Shir Levy^{1}, Darya Morozov^{1}, Inbar Seroussi^{2}, Leah Bar^{2}, Nir Sochen^{2}, and Yoram Cohen^{1,3}

Numerous different models provide detailed microstructure information from diffusion MRI data. In order to challenge them, there is a need for complex phantoms with known structural characteristics. For this purpose, we present a novel phantom, consists of spherical fixed yeast cells and cylindrical microcapillaries. Despite of its complexity, arising from the different size, geometry and size distribution of the restricted compartments, there is a good correlation between the known ground truth and the features that were extracted from fitting single diffusion encoding (SDE) MRI experimental data, assuming continued or discrete weight of size distribution.

Figure 1 shows the configuration of the phantom. The fixed yeast cells mixture was inserted into a 4 mm NMR tube that was inserted into an 8 mm glass sleeve filled with microcapillaries of 30±1 µm. This set-up was inserted into a 10 mm NMR tube.

Diffusion MRI experiments were
conducted on a 14.1 T NMR spectrometer equipped with 3 T/m gradients.
The pulsed-gradient-stimulated-echo (PGSTE) four
shots EPI experiments were performed perpendicular (x-direction) and parallel
(z-direction) to the main axis of the microcapillaries. One axial slice of 10
mm was acquired with the following parameters: matrix of 64×64 and
FOV of 8.5×8.5 mm^{2} resulting in an
in-plane resolution of 0.133×0.133 mm^{2}, TR/TE=3000/25, Δ/δ=100/3.2, G= [5…905] mT/m (23 equal steps, q_{max}=123.3
mm^{-1}) and NA=160. Note that the SNR's of the yeast cells and of the microcapillaries
were ~70 and ~5, respectively.

Light microscopy was used to study the yeast cells' diameter distribution before the MRI sessions.

The MRI signal was processed by using pixel-by-pixel
analysis as described previously^{3}. The
signal was modeled as a superposition of the MR signals arising from different restricted and
free diffusing compartments^{3,6,7}.
Here, we assume that the restricted compartments have
diameters in the range of 1-40 µm (50 steps) and a continued or a discrete weight distribution. Both fitting procedures were
performed using three apparent diffusion coefficients (ADC) of 1.0·10^{-3}, 1.5·10^{-3} and 2.0·10^{-3} mm^{2}/s. No other assumptions
were made.

Figure 2 shows the fractional diameter and free diffusion maps obtained by modeling the PGSTE MRI signals assuming two different weight distributions and two ADC values. It is clear that the sizes of both spherical and cylindrical compartments can be characterized accurately by both fitting procedures.

Significant populations of
yeast cells were observed in both directions as expected from their spherical geometry.
The yeast cells' average size that was extracted from the light microscopy is 5.00±0.36 µm, while the yeast cells' diameters that
were extracted from the MRI signals are between 4 to 6 µm. For the fitted SDE
signal of x-direction, the obtained mean sizes,
assuming continued weight distribution, were 4.36±0.06 µm and 4.79±0.07 µm
and the obtained mean sizes, assuming discrete weight distribution, were
4.48±0.06 µm and 4.86±0.07 µm, for ADC of 1.0·10^{-3} and 2.0·10^{-3} mm2/s, respectively.

As for the cylindrical compartment, a fraction of the diameters in the range of 29 to 31 µm appears in the area that corresponds to the location of the microcapillaries in the phantom only when diffusion was measured in the x-direction. In the z-direction, however, no notable populations are observed for the 29-31 µm diameters' range and only a free diffusing component is obtained there. These results match the excepted behavior of a compartment with cylindrical geometry.

A more detailed analysis of the
results shows that the yeast cells can be characterized accurately by the model
regardless of the assumed weight size distribution. The microcapillaries,
however, are better characterized by the discrete weight distribution.
Moreover,
it seems that the ADC of 1.0·10^{-3} mm^{2}/s
is more suitable for the
yeast compartment since for ADC of 2.0·10^{-3} mm^{2}/s a significant fraction of yeast is observed when the
diameters' range of 29 to 31 µm is inspected (Figure 2E). On the contrary, it
seems that the ADC of 2.0·10^{-3} mm^{2}/s is more suitable for the microcapillaries compartment
(Figure 2Q).

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