Linear-quadratic model isoeffect relations for proliferating tumor cells for treatment with multiple fractions per...

A modified linear-quadratic model isoeffect relation that includes the effect of proliferation is proposed. As for a planned course of therapy, the treatment time T and the number of fractions N are not independent variables; the new isoeffect relation involves only the fraction size d and the total dose D, but differs from the unmodified linear-quadratic model isoeffect relation and predicts higher isoeffect doses for small dose fractions. Using the new isoeffect relation it is explicitly shown, for a simple model, that decreasing the fraction size will improve the therapeutic ratio only if multiple fractions per day are given.