3. Oxygen diffusion in cells 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 ro that consists of tightly packed cells. Because cell membranes offer negligible resistance to O₂ diffusion, the sphere may be viewed as a homogeneous region in which O₂ is consumed at a constant rate ko (units of moles/volumetime). The O₂ 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 regi where oxygen is mplet depleted). (c) Oxygen consumption and diffusivity values representative of mammalian cells areko 30 μM/s and D = 2 10 ⁹m² s ¹. What is the maximum radius r that will be fully oxygenated if co 50 μM? What will the radius be if co = 200 μM? The lower value of co is representative of body tissues, and the higher one is approximately that for cells in contact with air. = =

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

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Transcribed Image Text:3. Oxygen diffusion in cells 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 ro that consists of tightly packed cells. Because cell membranes offer negligible resistance to O₂ diffusion, the sphere may be viewed as a homogeneous region in which O₂ is consumed at a constant rate ko (units of moles/volume*time). The O₂ 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). S (c) Oxygen consumption and diffusivity values representative of mammalian cells areko 30 μM/s and D = 2 * 10-⁹m². s-¹. What is the maximum radius r that will be fully oxygenated if со = 50 μM? What will the radius be if co = 200 µM? The lower value of co is representative of body tissues, and the higher one is approximately that for cells in contact with air.

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