Superficial white matter imaging: Contrast mechanisms and whole-brain in vivo mapping

Superficial white matter mapping provides the foundation for systematic studies of this crucial structure.


Supplementary Materials
Fig. S1. Orientation-dependent contribution to R2* in SWM. (a, b) Quantitative R2* measured at two different orientations of the sample with respect to the static magnetic field B0 (shown in the insert). (c) The difference of R2* between the two different orientations shows the orientation-dependent contribution to R2*. (d) Orientation-dependent contribution to R2* in SWM sampled along the sulcus. Top: The orientation of SWM surface with respect to magnetic field for all sampled positions and for the two orientations of the sample in the magnetic field (and are angles between the surface normal and the static magnetic field for two sample orientations). Bottom: Orientation-dependent contribution to R2* in SWM measured as the difference between the two sample orientations sampled along the sulcus. The sampled positions from 1 to 20 are marked in (a) with black dots. The orientation-dependent term β1 (sin 2 θ1-sin 2 θ2) + β2 (sin 4 θ1-sin 4 θ2) describing the mesoscopic contribution of iron and orientation-dependent contribution of myelin (Eq. M4, M6, S1.5 and S2.5) fitted the difference in R2* between two sample orientations very well explaining 78% of the variance in the orientationdependent R2* contribution.  . Classical histological iron stains for (a) ferric and (b) ferrous iron, and (c) a quantitative iron map obtained with LA-ICP-MSI in a post mortem brain tissue sample of the temporal lobe. Optical images of (a) Perls' and (b) Turnbull's stainings were converted into relative maps of iron concentrations of Fe 3+ and Fe 2+ , respectively, using the Beer-Lambert law. The Fe 3+ map revealed better correspondence to the quantitative iron map indicating that the majority of iron in the SWM was in the Fe 3+ state. Note that both histological methods underestimate the cortical iron concentration.  sampled at the SWM surface demonstrates low variation of myelin density in SWM and patterns distinct from iron-induced SWM contrast. in-plane angle between fiber bundle k and projection of the static magnetic field into the SWM plane is (b) Schematic representation of an MRI voxel containing a slab of the SWM (in gray) occupying a fraction p of the voxel volume. The angle between the SWM surface normal n and the static magnetic field b0 is . (c) The angular dependence of the mesoscopic contribution ∆R2'meso simulated using Eq. S1.5 for p=0.5, B0=7T, χ=1.3 10 -9 μg/g wtw, and the differences in the iron concentrations of SWM and DWM, measured with LA-ICM-MSI (22 ± 21 μg/g wtw).
SI.1 Iron-induced mesoscopic orientation-dependent contribution to R2* Assume that the SWM slab fills a fraction p of the voxel volume, the angle between the SWM surface normal and the static magnetic field is  (Fig. S6b) and the difference in the iron concentration between the SWM slab and surrounding tissue is cFe. The frequency shift between the SWM slab and surrounding tissue is given by: The gradient echo signal from the voxel will be proportional to a sum of the signal from the SWM slab and surrounding tissue: , where TE is the echo time. The signal magnitude is then given by: In our case, where TE<<1, 1 the Taylor expansion can be used: Merging Eq. S1.4 and Eq. S1.1 the mesoscopic contribution to R2*, can be written as: Eq. S1.5 The angular dependence of ∆R2'meso is plotted on Fig. S6c, assuming p=0.5, B0=7T, χ=1.37 10 -9 μg/g wtw, and the differences in the iron concentrations of SWM and DWM, measured with LA-ICM-MSI (22 ± 21 μg/g wtw,). Note that the orientation-dependent part of ∆R2'meso consists of a linear combination of sin 2 θ and sin 4 θ terms.

SI.2 Myelin-induced orientation-dependent contribution to R2*
The myelin contribution to R2*myelin can be described as a sum of orientation-dependent and orientation-independent terms (24): where CR2* is the orientation independent myelin contribution to R2*, θ* is the angle between a fiber bundle (Fig. S6a) and the static magnetic field and a1 and a2 are empirical coefficients.
Since most fibers in the SWM run parallel to the SWM surface (9), only the contribution of fibers pointing along the SMW surface are considered in the following. For these fibers running within the SWM plane the terms sin 2 θ*and sin 4 θ* can be rewritten as: sin * = 1 − cos * = 1 − sin cos sin * = (1 − sin cos ) = 1 − 2 sin cos + sin cos  

Eq. S2.2
where  is the angle between the SWM surface normal and the static magnetic field, and the angle between the fiber and projection of magnetic field onto the SWM plane is  (Fig.   S6a). For simplicity we assume that fibers are distributed isotropically with no preferential orientation within the plane. Performing the averaging over all fiber orientations within the plane is equivalent to integration over the angle . If the signal de-phasing due to the orientation dependent part of ΔR2*myelin is small 2 , the averaging over  can be performed directly on the terms in Eq. S2.1: Eq. S2.3 1 Using differences in the iron concentrations of SWM and DWM, measured with LA-ICM-MSI (22 ± 21 g/g wtw), magnetic field of 7T, and mass susceptibility of iron of 1.37 10 -9 g/g wtw  , and TE=0.021 s the product TE is estimated to be 2/3B0cFeTE=0.13, which is significantly less than 1. 2 The approximation in Eq. S1.3 is justified if (a1+a2)TE<<1. Estimating the orientation-dependent part of the R2* to be about 12 s -1 (as measured in the post mortem tissue Fig. S1) and multiplying it with the maximum TE value of 0.021 s (as used in vivo experiment) the product could be estimated to be about (a1+a2)TE =12 s -1 *0.021 s=0.168, which is significantly less than 1, so the approximation is valid.

SI.3 Physiology, chemical form and cellular distribution of iron accumulation in SWM
Additional insight into the physiology of iron accumulation in the SWM is provided by histological stains for the different iron forms, potentially iron-rich cells, and for proteins involved in iron metabolism (Figs. S3 and S4). Classical Perls' and Turnbull's histochemical iron stains, which are specifically sensitive to Fe 3+ and Fe 2+ forms, respectively, revealed elevated levels of iron in both oxidation states in the SWM (Fig. S3). Perls' staining revealed higher spatial correlation with overall iron concentrations measured by LA-ICP-MS compared to Turnbull's staining, consistent with previous reports that most iron in the brain is in the Fe 3+ form (25). Both classical histological stains systematically underestimated the iron concentration in the cortex compared to white matter (Fig. S3). This may be due to different staining efficiencies in WM and GM and emphasizes the necessity of quantitative histology for the study of contrast mechanisms in MRI.
The two most important proteins involved in iron storage and iron transport are ferritin and transferrin. It is known that ferritin contains more than 80% of the total tissue iron (25, 32). Interestingly, neither of the two proteins was present in the SWM in higher concentrations than in DWM (not shown), indicating that the elevated iron level in the SWM is more due to a higher iron loading of ferritin cores than to a higher concentration of ferritin proteins. Likewise, the density of microglia was not increased in the SWM (Fig. S4). Instead, microglia was rather homogeneously distributed across the cortex and the WM. A higher density of oligodendrocytes and activated astroglia was observed in the SWM (Fig. S4).

SI.4 Analysis of in vivo MRI data
Cortical curvature and thickness maps generated with Freesurfer ( Fig S5) were smoothed tangentially to the cortical surface (FWHM 6 mm), resampled to the template surface 'fsaverage' and averaged across subjects to allow comparison with the spatial pattern of the SWM mapping.

SI.5 Estimation of myelin volume fraction from sulfur and phosphor maps measured with LA-ICP-MSI
The myelin volume fraction was estimated based on quantitative maps of sulfur and phosphorus concentrations obtained with LC-ICP-MSI and the method proposed by Stüber et al. (21). This method assumes that (i) myelin has a constant ratio of sulfur to phosphorus, which is different from that of unmyelinated tissue; (ii) unmyelinated tissue (including proteins, non-lipid macromolecules, DNA) also has a constant ratio of sulfur to phosphorus concentrations; (iii) cortical layer II does not contain any myelin and can be used to determine sulfur to phosphorus ratio of unmyelinated tissue; (iv) myelin volume fraction of white matter is equal to 0.6. Based on these assumptions, the estimation of myelin volume fraction was performed in two steps. First the ratio of sulfur to phosphorus concentrations for unmyelinated tissue was obtained in manually segmented regions-of-interest located in cortical layer II: krest=n P layer II/n S layer II  where n P layer II and n S layer II are averaged values of phosphorus and sulfur concentrations obtained with LA-ICP-MSI in specific ROIs. In a second step the myelin volume fraction was calculated: cmye=n P -krest n S , where cmye is the relative myelin volume fraction. The obtained map of myelin fraction was normalized to provide an averaged value of 0.5 in deep white matter (21).