Synopsis

Mapping tissue microstructure in gray matter is becoming an important field of research in diffusion MRI. Previous studies have focused on characterizing different features separately, such as neurite density, branching order or soma size. However, the combined effect of different cell morphologies and sizes on the diffusion MRI signal has not yet been investigated. This work employs numerical simulations in more realistic cell configurations to investigate the effect of soma diameter, branch diameter and branching order, on the dMRI signal and its time dependence.

Introduction

Diffusion MRI (dMRI) is a popular non-invasive probe of tissue microstructure. Nevertheless, the relationship between the macroscopic signal and cellular architecture is not straightforward. Numerical simulations are playing a crucial role in dMRI research to understand the effect of various tissue features and/or acquisition parameters on the signal^1-8. Although many microstructural models are designed for white matter^3-6, recent studies have also focused on mapping gray matter tissue features, such as soma size⁷ or branching order⁸, which are important for characterizing different cortical areas and may reflect on brain development and pathology. However, the combined effect of different cell morphologies and sizes on the dMRI signal has not yet been investigated.

In this work, we employ the simulation framework described in¹, to systematically study for the first time the combined effect of soma diameter, branch diameter and branching order, on the dMRI signal and its time dependence.

Methods

Cellular configurations. 3D meshes are generated using the pipeline described in¹ for all combinations of the following parameters: soma diameter D_s={5,12,30} μm, branch diameter D_b={1,2,3} μm, number of branching points N_b={1,2,4} and whole-cell diameter of 200μm, resulting in 27 cellular configurations. Examples of synthetic cells are illustrated in Figure 1. For each configuration, 20 different instantiations were generated.

Diffusion simulations. Monte Carlo (MC) simulations in Camino⁹ were used to generate diffusion trajectories inside each synthetic cell, with the following parameters: duration 200ms, 2,000 time steps, diffusivity D=2μm²/ms and 5000 walkers for each cell instance resulting in 100,000 walkers for each configuration. The signal was then computed for single diffusion encoding (SDE) sequences with gradient duration δ=1ms, gradient separation Δ={5,10,15,…195}ms, diffusion weighting b={0,0.5,1,…5,6,..,10,15,...60} ms/μm² and 64 gradient directions. The signal is then averaged over directions and the 20 instantiations.

Results

Experiment I. The first experiment investigates the time dependence of apparent diffusion coefficient (ADC) at b=1ms/μm². Figure 2 plots the ADC dependence and example spin trajectories for cells with D_b=1μm, N_b={1, 4} and different soma sizes. The ADC dependence for diffusion inside spheres and finite cylinders of corresponding sizes is also shown. For N_b=1 (simple dendritic tree) and small soma diameter (D_s=5μm, relative volume ~18%), there is a peculiar increase in ADC with time which tends towards the ADC of finite cylinders. Considering the specific geometries investigated, this is due to ‘hopping’ of the diffusing spins between different stick-like branches (and soma), which increases the apparent displacement with time. For larger soma sizes (D_s=12 and 30μm, relative volumes ~48% and 53%), the effect of hopping is not apparent and the ADC time dependence is dominated by diffusion in spherical restriction. For cells with N_b=4 (complex dendritic tree), the ADC of diffusion in full cells at long diffusion times is larger than both the ADC in finite cylinders or spheres, reflecting the effect of moving between branches. Figure 3 plots the ADC time dependence for cells with N_b=1 and varying D_b, for three different soma sizes. For simple cells, the plots show that branch diameter has a larger impact on the ADC for small and medium soma sizes.

Experiment II.The second experiment investigates the b-dependence of the signal. Figure 4 and 5 plot the signal vs. b^-1/2 for different diffusion times, soma and branch diameters, in cells with N_b=1 and N_b=4, respectively. For simple cells with N_b=1 and D_s=5μm (Figure 4a-b), the b-dependence is mainly driven by diffusion in sticks/cylinders, with the function becoming convex (a signature of spherical compartment^7,10) only at high b-values. For cells with D_s=30μm (Figure 4c-d), and higher soma volume fraction, the function is convex over a wide range of b-values. As the diffusion time increases, the convexity shifts towards higher b-values. The more complex cells with N_b=4 (Figure 5a-d), show a highly diminished convexity, although in this case the soma volume fraction is lower, which likely influences the overall trend.

Discussion and Conclusion

Acknowledgements

References

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¹⁰ Palombo, M. et al, Abundance of cell bodies can explain the stick model’s failure to describe high b-value diffusion signal in grey matter. Proc. Int. Soc. Magn. Reson. Med. 2018, #1096.