The use of three-dimensional treatment planning and volume-reduction t
echniques in radiotherapy has prompted the development of a number of
mathematical models to describe the effect of changing treatment volum
e on the probability of associated complications in normal tissues. Ho
wever, limited data are available to test or support these models. One
prediction of the Probability model and analogous models, which descr
ibe 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 subun
its suggested to be arranged in series, using the incidence of obstruc
tions due to consequential fibrosis as the end point of damage. Variou
s lengths of the colorectum of C3Hf/Kam mice were irradiated with sing
le doses of 250 kVp X rays. A threshold length between 10 and 15 mm wa
s observed after 32 Gy. The Probability model could not describe the d
ata adequately, but a modified version that included a threshold volum
e term (the Threshold Probability model) provided an excellent fit. In
a separate experiment, epithelial regeneration (migration, extracrypt
al proliferation and formation of new crypts) was examined as a possib
le mechanism for the threshold length. Reepithelialization was complet
e after 32 Gy was delivered to lengths below (5 or 10 mm) but not abov
e (20 mm) the threshold for consequential obstruction. Proliferation o
f epithelial cells outside the crypt on the mucosal surface (i.e. extr
acryptal proliferation) may contribute to the regeneration process. Th
e 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 Probabi
lity model. (C) 1998 by Radiation Research Society.