Relating diffusion tensor imaging measurements to microstructural quantities in the cerebral cortex in multiple sclerosis

Abstract To investigate whether the observed anisotropic diffusion in cerebral cortex may reflect its columnar cytoarchitecture and myeloarchitecture, as a potential biomarker for disease‐related changes, we compared postmortem diffusion magnetic resonance imaging scans of nine multiple sclerosis brains with histology measures from the same regions. Histology measurements assessed the cortical minicolumnar structure based on cell bodies and associated axon bundles in dorsolateral prefrontal cortex (Area 9), Heschl's gyrus (Area 41), and primary visual cortex (V1). Diffusivity measures included mean diffusivity, fractional anisotropy of the cortex, and three specific measures that may relate to the radial minicolumn structure: the angle of the principal diffusion direction in the cortex, the component that was perpendicular to the radial direction, and the component that was parallel to the radial direction. The cellular minicolumn microcircuit features were correlated with diffusion angle in Areas 9 and 41, and the axon bundle features were correlated with angle in Area 9 and to the parallel component in V1 cortex. This may reflect the effect of minicolumn microcircuit organisation on diffusion in the cortex, due to the number of coherently arranged membranes and myelinated structures. Several of the cortical diffusion measures showed group differences between MS brains and control brains. Differences between brain regions were also found in histology and diffusivity measurements consistent with established regional variation in cytoarchitecture and myeloarchitecture. Therefore, these novel measures may provide a surrogate of cortical organisation as a potential biomarker, which is particularly relevant for detecting regional changes in neurological disorders.

We have previously applied postmortem (PM) diffusion imaging to the investigation of the relationship between cortical histology measures and white matter diffusion properties (Kolasinski et al., 2012).
The target was white matter tracts in multiple sclerosis, based on the established sensitivity of MD and FA to demyelination and other aspects of white matter degeneration (Beaulieu, 2002;Schmierer et al., 2008). Measurements in the white matter tracts between cortical and subcortical grey matter areas correlated with standard histological measures in those areas (cortical thickness and cell density), implicating Wallerian degeneration (Kolasinski et al., 2012). Given the increasing interest in the cerebral cortex in multiple sclerosis (Wegner, Esiri, Chance, Palace, & Matthews, 2006), we have extended this investigation of the relationship between DTI and histology to the grey matter of the cortex in the same cohort. Therefore, the present study aimed to identify variation in histological measurements of the radial elements of cortical structure corresponding to the diffusion signal. A fundamental structural unit of the cortex is the minicolumn, a vertical string of neurons, with associated dendrites and myelinated axon bundles Casanova, Konkachbaev, Switala, & Elmaghraby, 2008;Mountcastle, 1997). Although it may be expected that aspects of the axonal bundles (including membranes and myelination) descending from Layers III to VI are a significant contributor to diffusion in the cortex, the bulk of histological literature on cortical radial organisation depends on measurement of the minicolumns as assessed by Nissl staining of the cell bodies. This literature documents regional differences (Chance et al., 2011) and effects of both ageing (Chance et al., 2011;Chance, Casanova, Switala, Crow, & Esiri, 2006;Di Rosa, Crow, Walker, Black, & Chance, 2009) and pathology in other disorders (Casanova, Buxhoeveden, Switala, & Roy, 2002). Previous work has demonstrated almost identical spacing between the axon bundles and the minicolumns  supporting the idea that both are measuring different aspects of the same structure. Both cellular and axonal components were assessed in the present study and their correspondence to MRI diffusion measures was also examined. One recent study has reported on the quantitative relationship between FA and axon orientation in the cerebral cortex in multiple sclerosis (Preziosa et al., 2019). Here, we explored additional diffusivity metrics not previously reported in the cortex and their relationships with axon bundles and minicolumn structure in multiple sclerosis. Water molecules move approximately 10 μm during a typical MR measurement time (Mori & Zhang, 2006) which is about one-third the width of a minicolumn.
Although DTI is a relatively crude tool for analysing diffusion MRI, which is not well suited to modelling relationships with the underlying anatomy, it can nonetheless be useful for exploring markers of disease by virtue of its simplicity and wide applicability to a large variety of acquisition protocols, especially those common in the clinical realm.
This study set out to investigate the hypothesis that variation in the principal diffusivity relates to aspects of the best known radial cortical elements, the minicolumn, and axonal bundle organisation.
The study did not model or attempt to explore a deep interpretation of the cause of the relationship between histology and diffusivity, but was intended as a study to observe correlations and differences in disease that could be useful for developing biomarkers.

| Patients/samples
Fixed whole brains from nine multiple sclerosis patients (Table 1)

| MRI scanning
Nine multiple sclerosis patients and six control brains from a preexisting cohort in the Oxford Brain Bank, were used for the MRI comparison.
Scanning was carried out on a Siemens Trio 3T scanner using a 12-channel head coil. Scanning was conducted at room temperature and each scan session lasted approximately 24 h. Diffusion weighted data were acquired using a modified spin-echo sequence with threedimensional (3D) segmented EPI (TE/TR = 122/530 ms, bandwidth = 789 Hz/pixel, matrix size: 168 × 192 × 120, resolution 0.94 × 0.94 × 0.94 mm 3 ). Diffusion weighting was isotropically distributed along 54 directions (b = 4,500 s/mm 2 ) with six b = 0 images. This protocol takes approximately 6 h, and three averages were acquired for 18 h total diffusion imaging. Structural scans were acquired using a 3D balanced steady-state free precession sequence (TE/TR = 3.7/7.4 ms, bandwidth = 302 Hz/pixel, matrix size: 352 × 330 × 416, resolution 0.5 × 0.5 × 0.5 mm 3 ). Images were acquired with and without RF phase alternation to avoid banding artefacts. This was averaged over eight repeats to increase signal to noise ratio (SNR). For more details, see Miller et al. (2011).
Data were processed using the FMRIB software library (FSL) (Smith et al., 2004;Woolrich et al., 2009). The FSL diffusion toolbox was used to process diffusion weighted data, which incorporates an in house processing pipeline to compensate for gradientinduced-heating drift and eddy-current distortions, to produce maps of FA, MD, and the diffusion tensor components (Miller et al., 2011). F I G U R E 1 Example of the cortical diffusion data for one representative region (right), including an illustrative voxel example of the derived diffusion-based measures (left). A blue line indicates the principal diffusion vector in a voxel: on the right, only the direction is indicated, while on the left, the diffusion tensor component along the principal diffusion direction (PDD) vector (D PDD ) is shown. A red line indicates the radial direction within the cortex (CRadial). The angle of radiality, AngleR (notation θ R ), in a voxel is the angle between the red and blue lines. The perpendicular diffusivity, PerpPD (notation D1,⊥), was calculated by projecting D PDD onto the plane perpendicular to CRadial. The parallel diffusivity, ParlPD (notation D1,k), was calculated by projecting D PDD onto the CRadial. Quantities were averaged along the radial cortical profile across the cortical layers, reflecting the minicolumnar organisation, as indicated for a set of voxels by the yellow line

| Selection of brain regions
Measures of cortical thickness in dorsolateral prefrontal cortex (Area 9) and primary visual cortex (V1) and diffusion measures of connected white matter tracts (FA and MD) were correlated with histological myelination measures in our previous study (Kolasinski et al., 2012) and, as multiple sclerosis is a demyelinating disorder, these areas were chosen for further investigation in the present study. In addition, these areas are well characterised and are known to represent a range of cortical cytoarchitectural arrangements (i.e., wider minicolumns in Area 9 and narrower minicolumns in V1). An additional comparison region was included-the primary auditory cortex within Heschl's gyrus (Area 41)-because its columnar architecture is well characterised but there have been inconsistencies in previous reports on its PDD in healthy subjects (Kang et al., 2012;McNab et al., 2013). Investigation of multiple cortical regions allowed us to explore the sensitivity of measures of diffusion to regional differentiation, which would be of interest in future investigations of neurological disorders.  Averaging values reduced the influence of noise in the DTI data, effectively smoothing the data, and ensuring only directionality with some local coherence would dominate, guarding against the influence of random deflections from the radial direction. Averaging also provided consistency with the histological measurements, which similarly calculated a single value for each cortical region. Previous work has found that measures of the cytoarchitecture and myeloarchitecture are relatively stable within a cortical subregion (e.g., von Economo and

| Neurohistological sampling
Koskinas (1925)) indicating that it is valid to find an average value for that region.

| Minicolumn analysis
Minicolumn width, based on cell bodies, was assessed in the histological tissue sections using a semiautomated procedure that has been described in detail previously (Buxhoeveden, Switala, Litaker, Roy, & Casanova, 2001;Casanova & Switala, 2005). This procedure gives a value for the minicolumn width consisting of the cell dense core For each ROI, three digital photomicrographs were taken from a single slide where possible, each containing a region of about 1 mm 2 .
Image locations were selected using a random number generator, excluding areas of high curvature which have been shown to affect cell distribution (Chance, Tzotzoli, Vitelli, Esiri, & Crow, 2004). As minicolumns are clearest in Layer III, photographs were centred on that layer and obtained through a ×4 objective lens, with an Olympus BX40 microscope (more details can be found in Chance et al. (2004) and Di Rosa et al. (2009)). Values calculated from the three photographs were averaged to give a single value for each region.

| Quantification of myelin levels
Cortical myelin content was assessed using light transmittance to quantify the intensity of myelin stain in anti-PLP stained tissue sec-

| Axon bundle analysis
For each region, three photographs were obtained through a ×10 objective lens (resolution 1.10 μm) with an Olympus BX40 microscope, centred around Layer V as the axon bundles are clearest there.
Areas of extreme curvature were avoided where possible, as was done for the minicolumn measurements.
Measurements of axon bundle centre-to-centre spacing, and the width of the bundles themselves were made manually in AxioVision, using the in-built measurement tools ( Figure 2). The digital resolution of the analysed images was 0.67 μm/pixel. A sample line of standard length (590 μm; determined by the size of the image view) was drawn across the centre of the photograph, perpendicular to the bundle direction in order to identify the bundles to be measured. Only bundles intersecting this line were measured, those that passed out of the plane of sectioning above or below the line were not included. Single axons or pairs of axons crossing the line were not considered to constitute axon bundles for the purposes of this analysis.
Bundles (>2 axons) were identified and their centres marked. Bundle spacing measurements were then made from the centre of each bundle marked in this way to the centre of the adjacent bundle. The width of each axon bundle was also measured. For the width measurements, the edges of the bundles were marked at the point where they intersected the line, and the bundle width was determined as the distance between these two points. Edges of axon bundles were distinguished by the change in intensity of staining from the background, which identified the start of the more darkly stained axon bundle.
Pilot data revealed high reliability of this method, finding a high corre- bundles deviate from the radial direction across the cortex by an average of 3.50 (±2.68) degrees.

| Statistical analysis
All data were analysed using SPSS v22 for Windows and the R statistical package (version 3.3.3) (R Core Team, 2013).

| Relationship between histology and DTI
The relationship between the microanatomy and MRI diffusion measures across the full data set was investigated by correlation analysis  Table 5).
2.9.2 | Mean regional differences Regional differences in both histology and DTI measures within groups were assessed using repeated measures analysis of variances (ANOVAs) and significant main effects were followed up with post hoc t tests. Regional differences in DTI between groups were assessed using repeated measures ANOVA.

| Multiple sclerosis clinical correlates
Our previous study indicated a relationship between the degree of change in white matter and cellular organisation in Area 9 and V1 (Kolasinski et al., 2012). As disease duration was the only clinical measure available for all subjects (Table 1), the present study investigated whether there was a significant correlation between DTI derived measures and disease duration in these cortical regions (Area 9 and V1), and whether the correlations were different to that in the comparison region (Area 41). As age was expected to correlate with disease duration this was controlled for where appropriate using partial correlations using the standard SPSS recursive algorithm.

| Comparison of DTI and histology measures in MS brains
None of the cortical diffusion measures were significantly affected by PM interval (PMI) or scan interval (SI). The analysis of interactions between cortical diffusivity and minicolumn organisation are reported in Table 5; (significant p values after FDR correction are reported as p FDR ). In Area 9, Layer III showed significant direct correlations between AngleR and minicolumn width (r = .912, p = .001, p FDR = .030), and between AngleR and core width (r = .879, p = .002, p FDR = 0.045) (Figure 3 and Table 5 Concerning axon bundles, the correlation analysis revealed an association between AngleR and bundle spacing (r = .937, p = .000, p FDR = .000) in Area 9 ( Figure 3 and Table 5). No significant associations between AngleR and bundle measures were found in Area 41 and V1.
The relationship between cortical histology measures and the more commonly used DTI measure (MD) was not significant (see Table 5 for details).

| DTI differences between groups and brain regions
We used a pre-existent cohort of six controls to investigate the diffusiv-

| Histology differences between brain regions
Repeated measures ANOVA revealed a significant main effect of region on all histological measures (Tables 2 and 3 and Figure 4). Primary visual cortex had the narrowest minicolumns and narrowest axon bundles, with Area 41 having the widest spacing of axon bundles and the widest bundles (Table 4).

| Relationship between histology measures
A strong positive correlation was observed between the width of the minicolumns in the cortex, as assessed by cell bodies, and the spacing of myelinated axon bundles (r = .718, p < .001, p FDR = .000) ( Figure 5). Bundle width also showed a positive correlation with bundle spacing (r = .548, p = .003, p FDR = .0045) but the relationship between bundle width and minicolumn width assessed by cell bodies was not significant (r = .248, p = .222).

| Relationships with clinical variables
Due to the presence of a strong correlation between disease duration and age (r = .883, p = .002), partial correlations controlling for age were  F I G U R E 4 Regional differences in (a) AngleR, (b) minicolumn width, (c) axon bundle spacing, and (d) axon bundle width. Error bars show SD T A B L E 4 Overall region differences for histology measurements in the MS brains determined by repeated measures ANOVAs are reported in the first row (effect of region). Post hoc t-statistics are reported in the subsequent rows for specific region comparisons   Given previous histological findings of age-and pathology-related changes in the cortex Chance, Casanova, Switala, & Crow, 2008;Di Rosa et al., 2009;van Veluw et al., 2012), cortical diffusion surrogates could prove to be a powerful tool for investigating such changes without the destructive histological processing that limits tissue availability. It is therefore worth considering the feasibility of translating such markers into the in vivo clinical setting. The long acquisition times used in this study largely reflect the requirements of imaging PM tissue and are not necessary in vivo.
Changes in tissue diffusivity and T2 cause an extremely low SNR regime so that achieving a diffusion-weighted contrast comparable to in vivo scans requires long scan times (Miller et al., 2011) and alternative acquisition methods (Miller, McNab, Jbabdi, & Douaud, 2012). In vivo, the longer T2 and faster diffusion are much more conducive to imaging, and the primary challenge is to obtain sufficient SNR in a reasonable scan time. The diffusion scan SNR in the present PM study had an average SNR of 66.9 in B0 and 9.2 in b = 4,500 s mm 2 volumes. Similar SNR values (and at least greater than an SNR of 2) are achievable with in vivo acquisitions. Sotiropoulos et al. (2013) reported SNR values of 9 for b = 1,000 at high resolution using the previous generation of magnets, therefore the latest systems will deliver substantial improvements; note that the reduced ADCs (and anisotropy) in the present study place it roughly in the same domain as b = 1,000 data in vivo (e.g., Miller et al., 2011). The necessary spatial resolution for in vivo cortical analysis (~1 mm) is also achievable; for example, strong gradients and simultaneous multislice imaging in the Human Connectome Project has enabled 1.25 mm, whole-brain DTI acquisitions (U gurbil et al., 2013) that clearly demonstrate cortical anisotropy (Sotiropoulos et al., 2013). Several studies have achieved sub-millimetre resolution using ultrahigh field strengths (Dumoulin, Fracasso, van der Zwaag, Siero, & Petridou, 2018;Heidemann et al., 2012) and non-EPI acquisition schemes (Sarlls & Pierpaoli, 2009;Setsompop et al., 2018). Sufficient resolution has been achieved to enable similar diffusion analysis in the cortex in vivo with realistic acquisition times (Anwander et al., 2010;McNab et al., 2013). It will be necessary to take account of potential movement artefacts and we would expect that sophisticated methods for detecting and correcting for motion will likely be a key factor in future studies (e.g., Andersson, Graham, Zsoldos, & Sotiropoulos, 2016). Adaptation of our analysis for in vivo use would allow longitudinal investigation with potential prognostic and diagnostic value.

| Diffusion as an index of histology
Multiple anatomical correlations were found with the cortical diffusion signal-in particular, AngleR was found to correlate sensitively with changes in minicolumn width and axonal bundle characteristics.
Due to the relatively small sample size, a common challenge in PM studies of this kind, it can be difficult to reliably detect relationships between variables. Some individual data points may have a strong influence on the estimated effect sizes-for example, in the Area 9 results, it could be argued that data points appear to cluster with two subjects further from the others (Figure 3). However, correlations F I G U R E 5 Relationships between histological measures of cortical cytoarchitecture in MS brains, pooled across regions F I G U R E 6 Relationship between bundle width and disease duration in primary auditory cortex (Area 41) in MS brains in this region were statistically robust and survived FDR correction for multiple comparisons. The association with histological measures suggests the possibility that our DTI correlates may be sensitive to alterations of minicolumnar organisation produced by neurodegeneration.
Neuron loss is considered to be one of the most clinically relevant surrogate markers of disease progression (Fisher et al., 2002) and one of the causes of minicolumn disruption (Wegner et al., 2006). The increased AngleR value in multiple sclerosis patients compared with healthy controls describes an increased angle between the radial direction across the cortex and the PDD, perhaps due to minicolumn alteration.
The significant correlation between axon bundle spacing and AngleR, and between axon bundle width and ParlPD, may be due to the hindrance to water diffusion imposed by the axonal membranes Another study has attempted to relate cortical DTI in PM tissue to histological features in humans, finding that areas with high FA were also the areas where visual assessment of histology indicated radial organisation . Although studies have demon- Therefore, it may be premature to seek a hypothesis under which changes in PDD are not accompanied by specific changes in MD. Furthermore, the finding that the values relating to the direction of diffusion in the cortex did not seem to vary with PMI and SI suggests diffusion direction is amenable to study in PM tissue. The absence of a clear correlation between overall myelin density and the DTI measures is different from the picture generally reported by studies of white matter (e.g., Beaulieu, 2002;Song et al., 2002). A straightforward relationship may not be expected in grey matter given the far more complex structure of the cerebral cortex and the lower amount of myelin compared with white matter. The influence of cellular components, extracellular matrix, and dendritic structure is likely to be greater in cortical grey matter, constituting multiple interacting microstructural boundaries independent of myelin level.

| Regional differences
The difference between brain regions in cortical DTI characteristics and cytoarchitecture has potential clinical relevance as selective regional changes may be informative for investigating neurological disorders. The present study found regional differences in minicolumn width between Area 9 and V1 that are similar to those that have been well characterised previously van Veluw et al., 2012). In this study, Area 41 contained relatively wide minicolumns compared to Area 9 and V1, which may be explained by the agerelated minicolumn narrowing normally observed in regions other than Area 41 van Veluw et al., 2012). Axon bundle spacing showed a similar pattern, confirming the consistency between cell body and axon-bundle-based columnar measurements. The width of the axon bundles also differed between regions. Although this measure is uncommon, one study examining axon bundles in Area 41 found similar widths to those reported here (Seldon, 1981).
The current findings of regional differences in the values of cortical diffusion are consistent with a previous study which found that MD was different in frontal areas compared to occipital areas . The present study found regional differences in AngleR, in particular, a significant difference between Area 9, Area 41 (most radial), and V1 (most tangential). The more tangential diffusivity in V1 may be due to the presence of the stria of Gennari which is a myelinated tract running parallel to the cortical surface, roughly in the middle of the primary visual cortex. Area 41 has been shown to have strongly radially organised cytoarchitecture (Sigalovsky, Fischl, & Melcher, 2006;von Economo & Koskinas, 1925) and very directional diffusion (as suggested by high FA and low MD in the present study).

| Relationships between histology measures
The present finding of a correlation between spacing of the minicolumns based on cell bodies and axon bundles is consistent with what is known about the structure of the minicolumn Mountcastle, 1997) and previous work comparing the two measurements .
In the present study, the width of bundles increased with spacing between the bundles, but it is not known whether this reflected a greater number of individual fibres within the bundle or less dense packing of the same number of fibres. Understanding this may shed light on the functional implications of such regional variation. It has been suggested that narrowly spaced minicolumns have more overlapping activations and function less independently (Chance et al., 2013;Harasty, Seldon, Chan, Halliday, & Harding, 2003). Those minicolumns may have fewer axons in their bundles due to the greater redundancy in their information output. This would be of particular relevance to demyelination and conditions of brain damage, but also disorders such as autism where one of the most prominent neuroanatomical hypotheses is concerned with altered minicolumn organisation  and connectivity in fibre tracts (i.e., axon bundles) (Tommerdahl, Tannan, Holden, & Baranek, 2008).

| Clinically relevant variation in measurements
Overall, the cortical DTI markers showed a difference between controls and MS brains. Markers relating to myelinated components of the cortex may complement other methods for characterising brain regions, age-related changes, and the detection of pathology, particularly in multiple sclerosis. Cortical demyelination has been suggested to account for the moderate correlation between white matter damage and cognitive impairment (Kutzelnigg & Lassmann, 2006). Furthermore, changes in diffusivity in grey matter have been found to relate more closely to clinical measures than either changes or lesions in normal appearing white matter (Vrenken et al., 2006). shown to be more common in sulci and deep in-foldings of the cortical surface, particularly in the insula (Kutzelnigg & Lassmann, 2006).

| Limitations
The current study has been limited to investigating three regions of the cortex (Area 9, V1, and Area 41) due to the time-consuming nature of the manual steps involved in both histological and MRI analysis. Future studies across the whole brain would depend on development of robust, automated image analysis tools for segmentation and registration of PM data, as well as advances in histological processing hardware.
PM tissue is known to show altered diffusion properties (Miller et al., 2011;Shepherd, Thelwall, Stanisz, & Blackband, 2009). Studies examining these changes in WM have demonstrated reductions in both FA and MD, for example, (Miller et al., 2011;Schmierer et al., 2008), but this has been much less studied in GM. Cortical slices of fixed rat brain have shown increases in extracellular apparent diffusion coefficient and apparent restriction size, with evidence of increased membrane permeability (Shepherd et al., 2009). Future work would also benefit from broadening the acquisition to acquire either a range of diffusion times or q-values (i.e., multishell acquisitions). suggested that these remain relatively constant after fixation, for example, (Kim, Zollinger, Shi, Rose, & Jeong, 2009). It is worth noting that tissue volumetric change due to fixation (i.e., shrinkage) stabilises within a few weeks (Quester & Schröder, 1997) and all of the cases in this study had been fixed for little more than the 3 years that Dyrby et al (2011) suggest is the initial period of stable SI. In testing for correlations in the present study, only FA showed a relationship with SI.
The effect of PMI on diffusivity values in the cortical grey matter are likely to differ from those in WM due to cellular components as well as the fixation process itself. Immersion fixation causes the GM to come into contact with the fixative immediately whereas it has to penetrate through to the WM, effectively resulting in a more extended PMI. Overall, there are reasonable grounds to expect a correspondence between cortical diffusivity assessments obtained in vivo and those obtained from PM tissue, although future research should focus on clarifying this. The full range of factors influencing diffusion in the cortex is not fully understood and other factors such as the packing density of axons and other membranes, and the relative volume fractions of these components may also contribute.

| CONCLUSIONS
We describe an approach to the analysis of high-resolution MRI diffusion data in the cortex that is sensitive to cytoarchitecture and myeloarchitecture in the human brain using DTI. Histologically measured widths of cell minicolumns and axonal bundles were correlated with direction of diffusion in the cortex. Further, we demonstrate regional differences in these aspects of cortical diffusion. There are many potential causes for these differences, and this study does not interpret the cause nor does it attempt to model the anatomy and its effects. We do observe consistent differences and correlations, and this is what we report here as we believe that these may be useful