The dynamic behavior of the oxygen tension distribution in tumors during radiotherapy is studied by the development and solution of a diffusion with absorption model involving a moving free boundary. The oxygen uptake rates within the tumor are considered to be functions of the oxygen concentration and results are presented for zeroth-, half-, first- and second-order rates of absorption, as well as when the rate of oxygen absorption is described by the Michaelis-Menten expression. The results presented in this work may be used together with the data from the oxygen radiosensitivity curve of a tumor, in order to determine the proper radiation dosage that should be applied to the tumor during radiotherapy, so as to compensate for the lost killing effectiveness resulting from oxygen consumption by the tumor. The model used in this study may also be employed in examining the role of oxygen and hypoxia in chemotherapy, when cycle-specific chemotherapeutic agents are used. The numerical procedure developed for the solution of the equations of the model may become applicable to problems encountered in such diverse areas as statistical decision theory, heat transfer with changes of phase, thermal explosions, optimal control and fluid flow in porous media. © 1988.
B. H. Arve and A. I. Liapis, "Oxygen Tension Profiles In Tumors Predicted By A Diffusion With Absorption Model Involving A Moving Free Boundary," Mathematical and Computer Modelling, vol. 10, no. 3, pp. 159 - 174, Elsevier, Jan 1988.
The definitive version is available at https://doi.org/10.1016/0895-7177(88)90020-9
Chemical and Biochemical Engineering
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01 Jan 1988