Modeling diffusion of intracellular metabolites in the mouse brain up to very high b: diffusion in long fibers (almost) accounts for non-monoexponential attenuation
Marco Palombo1,2, Clémence Ligneul1,2, and Julien Valette1,2

1CEA/DSV/I2BM/MIRCen, Fontenay-aux-Roses, France, 2CNRS Université Paris-Saclay UMR 9199, Fontenay-aux-Roses, France

Synopsis

We investigate how metabolite diffusion measured up to very high b (60 ms/µm2) at relatively short diffusion time (63.2 ms) in the mouse brain can be explained in terms of simple geometries. We model cell fibers as isotropically oriented cylinders of infinite length, and show this can account very well for measured non-monoexponential attenuation. The only exception is NAA, for which the model extracts fiber diameter equal to 0. We show that is theoretically and experimentally compatible with a small fraction of the NAA pool being confined in highly restricted compartments (with short T2), e.g. a mitochondrial pool.

Purpose

It has been recently shown that the apparent diffusion coefficient (ADC) of intracellular metabolites in the primate brain1 and human2 grey and white matter is quite stable as the diffusion time td is increased from a few tens of ms to ~1 sec. This led us to conclude that the vastest fraction of each metabolite pool is not restricted in small subcellular domains (cell bodies, organelles…) but is instead “freely” diffusing along cell fibers. Here we investigate if this (admittedly) simplistic view is consistent with metabolite data collected up to unprecedented high b in the mouse brain, outside the low b monoexponential regime.

Methods

Data analyzed here are those reported in a separate abstract3. Briefly, acquisitions were performed in a large voxel of the mouse brain using our new STE-LASER sequence3, based on a diffusion-weighted stimulated echo block followed by a LASER localization block, yielding no cross terms. 10 mice were scanned at 11.7 T Bruker scanner (Gmax=752 mT/m) using a cryoprobe, at TE=33.4 ms and td=63.2 ms, up to bmax=60 ms/µm² (qmax=1 μm-1) (Fig.1). Individual scan phasing was performed and experimental macromolecule spectrum was included in LCModel’s basis-set. Unlike biological water, metabolites are mainly intracellular, and membranes are nearly impermeable to metabolites. Cellular processes can be described in first approximation as a collection of long cylinders (Fig.2A) with radius a, and intracellular diffusivity Dintracyl. We assume cylinders randomly oriented to calculate signal attenuation in the narrow pulse approximation5,6. This theoretical attenuation is used to fit experimental data as a function of q to estimate Dintracyl and a.

Results and Discussion

Signal attenuation as a function of q is reported in Fig.2B for each metabolite, together with best fits. Extracted parameters are reported in Table 1. Results show that randomly oriented cylinders account well for measured attenuation, giving fiber radii consistent with axons, dendrites and astrocytic processes, and Dintracyl in the expected range (0.30-0.45 µm2/ms 1,2,4,5). The only exception is NAA, for which the model extracts a=0. Although a=0 has been used as an assumptionto fit NAA diffusion in the past4, we think this is not satisfactory, considering that this does not hold for other metabolites (including glutamate which is supposed to be, like NAA, predominantly neuronal). Explanations based on finer structural features (e.g. spines6) affecting diffusion of a single cytosolic pool also seem unlikely, because they should apply to other metabolites diffusing in the same cells. NAA is synthetized in neuronal mitochondria, so it may be significantly present in mitochondria (which represent 5-10% of the cytoplasmic volume), resulting in a second NAA pool, with limited exchange with cytosolic NAA. As mitochondrial matrix is viscous7 and densely filled with membranes, it is expected that T2 is very short. Hence, mitochondrial NAA should become invisible at long TE. Consistently, we have measured that increased TE (73.4 ms) led to small but significantly stronger signal attenuation at high b for NAA (Fig.3B), but not for other metabolites3. When analyzing NAA signal acquired at longer TE with cylinders (Fig.3B-C), the model returns a=0.62 µm (and Dintracyl=0.335 µm²/ms), which is now realistic, strongly suggesting that a highly restricted NAA pool has become invisible. Going one step further, these a and Dintracyl values can be injected in a modified model, where a log-normal distribution of spherical compartments8 (accounting for organelles/mitochondria) is added to cylinders whose properties were determined at long TE, to fit data at short TE (Fig. 3A-B). New free parameters are the diffusivity inside spheres Dintrasph, the volume fraction of these spheres νsph, and the mean radius μ and s.d. σ of spheres. Best fit of NAA attenuation at short TE yields (Fig.3C): νsph=2.0%, Dintrasph=0.168 µm²/ms, μ=0.019 µm, σ=0.028 µm. Values of νsph and Dintrasph are consistent with the known mitochondrial volume fraction and the higher viscosity in mitochondria7. Extracted radii are much smaller than typical mitochondria size, but very consistent with the typical distance between cristae, which must cause most of the restriction inside mitochondria.

Conclusion

The non-monoexponential signal attenuation of intracellular metabolites in the mouse brain can be essentially described by diffusion in long and thin cylinders, yielding realistic Dintra and fiber diameters, thus consolidating what we had previously proposed based on ADC measurements performed at very long td (and low b). However, this simple model seems to require some small “correction” for NAA at very high b, under the form of a small fraction of the NAA signal originating from a highly restricted (with short T2) compartment, e.g. a mitochondrial pool.

Acknowledgements

This work was funded by the European Research Council (ERC-336331-INCELL).

References

1. Najac C, et al. NeuroImage 2014; 90: 374.

2. Najac C, et al. Brain Struct Fun DOI: 10.1007/s00429-014-0968-5 (in press).

3. Ligneul C, et al. “Metabolite diffusion up to very high b in the mouse brain in vivo: revisiting the correlation between relaxation and diffusion properties.” This symposium.

4. Kroenke C, et al. Magn Reson Med 2004;52:1052.

5. Ronen I, et al. Front Integr Neurosci 2013; 7:13.

6. Yablonskiy et al., NMR Biomed 2010; 23 :661- 681

7. Garcia-Perez A et al., Arch Biochem Biophys 1999;362:329.

8. Balinov B, et al. J Magn Reson A 1993; 104; 17.

Figures

Figure 1. Diffusion-weighted spectra obtained with the STE-LASER sequence described in Methods, at different b-values, during a single experiments. The selected voxel in the mouse brain is shown as green box.

Figure 2. (A) Schematic description of the randomly oriented cylinders (ROC) model used to fit experimental data. (B) DW signal attenuation (points) and corresponding fitted curves (lines) as a function of q for all the investigated metabolites. Error bars stand for s.d. of the mean.

Table 1. Estimated parameters from the fit of the randomly oriented cylinders model to experimental data of each metabolite. Dintracyl= intracellular diffusivity and a = cylinders radius.

Figure 3. (A) Schematic description of the modified-ROC model. (B) q dependence of the NAA DW signal attenuation (points) and corresponding fitted curves (ROC model, black line; modified-ROC model, red line) at short (red) and long (black) TE. Error bars stand for s.d. of the mean. (C) Estimated model parameters.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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