Linear-quadratic model underestimates sparing effect of small doses per fraction in rat spinal cord

The application of the linear-quadratic (LQ) model to describe iso-effective fractionation schedules for dose fraction sizes less than 2 Gy has been controversial. This paper describes experiments in which the effect of daily fractionated irradiation given with a wide range of fraction sizes was assessed in rat cervical spinal cord. The first group of rats were given doses in 1, 2, 4, 8 and 40 daily fractions. The second group of animals received three initial "top-up" doses of 9 Gy given once daily, representing three-quarters of tolerance, followed by doses in 1, 2, 10, 20, 30 and 40 daily fractions. The fractionated portion of the irradiation schedule therefore constituted only the final quarter of the tolerance dose. The endpoint of the experiments was paralysis of the forelimbs secondary to white matter necrosis. Direct analysis of data from experiments with full course fractionation up to 40 daily fractions (25.0-1.98 Gy per fraction) indicated consistency with the LQ model yielding an alpha/beta value of 2.41 Gy. Analysis of data from experiments in which the three "top-up" doses were followed by up to 10 fractions (10.0-1.64 Gy per fraction) gave an alpha/beta value of 3.41 Gy. However, data from "top-up" experiments with 20, 30 and 40 fraction (1.60-0.55 Gy per fraction) were inconsistent with the LQ model and gave a very small alpha/beta value of 0.48 Gy. It is concluded that the LQ model based on data from large doses per fraction underestimates the sparing effect of small doses per fraction provided sufficient time is allowed between each fraction for repair of sublethal damage.