Data on dose–volume effects in the rat spinal cord do not support existing NTCP models

To evaluate several existing dose–volume effect models for their ability to describe the occurrence of white matter necrosis in rat spinal cord after irradiation with small proton beams. A large number of dose–volume effect models has been fitted to data on the occurrence of white matter necrosis after irradiation with small proton beams. The fitting was done with the maximum likelihood method. For each model, the goodness of fit was calculated. An empirical tolerance dose–volume (eTDV) model was designed to describe data obtained after uniform irradiation. The eTDV model, the critical element model, and critical volume model with inclusion of the repair-by-migration principle described by Shirato, were able to describe the data obtained after irradiation with uniform dose distributions of varying sizes. However, none of the models under investigation was able to describe all the data. Extension of the developed empirical model with a repair mechanism with a limited range resulted in a good description of the tolerance doses. In the rat spinal cord, a nonlocal repair mechanism, acting from nonirradiated to irradiated tissue, plays an important role in the (prevention of the) occurrence of white matter necrosis after irradiation. Models that take into account this effect need to be developed.