Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension

Simpson, Matthew & Baker, Ruth (2015) Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension. Journal of Chemical Physics, 143, 094109.

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Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard nongrowing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here.

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ID Code: 91496
Item Type: Journal Article
Refereed: Yes
Keywords: Diffusion, Growing tissues, Growing domains, Survival, Survival probability
DOI: 10.1063/1.4929993
ISSN: 1089-7690
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: © 2015 AIP Publishing LLC
Deposited On: 04 Jan 2016 04:26
Last Modified: 04 Jan 2016 21:43

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