Masters Theses


"A mathematical model which describes the diffusion of oxygen in absorbing tissue is presented. The model accounts for the presence of a moving boundary which marks the deepest penetration of oxygen into the absorbing medium and predicts the steady state and unsteady state distribution of oxygen through the absorbing tissue.

Results are shown for zeroth, half, first, one and a half, and second order rates of absorption as well as when the rate of absorption is described by the Michaelis - Menten equation.

The model predictions show that the total time for the moving boundary to recede to the surface of the tissue and the innermost penetration of oxygen at steady state increases with absorption order when the initial surface concentration is less than unity, whereas the total time and oxygen penetration depth decreases with absorption order when the initial surface concentration is much larger than unity. It is also shown that for a first order absorption rate, the total time and innermost point of oxygen penetration is independent of the initial surface concentration.

The results may be used to develop a time varying radiation procedure in the treatment of tumors by radiotherapy, so as to compensate for the lost killing effectiveness resulting from oxygen consumption by the tumor. It was found that in certain cases constant radiation dosage may suffice. In addition, the results may be used to obtain estimates for the absorption rate constant and the absorption order in a tissue.

The modelling and solution procedure presented in this work may also be applicable to certain classes of systems involving mass diffusion and absorption or chemical reactions with a moving interface as well as thermal diffusion problems with a moving interface where heat is generated or dissipated"--Abstract, pages ii-iii.


Liapis, Athanasios I.

Committee Member(s)

Crosser, Orrin K.
Grimm, L. J.
Avula, Xavier J. R.


Chemical and Biochemical Engineering

Degree Name

M.S. in Chemical Engineering


University of Missouri--Rolla

Publication Date

Spring 1985


ix, 108 pages

Note about bibliography

Includes bibliographical references (pages 70-71).


© 1985 Bo Henrik Arve, All rights reserved.

Document Type

Thesis - Open Access

File Type




Subject Headings

Diffusion -- Mathematical models
Absorption -- Mathematical models
Oxygen -- Absorption and adsorption
Oxygen -- Physiological transport
Oxygen in the body

Thesis Number

T 5167

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