3-3. Oxygenation of Cell Aggregates Oxygen is consumed in body tissues or by cells in vitro at a rate that is nearly independent of the O2 concentration. As a model for either a small tissue region without blood vessels or a spheroidal aggregate of isolated cells, consider steady O2 diffusion in a sphere of radius r0 that consists of tightly packed cells. Because cell membranes offer negligible resistance to O2 diffusion, the sphere Problems 99 may be viewed as a homogeneous region in which O2 is consumed at a constant volumetric rate k0. The O2 concentration at the edge of the sphere is C0. (a) Determine the O2 concentration profile C(r), both when O2 is present throughout the sphere and when there is an anoxic core of radius rc. Show how to predict the value of rc. (b) Oxygen consumption and diffusivity values representative of mammalian cells are k0=30M/s and D=2109m2s1. What is the maximum radius r0 that will be fully oxygenated if C0=50M ? What radius will be oxygenated if C0=200M ? (The lower value of C0 is representative of body tissues and the higher one is approximately that for cells in contact with air.)