Characterizing transport through a crowded environment with different obstacle sizes
Ellery, Adam, Simpson, Matthew, McCue, Scott W., & Baker, Ruth (2014) Characterizing transport through a crowded environment with different obstacle sizes. Journal of Chemical Physics, 140(5), 054108.
Transport through crowded environments is often classified as anomalous, rather than classical, Fickian diffusion. Several studies have sought to describe such transport processes using either a continuous time random walk or fractional order differential equation. For both these models the transport is characterized by a parameter α, where α = 1 is associated with Fickian diffusion and α < 1 is associated with anomalous subdiffusion. Here, we simulate a single agent migrating through a crowded environment populated by impenetrable, immobile obstacles and estimate α from mean squared displacement data. We also simulate the transport of a population of such agents through a similar crowded environment and match averaged agent density profiles to the solution of a related fractional order differential equation to obtain an alternative estimate of α. We examine the relationship between our estimate of α and the properties of the obstacle field for both a single agent and a population of agents; we show that in both cases, α decreases as the obstacle density increases, and that the rate of decrease is greater for smaller obstacles. Our work suggests that it may be inappropriate to model transport through a crowded environment using widely reported approaches including power laws to describe the mean squared displacement and fractional order differential equations to represent the averaged agent density profiles.
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|Item Type:||Journal Article|
|Keywords:||diffusion, random walk, fractional differential equation, microenvironment, cancer, wound healing|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Biological Mathematics (010202)|
|Divisions:||Current > Institutes > Institute of Health and Biomedical Innovation
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
|Copyright Owner:||Copyright 2014 AIP Publishing LLC|
|Deposited On:||22 Jan 2014 22:48|
|Last Modified:||15 Apr 2014 14:15|
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