When tumors grow, they become vascularized so that the tumor cells can get adequate oxygen. We are interested in how large a tumor can become without having its own blood supply. Consider a spherical, avascular tumor of radius r under steady-state conditions. We would like to find how larger can become while still having the tumor receive an adequate oxygen supply. The tumor tissue consumes oxygen at a rate (per unit volume) of 10-5 g/cm³.s. Let the diffusivity of oxygen in the tumor be 2 x 10-5 cm²/s. The tissue surrounding the tumor has an oxygen concentration of 1.7 x 10-5 g/cm³. Consider two possible boundary conditions at the surface of the tumor. (a) Let the concentration of oxygen at the surface of the tumor be the same as that in the surrounding tissue (1.7 x 10-5 g/cm³). For this boundary condition, find the maximum radius (r) of the tumor such that all the tumor cells receive an adequate oxygen supply. (b) Let the flux of oxygen that is supplied to the tumor by blood in the tissue surrounding the tumor be 8.5 x 10-8 g/cm²-s. For this boundary condition, find the maximum radius (r) of the tumor such that all the tumor cells receive an adequate oxygen supply.
When tumors grow, they become vascularized so that the tumor cells can get adequate oxygen. We are interested in how large a tumor can become without having its own blood supply. Consider a spherical, avascular tumor of radius r under steady-state conditions. We would like to find how larger can become while still having the tumor receive an adequate oxygen supply. The tumor tissue consumes oxygen at a rate (per unit volume) of 10-5 g/cm³.s. Let the diffusivity of oxygen in the tumor be 2 x 10-5 cm²/s. The tissue surrounding the tumor has an oxygen concentration of 1.7 x 10-5 g/cm³. Consider two possible boundary conditions at the surface of the tumor. (a) Let the concentration of oxygen at the surface of the tumor be the same as that in the surrounding tissue (1.7 x 10-5 g/cm³). For this boundary condition, find the maximum radius (r) of the tumor such that all the tumor cells receive an adequate oxygen supply. (b) Let the flux of oxygen that is supplied to the tumor by blood in the tissue surrounding the tumor be 8.5 x 10-8 g/cm²-s. For this boundary condition, find the maximum radius (r) of the tumor such that all the tumor cells receive an adequate oxygen supply.
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:When tumors grow, they become vascularized so that the tumor cells can get adequate
oxygen. We are interested in how large a tumor can become without having its own blood
supply. Consider a spherical, avascular tumor of radius r under steady-state conditions. We
would like to find how larger can become while still having the tumor receive an adequate
oxygen supply.
The tumor tissue consumes oxygen at a rate (per unit volume) of 10-5 g/cm³.s. Let the
diffusivity of oxygen in the tumor be 2 x 10-5 cm²/s. The tissue surrounding the tumor has an
oxygen concentration of 1.7 x 10-5 g/cm³. Consider two possible boundary conditions at the
surface of the tumor.
(a) Let the concentration of oxygen at the surface of the tumor be the same as that in the
surrounding tissue (1.7 x 10-5 g/cm³). For this boundary condition, find the maximum
radius (r) of the tumor such that all the tumor cells receive an adequate oxygen supply.
(b) Let the flux of oxygen that is supplied to the tumor by blood in the tissue surrounding the
tumor be 8.5 x 10-8 g/cm².s. For this boundary condition, find the maximum radius (r) of
the tumor such that all the tumor cells receive an adequate oxygen supply.
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