Effect of heterogeneity in radiosensitivity on LQ based isoeffect formalism for low alpha/beta cancers

Change of fractionation for external beam radiation therapy based on linear-quadratic (LQ) formalism assumes that a single alpha/beta is sufficient to characterize tumour response to dose fractionation. In reality, both inter-patient and intra-tumour heterogeneity might affect the applicability of isoeffectiveness formalism. The impact of heterogeneity on recently proposed hypofractionation schemes for the prostate has been analysed. The alpha/beta ratio was assumed to be Gaussian distributed with a mean value of 1.5 Gy. Gaussian and lognormal distributions for alpha were modelled. TCP model parameters were adjusted to lead to TCP = 0.80 for 70 Gy at 2 Gy per fraction. TCP loss from heterogeneity and doses required to restore TCP = 0.80 were calculated. The effect of heterogeneity was moderate. Doses to restore TCP = 0.80 in most cases were less than 1 Gy. The largest TCP loss was 4%. The difference between predictions of single alpha/beta and heterogeneity models is too small to be detected in a clinical trial.