Sheryl L Herrera^{1,2}, Morgan E Mercredi^{3}, Henri R Sanness Salmon^{1}, Guneet Uppal^{1}, Domenico L Di Curzio^{4}, and Melanie Martin^{1}

Temporal diffusion spectroscopy (TDS) can be used to infer sizes of cells in samples. It relies on a geometric model to relate the MRI signal to the cell sizes. Celery collenchyma tissue and vascular bundles have long cells while parenchyma cells are rounder. We compared a cylindrical and spherical geometric model in temporal diffusion spectroscopy to determine how important the geometrical model was for celery. The inferred diameters of cells in celery (14±6µm to 20±12µm) were not statistically different when using the two different geometric models. This is the first step toward understanding the importance of geometric models for TDS.

Sample: A small section of a celery stalk was cut to fit inside a 15 mL sample tube filled with water. The image slice was chosen to be perpendicular to the length of the celery stalk.

MRI: The sample was imaged using a 7T Bruker AvanceIII
NMR system with Paravision 5.0 and BGA6 gradient set with a maximum gradient
strength of 430357 Hz/cm, and a 3.5 cm diameter bird cage RF coil. Each 20 ms apodised cosine
gradient pulse^{5,6} ranged from n = 1-20, in steps of 1. Two
different gradient strengths were used for each frequency and gradient pulses
were separated by 24.52 ms. One image was collected at the first gradient
strengths of 0. Four images were collected at the second gradient strength for
each frequency. The gradient strength was chosen to keep b ≈ 130 s/mm^{2} constant
for the frequencies from n=1-9. For n>9 the gradient strength was held
constant at 90% maximum because we could not get to the desired b-value.

Imaging parameters: 2 averages, 2.56 cm^{2} FOV, TR =
1250 ms, TE = 50 ms, matrix 128 x 128, 200 μm in plane
resolution, acquisition time 26.67 minutes per scan (scans performed = 40, 17.78
hours) were used. A 1 mm thick slice of interest was imaged as shown in Figure 1.

Image
Analysis: Prior to fitting, a custom-built image
registration tool was used^{7} to align all images to the b=0
diffusion-weighted images using a rigid affine transformation matrix determined
automatically by maximizing the 2D correlation coefficient.

Analysis: Regions of interest (ROIs) were drawn in the vascular bundles, collenchyma and parenchyma tissue, as well as within the noise. The mean ± standard deviation of the signal in the ROIs was calculated. The signal was assumed to be described by a two compartment model of the form $$$ E(ω= 2πn⁄σ,g)=(1-f_{cel} ) e^{bD_h}+f_{cel} e^{-β(D_i,AxD)}$$$

where
f_{cel }is the packing
fraction of cells, _{Di} is
the intra-cellular diffusion coefficient, D_{h}
is the hindered diffusion coefficient, and AxD
is the effective mean cell diameter^{3,8}. Signals were fitted to the
two compartment model using least squares minimization to extract AxD.
The
data were fitted to two different models, one with cylindrical cells and one
with spherical cells. We hypothesized that the vascular bundle and collenchyma
tissue would be better modelled with cylinders and the parenchyma would be
better modelled with spheres.

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Figure 1: Slice selection and the ROIs drawn.
ROIs 1,2,6,7,and 8 contain the vascular bundles, ROIs 9-11 contain the
collenchyma tissue, ROI 3 and 5 contain the parenchyma tissue, and ROI 4 is in
a broken region of the celery.

Figure 2:
Table of AxD results based on
the ROIs in Figure 1. No significant difference is seen between the
inferred diameter of the cells in the two geometric models (cylinders vs.
spheres). For the five ROIs without >100% uncertainties, the inferred cell
sizes are in the range expected. The OGSE sequence targets smaller cell sizes
so the cell sizes in the parenchyma tissue could not be inferred. We believe
that the small size of the collenchyma ROIs and possible partial-volume effects
led to difficulty in inferring cell sizes in most of the collenchyma ROIs.