A Model of Oxygen Diffusion in Absorbing Tissue
A mathematical model is presented which describes the diffusion of oxygen in absorbing tissue, and numerical solutions of its partial differential equation are obtained by orthogonal collocation. The diffusion with absorption model accounts for the presence of a moving boundary which marks the furthest penetration of oxygen into the absorbing medium and also allows for an initial distribution of oxygen through the absorbing tissue. The model predictions may be used in the development of time variant radiation treatments of cancerous tumors, so that the dosage of radiation could be varied with the changing oxygen concentration. Simple expressions are also presented for evaluating the surface oxygen concentration, the rate of consumption of oxygen per unit volume of absorbing tissue, and the point of innermost oxygen penetration.
E. Tsiroyianni-Liapis et al., "A Model of Oxygen Diffusion in Absorbing Tissue," Mathematical Modelling, Elsevier, Jan 1982.
The definitive version is available at http://dx.doi.org/10.1016/0270-0255(82)90014-8
Chemical and Biochemical Engineering
Keywords and Phrases
Cancer; Mathematical Model; Nonbiological Model; Oxygen Consumption; Oxygen Diffusion; Oxygen Tissue Level; Radiotherapy; Theoretical Study; Therapy
Article - Journal
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