apoptosis in late reacting tissue and a common value of a//? (of the modified LQ model). ... Apoptosis and the biological effect of fractionated radiotherapy.
1995, The British Journal of Radiology, 68, 1230-1236
Calculation of the biological effect of fractionated radiotherapy: the importance of radiation-induced apoptosis D R O L S E N , MSc Department of Medical Physics, The Norwegian Radium Hospital, Box 20, Montebello, N-0310 Oslo, Norway 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 (F a ). Also, the TE increases with increasing a//? 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 a//? (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 F a . Assuming a consecutive fractionation mechanism, the TE formalism is unable to predict a log cell kill of more than 3 for /? values of 0.010-0.028. It is less dependent on dose per fraction and F a than the repetitive fractionation mechanism. The biological effect ratio is only slightly higher than 1, and is less influenced by F a , dose per fraction and a//? 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. „
Calculations of the biological effect of fractionated radiotherapy are currently predominantly performed using an extension of the linear quadratic (LQ) model, introduced by Douglas and Fowler [ 1 ] . Here, the biological effect is related to the surviving fraction of cells after n fractions of therapy, each of dose d. The linear quadratic model assumes that the logarithm of the surviving fraction is partly a linear and partly a quadratic function of the absorbed dose. This model does not specify the cell inactivation mechanism responsible for cell kill. In a tentative explanation of the model, the linear and the quadratic terms are related to radiation induced DNA strand brakes [ 2 ] . If not repaired or misrepaired, these lesions will evidently lead to cell inactivation during mitosis. Although not specified, the linear quadratic model assumes a mitotic cell death, but when fitted to experimental data the parameters of the model obtained are characteristic for the overall cell inactivation. Biologists have been aware that programmed cell death, apoptosis, is a major cell inactivation mechanism present in normal tissue. Research over the past few years has revealed that in radiation induced cell inactivation, apoptosis may be a most important component [ 3 - 6 ] . A recent clinical study also indicated that the pre-treatment apoptotic fraction may predict the Received 17 March 1995 and in revised form 5 July 1995, accepted 21 July 1995. 1230
outcome after radiotherapy of patients with cancer of the cervix [ 7 ] . Since the overall cell inactivation in both normal and tumour tissues may be dependent on mitotic cell death as well as apoptosis, it is most important that the radiation induced apoptosis of cells is well understood. Ling et al have recently presented an empirical model modifying the linear quadratic model to account for the radiation induced apoptosis [ 8 ] . When calculating the effect of multiple fractions of exposure to radiation using the linear quadratic model, it is assumed that each fraction may be regarded as an independent event. The probability of cell survival after n fractions will therefore be the probability of cell survival after one fraction raised to the power of n. This effect of fractionated radiation therapy may be described as a repetitive mechanism. Conclusive experimental data able to verify whether this mechanism will also be valid for radiation induced apoptosis is not available at the present time. An alternative mechanism of fractionated irradiation induced apoptosis may be a consecutive inactivation mechanism, where the effect of n fractions of dose d will be equal to the effect of one fraction of dose n • d. Ling et al have reported preliminary results which show an increased effect of four fractions of 5 Gy each, compared with single fraction irradiation of 20 Gy [8]. These results are an indication of a fractionation mechanism of apoptosis of a repetitive nature. However, Ling et al have also shown that radiation induced apoptosis is
The British Journal of Radiology, November 1995
Apoptosis and the biological effect offractionated radiotherapy
probably dose rate independent [ 5 ] . If continuous irradiation with dose rates of less than 1 Gy h " 1 are regarded equal to an infinite number of fractions, these results indicate that radiation induced apoptosis may be of a consecutive nature. It is the aim of this study to consider the influence of apoptosis in calculations of the biological effects of fractionated radiotherapy, and the possible fractionation mechanisms involved. Materials and methods Calculation of biological effect The overall surviving fraction of cells (S) after a single fraction irradiation to a dose d, according to Ling et al. [8], is assumed to be:
importance in the development of late reactions in normal tissue [8,10,11], and that the a//? ratio of mitotic inactivation dependent late and acute reactions or tumour effects, do not differ significantly from each other [ 8 ] . This implies that the difference in the radiation effect of late and early effects in normal tissue, and the difference between late normal tissue reactions and tumour response is assumed to be due mostly to differences in apoptotic fraction and due less to differences in mitotic radiation sensitivity. Under the conditions of a repetitive fractionation mechanism, the BR of a fractionated radiotherapy regime can be written as (see Appendix): (8)
while the BR for a consecutive fractionation mechanism where Fa is the maximal apoptotic fraction of cells,
