TY - JOUR
T1 - Restricted Diffusion in Cellular Media
T2 - (1+1)-Dimensional Model
AU - Huang, Huaxiong
AU - Wylie, Jonathan J.
AU - Miura, Robert M.
PY - 2011/7
Y1 - 2011/7
N2 - 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.
AB - 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.
KW - Nuclear magnetic resonance imaging
KW - Restricted diffusion in cellular media with permeable membranes
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-79956146367&origin=recordpage
U2 - 10.1007/s11538-010-9589-1
DO - 10.1007/s11538-010-9589-1
M3 - RGC 21 - Publication in refereed journal
C2 - 20953725
VL - 73
SP - 1682
EP - 1694
JO - Bulletin of Mathematical Biology
JF - Bulletin of Mathematical Biology
SN - 0092-8240
IS - 7
ER -