Nicolas Moutal^{1}, Denis Grebenkov^{1}, Sylvie Clerjon^{2}, Guilhem Pages^{2}, and Jean-Marie Bonny^{2}

We present an application of diffusion MRI at high
b-values to a non-invasive quantification of micron-sized organelles such as
mitochondria. The experiments were conducted *ex vivo* on pork muscle and analyzed with a
bi-exponential tensorial model, which allows us to estimate the mitochondria
content in the muscle. Even though a more systematic comparison between
mesoscale diffusion and microscale histology is deserved, this work is a proof
of concept and a prerequisite for developing *in vivo* methods for quantifying the content of various organelles
in muscles, e.g. for studying mitochondrial dysfunction in aging.

The
signal has a “fast” contribution from the intracellular water almost freely
diffusing in large (~50µm) muscle cells, and a “slow” contribution from
restricted diffusion of mitochondrial water and possibly from residual lipids
in IMCL^{2}. We employ thus a bi-exponential tensorial fit

$$S=S_0\cdot \left[(1-\rho)\exp\left(-b\sum_{i,j}e_iD^f_{i,j}e_j\right)+\rho \exp(-bD^s)\right], \quad(1)$$

where S_{0}
is the reference signal, 1-ρ is the
volume fraction of the intracellular water, D^{f} is the apparent diffusion tensor for the
intracellular water inside the anisotropic fibrillar structure of the muscle
cells, e_{i} is the unit direction of the gradient, and
D^{s} is the apparent diffusion coefficient of the “slow”
component. In a first approximation, mitochondria can be treated as isolated
micron-sized compartments, in which the motional narrowing regime is expected,
with

$$D_s=\frac{2\zeta_{-1}L^4}{D\delta(\Delta-\delta/3)}, \quad (2)$$

where L is the size of the compartment, and ζ_{-1}
is a numerical shape-dependent coefficient^{3}. Since this signal is
very sensitive to the size L, only relatively small organelles (whose size is
inferior to 7µm) can provide a non-negligible signal at high b-values that
excludes e.g. blood vessels. As mitochondria are filled with around 65% of
water^{4}, the mitochondria volume fraction (MVF) would be given by $$$MVF=1.5\cdot \rho$$$ , if the
contribution from the IMCL was fully eliminated. In practice, $$$1.5\cdot\rho$$$ is the upper bound of the MVF.

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Figure 1: Example
of a bi-exponential tensorial fit of the data for the six gradient directions. The value of ρ is 2.9% and thus MVF is 4.4%. The level of noise (dashed line) is
about 0.5% of the reference signal. Gray shadowed region indicates the 67%
confidence interval (fitted curves ± noise level).

Figure 2: Map
of the estimated mitochondria volume fraction.
The image is not homogeneous, the values range typically from 3% to 6%.