Random Permeable Barrier Model, Matlab Code

Random Permeable Barrier Model, Matlab Code

Gregory Lemberskiy

The following scripts are intended for the use in modeling the dependence of diffusion on diffusion time, D(t), within permeable anisotropic microstructure. This model was motivated by the necessessity to characterize "disordered" microstructure. Prior to the publication (1) of this Random Permeable Barrier Model, the only proposed solution to a time-varying diffusion coefficient in biological tissue was derived from periodic boundaries (Tanner et al (1979)).

Moreover, the RPBM has been identified as a powerful model to describe the microstructure of muscle tissue. It has been applied in-vivo for quantifying muscle myofiber diameter and sarcolemma membrane permeability (3,4).


  1. Novikov DS, Fieremans E, Jensen JH, Helpern JA. Random walk with barriers. Nat Phys 2011; 7(6): 508–514. DOI:10.1038/nphys1936.6.
  2. Novikov DS, Jensen JH, Helpern JA, Fieremans E. Revealingmesoscopic structural universality with diffusion. Proc Natl Acad SciU S A 2014; 111(14): 5088–5093. DOI:10.1073/pnas.1316944111.7.
  3. Fieremans, E., Lemberskiy, G., Veraart, J., Sigmund, E. E., Gyftopoulos, S., and Novikov, D. S. (2017) In vivo measurement of membrane permeability and myofiber size in human muscle using time-dependent diffusion tensor imaging and the random permeable barrier model. NMR Biomed., 30: e3612. DOI:10.1002/nbm.3612.
  4. Sigmund EE, Novikov DS, Sui D, Ukpebor O, Baete S, Babb J, Liu K,Feiweier T, Kwon J, McGorty K, Bencardino J, Fieremans E. Time-dependent diffusion in skeletal muscle with the random permeablebarrier model (RPBM): application to normal controls and chronic ex-ertional compartment syndrome patients. NMR Biomed 2014; 27(5):519–528. DOI:10.1002/nbm.3087.



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 (Gregory Lemberskiy) 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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Philanthropic Support

We gratefully acknowledge generous support for radiology research at NYU Langone Health from:
• The Big George Foundation
• Bernard and Irene Schwartz

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