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 brain
1
and human
2 grey and white matter is quite stable as the diffusion
time t
d 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 abstract
3. Briefly, acquisitions were
performed in a large voxel of the mouse brain using our new STE-LASER sequence
3,
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 (G
max=752 mT/m) using a cryoprobe,
at TE=33.4 ms and t
d=63.2
ms, up to b
max=60 ms/µm² (q
max=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 D
intracyl.
We assume cylinders randomly oriented to calculate signal attenuation in the
narrow pulse approximation
5,6. This theoretical attenuation is used
to fit experimental data as a function of q
to estimate D
intracyl 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 D
intracyl in the expected range (0.30-0.45 µm
2/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 past
4, 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. spines
6)
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 viscous
7 and
densely filled with membranes, it is expected that T
2 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
metabolites
3. When analyzing NAA signal acquired at longer TE with cylinders
(Fig.3B-C), the model returns a=0.62 µm (and D
intracyl=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 D
intracyl values
can be injected in a modified model, where a log-normal distribution of spherical
compartments
8 (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 D
intrasph, the volume fraction
of these spheres ν
sph, and
the mean radius μ and s.d. σ of spheres. Best fit of NAA
attenuation at short TE yields (Fig.3C):
ν
sph=2.0%, D
intrasph=0.168
µm²/ms, μ=0.019 µm, σ=0.028 µm. Values of ν
sph
and D
intrasph are consistent with the known mitochondrial
volume fraction and the higher viscosity in mitochondria
7. 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 D
intra and fiber diameters,
thus consolidating what we had previously proposed based on ADC measurements
performed at very long t
d
(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 T
2) compartment,
e.g. a mitochondrial pool.
Acknowledgements
This work was funded by the European Research Council (ERC-336331-INCELL).References
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