Oxygen tension profiles in tumors predicted by a diffusion with absorption model involving a moving free boundary
type: Item
instance of: scholarly article
title: Oxygen tension profiles in tumors predicted by a diffusion with absorption model involving a moving free boundary
zbMATH Open document ID: 0644.92004
DOI: 10.1016/0895-7177(88)90020-9
author: B. H. Arve
author: A. I. Liapis
published in: Mathematical and Computer Modelling
publication date: 1988-01-01T00:00:00Z
review text: 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-, and 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.
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 92-08
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 65N35
zbMATH DE Number: 4051400
zbMATH Keywords: oxygen tension distribution in tumors
zbMATH Keywords: radiotherapy
zbMATH Keywords: diffusion with absorption model
zbMATH Keywords: moving free boundary
zbMATH Keywords: oxygen uptake rates
zbMATH Keywords: oxygen concentration
zbMATH Keywords: rate of oxygen absorption
zbMATH Keywords: Michaelis-Menten expression
zbMATH Keywords: oxygen radiosensitivity curve
zbMATH Keywords: radiation dosage
zbMATH Keywords: hypoxia
zbMATH Keywords: chemotherapy
MaRDI profile type: Publication
full work available at URL: 0895-7177(88)90020-9
OpenAlex ID: W2075538270
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description: scientific article; zbMATH DE number 4051400