Disentangling white-matter damage from physiological fibre orientation dispersion in multiple sclerosis

Abstract Multiple sclerosis leads to diffuse damage of the central nervous system, affecting also the normal-appearing white matter. Demyelination and axonal degeneration reduce regional fractional anisotropy in normal-appearing white matter, which can be routinely mapped with diffusion tensor imaging. However, the standard fractional anisotropy metric is also sensitive to physiological variations in orientation dispersion of white matter fibres. This complicates the detection of disease-related damage in large parts of cerebral white matter where microstructure physiologically displays a high degree of fibre dispersion. To resolve this ambiguity, we employed a novel tensor-valued encoding method for diffusion MRI, which yields a microscopic fractional anisotropy metric that is unaffected by regional variations in orientation dispersion. In 26 patients with relapsing-remitting multiple sclerosis, 14 patients with primary-progressive multiple sclerosis and 27 age-matched healthy controls, we compared standard fractional anisotropy mapping with the novel microscopic fractional anisotropy mapping method, focusing on normal-appearing white matter. Mean microscopic fractional anisotropy and standard fractional anisotropy of normal-appearing white matter were significantly reduced in both patient groups relative to healthy controls, but microscopic fractional anisotropy yielded a better reflection of disease-related white-matter alterations. The reduction in mean microscopic fractional anisotropy showed a significant positive linear relationship with physical disability, as reflected by the expanded disability status scale. Mean reduction of microscopic fractional anisotropy in normal-appearing white matter also scaled positively with individual cognitive dysfunction, as measured with the symbol digit modality test. Mean microscopic fractional anisotropy reduction in normal-appearing white matter also showed a positive relationship with total white-matter lesion load as well as lesion load in specific tract systems. None of these relationships between normal-appearing white-matter microstructure and clinical, cognitive or structural measures emerged when using mean fractional anisotropy. Together, the results provide converging evidence that microscopic fractional anisotropy mapping substantially advances the assessment of cerebral white matter in multiple sclerosis by disentangling microstructure damage from variations in physiological fibre orientation dispersion at the stage of data acquisition. Since tensor-valued encoding can be implemented in routine diffusion MRI, microscopic fractional anisotropy mapping bears considerable potential for the future assessment of disease progression in normal-appearing white matter in both relapsing-remitting and progressive forms of multiple sclerosis as well as other white-matter-related brain diseases.


Introduction
Multiple sclerosis is a heterogeneous neurodegenerative and inflammatory disease, causing wide-spread pathology in the central nervous system (Thompson et al., 2018). MRI plays a critical role in the clinical assessment of multiple sclerosis revealing spatial dissemination and load (Filippi et al., 2019). Lesion load correlates with clinical scores and disease progression (Bodini et al., 2011;Matias-Guiu et al., 2018). However, correlation is often rather poor and routine MRI lacks specificity to the underlying pathological mechanisms of multiple sclerosis (Poloni et al., 2011). Multiple sclerosis lesions also give rise to wide-spread changes in the surrounding normalappearing white matter (NAWM) such as axonal degeneration and demyelination, however, these changes are poorly visualized and quantified by standard diagnostic MRI techniques (Lassmann, 2011;Filippi et al., 2012;van Horssen et al., 2012;Kutzelnigg and Lassmann, 2014). These limitations explain why the pathological changes, as revealed by clinical MRI, only show a relatively poor correlation with individual clinical disability, contributing to the so-called clinico-radiological paradox (Chard and Trip, 2017).
Diffusion MRI measures the regional mobility of water molecules and has the potential to offer more specific insights into the underlying microstructural changes (Alexander et al., 2019;Dyrby et al., 2018). The diffusion of water molecules is higher along than perpendicular to axons, causing a high degree of diffusion anisotropy in cerebral white matter (WM). Fractional anisotropy (FA) of WM obtained from diffusion tensor imaging (DTI) (Basser and Pierpaoli, 1996) is tightly associated with the presence of the densely packed and myelinated axonal structures, but also the presence of glial cells in disease (Beaulieu, 2002). DTI in combination with tractography is highly sensitive and has enabled quantification of tract-related microstructural changes in multiple sclerosis, which correlate with lesion load (Droby et al., 2015), clinical scores (Pagani et al., 2005), cognitive measures (Bester et al., 2013) and tract-specific physiological measures (Wahl et al., 2011). However, consistent conclusions between similar studies are not guaranteed (Sbardella et al., 2013). For example, DTI group differences between healthy controls and relapsingremitting multiple sclerosis patients have been found in some studies (Preziosa et al., 2011), but not all (Nusbaum et al., 2000;Wilting et al., 2016).
The FA metric is challenging to interpret since it intermingles mesoscopic tissue architectonic features (i.e. fibre orientation dispersion and crossings) with microscopic tissue features (i.e. axons, cells and their density). Both can lead to changes in FA that can be interpreted as pathology as illustrated in Fig. 1. Since 90% of WM voxels contain crossing fibres (Jeurissen et al., 2013;Schilling et al., 2017), axonal fibres are never perfectly aligned, making it almost impossible to disentangle tissue microstructural anisotropy from macrostructure using FA (Basser and Pierpaoli, 1996;Oouchi et al., 2007;Wheeler-kingshott and Cercignani, 2009;Vos et al., 2011;Wang et al., 2015). For example, increased FA was reported in Alzheimer's disease but was attributed to changes in fibre orientation dispersion rather than to changes in microscopic anisotropy (illustrated in Fig. 1, environment B versus E) (Douaud et al., 2011;Teipel et al., 2014).
The problems inherent to FA are introduced at the acquisition level since only a standard linear diffusion MRI (dMRI) scheme is used. However, the inherent ambiguity of FA as a microstructural measure can be circumvented by optimizing the acquisition scheme. Recently, the conventional DWI acquisition scheme has been combined with an additional tensor-valued acquisition scheme, called spherical tensor encoding (STE) (Mori and Van Zijl, 1995;Eriksson et al., 2015;Westin et al., 2016;Topgaard, 2017). The combination of the two dMRI and damaged multiple sclerosis tissue. In addition, the figure includes voxel-wise averages of FA and lFA. In straight fibre environments (A) it is expected that both FA and lFA will be high and approximately equal, but crossing (B) and fanning (C) fibre situations will expectedly decrease FA but keep lFA high. In straight degenerated fibre bundles (D) both FA and lFA will be lower as compared with the normal tissue (A). In crossing fibres when one fibre bundle is degenerated (E) FA may be higher and lFA lower as compared with the normal tissue (B). Lesions in straight fibre bundles (F) will decrease both measures equally. FA ¼ fractional anisotropy; lFA ¼ microscopic fractional anisotropy. acquisitions allows the estimation of a micro-FA (lFA) map which decouples fibre orientation dispersion from microstructural tissue features without the need of advanced modelling (Cory et al., 1990;Jespersen et al., 2014;Lasi c et al., 2014;Shemesh et al., 2016). Until now, lFA mapping has only been applied in a few case studies of multiple sclerosis (Yang et al., 2018), cancer Nilsson et al., 2020) and with related techniques in ageing (Lawrenz et al., 2016). Therefore, it remains to be clarified whether lFA can advance microstructural mapping of disease-related tissue damage in multiple sclerosis disease progression and whether the lFA metric correlates more closely with clinical scores than the standard FA metric.
In this study, we employed lFA mapping to resolve the ambiguity of microstructural anisotropy mapping in multiple sclerosis by disentangling disease-related tissue damage from fibre orientation dispersion. We hypothesized that lFA mapping will improve the sensitivity of diffusion MRI to detect regional microstructural tissue pathology and improve the correlation of WM tissue damage with clinical scores in individual patients relative to standard FA mapping. We applied standard dMRI (DTI) for FA mapping and tensor-valued dMRI for lFA mapping (Lasi c et al., 2014) in three subject groups including relapsing-remitting and primary-progressive multiple sclerosis and age-matched healthy controls. Both FA and the novel lFA were evaluated in regions of interests (ROIs) including the total NAWM as well as in three fibre tracts with different known functional relations to multiple sclerosis, and complexity in structural architecture that the lFA is expected insensitive to but not the FA. These are the corticospinal tract (CST), superior longitudinal fasciculus (SLF), and cingulum (CING). In addition, we performed correlations with clinical disability as measured with the expanded disability status scale (EDSS), cognitive processing as measured with the symbol digit modality test (SDMT).

Subjects
The study included 45 multiple sclerosis patients and 28 healthy controls (Table 1). Five multiple sclerosis patients and one healthy control were excluded from data analysis because of missing data (data were not exported correctly from the scanner), thus the final analyses included data from 40 multiple sclerosis patients (26 relapsing-remitting multiple sclerosis, 14 primary-progressive multiple sclerosis) and 27 healthy controls. Approval was given by the Ethics committee of the Capital Region of Denmark (Protocol H-15006964) and written informed consent was obtained from all subjects before inclusion in the study according to the Declaration of Helsinki.

Clinical and cognitive assessments
The EDSS (Kurtzke, 1983) was performed by a trained neurologist and used to examine the multiple sclerosis patients' physical disability. The SDMT (Smith, 1982) was performed to evaluate cognitive processing speed. The multiple sclerosis patients performed the SDMT test orally, where the patients had the paper in front of them and spoke out the answer to the examiner, who noted the answer. The healthy controls did a written version of the test and wrote down the answers themselves.

Magnetic resonance imaging
All MR images were acquired on a Philips Achieva 3T scanner using a 32-channel head-coil. Three different protocols were acquired: (i) standard clinical structural MRI for lesion drawing and segmentation of the brain's WM; (ii) multi-shell dMRI for FA and tractography; and (iii) tensor-valued dMRI for lFA estimation. The protocols were a subset of a more comprehensive multiple sclerosis study.
Tensor-valued dMRI was acquired using two tensor shapes of diffusion encodings i.e. LTE and STE for six bvalues (100, 500, 900, 1200, 1600 and 2000 s/mm 2 ). The LTE acquisition was performed in 15 non-collinear directions for each shell distributed on the unit spheres as described in Szczepankiewicz et al. (2019) (scan time around 16.2 min). The STE uses an isotropic diffusion encoding (Mori and Van Zijl, 1995) based on the magic angle spinning of the q-vector (qMAS) (Eriksson et al., 2013;Topgaard, 2013), and was acquired in 15 repetitions. Spin-echo-based echo-planar imaging was used, with TR ¼ 5400 ms, TE ¼ 147 ms, 2.5 mm isotropic resolution, slice gap ¼ 0.1 mm, 14 axial slices, 90 images, FOV ¼ (240, 240, 36.3) mm 3 . The FOV (shown in Fig. 2A) covered the axial plans of corpus callosum where lesions typically are to be found. Here we used the Philips scanner implementation of the tensor-valued dMRI sequences that also are available for other scanner platforms as described here: https://github.com/filip-szcze pankiewicz/fwf_seq_resources.

Structural MRI processing
In multiple sclerosis patients, lesions were segmented using a semi-automated method in native space. This included co-registration of the T 2 -weighted and FLAIR images to the T 1 -weighted image followed by rigid-body co-registration to the Montreal Neurological Institute (MNI) template using SPM12 software version 6470 (Welcome Department of Imaging Neuroscience, London, UK). Note that no warping was involved during this step but only rigid-body translation/rotations to align the brains best possible to standard space. Then lesions were segmented using a local thresholding technique based on the FLAIR image (Jim 6.0 Xinapse System, Leicester, UK) by a single experienced observer blinded to the subject identity. The T 1 -weighted and T 2 -weighted images were used to guide the lesion delineation. For each subject, the total number of lesions and their volume was calculated. Healthy controls also followed the first initial co-registration between T 1 -weighted, T 2 -weighted and FLAIR images. However, WM abnormalities were not manually delineated in healthy controls.
Freesurfer's recon_all (version 5.3.0; http://surfer.nmr. mgh.harvard.edu) (Dale et al., 1999) was used for brain segmentation to obtain WM ROIs for both left and right hemispheres. Multiple sclerosis lesions, as defined by the semi-automated method described above, were excluded from the WM to provide ROIs for NAWM. ROIs were then eroded by 2 voxels to reduce partial volume effects from CSF, GM and lesions. These ROIs were used as WM ROIs for healthy controls, and as NAWM ROIs for multiple sclerosis patients.

Multi-shell dMRI dataset processing and FA estimation
Data were corrected for susceptibility artefacts using FSL's topup based on the sets of b ¼ 0 images with opposite phase encoding (Andersson et al., 2003) and corrected for motion and eddy current artefacts using FSL's eddy (Andersson and Sotiropoulos, 2016). This was followed by linear co-registration to the subject's T 1weighted scan including re-slicing to 1 mm isotropic resolution using FSL's FLIRT with sinc interpolation .
Voxel-wise FA maps we estimated based on co-registered and interpolated dMRI data using MRtrix3's dwi2tensor (http://www.mrtrix.org/). For the FA parameter estimation, only the b ¼ 1000 s/mm 2 and b ¼ 0 s/mm 2 images from the multi-shell dMRI protocol were used.

Tensor-valued dMRI data processing and lFA estimation
The tensor-valued data were corrected for motion and eddy-currents in ElastiX  using extrapolated reference images . After correction, a mild smoothing (1.25 mm FWHM) was applied using a Gaussian kernel. The lFA map was then estimated using the Multidimensional diffusion MRI toolbox, available at https://github.com/markus-nilsson/mddmri (Nilsson et al., 2018). First, the LTE data were powder (directionality) averaged for each b-value, and the repeated STE dataset was averaged to gain signal-tonoise ratio. Laplace transform of gamma distribution was first fitted to the data points of LTE and STE using nonnegative least-squares fitting and voxel-wise lFA maps were estimated (Lasi c et al., 2014). After fitting, linear co-registration to the subject's T 1 -weighted space was performed by first co-registering the b ¼ 100 s/mm 2 image to the T 1 -weighted registered b ¼ 0 s/mm 2 image from the multi-shell dataset and then applying the same transformation to the lFA image including re-slicing to 1 mm isotropic resolution using FSL's FLIRT with sinc interpolation.
Since lFA data were only acquired in a 36.4 mm slab covering the corpus callosum, we averaged FA both in the same slab as well as in the whole NAWM. The FA results are consistent for both the whole brain as well as the slab, so we only report statistics for the slab NAWM but visualize the results for both analyses.

Tract-based segmentation using tractography
Constrained spherical deconvolution using all b-values from the whole brain multi-shell dataset was used to estimate individual subjects' fibre orientation distribution images using MRtrix3's dwi2response (dhollander method) and dwi2fod. A group fibre orientation distribution template from 65 subjects (including both multiple sclerosis patients and healthy controls) was generated using MRtrix3's population_template. In this group template space, whole-brain probabilistic tractography was performed using default parameters (step size: 0.5 mm, max angle: 45 degrees, fibre orientation distributionthreshold ¼ 0.1) and 10 million streamlines to estimate consistent tract systems of the brain. Post hoc, streamlines belonging to either SLF, CST or CING in each hemisphere were extracted by filtering the set of all streamlines. These tracts have shown to be affected and show relation to cognitive and clinical scores in multiple sclerosis patients (Liu et al., 2012;Onu et al., 2012;Koenig et al., 2015;Tovar-Moll et al., 2015;Deppe et al., 2016). For each tract, this was done by manually placing four different inclusion ROIs along the tract. Finally, the number of streamlines passing through each imaging voxel was counted and thresholded to obtain a binary mask of each tract (see Supplementary Fig. 1). The thresholds used were 50 streamlines for SLF and CING and 500 for CST. The binary masks were then warped back into each individual subjects' T 1 -weighted space. In multiple sclerosis patients, individual subject lesions overlaying any of the masks were excluded to only include NAWM with each tract. Finally, the masks were eroded by 1 voxel to reduce partial volume effects.

Statistical analysis
Mean FA and lFA were calculated in each subject's NAWM, CST, SLF and CING masks for both hemispheres separately. Repeated measures 'hemisphere' (left, right) by 'group' (RRMS, PPMS, healthy controls) ANOVA was performed in SPSS version 25 with age and gender as covariates. This analysis was performed separately for the total WM and NAWM ROI as well as for the CST, SLF and CING. Analysis of the linear correlation (Pearson) for FA and lFA with age, SDMT and EDSS were performed in MATLAB. Total lesion load (volume) was correlated with FA and lFA in the specific ROIs using Spearman's rank correlations in MATLAB. In addition, lesion load was correlated with FA and lFA within ROIs. We set the significance level to P < 0.05 and follow-up t-tests in the ANOVA analyses were corrected for multiple comparisons using Bonferroni correction. SPSS provides Bonferroni corrected P-values (P bonf ) by multiplying the un-corrected P-values with the number of comparisons performed, so the same significance level (P bonf < 0.05) still holds for the follow-up tests.

Data availability
Fully anonymized post-processed data will be made available on reasonable request.

Results
Disease phenotype reflected by lFA, but not FA Voxel-wise group average maps of FA and lFA values obtained in healthy controls are shown in Fig. 1 (left  panel). These group averages illustrate the difference between mean FA and lFA in relation to WM anatomy: FA values are low in regions with orientationally dispersed fibre populations, whereas lFA values are relatively homogeneous in the whole WM. Regional FA is lower than regional lFA, especially in regions with known fibres crossings, e.g. in the centrum semiovale, where corpus callosum projection and the associative fibres are crossing (Fig. 1, arrowhead B).
Repeated measures ANOVA revealed significant differences between groups, when comparing mean lFA and FA in the NAWM slab covered by dMRI, but the pattern differed for the two measures (Fig. 2). The between-group difference in lFA [F(2,63) ¼ 9.00, P < 0.001] was driven by higher mean lFA values in the NAWM in healthy controls relative to patients with relapsing-remitting multiple sclerosis (P bonf ¼ 0.002) and primary-progressive multiple sclerosis (P bonf ¼ 0.006). Mean lFA values in the NAWM did not differ significantly between the two patient groups. Mean FA values in NAWM also showed a main effect of group [F(2,63) ¼ 3.63, P ¼ 0.03], but follow-up t-tests showed only trend-wise differences in mean FA between groups. Patients with relapsing-remitting multiple sclerosis tended to have lower FA values than healthy controls (P bonf ¼ 0.07) and patients with primary-progressive multiple sclerosis (P bonf ¼ 0.08). In contrast to mean lFA values in the NAWM, mean FA values of patients with primary-progressive multiple sclerosis did not differ from mean FA values of healthy controls. For mean lFA and FA of NAWM, ANOVA revealed no main effect of hemisphere nor group by hemisphere interaction (Fig. 2A).

Thresholding FA impacts diseaserelated information
In the analysis above, we averaged FA and lFA values across all voxels in NAWM. The left panel in Fig. 2B shows the within-group average histograms of both FA and lFA measures across the whole bilateral NAWM mask. The FA histograms for the three groups overlap each other almost perfectly. However, the histograms for lFA are clearly different between the groups with primary-progressive multiple sclerosis showing a larger tail towards smaller lFA values and a lower and more leftskewed peak compared to the relapsing-remitting multiple sclerosis distribution.
A common approach to overcome the crossing-fibre problem in FA analyses is to limit the regions of interest to only include voxels with FA greater than a given threshold. Therefore, we investigated the effect of removing voxels with low FA values before calculating the mean lFA and FA values in the WM. When discarding voxels from the analysis, where FA is, respectively, lower than 0.2, 0.4 and 0.6, the between-group differences in mean FA remained the same, but group means are shifted towards higher values ( Supplementary Fig. 2, left panel). The right panel in Supplementary Fig. 2 shows group means for lFA values, again, when removing voxels with low FA values. In this analysis, the group difference between the two multiple sclerosis groups was diminished when voxels with FA values <0.4 were removed, suggesting that this approach of restricting the ROI is removing microstructure information for primary-progressive patients only.

Correlation between lFA measures and clinical rating scales
In the combined multiple sclerosis group (relapsing-remitting and primary-progressive multiple sclerosis) as well as in the group of healthy controls, lFA averaged in NAWM correlated negatively with age (first row in Fig. 3 and Supplementary Table 1), whereas for FA, the age relationship was only significant in the healthy control group (first row in Fig. 4 and Supplementary Table  1). However, post hoc tests revealed no interactions between group and age for lFA and FA. In the combined multiple sclerosis group, lFA, but not FA, was negatively correlated with physical disability as measured with the EDSS in both hemispheres. This means that lower lFA values were associated with higher disability (second row in Figs 3 and 4 and Supplementary Table 1). The correlation, however, was not significant when adjusting for age, suggesting a relation between age and EDSS. Additionally, lFA values showed significant correlations with cognitive performance as measured with the SDMT in both healthy controls and in multiple sclerosis (third row in Fig. 3), which remained significant when controlling for age in the multiple sclerosis group. Again, no significant correlations between FA and cognitive performance were found (third row in Fig. 4).

Tract-specific group analyses
To investigate how fibre crossings along specific tracts might affect group results of FA mapping but not lFA, we performed the same set of analyses which we had performed for the entire NAWM for the NAWM belonging to specific WM tracts having different degrees of architecture complexity. The CING bundle on the part superior to mid-sagittal corpus callosum fibres was selected, because it contains (in that region) a limited number of crossing fibres. In addition, we selected the SLF and CST, both having trajectories projecting through regions where other fibre bundles are crossing e.g. with the corpus callosum (Schmahmann and Pandya, 2006).
We found no significant differences in regional lFA values among the three groups in any of the three tracts (right column in Supplementary Fig. 3 and Table 2). Yet there was a trend towards a between-group difference for lFA values in the SLF (P ¼ 0.085) as well as a trend towards an effect of hemisphere in the CST (P ¼ 0.062). Interestingly, albeit not being significant, regional lFA values showed a consistent similar pattern in all tract systems with a relative decrease in lFA values from healthy controls to relapsing-remitting to primary-progressive multiple sclerosis. In contrast, regional FA values showed significant group differences in the CST (main effect of group: P ¼ 0.007). This between-group difference was caused by higher FA values in patients with primaryprogssive multiple sclerosis relative to patients with relapsing-remitting multiple sclerosis (P bonf ¼ 0.024) and healthy controls (P bonf ¼ 0.006). Increase in FA with disease progression could indicate degeneration of a crossing-fibre tract (Fig. 1E). When considering all patients with multiple sclerosis together, we found negative correlations between age and lFA values in SLF (both hemispheres) and left CING (Supplementary Table 1). Similarly, lFA values in left CING of healthy controls also correlated with age. In the multiple sclerosis group, disability as measured with EDSS correlated negatively with lFA values in the left CING. Trends towards significant correlations were also found in left CST and right SLF. However, when controlling for age these effects were no longer significant. FA values in the left SLF (whole brain) correlated positively with EDSS, which also persisted after controlling for age.
Both, tract-specific lFA and FA values, scaled with cognitive processing speed in patients with multiple sclerosis, as measured with SDMT. SDMT correlated positively with tract-specific lFA values in bilateral CING and SLF. Trends towards significant correlation between tractspecific lFA values and cognitive processing speed were also found in the right CST. In healthy controls, significant correlations between tract-specific lFA values and cognitive processing speed were observed in the right CING and right SLF. There, was also a significant relationship between cognitive processing speed and tract-specific FA values, but this correlation was only found for the left CING and was present in both, multiple sclerosis and healthy controls.
Whole-brain lesions-load correlates with mean lFA but not FA of NAWM The hallmark of multiple sclerosis is the focal lesions, which are distributed diffusely in the brain. Lesions are areas with a high degree of demyelination and axonal degeneration and will thus also affect the remaining part of the NAWM. We correlated lesion load, that is the total lesion volume, with lFA values in the different regions of interest to investigate whether a larger number of lesions would result in greater decrease of microstructural anisotropy.

Discussion
We show that lFA mapping substantially advances microstructural imaging of cerebral WM with multiple sclerosis compared to standard DTI-based FA mapping. Tensor-valued dMRI minimized the influence of fibre dispersion to the estimation of regional anisotropy already at the data acquisition stage (Lasi c et al., 2014). This rendered diffusion-based microstructural mapping more sensitive to microstructural alterations directly caused by pathology and overcome the ambiguity from fibre architecture inherent to standard FA mapping. Importantly, the lFA mapping showed a consistent reduction in 'microscopic' anisotropy of NAWM in patients with relapsing-remitting and primary-progressive multiple sclerosis relative to the healthy control group. This significant difference between healthy individuals and patients affected by multiple sclerosis was not evident, when quantifying 'macroscopic' anisotropy of NAWM with DTI-based FA mapping that also is sensitivity to complex fibre architecture. Correlational analysis showed that mean lFA of NAWM scales with physical disability, cognitive dysfunction and the participant's age. These relationships between WM microstructure and clinical variables were not evidenced by mean FA. In the correlation analyses, we pooled patients with relapsing-remitting and primary-progressive multiple sclerosis into a single patient group. We acknowledge that the two multiple sclerosis groups are two distinct phenotypes and, in our study, differed in age and EDSS distribution. Nonetheless, individual NAWM lFA values scaled linearly with patient-specific disease and clinical variables, while NAWM lFA value did not. This observation in a heterogenous patient group highlights the potential of NAWM lFA measurements to provide an MRI-based estimate of multiple sclerosis-related impairment.
Axonal degeneration and indirectly demyelination effects should reduce regional FA because of changes in the volume fractions of the cellular spaces (Beaulieu, 2002;Tuch, 2004;Wheeler-kingshott and Cercignani, 2009). Practically, our results prove that this is not necessarily the case. Most WM voxels contain crossing fibres with a considerable amount of fibre orientation dispersion (Jeurissen et al., 2013;Schilling et al., 2017). In these voxels, regional FA is determined by two tissue properties, namely microscopic diffusion anisotropy and fibre orientation dispersion. This renders the interpretation of regional FA values inherently ambiguous in the context of neuroinflammatory and neurodegenerative diseases. For instance, these two features may exert opposing effects on regional FA. On the one hand, axonal degeneration and demyelination effects may lower FA. On the other hand, axonal degeneration of a single fibre bundle in a crossing-fibre region may reduce the regional dispersion of fibre orientation dispersion and hereby increase regional FA (Pierpaoli et al., 2001;Douaud et al., 2011;Teipel et al., 2014). The ambiguity of the FA metric may explain why tract-specific analysis showed higher mean FA values in patients with primary-progressive multiple sclerosis as compared with patients with relapsingremitting multiple sclerosis and healthy controls. This effect was especially pronounced in the SLF due to its high degree of fibre orientation dispersion, underlining that regional FA is less suited to detect fibre damage in regions with large fibre orientation dispersion. Actually, the observed increasing FA value in primary-progressive multiple sclerosis could indicate a crossing-fibre environment where one fibre tract has degenerated and the fibre orientation dispersion decreases (illustration Fig. 1E), which was previously described in Alzheimer's disease (Douaud et al., 2011;Teipel et al., 2014). On the other hand, regional FA and lFA in CING, a relatively homogenous fibre bundle, resembled each other due to relatively wellaligned fibres, showing a stronger relative decrease in anisotropy in patients with primary-progressive than relapsing-remitting multiple sclerosis.
We found that the total lesion load correlates negatively with lFA in the remaining NAWM as well as in different tract systems ( Supplementary Fig. 2). Multiple sclerosis lesions are focal areas with demyelination and axonal degeneration, but degeneration spreads out from the lesions to the rest of the brain, affecting the microstructure of NAWM. We argue that the degree of axonal degeneration in NAWM scales with lesion load and this mechanism may account for lower mean lFA values in the NAWM of patients with high lesion load. Especially in primary-progressive multiple sclerosis, primary microscopical changes observed with histology in non-lesioned WM may also contribute to the observed lFA decrease in the NAWM (Lassmann, 2019). In our study, we did not find the same relation with FA, which only correlated negatively with global lesion load in the right SLF (as well as a trend towards negative correlation in left SLF).
Only mean lFA but not FA scaled with cognitive processing speed in patients and healthy controls. The higher the individual SDMT score, the higher was mean lFA of the NAWM. The same positive relationship was found when considering the mean lFA of the CING or SLF. Similar correlations have been described previously between SDMT and mean FA in CING (Lin et al., 2014;Koenig et al., 2015) and corpus callosum (Pokryszko-Dragan et al., 2018). However, in our study, mean FA only correlated with SDMT in the left CING.
Mean lFA but not mean FA showed an inverse linear relationship with physical disability as measured with the EDSS score. This effect was found when using the total NAWM mask but was also present when using the NAWM in the left CING. In the existing literature, the relation between FA of NAWM and physical disability is conflicting with some studies reporting significant correlations (Liu et al., 2012;Onu et al., 2012;Tovar-Moll et al., 2015;Deppe et al., 2016) while others did not (Griffin et al., 2001;Fink et al., 2010;Daams et al., 2016). Together, our findings suggest that lFA may better reflect disease-related functional impairment than conventional FA because it reveals changes in microstructure anisotropy independent of fibre architecture.
Both, mean lFA and mean FA correlated with age, showing lower anisotropy with increasing age in healthy controls. This finding replicates previous studies showing similar age-related effects of FA (Sullivan and Pfefferbaum, 2006) or lFA (Lawrenz et al., 2016). Reduced microscopic anisotropy with age suggests a change in the volume fraction of the cellular spaces due to axonal degeneration or changes in myelination. In addition, more supporting cells, e.g. glial cells, in the microstructural environment would result in lower microscopic anisotropy (Lynch et al., 2010;Al-Mashhadi et al., 2015). We observed that patients with multiple sclerosis also showed lower WM anisotropy with age, but only when using lFA and not FA as anisotropy measure. The absence of a change in WM FA with patient's age may be caused by disease-related architectural change (degeneration of a single tract in a crossing tract environment) that cause an apparent increase in FA, obscuring the ageassociated reduction in anisotropy.
A common approach to overcome the crossing-fibre problem in FA analyses is to limit the regions of interest to only include voxels in which FA exceeds a given threshold (e.g. FA > 0.2). Interestingly though, our analyses showed that this did not change the relations between groups ( Supplementary Fig. 2), showing consistent results across different FA-thresholds. An alternative strategy to overcome the crossing-fibre problem is to extract FA in coherent WM structures, e.g. using tract-based spatial statistics (Smith et al., 2006). However, both ways of limiting the analysis to voxels with coherent fibre orientation have the disadvantage of lowering the signal to noise ratio since fewer voxels are used to compute the mean statistic. Moreover, this approach excludes relevant portions of WM. Regardless of these strategies to mitigate the fibre dispersion problem, FA is modulated by effects of crossing fibres and thus cannot reflect the true underlying microscopic anisotropy due to limited spatial resolution (Budde and Frank, 2012;Schilling et al., 2017). Taken together, our observations suggest that lFA better reflects the true underlying microstructural anisotropy and thus also the disease condition.
It has been proposed that lFA can be obtained using linear tensor encoding data only (Kaden et al., 2016). However, this approach has been showed to be invalid (Henriques et al., 2019). It has also been proposed that orientation dispersion can be accounted for by the use of biophysical models with linear tensor encoding data only (Zhang et al., 2012;Kaden et al., 2016), however, the result from such approaches depends as much on the assumptions in the model as on the underlying microstructure (Lampinen et al., 2017(Lampinen et al., , 2019Dyrby et al., 2018;Novikov et al., 2019). The approach in this study did not make any assumptions on the configuration of the microstructure but instead relied on additional information provided by the STE collected at the acquisition.
Our lFA and FA results were obtained in a slab of slices covering part of the brain hence only the part of a tract projecting through the slab of slices was investigated. Focal pathological effects on the tract outside the NAWM volume covered by our slab of slices could impact our correlation results with clinical scores. However, any neuronal degeneration caused by focal attacks outside the volume covered by the NAWM slab will affect the microstructure along the entire tract also within the NAWM slab (Pierpaoli et al., 2001). Therefore, tractrelated NAWM changes within the slab are expected to correlate with neurodegenerative effect changes appearing along the whole tract hence to representative correlated with clinical scores.
In conclusion, lFA mapping is not affected by fibre architecture effects as conventional DTI-based FA mapping. Therefore, it is a more specific imaging tool to better capture microstructure anisotropy changes in NAWM multiple sclerosis pathology by demonstrating better group statistics in phenotype detection independent of the complexity of the tract system investigated. The lFA mapping also gives a better reflection of disease-related functional impairment when correlated with clinical scores. This motivates the future use of lFA mapping acquisitions as a complementary MRI modality to track the course of pathology dynamics and to test the efficacy of new treatments.

Supplementary material
Supplementary material is available at Brain Communications online.