A mathematical model of the volume effect which postulates cell migration from unirradiated tissues.

Abstract

In order to simulate the large variation in tolerance doses for very small treatment volumes, we introduce a model which assumes the presence of cells which have migrated from unirradiated tissues. In order to represent serial architecture, the new model adds a new parameter to the familiar expression for serial architecture. Data derived from the model is fitted to the dose-response data developed by Hopewell et al. (Hopewell, J.W., Morris, A.D. and Dixon-Brown, A. The influence of field size on the late tolerance of the rat spinal cord to single doses of X rays. Br. J. Radiol. 60: 1099-1108, 1987) using white matter necrosis of rat spinal cord. The new model with a cell-migration term more accurately describes the large differences in threshold doses for a very small treatment volume than a model without a cell-migration term. Although these results do not prove that cell migration is the mechanism behind the volume effect for very small volume, they do suggest that the probability of normal tissue complication is more accurately predicted by the new model.