The use of three-dimensional treatment planning and volume-reduction techniques in radiotherapy has prompted the development of a number of mathematical models to describe the effect of changing treatment volume on the probability of associated complications in normal tissues. However, limited data are available to test or support these models. One prediction of the Probability model and analogous models, which describe the volume-effect relationship for late end points in tissues with a series-type arrangement of functional subunits, is that there is no threshold volume in the development of the end point. This hypothesis was tested in mouse colorectum, a normal tissue with functional subunits suggested to be arranged in series, using the incidence of obstructions due to consequential fibrosis as the end point of damage. Various lengths of the colorectum of C3Hf/Kam mice were irradiated with single doses of 250 kVp X rays. A threshold length between 10 and 15 mm was observed after 32 Gy. The Probability model could not describe the data adequately, but a modified version that included a threshold volume term (the Threshold Probability model) provided an excellent fit. In a separate experiment, epithelial regeneration (migration, extracryptal proliferation and formation of new crypts) was examined as a possible mechanism for the threshold length. Reepithelialization was complete after 32 Gy was delivered to lengths below (5 or 10 mm) but not above (20 mm) the threshold for consequential obstruction. Proliferation of epithelial cells outside the crypt on the mucosal surface (i.e. extracryptal proliferation) may contribute to the regeneration process. The data indicate that regeneration of the epithelium after irradiation results in a threshold length of the colorectum in the development of consequential fibrosis, in contradiction to predictions of the Probability model.

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