Oxygen diffusion in large single-celled organisms

Bulletin of Mathematical Biology (Impact Factor: 1.29). 01/1969; 31(2):327-340. DOI: 10.1007/BF02477010

ABSTRACT The functional relationship between the oxygen uptake rate of a spherical, single cell organism and the external oxygen tension
is shown to be related to the dependence of the specific oxygen consumption rate, that is, the consumption rate of an infinitesimal
volume element of cellular material, on the external oxygen tension. Analytical solutions of the governing steady state diffusion
equation are obtained by dividing the system into three regions, an inner region of the sphere in which oxygen consumption
rate depends upon oxygen tension, an outer region of the sphere in which oxygen consumption rate is constant (independent
of oxygen tension), a nonconsuming membrane over the sphere that offers only resistance to oxygen diffusion, and an infinite
region outside the sphere and membrane supplying oxygen to the system. The solutions show the oxygen tension as a function
of position inside the spherical cell for a variety of system parameters.

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