The code re-implements 2d Monte Carlo simulations originally developed in Fieremans, et al., NMR Biomed, 2010 and Novikov, et al., Nature Physics, 2011, illustrating the examples in Figure 4 of Fieremans and Lee, NeuroImage 2018 with more details in supplmentary information.
- Example 1 (Figure 4, point 1): Free diffusion in 2d
- Example 2 (Figure 4, point 2): Check short-time limit of diffusion in a geometry composed of randomly packed impermeable cylinders (2d)
- Example 3 (Figure 4, point 3): Check against analytical formulas for diffusion within an impermeable non-absorbing cylinder (2d)
- Example 4-5 (Figure 4, point 5): Calculate membrane's permeability by starting diffusing particles from the center of permeable cylinders (2d)
- Analytical solution of time-dependent diffisivity and kurtosis between parallel planes, inside cylinders, and inside spheres.
- Densely packed cylinders: Generation of randomly packed cylinders with the freedom of tuning axonal water fraction, inner diameter distribution, and g-ratio. Packing geometry is generated as in Donev, et al., J Comput Phys, 2005. Axonal diameter histogram comes from Aboitiz, et al., Brain Research, 1992.
These are good exercises if you just start your own MC simulation codes. Some results can suprise you, even if you are well experienced!!
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Monte Carlo simulation
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Random packing generation
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Axonal diameter histogram in corpus callosum
This project is licensed under the LICENSE.