Volume and heterogeneity dependence of the dose-response relationship for head and neck tumours.

Based on the Poisson statistics of cell kill a model for the response of heterogeneous tumours to non-uniform dose delivery have been developed. The five parameters required to characterize the response are the 50% response dose, D50, the normalized dose-response gradient, gamma, the tumour heterogeneity factor, h, the relative volume, v and the extra daily dose required to counteract the tumour cell proliferation, delta. The model has been fitted to data from a number of clinical investigations to allow the derivation of clinically relevant radiation response parameters for head and neck tumours. The D50 value for T2 larynx cancers is 59.9 Gy in 41 days with a relative standard deviation of 2.1 Gy and the gamma value is 2.9 with a relative standard deviation of 0.3. The value of delta, which is most consistent with the clinical data for laryngeal tumours, is 0.35 Gy/day and this value should be used if the treatment time is changed from the 41 days normalization. The heterogeneity factor, h, is close to zero for laryngeal tumours which indicates that their response is basically governed by Poisson statistics. Nasopharyngeal tumours, on the other hand, exhibit h values around 0.2 which indicates that these tumours are more heterogeneous in their internal organization and so are their responses to radiation.