Diffusion in deforming semi-permeable media: a Monte Carlo random walk approach
- 1Department of Aeronautics, Imperial College London, London, UK
- 2Cardiovascular Magnetic Resonance Unit, Royal Brompton Hospital, Guy’s and St Thomas’ NHS Foundation Trust, London, UK
- 3National Heart and Lung Institute, Imperial College London, London, UK
Abstract
Diffusion processes in deforming media with semi-permeable barriers are fundamental to understanding many biological and physical systems. The presence of semi-permeable barriers causes temporal and spatial departures from normal diffusion. We present an analytic expression for diffusion in a dynamically strained cuboidal cell that demonstrates one extreme of behaviour. Unfortunately however, analytical models cannot represent the effects of dynamic strain in microscopically restrictive media with varying permeability. To address these limitations, we explore how different cyclical strain patterns affect the apparent diffusion tensor in a simplified microstructure inspired by cardiac tissue. We show how the diffusion tensor in a dynamically strained medium may be derived for a Monte Carlo Random Walk (MCRW) model. The MCRW procedure is readily adaptable to more complex geometries and to cyclic and non-cyclic strains. Computations using the MCRW method show that the effects of physiologically relevant strain (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}∼ 20%\end{document}) are significantly attenuated by semi-permeable barriers. Strain correction methods, derived for homogeneous diffusion, are found to systematically overcorrect as barrier permeability decreases. These findings are significant for interpreting measurements, particularly in biology, where both microstructural barriers and dynamic deformation alter observed diffusion properties.
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BibTeX
@article{alemany2026diffusion,
title = {{Diffusion in deforming semi-permeable media: a Monte Carlo random walk approach}},
author = {Ignasi Alemany and Andrew D. Scott and Denis J. Doorly},
journal = {Scientific Reports},
year = {2026},
month = aug,
doi = {10.1038/s41598-026-64054-1},
url = {https://doi.org/10.1038/s41598-026-64054-1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Diffusion in deforming semi-permeable media: a Monte Carlo random walk approach
AU - Ignasi Alemany
AU - Andrew D. Scott
AU - Denis J. Doorly
PY - 2026
DA - 2026/08/07
JO - Scientific Reports
DO - 10.1038/s41598-026-64054-1
UR - https://doi.org/10.1038/s41598-026-64054-1
AB - Diffusion processes in deforming media with semi-permeable barriers are fundamental to understanding many biological and physical systems. The presence of semi-permeable barriers causes temporal and spatial departures from normal diffusion. We present an analytic expression for diffusion in a dynamically strained cuboidal cell that demonstrates one extreme of behaviour. Unfortunately however, analytical models cannot represent the effects of dynamic strain in microscopically restrictive media with varying permeability. To address these limitations, we explore how different cyclical strain patterns affect the apparent diffusion tensor in a simplified microstructure inspired by cardiac tissue. We show how the diffusion tensor in a dynamically strained medium may be derived for a Monte Carlo Random Walk (MCRW) model. The MCRW procedure is readily adaptable to more complex geometries and to cyclic and non-cyclic strains. Computations using the MCRW method show that the effects of physiologically relevant strain (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}∼ 20%\end{document}) are significantly attenuated by semi-permeable barriers. Strain correction methods, derived for homogeneous diffusion, are found to systematically overcorrect as barrier permeability decreases. These findings are significant for interpreting measurements, particularly in biology, where both microstructural barriers and dynamic deformation alter observed diffusion properties.
SN - 2045-2322
ER -