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Investigating exchange, structural disorder and restriction in Gray Matter via water and metabolites diffusivity and kurtosis time-dependence1Université Paris-Saclay, Commissariat à l’Energie Atomique et aux Energies Alternatives (CEA), Centre National de la Recherche Scientifique(CNRS), Molecular Imaging Research Center (MIRCen), Laboratoire des Maladies Neurodégénératives, Fontenay aux Roses, France, 2Centre for Medical Image Computing (CMIC), Department of Computer Science, University College London, London, United Kingdom, 3Cardiff University Brain Research Imaging Centre (CUBRIC), School of Psychology, Cardiff University, Cardiff, United Kingdom, 4School of Computer Science and Informatics, Cardiff University, Cardiff, United Kingdom
Synopsis
This work reports first-time measurements of the time-dependent diffusivity and kurtosis of both water and metabolites in vivo in the mouse gray matter (GM). Our aim is to exploit the complementary information provided by the diffusion of water and intracellular metabolites to investigate and potentially disentangle the role of exchange, structural disorder and restriction in GM. Our results show evidence that water diffusion-time dependence in GM is mostly driven by 1D short-range disorder, potentially alongside exchange. Conversely, metabolites’ diffusion-time dependence is exclusively driven by cellular restrictions, paving a new way to quantify noninvasively microstructural restrictions in GM.
Introduction
Measurement of the time-dependent diffusion-weighted MRI (dMRI) signal has been used to quantify brain tissue inter-compartmental exchange1-7, structural disorder8-10 and micrometric restrictions11-16. Particularly, measurements of the diffusion-time (td) dependence of water diffusivity13,17-20, Dw(td), and kurtosis21-24, Kw(td), provide unique insight into these tissue properties.However, due to water presence within all tissue compartments and its ability to exchange between them, interpreting the measured Dw(td)-Kw(td) in terms of the underpinning tissue microstructure is challenging. This is particularly true for the gray matter (GM), whose complex microstructure comprises restrictions on multiple length-scales, different classes of structural disorder and intra/extracellular exchange times perhaps comparable to typical dMRI’s td25,26.
Complementary to water, measurements of the diffusion of purely intracellular metabolites through dMRS offer information on the brain microstructure which is specific to the intracellular space and unaffected by inter-compartmental exchange27,28. Thus, comparing the time-dependent diffusivity, Dm(td), and kurtosis, Km(td), of intracellular metabolites with Dw(td)-Kw(td) one can potentially separate and quantify the relevant mechanism(s) driving each time-dependency in GM.
The aim of this work is to shed some light on the role of exchange, structural disorder and restriction in GM, by exploiting the complementary information from both Dw(td)-Kw(td) and Dm(td)-Km(td) measured through dMRS.
Methods
dMRS acquisitionWe scanned anesthetized C57/BL6 wild-type mice (Isoflurane ~1.6%) on a Bruker Biospec at 11.7 T equipped with a cryoprobe, using a diffusion-weighted-stimulated-echo sequence coupled to a LASER module, with TE/TR=33.4/2500 ms; δ=3 ms.
We measured water diffusion in four mice within a 2.4-µL voxel in the hippocampus (Fig.1). For each td=[11.7;15.5;20.8;30;42.5;100;250;500] ms, we acquired eight repetitions with diffusion-weightings b=[0.2;0.7;1.2;2.0;2.5] ms/µm2 along one fixed direction.
For metabolites, we scanned seven mice with a 31.5-µL voxel in the hippocampus, containing [GM,WM,CSF]~[94%,5%,1%] (Fig.2). For each td=[42.5;100;250;500] ms, we acquired two blocks of 32 repetitions (plus an extra block for the longest td) with b=[0.2;1.0;2.0;3.2;4.5;6.0;8.0] ms/µm2 along one fixed direction.
Data processing and analysis
Spectra were analyzed with LCModel29 (including experimental MM spectra in the basis-sets) to estimate metabolite concentrations and water-peak integral at each b and td.
Water and metabolites time-dependent apparent diffusivity Dapp(td) and kurtosis Kapp(td) were estimated by fitting to the corresponding diffusion-weighted signal S as a function of b at each td the following equation30:
$$S(b,td)=S(b=0,td) \times exp(-bD_{app}(td)+\frac{1}{6}K_{app}(td)(bD_{app}(td))^2))$$.
Results and Discussion
SummaryBriefly, our results suggest that water diffusion-time dependence in GM is mostly driven by 1D short-range disorder (potentially alongside exchange), while metabolites’ one exclusively by cellular restrictions, which may mask any signature of existing structural disorder.
1D short-range disorder dominates water diffusion-time dependence
Exemplar fits of Eq.1 to the measured S(b,td) are shown in Fig.1. We observe a decrease of Dapp(td) and Kapp(td) with increasing td (Fig.1), in line with13,17-24.
To assess whether there is any signature of structural disorder, in Fig.2 we report Dapp(td) and Kapp(td) as a function of td-0.5 and td-1, the functional forms for 1D and 2D/3D disorder9,24. We observe a cleaner td-0.5 trend. Fitting to these data the power-law time-dependence proposed in9,24, we estimated a dynamical exponent ϑ=0.30±0.15 and a dimensionless ratio $$$\xi=\frac{C_KD_\inf}{C_D}=2.1±0.8$$$ (ξ=2.3±0.9, when imposing ϑ=0.50). These agree with theoretical predictions for 1D short-range disorder9,24 (ϑ=0.5, ξ=2), and7,24.
Nevertheless, at long td, both structural disorder and exchange could compete. Unless all molecules have already exchanged (i.e. td>>tex, exchange-time), the overall Dapp(td) and Kapp(td) would still scale with the same ϑ<1 , dominated by the smallest ϑ , hence 0.59,24. Fig.2 additionally suggests that, in the in vivo mouse GM, tex~[12-500] ms, which is in line with recent findings5,7.
Restrictions dominate metabolites diffusion-time dependence
Fig.3 shows exemplar metabolites S(b,td) together with the fit of Eq.1. In contrast to water, for all metabolites, we observe a decrease of Dapp and an increase of Kapp with td, with Kappmax~2.6 (Fig.4). This trend is noisier for supposedly glial metabolites (e.g. Ins and tCho).
The observed metabolites Dapp(td)-Kapp(td) suggest that restriction is the dominant mechanism (e.g. over structural disorder) impacting intracellular metabolites diffusion within the investigated td range. Indeed, the presence of non-negligible fraction of restricting compartments of radius R, like soma and projections, would lead to an increase of Kapp with increasing td for td≤R2/Dapp(td->0)24. On average31, neural soma’s R~8 µm and projections’ R~1 µm, suggesting that most of the probed td falls within this regime (i.e., td≤200 ms for Dapp(td->0)=0.35 µm2/ms32,33).
To assess the validity of this picture, we modeled the average Dapp(td) and Kapp(td) for joint tCho and Ins (mostly intra-glial), and tNAA and Glu (mostly intra-neuronal), using diffusion in randomly oriented cylinders and spheres34-36. This model well described the ‘glial’ and ‘neuronal’ data (Fig.5), with estimated intracellular diffusivities 0.17±0.05 and 0.34±0.03 µm2/ms, respectively. Moreover, the estimated cylinder radii (2.4±0.8 and 0.3±0.2 µm) and sphere radii (19±11 and 5.4±0.9 µm) for the ‘glial’ and ‘neuronal' metabolites, respectively, match microscopy estimates of projections and soma radii31.
Conclusion
To our knowledge, this is the first study reporting both Dw,m(td) and Kw,m(td) in-vivo in the mouse brain GM.These new results can help interpreting measured Dw(td)-Kw(td) in terms of the underpinning brain microstructure and suggest that measurements of Dm(td)-Km(td) can offer a new way to quantify microstructural restrictions in GM.
Acknowledgements
MP is supported by UKRI Future Leaders Fellowship (MR/T020296/1). JV and EM receive support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programmes (grant agreement No 818266).References
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