David Romascano^{1,2}, Jonathan Rafael-Patino^{1}, Ileana Jelescu^{3}, Muhamed Barakovic^{1}, Tim B. Dyrby^{2,4}, Jean-Philippe Thiran^{1,5}, and Alessandro Daducci^{1,5,6}

Monte Carlo simulations provide diffusion MRI signals that can be used to evaluate microstructure models, but that can also be incorporated into microstructure reconstruction methods. It is therefore important for the generated signals to be as realistic as possible. This work shows preliminary evidence that, in the case of white matter models, the symmetry of the perpendicular extra-axonal signal generated with Monte Carlo simulations depends on the voxel size. Simulations corresponding to millimeter-sized voxels should therefore be computed using substrates of equivalent size, or by averaging signals generated from multiple small voxels.

Figure 1 shows samples of cylinder positions for three different substrates, as well as the corresponding EA signals. Figure 2 shows the mean and standard deviation of the EA signal as a function of substrate size. Overall, our experiments show that EA signals from real acquisitions (voxel sizes of the order of millimeters) cannot be approximated by using Monte Carlo simulations in small voxels. Indeed, small voxels present EA signals that are not symmetric, and with reduced mean amplitude compared to signals from bigger voxels. Voxel sizes of the order of 400x400μm^{2}, which is the typical voxel size for animal imaging, are therefore required to be able to generate realistic EA signals that are in accordance with biophysical models for hindered compartments.

The symmetry of the EA signal can also be recovered by averaging many small substrates. We averaged the signals of 100 substrates of size 40.5x40.5μm^{2} (each with different cylinder positions) and obtained an EA signal with standard deviation and amplitude equivalent to the signal obtained for a voxel of 406x406μm^{2}. Our observations regarding single voxels might therefore be linked to the limited number of cylinders in small voxels, which limits the diversity of local environments explored by the spins when the voxel size is small.

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Figure 1: (Up) Positions of cylinders for different substrate sizes: 406x406μm^{2}, 181x181μm^{2} and 40.5x40.5μm^{2}. Dotted blue lines show the size of the voxels (voxel boundaries for the 1st voxel are out of the plot). (Bottom) corresponding EA signal profiles. The dMRI signal for a voxel of 406x406μm^{2} is symmetric, as expected for real acquisitions. The anisotropy in the smaller voxels show that they cannot be used to approximate the signal of millimeter-sized voxels

Figure 2: (Left) Mean EA signal for different voxel sizes. The mean signal is decreased for smaller voxel sizes. (Right) standard deviation of the shell’s signals, for different voxel sizes, showing the increased anisotropy for smaller substrates. Given our settings, voxel size should be above 300x300μm^{2} in order to recover the highest symmetry.