Calculation of the biological effect of fractionated radiotherapy: the importance of radiation-induced apoptosis

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Abstract
The total effect (TE) has been calculated for two different fractionation formalisms: the consecutive and repetitive fractionation mechanism, using a modified linear quadratic (LQ) model which includes the effect of apoptosis. For a given total dose, an increase in TE is seen when increasing the dose per fraction as well as the apoptotic fraction (Fa). Also, the TE increases with increasing alpha/beta ratio (of the modified LQ model). The ratio of TE for tumour tissue and TE for late reacting tissue is calculated assuming the absence of apoptosis in late reacting tissue and a common value of alpha/beta (of the modified LQ model). The biological effect ratio (BR) is higher for a large Fa and low doses per fraction, than for large doses per fraction and a small Fa. Assuming a consecutive fractionation mechanism, the TE formalism is unable to predict a log cell kill of more than 3 for beta values of 0.010-0.028. It is less dependent on dose per fraction and Fa than the repetitive fractionation mechanism. The biological effect ratio is only slightly higher than 1, and is less influenced by Fa, dose per fraction and alpha/beta ratio. A repetitive fractionation mechanism is also consistent with the preliminary results of published fractionation experiments. The calculations indicate that designing fractionation regimes for optimization of biological effect is a process where the role of apoptotic cell inactivation must be maximized, and where the influence of mitotic cell inactivation may be of less importance.

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