Compartmental diffusion and microstructural properties of human brain gray and white matter studied with double diffusion encoding magnetic resonance spectroscopy of metabolites and water

Double diffusion encoding (DDE) magnetic resonance measurements of the water signal offers a unique ability to separate the effect of microscopic anisotropic diffusion in structural units of tissue from the overall macroscopic orientational distribution of cells. However, the specificity in detected microscopic anisotropy is limited as the signal is averaged over different cell types and across tissue compartments. Performing side-by-side metabolite DDE spectroscopy (DDES) and water DDES in which a wide range of b-values is used to gradually eliminate the extracellular contribution provides complementary measures from which intracellular and extracellular microscopic fractional anisotropies ($\mu$FA) and diffusivities can be estimated. Metabolites are largely confined to the intracellular space and therefore provide a benchmark for intracellular diffusivity of specific cell types. Here, we aimed to estimate tissue- and compartment-specific human brain microstructure by combining water and metabolites DDES experiments. We performed DDES in human subjects in two brain regions that contain widely different amounts of white matter (WM) and gray matter (GM): parietal white matter (PWM) and occipital gray matter (OGM) on a 7 T MRI scanner. Results of the metabolite DDES experiments in both PWM and OGM suggest a highly anisotropic intracellular space within neurons and glia, with the possible exception of gray matter glia. Tortuosity values in the cytoplasm for water and tNAA, obtained with correlation analysis of microscopic parallel diffusivity with respect to GM/WM tissue fraction in the volume of interest, are remarkably similar for both molecules, while exhibiting a clear difference between gray and white matter, suggesting a more crowded cytoplasm and more complex cytomorphology of neuronal cell bodies and dendrites in GM than those found in long-range axons in WM.


Introduction
Diffusion-weighted MRI (DW-MRI) sensitizes the signal to molecular displacement on length scales comparable to cell morphological features, making DW-MRI a sensitive tool for tissue characterization on a microscopic scale 1 . Inferring specific cytomorphological properties from DW-MRI is not straightforward, as diffusion measurements reflect the average properties across a large volume compared to cellular dimensions. This average reflects properties that range from the microscopic shape and size of restricting geometries of different cell types to the heterogeneous organization over the entire voxel. Some microstructural information may be retrieved from modeling conventional diffusion data, thereby accounting for the heterogeneity across the imaging voxel. This, however, heavily relies on model assumptions that are difficult to validate with the ambiguous and sparse histological data A different approach is to increase specificity to the underlying cytomorphological features at the data acquisition stage. Several methods have been suggested to separate anisotropic diffusion on the microscopic scale, reflecting the presence of thin fibers such as axons and astrocytic processes, from macroscopic anisotropy, which reflects co-alignment of fibers across the acquisition volume. These methods include double diffusion encoding (DDE) experiments 4,5 , related tensor valued encoding methods in multiple directions with tailored gradient waveforms 6 , and analysis of the nonmonoexponential attenuation of disordered samples or the so-called "powder average" of diffusion measurements in multiple directions with respect to the b value in conventional diffusion experiments [7][8][9][10][11][12] . Microscopic anisotropy (µFA) and derived microscopic axial (D//) and transverse (D┴) diffusivities can be calculated from these measurements, and these reflect the diffusion properties within cytomorphological units on the length scale of the diffusion process, regardless of their mutual orientation on larger length scales ( Figure 1A) [13][14][15] . Compartmental and cell-type selectivity, and in some cases specificity, can be obtained with diffusion-weighted magnetic resonance spectroscopy (DW-MRS) 16,17 , where the diffusing microstructural probes are intracellular metabolites. DW-MRS is thus not only specific to the intracellular space but also allows studying cytomorphology of different cell populations such as neurons and glia across species (figure 1B) 18 . The compartmental specificity of DW-MRS extends beyond obtaining standard diffusional metrics such as metabolite apparent diffusion coefficients (ADC). The combination of DDE and DW-MRS (DDES) [19][20][21][22] can yield cell-type-specific microscopic diffusion metrics of the intracellular space, and contribute to a more detailed characterization of cytomorphology in neural tissue.
The morphological properties of the intracellular and extracellular spaces are not independent of one another, especially in white matter (WM), where the dominant structural unit is long-range axons in WM tracts. The relatively compact packing of axons in WM suggests the possibility of microscopic anisotropy also in the extracellular space 23,24 . Earlier work interpreting conventional DW-MRI with biophysical models suggests that in WM the diffusivity in the extracellular space (D//(extracellular water) ~ 2 µm 2 /ms and D┴(extracellular water) ~ 0.5 µm 2 /ms for an overall D(extracellular water) ~ 1 µm 2 /ms) is higher than in the intracellular space (D//(intracellular water) ~ 2 µm 2 /ms and D┴(intracellular water) ~ 0 µm 2 /ms for an overall D(intracellular water) ~ 0.67 µm 2 /ms) 25- 28 . This suggests that diffusion weighting modulates, and at high b value effectively eliminates, the contribution from the extracellular space. This has inspired the notion of using large diffusion weightings as a filter to target measurements of intra-axonal water 12,29-31 (figure 1C). For a quantitative assessment of the elimination of extracellular water in our experiments, see figure S1 in the appendix.
The microstructural characterization of both the intracellular and the extracellular spaces in gray matter (GM) has been less investigated. The microstructural heterogeneity of human GM, in addition to the lack of evidence of macroscopic anisotropy except for that found in neonates 32 and some cortical regions 33 , has discouraged researchers from further exploring the microstructural properties of GM in detail with DW-MRI. Pioneering work with DDE demonstrated the presence of microscopic anisotropy in GM of excised pig spinal cord and brain samples [34][35][36] . Only recently have attempts been made to characterize microscopic anisotropy in human GM in vivo, either with tensor valued encoding techniques 37 or with DDE 38 . In this study, we present a DDES approach to characterize the microscopic anisotropy and diffusivities of the intracellular and the extracellular spaces in the human brain. The complementarity of the DDES water measurements at low b values, which includes contributions from both the intra-and extracellular spaces, with the intracellular-specific DDES measurements of metabolites and water at high b values results in a set of unique quantitative insights on the morphology of the intracellular space in gray and white matter. In addition, qualitative assessments of the microstructural characteristics of the extracellular space are also derived.

Human subjects
A total of 20 healthy volunteers (age 33±12 years, 11 females) participated in the study, with 2 volunteers participating twice for acquisitions in two different regions (see description below). The study adhered to the guidelines of the Leiden University Medical Center Institutional Review Board (The Netherlands).
Informed consent was obtained from all subjects prior to the session.

MRI scanner/hardware
All experiments were performed on a 7T Philips Achieva whole-body MRI scanner (Philips Healthcare, Best, The Netherlands) equipped with a volume transmit/32-channel receive head coil (Nova Medical, Wilmington MA, USA) and gradient coils with a maximum gradient strength of 40 mT/m and a slew rate of 200 T/m/s. A high permittivity dielectric pad (suspension of barium titanate in D2O) was used to maximize the transmit magnetic field (B1 + ) homogeneity and efficiency in the parietal and occipital regions as previously described 39,40 .

MRI/DW-MRS data acquisition
The acquisition time for the entire protocol averaged approximately 55 minutes and comprised the following scans.

Anatomical Images
A short survey scan and a sensitivity encoding (SENSE) reference scan followed by a 3D T1-weighted gradient-echo acquisition were conducted to allow for the planning of the volumes-of-interest (VOIs) for the DDES experiments (figure 2). Imaging parameters for the 3D-T1 weighted scan were: field-of-view (a-p, f-h, r-l): 246x246x174 mm 3 , in-plane resolution: 1x1x1 mm 3 , repetition time (TR)/echo time (TE): 4.9/2.2 ms, total scan duration: 1:55.

Water and metabolite DDES
Pulse sequence: DDES data were acquired using a DDE-sLASER sequence 41 . The sequence diagram is shown in figure 3A. The following acquisition parameters were used: TE: 185 ms, spectral width: 3000 Hz, number of time-domain points: 1024. Each of the two diffusion weighting modules within our DDES sequence consisted of a double spin-echo with a bipolar diffusion weighting scheme. Using the conventions established for DDE sequences 4 adapted to a bipolar DW scheme: for both DW modules, single gradient lobe duration δ1/2 = δ2/2 = 15.5 ms; bipolar gap τ1 = τ2 = 10 ms; gradient separation time Δ1 = Δ2 = 45 ms; mixing time tm = 5.3 ms (see figure 3A for definitions of timing parameters).

Volumes of interest:
We examined two different brain regions: a WM region within the left parietal lobe (PWM) and a GM cortical region within the occipital lobe (OGM). 9 subjects were scanned with a 9 cm 3 VOI in the PWM region (3cm (a-p), 2 cm (f-h), 1.5 cm (r-l)); 9 subjects were scanned with a 9 cm 3 VOI in the OGM region (3cm (a-p), 1.5 cm (f-h), 2 cm (r-l)). To increase the specificity to GM in the OGM, 4 subjects were scanned with a smaller OGM VOI (sOGM) of 2.5 cm 3 (2.5 cm (a-p), 1 cm(f-h), 1cm (r-l)).
Two subjects participated twice: one was scanned with PWM and OGM VOIs and another was scanned with OGM and sOGM VOIs. Due to the limited SNR, only water acquisition was possible in the smaller VOI. The positions of the VOIs are illustrated in figure 2. Due to time constraints, metabolites and water DDES scans at all b values were also not acquired in all subjects. Table 1 summarizes the sample size for each acquisition performed in PWM and OGM VOIs.   Water suppression, B0 shimming, and scan synchronization: VOI-localized B0 shimming up to second order was performed. To minimize signal fluctuations due to cardiac pulsation, cardiac triggering was achieved using a peripheral pulse unit (trigger delay: 250 ms, TR: 5 cardiac cycles). For metabolite acquisitions, water suppression was achieved using two frequency-selective excitation pulses, each followed by a dephasing gradient.

Data processing and analysis
Image processing: T1-weighted images were segmented into tissue maps for GM, WM and cerebrospinal fluid (CSF) using FSL (Brain extraction Tool 43 and FAST 44 algorithm in the FMRIB Software Library). Each voxel contains a value in the range 0-1 that represents the proportion of each tissue. An in-house Matlab routine (MathWorks, Inc., Ma, USA) was then used to quantify the tissue volumes within each spectroscopic VOI. One subject was excluded from the tissue analysis due to the poor quality of the segmentation.
DDES Data pre-processing: Individual spectra were corrected for eddy currents, phase, and frequency drifts using in-house Matlab routines as previously described 45 . Averaged metabolite data sets consisted of 49 individual spectra: one acquired with b = 0 s/mm 2 and two sets of 24 (3 (Gd1) x 8 (Gd2)) DW spectra at b = 7199 s/mm 2 , each set acquired with two gradient polarities. DW spectra were subsequently averaged across the three Gd1 directions to provide an emulated powder average, resulting in two sets of 8 DW spectra. These spectra and the one acquired at b = 0 s/mm 2 were subsequently quantified with LCModel 46 , resulting in signal amplitudes of total N-acetyl-aspartate (tNAA = N-acetyl aspartate (NAA) + N-acetylaspartylglutamate (NAAG)), total creatine (tCr = creatine (Cr) + phosphocreatine (PCr)) and total choline (tCho = choline (Cho) + phosphocholine (PCho) + glycerophosphocholine (GPC)) for each value of b, θ and gradient polarity. The LCModel basis set included a total of 16 metabolites and a control node spacing of the spline function for fitting the baseline (dkntmn) of 0.5. Finally, the geometric mean of the LCModel estimates was calculated for each pair of spectra acquired with the same (b, θ) acquired with opposite sign of the gradient polarity, thereby reducing the effect of cross-terms with background and sequence gradients. An evaluation of this effect on phantom data is shown in figure S2 in the appendix. The resulting diffusion-weighted metabolite signals were finally normalized to their respective signal at b = 0 s/mm 2 . The post-processing scheme is depicted in figure 4.
The water signal was preprocessed similarly, and water spectra acquired with the same diffusionweighted condition (b, θ, gradient polarity) were averaged. The amplitude of the water signal for each averaged spectrum was obtained by integrating the area under the water peak in Matlab. The remaining post-processing procedure for the water data at each of the 4 b values followed the one described above for the metabolites, resulting in a single water signal value for b = 0 s/mm 2 and 4 sets of 8 water signal values, for each value of b and θ, respectively. All DW water signals were normalized to the signal at b = 0 s/mm 2 . A short representation of the raw data is available in tables S2 and S3 in the appendix. The raw data and associated analysis code is available from Itamar Ronen (i.ronen@lumc.nl) upon request and data handling agreement.

Analyses and interpretation of DDES data
Under the assumption of mono-disperse, axially symmetric diffusion tensors ! with axial and radial diffusivities D// and D┴, the b value and θ-dependent DDE signal from an ensemble of N different orientations described by the rotation matrices " ! can be calculated as: The two orthogonal unit vectors : # and : & span the encoding plane. The signal from a powder average was emulated with N = 256 uniformly distributed rotations with respect to the axial direction of an axially symmetric diffusion tenor. The two exponentials in the summation reflect the signal attenuation from the first and second diffusion encoding gradient acting on each rotation " ! of the diffusion tensor !. While the signal of a powder average at low b values reflects the initial slope or the mean diffusivity of the ensemble, the different angular modulation of anisotropic components with different orientations gives a multiexponential behavior that becomes more apparent at higher b values (shown schematically in figure 3C and simulated for monodisperse diffusion tensors in figure 3D).
For metabolites, the single compartment diffusivity was estimated from the b = 0 s/mm 2 normalized signal (#(%, ')/# " ) with the axial (D//) and radial (D┴) microscopic diffusivities as fitting parameters. A similar assumption for the water signal is not expected to be valid, as multiple signal components from CSF and different intra-and extracellular environments violate the monodisperse assumption. However, residual restricted and anisotropic components would be expected to dominate the signal at larger b values. Here, the water signal was fitted using data from two subsequent b values with # " as an additional fitting parameter. For mixed components with well-separated diffusivities, the fitted # " at high b values thus reflects the residual volume of slow and anisotropic signal components. Some hypothetical considerations for signal contributions from different environments are shown in figure S1 in the appendix. All fitting procedures were performed using non-linear sum of squares error minimization with D// = 1 µm 2 /ms, D┴ = 0 and # " = 1 as initial values. The microscopic fractional anisotropy (µFA) was calculated analogous to the fractional anisotropic (FA) from DTI analyses:

Statistical analysis
Results are expressed as mean ± standard deviation. Statistical significance was tested using GraphPad Prism 7 using an unpaired Student's t test with unequal variance (GraphPad Software, USA). A threshold of p < 0.05 was considered significant, the following symbols where used to indicate the significance: *p < 0.05, **p < 0.01, ***p < 0.001, ****p ≤ 0.0001. Correlation between intracellular tortuosity and D|| with tissue fraction were obtained with linear regression using GraphPad Prism 7. Table 2 shows the average percentages of WM, GM, and CSF within our two VOIs. The average WM fraction in the PWM VOI is above 80% while the average GM fraction is about 15%. In comparison, the average WM fraction in the OGM VOI is lower than 40% and the average GM fraction is around 50%.

Volume Fraction of GM, WM, and CSF
To increase the specificity to GM, a subset of data was acquired in a smaller OGM VOI (sOGM), which contained on average around 70% GM and 20% WM (see  Values refer to measurements at b=7199 s/mm 2 and were averaged across subjects and values of θ. Panels C and D in figure 5 show the fitting results of the θ-modulated signal (averaged over subjects) for the PWM and the OGM VOIs. Figure 6 reports the averaged values for metabolite D//, D┴, and μFA and the results of the statistical analysis. For all three metabolites, D// was significantly lower in OGM compared to PWM (p ≤ 0.024). D┴ and μFA were not significantly different between the two VOIs, except for tCho (p ≤ 0.043 for both D┴ and μFA). D//(tCho) was significantly lower than D//(tNAA) in both PWM

D//, D┴ and μFA from water DDES data over a range of b values
Water DDES at the highest b value The water signal was quantified over a range of b value in the PWM and OGM VOIs (figure 7). Table 3 reports the averaged values and statistical analyses for S0, D//, D┴, and μFA. S0 was evaluated from each consecutive pair of b values and normalized to the S0 at the lowest b (918 s/mm 2 ) as explained in the methods section, and is referred to as "fitted S0" from here on. At the highest b, the fitted S0 was significantly lower in OGM VOI compared to PWM VOI. In both VOIs, μFA(water) > 0.8 at the highest b, and significantly higher in the PWM VOI (p = 0.0008). Differences in μFA(water) were associated with differences in D//(water) as well as in D┴(water). D//(water) was significantly higher in the PWM VOI compared to OGM VOI (p < 0.0001). D//(water) was also significantly higher than D//(tNAA) in both PWM and OGM VOIs (p < 0.0001). Finally, D┴(water) was significantly lower in PWM VOI compared to OGM VOI (p < 0.0009). D┴(water) was significantly higher than D┴(tNAA) in OGM VOI (p < 0.0003). Values for the sOGM VOI are reported in appendix (table S1), however due to the small sample size no statistical test were performed. For each tissue type (100% WM and 100% GM), similar tortuosity values for tNAA and water were obtained. Tortuosity values for OGM were significantly higher than those in PWM (p < 0.003 for both water and tNAA). D// for tCr and tCho were also estimated, both indicating lower D// for these metabolites in GM than in WM.

Water DDES across b values
We observed a significantly lower μFA(water) at all b < 7199 s/mm 2 in OGM VOI (p <0.0008) when compared to the μFA(water) at the highest b value(see table 3

Discussion
In this work we demonstrate an approach for studying local microstructural features of brain tissue compartments by measuring and analyzing side-by-side water and metabolite DDES data. While metabolite DDES measurements provide an unequivocal empirical benchmark for intracellular diffusion metrics of neuronal and glial metabolites, water DDES measured with a range ofvalues enables the gradual elimination of the CSF and extracellular contributions, offering a reading of the intracellular diffusivity alone, as well as indirect information on the local geometry of the extracellular space. We used this approach to study the characteristics of intracellular diffusion processes of water and metabolites in GM and WM, highlighting common features as well as stark differences between the compartmental properties of these two tissue types. Table 4 summarizes the salient microstructural metrics obtained from the DDES measurements of metabolites and those of water at the highest b, highlighting our findings that pertain to the intracellular space in both GM and WM.

Intracellular spaces are highly anisotropic but different in GM and WM
With the exception of μFA(tCho) in OGM, the μFA of all three metabolites was higher than 0. The high μFA in GM is in stark contrast to the overall low macroscopic anisotropy in GM obtained from DTI measurements, which reflects the overall lack of directionality in neurite propagation across the measurement volume, even at the millimeter scale. This has been alluded to in studies that investigated microscopic anisotropy in post-mortem tissue 35,36,52,53 as well as from DDE imaging studies in the human brain performed at low b values 38 , and is strong supported by this current study, with the added value of cross-validation between water and metabolite data.
Noteworthy is that the μFA(water) values obtained in GM in a previous report 38 are lower than those found in WM and lower than those reported here. At the b value in which these experiments were performed (total diffusion weighting of b < 1000 s/mm 2 ) it is likely that signal from the more isotropic extracellular space in GM significantly contributed to the overall signal.
The only exception to high intracellular μFA in GM in our measurements was the μFA(tCho). This can be interpreted in two possible ways. One is the lower tCho signal to noise ratio (SNR) for the single measurement, resulting in higher variability of the tCho signal across gradient orientations in the DDES results. The other possibility is that in GM, a significant fraction of the predominantly glial tCho is found in protoplasmic astrocytes. These astrocytes, found extensively in human GM, are highly branched cells, significantly more so than their fibrous counterparts in WM 48 . It is plausible that the effective μFA(tCho) is low because the average diffusion length of tCho is comparable or higher than the distance between branching points on processes in protoplasmic astrocytes. Additional support for this explanation is also provided by the lower D// of tCho in GM compared to the one in WM, mentioned in the following paragraph. The uniqueness of diffusion properties of tCho in human GM has been previously reported 40 , where the sub diffusion index α for tCho in GM was significantly lower than that of tCr and tNAA in GM and all three metabolites in WM. In figure 10 are shown schematic representations of microstructural features such as deviation from propagation along a straight line and branching processes, that may affect microscopic diffusion metrics at different diffusion lengths. We used the strong correlation between D// of both water and metabolites at the highest b value with tissue type fraction to estimate intracellular D// of water and the three metabolites in pure GM and WM. Assuming that within the diffusion encoding times (~45 ms) in our experiments the diffusion length along the neurite represents a path along a straight-propagating unbranched fiber (< 15 μm), D// can be seen as the cytoplasmic diffusion coefficient for the metabolites and the intracellular water. When branches and deviation from straight propagation occur within the diffusion length at a given td, these geometric features will influence D// as well (see figure 10).
We observed a lower GM D// for all metabolites, as well as for water at high b. Differences in D// of tNAA between GM and WM may reflect differences in mitochondrial density between WM axonal fibers and GM neurons 54 as well as morphological differences between long propagating WM axons and highly branched dendritic trees in cortical neurons. Differences in D// of tCr, and mostly of tCho between the two regions may also reflect cytomorphological differences between astrocytes in both regions, as mentioned in the previous paragraph regarding µFA(tCho). Similarly, the values for free diffusivity of tCr and tCho require better assessment in phantom experiments with a realistic combination of co-measured metabolites that represents these combinations in vivo in GM and WM. We intend to pursue the investigation of the unique diffusion properties of tCr and tCho more thoroughly in future studies.
Values for D//(water) in WM we report here align well with earlier studies using different approaches for filtering extracellular and CSF contributions 12,29,30 . Similar values have also been found in more model-driven analyses of conventional DWI data, which also suggest two-fold differences in axonal and dendritic intracellular diffusivities 28 . Estimating all contributions to the water signal from different tissue compartments provides a rather flat fitting landscape for selecting the right combination of fractions and diffusivities 28,60 , making the fitting procedure for compartment-specific microscopic diffusion metrics fairly unstable. The spatial resolution of conventional DWI is in general on the order of the cortical thickness, making direct measurements without contaminations from CSF and WM all but impossible. In our study, we operated on an even coarser resolution, many times over the cortical thickness. We demonstrated that taking into account tissue fractions within the VOI, it is possible to obtained consistent and reliable microstructural details on GM via correlation analyses. This can be easily extended to imaging studies where partial volume within DWI voxels can be obtained in a similar way to the one we to a lower SNR in our present study. We estimated the effect of SNR on the estimation of D// and D┴ of tNAA with a simulation that takes into account our experimental settings ( figure 11). We assumed that D┴ = 0 (displacement RMS perpendicular to the fiber wall >> fiber diameter) and D// = 0.5 µm 2 /ms which are representable values for tNAA 19,67 . SNR is defined here as the tNAA signal relative to the standard deviation of the noise in the b = 0 condition. In our experiments, SNR for the tNAA peak estimated by LCModel was in the range of 30-45 for the data averaged across DW conditions. The simulation shown here indicates that D┴ of tNAA would be overestimated to about 0.02-0.03 µm 2 /ms, with a standard deviation on the same order. These estimates are slightly lower but in the same range of our D┴(tNAA) as estimated from our current data. A similar low D┴(water) was estimated in PWM but with a 2-3 fold increase in the more GMrich OGM and sOGM voxels. We speculate that this may reflect residual extracellular signal, either from non-complete filtering or comparably higher transmembrane exchange in the unmyelinated dendrites. Additional intracellular contributions from protoplasmic astrocytes contributing to the lower μFA(tCho) discussed above may also play a role. It is expected, however, that the effect of a nonfinite axonal radius on D┴ is small 68 within the range of diffusion times and diffusion coefficients in our experiments.

Morphology of the extracellular space varies significantly between WM and GM
A significantly lower μFA in both PWM and OGM VOIs was observed at lower b values. Under the assumption that the contribution of the extracellular space to the measured signal decreases with increasing b value, this suggests that the extracellular space is less microscopically anisotropic than the intracellular space in both WM and GM, but that there is a significant degree of microscopic anisotropy in the extracellular space in WM, absent in GM. At the lowest b, water μFA is more than three times lower in OGM than in the PWM VOI, suggesting that the extracellular space in WM is highly anisotropic, or conversely, that the tortuosity in the direction perpendicular to the fiber direction significantly affects water diffusion in WM. This result is consistent with the fact that long axons are the dominant structural feature in WM and are relatively densely packed, resulting not only in a high intracellular anisotropy but also in a significant extracellular anisotropy. Our data fitting approach differs slightly from the original definition of µFA based on contrasting b 2 -terms (kurtosis) at low b values reflecting variance in mean displacements across either directions or domains [13][14][15] . While this provides a stringent theoretical description, larger b values might be needed to provide sufficient contrast-to-noise (see figure 3D), which in turn leads to the increasing influence of higher-order terms 53 . Here we followed an approach valid at all b, but under the assumption of mono-disperse gaussian domains, which was also applied in previous DDES studies 19,20 . Given the numerous potential interpretations of DDE/DDES data, a model-free representation of the data is given in the appendix (tables S2 and S3).
Finally, it is likely that the microstructural and diffusional properties in gray and white matter will vary across the brain and will be dictated by local myelo-and cytoarchitecture. This calls for expanding this type of investigations to other brain regions, or to incorporate DDES experiments in spatially resolved techniques such as magnetic resonance spectroscopic imaging (MRSI).

Possible time-dependence effects
While this study focused on the effects of microscopic anisotropy, the DDE experiment may entangle different temporal fingerprints of time-dependent diffusion phenomena, such as exchange across different domains 70 or reflections from restrictive barriers 71 . These effects could bias measurements of microscopic anisotropy but could also provide rich additional information regarding microstructure or physiological processes. Our measurement was performed at a relatively short and fixed mixing time (~5.3 ms) which will neither modulate nor capture exchange on longer time scales, e.g. between branches of highly arborized cells such as protoplasmic astrocytes in GM or transmembrane exchange in non-myelinated fibers.
Time-dependent effects from restrictions could however potentially generate a difference between the signal intensity at parallel (θ=0º) and anti-parallel (θ=180º) directions with a lower signal in the latter 71,72 . We investigated the size of this contrast (see figure S3 in the appendix), but found no significant difference for the metabolites, in contrast to results reported in a recent DDES study in rodents. Higher SNR or shorter and stronger gradient pulses in the animal setting could reflect a different spatial scale and explain this difference. We did find a significant difference between

Conclusion
We presented here a comprehensive approach for combining water and metabolite DDES to investigate the local microstructural and cytoplasmic features of extra-and intracellular spaces in the human brain. We demonstrated the usefulness of this approach by shedding light on differences as well as similarities in local anisotropy and cytoplasmic properties in different cell types in gray and white matter, and inferred on differences in local geometry between the two tissue types. This approach can be extended to combine other microstructural probes, such as

Multi-compartmental effects
A simple model can serve as a hypothetical model of the contributions of intracellular, extracellular, and CSF components of the signal at different b values. Simulated signals are shown in figure S1. Here, the intracellular diffusivity is modeled as a "stick" with zero axial diffusivity, the extracellular space as an anisotropic tensor, and CSF as an isotropic tensor. Examples

Effect and correction of contaminating gradient fields -phantom data and simulations
Cross-terms between the diffusion gradients and static background gradients or imaging gradients (such as the crushers and slice-selection gradients) may bias the measurement of D//, D┴ and μFA. To investigate this effect we acquired all data with both positive and negative diffusion gradient polarities. The geometric mean of the signal over both conditions was then calculated which cancels out cross-terms to first order in b value. Our sequence and approach were validated in vitro using the "BRAINO" phantom (GE Medical Systems, Milwaukee, WI, USA).
Water DW-spectra were acquired with two b values (0 and 1111 s/mm 2 ) and both diffusion gradient polarities. For each condition, the water signal was calculated as the peak integral. As illustrated in figure S2A, the behavior of the water signal as a function of θ changes with gradient polarities and as expected becomes independent of θ when taking the geometric mean of the signal acquired with both polarities. This demonstrates that the effects of cross-terms between diffusion and imaging gradients are then corrected. We further validated this using Matlab simulations calculating the signals from b tensors with and without contributions from background or imaging gradients. Diffusion and imaging gradients were extracted from a simulation of the sequence on the scanner software as described earlier. This showed that all cross-terms between diffusion and imaging gradients are canceled as well as cross-terms with spatially constant background gradients ( figure S2B and C). However, the effects spatially varying microscopic background gradients on the length scale of the diffusion pathway are not cancelled.

Time dependence
If the mixing time in a DDE experiment is short compared to the characteristic length of a restriction a difference in signal between the anti-parallel and parallel conditions will be observed 2,3 . Diffusion in the proximity of barriers is likely to change direction from boundary reflections, leading to a larger signal attenuation when the encoding direction change is in the anti-parallel condition. In contrast, the anti-parallel condition is velocity compensated which will be rephased leading to the opposite pattern 4,5 . Pairwise comparison of the two conditions is shown in figure S3. We observe significantly lower anti-parallel signals in the order of ~1% signal difference in the lower b values of the water acquisition in both PWM and OCC which support apparent effects from restrictions/reflections rather than IVIM effects.

Small OGM VOI data
Additional water data from 4 participants with a smaller VOI was collected in OGM to achieve a larger relative fraction of gray matter. The data is included in figure 8 in the main paper. Tissue volume fractions and fitted model parameters are shown in table S1.