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A compartment based model for non-invasive cell body imaging by diffusion MRI
Marco Palombo1, Noam Shemesh2, Andrada Ianus1,2, Daniel C. Alexander1, and Hui Zhang1

1Computer Science Department and Centre for Medical Imaging Computing, University College London, London, United Kingdom, 2Champalimaud Neuroscience Programme, Champalimaud Centre for the Unknown, Lisbon, Portugal

### Synopsis

This study aims to open a new window onto brain tissue microstructure by proposing a new technique to estimate cell body (namely soma) size/density non-invasively. Using Monte-Carlo simulation and data from rat brain, we show that soma’s size and density have a specific signature on the direction-averaged DW-MRI signal at high b values. Simulation shows that, at reasonably short diffusion times, soma and neurites can be approximated as two non-exchanging compartments, modelled as “sphere” and “sticks” respectively. Fitting this simple compartment model to rat data produces maps with contrast consistent with published histological data.

### Introduction

This work introduces a biophysical model for estimating neurite density and cell body (namely soma) size/density non-invasively by using diffusion-weighted MRI (DW-MRI). The existing conjecture1-4 considers water diffusion in white (WM) and grey (GM) matter as restricted diffusion in neurites, modelled by “sticks” embedded in the hindered extra-cellular water. However, recent studies5,6 suggest that the stick assumption, which appears to hold in WM, fails in GM. A plausible explanation for this failure is the abundance of soma in GM relative to WM. Here we show that soma size/density have indeed a specific signature on the direction-averaged DW-MRI signal at high b-values. Using Monte-Carlo simulations and data from rat brain, we show that, at reasonably short diffusion times (td), the water exchange between neurites and soma can be ignored, supporting the design of a simple compartment model to quantify the presence of soma.

### Methods

Microstructure Model. The proposed microstructure model is based on two commonly accepted assumptions:

a) at high b-values (≥3 ms/µm2) the extracellular water signal is negligible7;

b) at short td (≤40 ms) the effect of cell membrane permeability is negligible8.

An additional assumption, the validity of which is investigated in this work by numerical simulations (Fig.1 and 2), is that at short td (≤40 ms), soma and neurites can be approximated as two non-exchanging compartments, modelled as “sphere” and “sticks” respectively. Under these assumptions, the normalized direction-averaged DW-MRI signal at high b-values is expressed as:

S*(b)=fneuritesSneurites(b,Dintra)+fsomaSsoma(b,Dintra,rsoma) (1)

with fneurites+fsoma≤1, fneurites and fsoma the neurites and soma volume fractions, Dintra the intracellular diffusivity, Sneurites(b,Dintra)=[π/(4bDintra)]1/2erf[(bDintra)1/2] and Ssoma(b,Dintra,rsoma) the signal for restricted diffusion within a sphere of radius rsoma, as computed by multiple correlation function approach9, chosen to accurately model high b-value signals.

Numerical simulation. The validity of the non-exchange assumption was investigated by numerical simulation. Three-dimensional meshes of realistic cellular structures were implemented in CAMINO7 (Fig.1-a). Different (rsoma,fsoma) scenarios were simulated, and the direction-averaged DW-MRI signal was computed from a Pulsed-field-Gradients Spin-Echo (PGSE) sequence with 20 b-values=0-30 ms/µm2 and 60 directions, uniformly distributed over the full sphere (Fig.1-b). Gradient-pulse duration/separation, δ/Δ=4/7 ms. Model accuracy was evaluated by comparing model parameters’ values estimated by relation (1) with ground truth values (Fig.2).

Experimental Data. A healthy ex-vivo rat brain was investigated with a PGSE sequence at 16.4T (Bruker/Aeon): TE/TR=18/8000 ms; δ/Δ=4/7 ms; 16 b-values=0-15 ms/µm2, 10 uniformly distributed diffusion-encoding directions over a full sphere. The dataset was corrected for eddy-currents using FSL (https://fsl.fmrib.ox.ac.uk/fsl), and the direction-averaged DW-MRI signal computed.

Data analysis. Parametric maps of fneurites,fsoma,Dintra,rsoma and fextra=1-fneurites-fsoma were computed by voxel-wise fitting relation (1) to signals from the experimental data for b>3 ms/µm2 using in-house Matlab script (Fig.3). These estimated model parameters were then fixed to estimate the extracellular water mean diffusivity, Dextra, by solving the linear system with positivity constraint using all the b-values:

-ln{[S(b)-S*(b)]/fextra}=bDextra (2)

From fneurites,fsoma,fextra, the whole brain average tissue composition was computed and compared with published histological values10-15. The fsoma map was directly compared with publicly available histology10,16 of the rat brain (Fig.4).

### Results

Results (Fig.1-b and 2) show that the proposed model can closely approximate (within 10% accuracy) the connected cellular structure in the ideal case (SNR=$\infty$), and maintains good accuracy in the worse-case scenario (SNR=5). Quantitative maps of neurites and soma density match well the expected values from histology10-16 (Fig.4). Since DW-MRI cannot disentangle the component of neuronal from glial soma, the observed differences in DW-MRI and neuronal histology along the hippocampus profile (Fig.4-a) may be due to the larger presence of glial cells in that region. This hypothesis is supported by a second comparison with a combined “neurons+glia” histological density map, adapted from16 (Fig.4-b). Finally, the average estimated rsoma (6±1 µm) is also in good agreement with published histological estimates11,12.

### Discussion and Conclusion

Here we show that, according to the microstructure model we construct, from the intracellular water diffusion standpoint, the contribution of soma and neurites can be modelled as two non-exchanging compartments, suggesting that it is possible to quantify soma features in real tissue. However, our simulation ignores other potential effects, such as cell projections’ curvature and branching, and further validation will be required to assess the accuracy of the quantification.

While our results will require direct histological validation, the maps here reported already show some plausible contrast that might provide new insight into tissue architecture and provide markers of pathology. With the availability of powerful human scanners like the Connectom, this technique has the potential for translation into the clinic, opening a promising avenue for more in-depth assessment of cellular microstructure in-vivo in human brain.

### Acknowledgements

This work was supported by EPSRC (EP/G007748, EP/I027084/01, EP/L022680/1, EP/M020533/1, N018702), EPSRC EP/M507970/1 and ERC under the European Union’s Horizon 2020 research and innovation programme (Starting Grant, agreement No. 679058). We like to acknowledge Dr. Ekaterina Vinnik for ex-vivo data acquisition.

### References

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8 Yang D M, Huettner J E, Bretthorst G L, Neil J J, Garbow J R, Ackerman J J H. Intracellular water preexchange lifetime in neurons and astrocytes. Magn. Reson. Med. 2017; doi:10.1002/mrm.26781

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### Figures

Fig.1 a) Many randomly oriented cylindrical segments 200 µm long and of radius 0.50 µm (neurites) were connected through a spherical compartment (soma) of radius rsoma=2,5,10 µm, and relative volume fraction fsoma=0.01,0.05,0.10,0.20,0.35,0.50,0.70,0.80,0.95. The diffusion of 5x105 non-interacting spins was simulated within the synthetic mesh with bulk diffusivity 1 µm2/ms. b) From the spin trajectories, the normalised direction-averaged DW-MRI signal as measured by a PGSE sequence (data points) was computed for different (rsoma,fsoma) scenarios, together with the corresponding predictions according to the “sticks model” with Dintra=1 µm2/ms (dashed line) and the fit of “sticks+sphere” model (1), with fneurites=1-fsoma (solid line).

Fig.2 Correlation accuracy plot. fsoma, rsoma and Dintra estimated using relation (1) and labelled with the superscript “fitted” are plotted against the ground truth values. The correlation line (solid line) and ±10% error (dashed lines) are plotted. In infinite SNR case, the correlation is very high (R2>0.95) and accuracy within 10%. In the worse-case scenario of SNR=5, the correlation is still high (R2>0.85) and accuracy within 10% and 20%. Error bars on data points indicate uncertainty in model parameter estimation as evaluated by Monte Carlo approach (2500 random drawn).

Fig.3 Quantitative maps of microstructure parameters estimated by fitting relation (1) and (2) to experimental data from ex-vivo rat brain, as described in the methods.

Fig.4 a) Left-The soma (fsoma), neurites (fneurites) and extracellular space (fextra) volume fractions estimated by the proposed DW-MRI method are compared with published histological values10-15 referring to neurons only, for the whole rat brain (mean±SD). Center-fsoma maps obtained by the proposed DW-MRI method is compared with a Nissl stained histological slide of a similar region of the rat brain (adapted from10). Right-fsoma values along seven specific profiles (units 2xµm) within the corresponding DW-MRI and histology maps. b) Glia only, neuron only (both from16) and derived combined glia and neuron density images from histology compared to the DW-MRI derived fsoma map.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)
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