Recipes of Monte-Carlo Simulations, Matlab Code

Recipes of Monte-Carlo Simulations, Matlab Code

Author: 
Hong Hsi Lee

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!!

References

 

PLEASE NOTE: The software available on this page is provided free of charge and comes without any warranty. CAI²R and the NYU School of Medicine do not take any liability for problems or damage of any kind resulting from the use of the files provided. Operation of the software is solely at the user's own risk. The software developments provided are not medical products and must not be used for making diagnostic decisions.

The software is provided for non-commercial, academic use only. Usage or distribution of the software for commercial purpose is prohibited. All rights belong to the author (Hong Hsi Lee) and the NYU School of Medicine. If you use the software for academic work, please give credit to the author in publications and cite the related publications.

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We gratefully acknowledge generous support for radiology research at NYU Langone Health from:
 
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