Oxygen is consumed in body tissues or by cells in vitro at a rate that is nearly independent of the Oz concentration. As a model for either a small tissue region without blood vessels or a spheroidal aggregate of isolated cells, consider steady O$2$ diffusion in a sphere of radius to that consists of tightly packed cells. Because cell membranes offer negligible resistance to $02$ diffusion, the sphere may be viewed as a homogeneous region in which O$,$ is consumed at a constant rate ko $($units of moles$/$volume$*$time$).$ The O$2$ concentration at the edge of the sphere is co$.($a$)$ Write the differential equation and boundary conditions for the concentration profile of oxygen c$($r$)$ when the gas is present throughout the sphere.$($b$)$ Solve for c$($r$),$ and determine the largest radius of the cell mass that can be allowed before an anoxic core starts to form $($i$.$e$.,$ a region where oxygen is completely depleted$).($c$)$ Oxygen consumption and diffusivity values representative of mammalian cells areko $=30$ MM$/$s and D $=2*10-9$m$?.$ s$-1.$ What is the maximum radius ro that will be fullyoxygenated if Co $=50$ M$?$ What will the radius be if co $=200$ uM$?$ The lower value of cois representative of body tissues, and the higher one is approximately that for cells in contact with air.