typical DTI measures, MWF calculated based on mcDESPOT generally showed more asymmetry. Furthermore, when taking the average of each tract, in five out of the seven WM tracts investigated, the mcDESPOT MWF
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required a larger sample size than FA to reach significant results. While their work was aimed at disentangling the interrelations between different measures of white matter integrity in several ROIs, they only examined variations in measures along fibre tracts for their asymmetry analysis between hemispheres. Another study investigated MWF and radial diffusivity (RD) along a selection of fibre tracts in both MS and healthy subjects and could pinpoint differences along
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tract profiles that coincided with lesion locations [35]. In this work, we aimed to characterise the basic spatial structure of MWF maps with respect to
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white matter structural organisation and relate the spatial structure of MWF maps to that of FA
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maps. To this end, we examined whether the MWF variance within major WM fibre bundles is
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less than in regions immediately surrounding the fibre bundle. Additionally, we explored if
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MWF maps follow a tight spatial pattern that follows the underlying fibre organisation, and therefore the MWF variance gradient along fibre bundles should be smaller compared to an
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orthogonal direction. Furthermore, we investigated if different major white matter tracts have a
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characteristic pattern of MWF values along their trajectories allowing for the identification of local changes that may be of diagnostic value and related this to structure and patterns in FA
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maps. Finally, to determine if there was biological significance to the characteristic pattern along the fibre bundles we investigated the capabilities of tract MWF profiles versus tract MWF averages to estimate subjects age and differentiate between sex.
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2. Materials and Methods All subjects provided written, informed consent. We acquired data from a total of 41 healthy subjects (18 M and 23 F), with median age of 28 years with a total age range of 32 years from 20 to 52 years. All subjects had no known history of neurological disease. All data were acquired on a Philips (Netherlands) Achieva 3T MRI scanner with an 8 channel head coil. We acquired a full brain 3DT1-weighted scan for structural references with an MPRAGE sequence TI=808ms,
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TR=1800ms and an isotropic voxel size of 1mm3. T2 relaxation data were collected using a
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modified GRASE sequence with 32 echoes with 10ms echo spacing and TR=1000ms. Twenty
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slices were acquired at 5mm slice thickness and reconstructed to 40 slices at 2.5mm [15]. The in-
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plane voxel size was 1x1mm. Twenty subjects (mean age 26.8 5.4 years, 9 females) had DTI
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data sets with TE=69ms, TR=6179ms, with 32 gradient orientations, a b value of 700 s/mm2 and one b0 volume. The remaining 21 subjects (mean age 35.6 9.9 years, 14 females) had diffusion
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tensor imaging data sets acquired with TE=75ms, TR=7465ms, 16 directions, with a b value of
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900 s/mm2 and one b0 volume. Both DTI sequences were acquired at a 2.2 x 2.2mm in-plane
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resolution and reconstructed to 0.8 x 0.8mm in-plane resolution with a 2.2mm slice thickness.. The multi-echo GRASE sequence was analysed using in-house written MATLAB (Natick, MA, USA) code which uses an NNLS fitting method to approximate the multi-exponential decay curve with a number of basis functions, including corrections for stimulated echoes as well as a regularizer to make the fit more robust against noise in the time domain [36], resulting in one MWF map per subject. DTI data were corrected for geometric distortions and subject motions using FSL’s DTIFIT [37] prior to fitting the tensors and performing whole brain deterministic tractography using
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mrDiffusion, part of vistasoft (http://white.stanford.edu/software/). Sixteen major white matter tracts were segmented in both hemispheres with the AFQ toolbox [17]. Briefly, AFQ uses whole brain fibres and segments major fibre bundles based on predefined waypoint region-of-interest (ROIs), after which it compares the selected fibre bundles to a probabilistic atlas to remove potential outliers. Once the fibre tracts have been segmented, they are clipped to contain the fibres in between two defining waypoints per tract, as the intersubject variability beyond those
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endpoints was too large to robustly segment the tracts, precluding any quantitative attempt for
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characterization.
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In order to apply the fibre bundle masks to the MWF maps, for each subject the first echo of the
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GRASE data was registered to the non-diffusion weighted scan from the DTI acquisition (b = 0
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s/mm2 or b0) and the resulting transformation matrix was then applied to each MWF map. Registrations were done with FLIRT [37]. A white matter mask was generated using FSL’s
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FAST [37] on the high resolution and skull-stripped 3DT1-weighted images and registered to the
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b0 image using a transformation matrix generated by registering the 3DT1-weighted image to the b0 image. All registrations were visually checked for accuracy and, if needed, performed again
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with tweaked parameters in order to obtain well aligned images. In order to compare the spatial smoothness of MWF and FA maps, we first computed the local coefficients of variation (CoV) in a 9x9 voxel neighbourhood, on axial slices, across all white matter. The coefficient of variation was selected for a fair comparison to compensate the different plausible numerical ranges between the MWF and FA maps that will be accounted for in the CoV. Note that this comparison was done on a MWF map that went through a coregistration process to DTI space, so that the spatial resolutions are the same, and thus some
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degree of smoothing occurs during this procedure. Nevertheless, this should only impact the result slightly, and if anything, increase the spatial smoothness of MWF maps. Following this, we compared the variances of MWF and FA values in WM fibre bundles to their respective “tubes” – i.e. one-voxel layer of WM voxels surrounding each tract. To account for possible partial volume effects, imperfect fibre tracking, and registration misalignments between
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the b0 and myelin data, we introduced a gap of one voxel between the fibre bundles and their enclosing tubes (see Figure 1 for a schematic illustration). To further limit the influence of
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potential partial volume effects, we masked the generated tubes with the individuals WM mask
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to ensure that only WM voxels were being considered. The WM masks were based on the
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probabilistic output from FAST and only voxels with a probability of 95% or greater were
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retained. Note that this may lead to incompletely closed tubes in some fibre bundles that were close to the grey/white matter interface but allows for a fairer comparison between tracts and
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their enclosing tubes since only WM voxels are being examined.
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We further tested if the gradients of MWF and FA CoVs along adjacent segments of fibre
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bundles differed compared to perpendicular directions. More specifically, we calculated the differences of CoV between two adjacent segments along each tract and compared this gradient to the differences between a fibre segment and its immediate tube-segment neighbour (voxels enclosing the fibre bundle voxels, in perpendicular direction to the main fibre bundle direction). We divided each fibre bundle into 15 equidistant sub-regions and extracted the averages and CoVs of MWF and FA values in each segment. We used fibre bundles to create a weighted mask to subsequently interrogate MWF and FA values.
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Finally, we determined the biological significance of sampling MWF values along fibre bundles in two ways: 1) we examined if the age of a subject could be better estimated by average MWF in segments along a fibre bundle compared to the average MWF of the whole bundle and 2) we investigated if a classification by sex was more accurate with tract profiles than with tract averages.
2.1 Statistical Tests
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All statistical tests were performed using MATLAB v2015a (Natick, MA, USA). Results were
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deemed statistically significant at p<0.05 without correction for multiple comparisons in this
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exploratory analysis. A two sample t-test was used to compare the local, slice-by-slice computed
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CoVs between one representative MWF and FA map. Differences in variance of the WM tracts, and tubes were assessed with a two-sample t-test. A multiple linear regression model was used to
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examine the relation between age and the 15 segments per tract where all segments per tract
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served as predictors. In the case of the average MWF per fibre bundle, a simple linear regression was performed with the average MWF per tract as predictor and age as the outcome variable. A
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Linear Discriminant Analysis (LDA) was performed with the goal to differentiate males and
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females based on their MWF. Two LDAs per tract, with either its segments or whole average as features, and with subjects as observations were performed. LDA maximises the ratio of between-class variance to within-class variance, thus finding the most discriminative projections of data features so that the projected data is well distinguished between classes. We compared the accuracy of sex classification between tract profiles and tract averages as well as computing the Akaike Information Criterion (AIC) for both, the regression and LDA in order to test whether the models utilizing tract profiles were more appropriate. Statistical significance is marked with
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black stars in all figures. The significance level was set to p<0.05 without correction for multiple
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comparisons in this exploratory analysis.
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3. Results Despite the differences in DTI acquisition parameters in the two cohorts, the extracted fibre bundles were visually comparable across subjects. An individual analysis of MWF variances in fibre bundles and tubes in both cohorts demonstrated similar behaviour, so that the results shown here are from the combined cohort. Individual plots of the main findings can be seen in the
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supplementary material.
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Figure 2 shows the histograms of accumulated local CoVs for both maps, normalized to
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probabilities, in WM voxels only. It is apparent that MWF maps have higher CoV than FA maps,
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consistent with the empirical observation that the maps appear less spatially smooth.
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All extracted major white matter fibre bundles from one representative subject can be seen in Figure 3.
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Comparing the CoV of MWF values between fibre bundles and their respective tubes revealed
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that the CoV of tubes was higher in all WM tracts except the callosum forceps minor, but only
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the left/right thalamic radiation, left/right corticospinal tract, callsoum forceps major, right ILF, left/right SLF, as well as left/right arcuate showed significance (p<0.05), see Figure 4a. A comparison of FA CoV between fibre bundles and their respective tubes revealed that all tubes show higher CoV than major WM tracts (p<0.001 for all comparisons), Figure 4b. Comparing the CoV gradient along WM fibre bundles to the perpendicular direction revealed a consistently lower variance gradient between adjacent fibre segments than between fibre segments and tubes (Figure 5). While this was true for both MWF and FA, the MWF maps displayed slightly larger CoV gradients in most WM tracts. CoV gradients in MWF maps were significantly lower along fibre bundles than in perpendicular directions in all examined WM
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tracts except in the cingulum cingulate and callosum forceps minor where some pairs of segment-to-segment and segment-to-tube gradients did not display significant differences. The CoV gradients in FA maps exhibited a very similar behaviour in all tracts where the CoV gradient was lower between segments than between segments and tubes. The across-subject averages of MWF and FA along major fibre bundles are displayed in Figure
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6. Note a characteristic pattern along major fibre bundles. Some tracts such as the callosum forceps minor and major as well as the inferior fronto-occipital fasciculus were very consistent
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across subjects as indicated by low standard errors. This qualitative comparison held true for
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both MWF and FA patterns along the WM tracts. Further, some fibre bundles show a similar
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behaviour for both MWF and FA such as the callosum forceps major or the inferior longitudinal
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fasciculus (ILF). Others, such as the thalamic radiation or inferior fronto-occipital fasciculus (IFOF), show only some commonalities between MWF and FA patterns. In the case of the
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thalamic radiation, both show an increase of MWF and FA until roughly to the middle of tract
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decreases and increases.
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where the FA pattern shows a monotone decrease while the MWF pattern shows more complex
Note all Figures displaying either the CoV gradients or the averages of segments along each fibre bundle are showing results from the left hemisphere WM tracts. Please refer to supplementary Figures S1-S4 for results of right hemisphere tracts. To determine if there was biological significance to the characteristic pattern along the fibre bundles, we performed a multiple linear regression in an effort to estimate the subjects’ age, as this is known to robustly influence myelin [8–10] and compared the performance between including the individual averages of all segments per tract or the average of all segments per tract
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as predictors. We found that using fibre segment averages was more predictive of age than a single average per tract. We found that the callosum forceps major (R2adj=0.41, p=0.012), left IFOF (R2adj=0.36, p=0.035), and left arcuate (R2adj=0.54, p=0.003) could significantly estimate age (Figure 7). To ensure that the improved estimations were not only due to the increased number of predictors,
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outperformed the model using only the average (Figure 7).
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we compared the AIC between the two models and found that the model including the segments
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Additionally, we compared the tracts in which MWF values could estimate age with the corresponding FA tract profiles in order to identify regional differences. Figure 8 illustrates the
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MWF profiles (green) and FA profiles (orange) in the three tracts. Stars indicate significant
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segments in the multiple linear regression estimating age using MWF values. The MWF profiles demonstrated mostly adjacent segments that were significant predictors, except in the left IFOF.
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their general trend.
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Furthermore, significant segments can be observed where the MWF and FA profiles differ in
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The results from the LDA are shown in Figure 9a, where the accuracy of differentiating males from females was higher for tract profiles in each tract. The lower AIC as seen in Figure 9b indicates a superior model for the tract profiles as well. Figure 10 displays the receiver operator curves (ROC) for each LDA performed using either the tract profiles (blue) or whole tract (red). LDA models performed on the tract profiles consistently outperformed the models utilizing only the tract averages. The average area under the curve (AUC) for tract profiles was 0.87 while the average AUC for the whole tracts was 0.69 (p<0.0001). A table with individual sensitivity and specificity values can be found in the supplementary information (Supplementary Table T1).
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4. Discussion We have shown that MWF maps, despite their spatially unsmooth appearance, possess a spatial structure that substantially follows tracts derived from DTI. This draws into question how informative simply averaging MWF values over broad volumes really is. We have demonstrated MWF values are more consistent along a fibre bundle compared to “tubes” surrounding the fibre
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bundles, although MWF values are still more variable than FA values. Furthermore, we report that the variances of MWF as well as FA values exhibit a spatial gradient in major white matter
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(WM) fibre bundles that is lower along fibre tracts compared to perpendicular directions. This
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lower gradient along axonal pathways indicates a central role of MRI-derived major white matter
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tracts in the overall microstructural organisation of the cerebral WM and that indices of WM
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integrity should be evaluated with care to the underlying microstructure.
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While MWF CoVs were typically less in fibre bundles than their surrounding tubes, only 10 out of the total 16 fibre bundles exhibited significant differences. In contrast, FA CoVs displayed
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significant differences in all fibre bundles, making them appear to be a more stable measure of
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characterising WM microstructural integrity, albeit less biologically specific. However, it should be noted that the extraction of fibre bundles is directly biased towards FA values in terms of selecting voxels to fibre tracking as well as indirectly when tracing each fibre. Additionally, the left/right IFOF are one of the longest bundles and tend to be more difficult to track from occipital to frontal areas. In conjunction with the generally observed pattern of higher MWF values in posterior regions compared to anterior regions, these fibre bundles cover a wide range of MWF values.
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The lower CoV gradients along fibre tracts suggest evidence of MWF values following a pattern of microstructural WM organisation, highlighting the importance of WM fibre bundles. Both MWF and FA followed the same trend, in that the CoV gradient was lower between fibre bundle segments than in perpendicular directions with the difference being usually more pronounced in FA maps indicative of a steeper change of FA values from within fibres to its surroundings.
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We have demonstrated that each major fibre bundle has its own specific pattern of myelination, which is relatively consistent across subjects, with a general observation of higher to lower
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MWF values when one moves from posterior to anterior. Some structures such as the callosum
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forceps major/minor have quite intricate spatial patterns, which are completely lost when simply
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averaging over the entire tract. Thus, studies investigating age effects on myelination or inferring
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disease progression based on tract informed analysis may potentially more sensitive to subtle local changes in MWF. While it might be apparent that including more information about MWF
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values would increase predictability of a clinical index such as age, the key point is that the
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enhanced predictability implies consistency across subjects of MWF segments within a fibre bundle. It should be noted that MWF tract profiles has been computed before, with the focus
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there on four fibre bundles of the right hemisphere that were relevant to their specific MS cohort at hand [35]. In this work, we focused on characterising 16 major fibre bundles in a healthy cohort in order to outline the majority of healthy WM. We note that the overlapping investigated fibre bundles show qualitative similarities. The MWF tract profiles were able to significantly estimate age in three fibre tracts, the callosum forceps major, left IFOF and left arcuate. The most important segments in the left arcuate were segments exhibiting a steady decline in MWF profiles but showed a large variability in FA profiles. Similarly, the important segment in the left IFOF marked the point of a steep increase in
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the FA profile while in the MWF profile it was the start of a plateau. In case of the callosum forceps major, both profiles showed a similar behaviour, however the steep increase and decrease around the midline in the MWF profile seems to have profound effects in age estimation. Further, the MWF tract profiles could consistently better separate male and female sex when
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compared to using the tract average MWF and could present a method to gain more detailed insight into WM microstructural differences based on sex. While sex differences in MWF of the
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corpus callosum have been previously reported [12], other human adult studies of sex differences
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in MWF are scarce, potentially due to the limitation of commonplace ROI/tract average
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measures used in statistical analysis. Additionally, since LDA estimates a projection which
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maximises within to between class variance, it may be able to detect subtle sex differences more robustly than more traditional methods such as simple t-tests or logistic regression.
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We recognize that the true biological origin of the tract profiles cannot be fully determined in
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this study. The tract profiles could stem from differing myelination patterns along the axons that
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in sum produce a characteristic pattern of MWF values along each tract, in line with the synchronicity theory. Another explanation for the tract profiles we observed could be due to different fibre bundles crossing and merging into each other creating a heterogeneous microstructure which may not be resolved with the current MWF maps. The MWF profile of the callosum forceps minor/major, fibre bundles with little crossing or merging fibres, however do suggest a distinct myelination pattern. Further studies with higher spatial resolution in both MWI and DTI as well as more DTI gradient directions are needed to obtain a more detailed description of the trajectories myelination patterns of WM fibre bundles.
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We note that there are a number of limitations to this study. We had a rather narrow age range that may have limited the capacity of the regression analysis to predict age in some WM tracts. The use of two different DTI data sets with different acquisition parameters may introduce some confounding factors, namely in the accuracy of fibre tracking. However, examining these two
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sub-data sets separately did not reveal striking differences (see Supplementary Material) except possibly the thalamic radiation. A possible explanation could be imperfect fibre tracking
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in the thalamus, which is known to be a mixture of white- and grey matter tissue and thus finding
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a principal diffusion direction is always challenging and directly relates to the number of
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diffusion gradient used during data acquisition (16 vs 32 directions in our cohorts). Since our
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main focus was to establish a biological significance of the tract profiles, this difference does not appear to affect our conclusions. Future studies may use diffusion spectrum imaging (DSI) in
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order to mitigate the effects of crossing fibres and thus getting more accurate fibre tracking and
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consequently more robust measures. This could then be used to look further into the differences between the MWF and FA profiles as an area with crossing fibres should influence FA more than
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MWF and thus provide information whether or not crossing fibres are a dominant factor in the discrepancies between MWF and FA tract profiles. It should be noted that due to the healthy cohort, age and sex were the only available demographic variables to test usefulness of the tract profiles. This can easily be extended to a patient population with various clinical and behavioural data in order to pinpoint specific segments most associated with aberrant behaviour. Regarding the contribution of individual segments of the left IFOF in the estimation of age, the only segment significantly contributing may be influenced by partial volume effects as this part of the
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tract is running through the external capsule, a very thin WM structure that may not be purely WM with a 5 mm slice thickness. In summary, our results suggest that there is a deterministic spatial pattern in MWF despite the apparent unsmooth appearance of MWF maps. Our results indicate that when performing an ROI based analysis, one should be aware to the underlying white matter microstructure when
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investigating large ROIs containing multiple fibre tracts. When investigating whole fibre tracts, it may be inadvisable to integrate the MWF over the entire tract length rather than looking at
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smaller segments within each tract. The number of sections to divide each fibre bundle that we
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chose is somewhat arbitrary; further work will be required to determine the optimal number of
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segments.
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Acknowledgements: We are grateful to Saurabh Garg for the meaningful discussions during the
acquiring the data.
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course of this study. We thankfully acknowledge the help of all the MR technologists for
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Conflict of interest: None
Grant support: This work was partially supported by a Multiple Sclerosis of Canada Operating grant awarded to Professors McKeown and MacKay. MJM was supported by the PPRI/UBC Chair in Parkinson’s Research. Dr. Kolind has received research support from Roche, Genzyme, the MS Society of Canada, NSERC, VCHRI, MSFHR and Milan & Maureen Ilich Foundation, and consultancy fees for Acorda, Genzyme.
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Figure Captions
Figure 1: Schematic illustration explaining the subdivision of a fibre bundle (blue) into segments as well as the "tubes" (red), i.e. voxels enclosing the fibre bundle with a one voxel gap (grey) in between.
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Figure 2: Histogram of local CoV in a 9x9 voxel rectangle comparing MWF and FA maps. Significantly lower variances can be observed in FA maps, indicating an overall smoother spatial appearance.
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Figure 3: Rendering of the extracted major fibre bundles. a) blue: callosum forceps minor/major, red: thalamic radiation, green: cingulum cingulate, orange: superior longitudinal fasciculus (SLF). b) blue: inferior fronto-occipital fasciculus (IFOF), red: corticospinal tract, green: inferior longitudinal fasciculus (ILF), orange: arcuate
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Figure 4: Coefficient of Variation (CoV) of whole tracts and tubes in a) MWF and b) FA.
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Figure 5: CoV gradients between adjacent fibre segments (blue) and between fibre segments and tube segments perpendicular to fibre tract orientation (red). MWF CoV shown in a) and FA CoV shown in b). In both cases the majority of segment-to-segment and segment-to-tube pairs show significant differences. Errorbars depict standard errors across subjects. Shown are tracts from the left hemisphere.
Figure 6: Tract profiles of MWF and FA measures. a) average MWF and b) average FA in segments along each tract. Segments are shown along the x-axis indicating relative directions in the brain (A=anterior, P=posterior, L=left, R=right, I=inferior, S=superior). Errorbars show standard errors across subjects. Shown are tract profiles of left hemisphere tracts.
Figure 7: Age estimations based on multiple linear regression using tract profiles as predictors (blue) versus using only the tract average as a predictor (red). Shown are the significant
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estimation based on segments. The AICs for each model are listed below and showing lower values for the tract profile models, indicating favorable models.
Figure 8: MWF (green) and FA (orange) tract profiles of tracts able to significantly estimate age based on MWF predictors. Stars indicate significant segments in the model along the MWF profile
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Figure 9: Linear Discriminant Analysis (LDA) results for differentiating sex based on MWF. a) shows the accuracy of LDA when using the MWF tract profile (blue) or MWF tract average (red). Higher accuracy can be seen for all tract profiles. b) AIC per tract model, the model utilizing the tract profiles show a smaller AIC and are thus preferred.
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Figure 10: ROC plots for each LDA. Light blue and light red show the ROCs for each LDA per tract, thicker lines show the average. Mean AUC for tract profiles: 0.87, mean AUC for whole tracts: 0.69