Oxygen diffusion and the distribution of cellular radiosensitivity in tumours

The diffusion equation has been solved for radially symmetric diffusion of oxygen and other metabolites to and from tumour blood vessels. Estimates of the radial distance from a vessel at which the oxygen tension is expected to become zero are listed for a number of different conditions. It is suggested that oxygen deficiency is a major factor in the causation of cell deaths and necrosis. Relations between oxygen tension, radiosensitivity and radial displacement from an isolated blood vessel were derived. It is shown that there are likely to be many cells in regions of tumours where the oxygen tension has values conferring radiosensitivity which is intermediate between its minimum and maximum values. Thus, tumours cannot be represented accurately by only assuming subpopulations of maximally radiosensitive, well-oxygenated cells, and maximally resistant, anoxic cells. The limitations of this two-compartment model are discussed, and it is suggested that its use may sometimes give misleading conclusions. Radiation cell survival curves are derived for model tumours from the distributions of cellular radiosensitivity estimated by considering oxygen diffusion; these curves do not resolve into two components. Using the “diffusion model” cell survival curves are fitted to experimental data for a number of different tumours.