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It is demonstrated that the surviving fraction of a population of cells with heterogeneous radio sensitivity, like that composing most malignant tumors, conforms to a different linear quadratic survival relation for dose less than about 3-5 Gy and dose greater than about 7-9 Gy. In the intermediate range of dose the survival relation for the population, as a whole, is not linear quadratic. Consequently, the value of the alpha beta ratio and the associated biologically effective dose calculation are different for the low and high dose range for most malignant tumors. Normal tissue cell populations responsible for organ function also have heterogeneous radio sensitivity, though to less degree than most malignant tumors. Consequently, the alpha beta ratio and associated biologically effective dose calculation related to the development of some acute early and chronic late developing radiation injuries are not the same in the low and high dose range. Variance of the distribution of α of a heterogeneous cell population lowers the effective value of the quadratic survival constan β of the population, as a whole, and increases the α / β ratio in the low dose range. Heterogeneous appearance of tumor cells (pleomorphism) and necrosis on biopsy or imaging studies reflect heterogeneity of the radio sensitivity of the cells. Greater heterogeneity implies a tendency to higher α / β ratio. This may furnish a clinically accessible way to estimate a value of the α / β ratio specific to an individual patient and tumor.

clinical and translational radiation oncology

Effect of heterogeneous radio sensitivity on the survival, alpha beta ratio and biologic effective dose calculation of irradiated mammalian cell populations