Diffusion in deforming semi-permeable media: a Monte Carlo random walk approach
File(s)
Article in press
Author(s)
Alemany, Ignasi
Scott, Andrew
Doorly, Denis
Type
Journal Article
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 (∼ 20%) 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.
Date Issued
2026-08-07
Date Acceptance
2026-07-22
Citation
Scientific Reports, 2026
ISSN
2045-2322
Publisher
Nature Portfolio
Journal / Book Title
Scientific Reports
Copyright Statement
© The Author(s) 2026. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
10.1038/s41598-026-64054-1
Publication Status
Published online
Date Publish Online
2026-08-07