• Radiation Oncology Journal
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• v.7 no.2
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• pp.171-183
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• 1989

A general effect for cell proliferation has been incorporated into Roesch's survival equation (Accumulation Model). From this an isoeffect formula for the low dose-rate regimen is obtained. The prediction for total doses equivalent to 60Gy delivered at the constant dose-rate over 7 days agrees well with the dose-time data of Paterson and of Green, when the parameter ratio A/B (${\approx}{\alpha{\mu}}/2{\beta}\;where\;{\mu}$ is the repair rate) is chosen to be 0.7Gy/h. When a constant proliferation rate and known facts of division delay are assumed, an isoeffect relation between low dose-rate treatment and acute dose-rate treatment can be derived. This formula in the regimens where proliferation is negligible predicts exactly the data of Ellis that 8 fractions of 5 Gy/day for 7 days are equivalent to continuously applied 60Gy over 7days, provided the A/B ratio is 0.7 Gy/h and the $\alpha/\beta$ ratio is 4Gy. Overall agreement between the clinical data and the predictions made by the formula at the above parameter values suggests that the biologcal end points used as the tolerance level in the studies by Paterson, Green, and Ellis all agree and they are not entirely the early effects as generally assumed. The absence of dose-rate effects observed in the mouse KHT sarcoma can better be explained in terms of a large value for the A/B ratio. Similarly, the same total dose used independently of the dose-rate to treat head and neck tumors by Pierquin can be justified.