Restricted Diffusion in Cellular Media: (1+1)-Dimensional Model

Document Type

Article

Publication Date

7-1-2011

Abstract

We consider the diffusion of molecules in a one-dimensional medium consisting of a large number of cells separated from the extra-cellular space by permeable membranes. The extra-cellular space is completely connected and allows unrestricted diffusion of the molecules. Furthermore, the molecules can diffuse within a given cell, i. e., the intra-cellular space; however, direct diffusion from one cell to another cell cannot occur. There is a movement of molecules across the permeable membranes between the intra- and extra-cellular spaces. Molecules from one cell can cross the permeable membrane into the extra-cellular space, then diffuse through the extra-cellular space, and eventually enter the intra-cellular space of a second cell. Here, we develop a simple set of model equations to describe this phenomenon and obtain the solutions using an eigenfunction expansion. We show that the solutions obtained using this method are particularly convenient for interpreting data from experiments that use techniques from nuclear magnetic resonance imaging. © Society for Mathematical Biology 2010.

Identifier

79956146367 (Scopus)

Publication Title

Bulletin of Mathematical Biology

External Full Text Location

https://doi.org/10.1007/s11538-010-9589-1

e-ISSN

15229602

ISSN

00928240

PubMed ID

20953725

First Page

1682

Last Page

1694

Issue

7

Volume

73

Grant

1022848

Fund Ref

National Science Foundation

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