A C3H mouse mammary carcinoma (8-mm isotransplants growing in the leg, volume-doubling time of 2.5 days, median cell cycle time of 12 hr) has been used to investigate the relationships between total radiation dose required to achieve tumor control (<tex-math>${\rm TCD}_{50}$</tex-math>) and: number of equal dose fractions (v), time between fractions (ti), dose per fraction (Di), and total time of treatment (T). Radiation was administered under conditions of: acute local hypoxia produced by clamping; normal air breathing; respiration of 100% O2 at 30 psi. Assays were performed for: v values of 1, 2, 5, 10, and 20, and ti values of 1, 2, 3, or 5 days; in addition radiation was given in 2 or 3 fractions per day with 4 hr between treatments. Under hypoxic conditions and daily irradiations, <tex-math>${\rm TCD}_{50}$</tex-math> and v could be related by a power law with an exponent of 0.27 over the range of v from 1 to 10. With aerobic or hyperbaric oxygen conditions, the relationships were more complex due to interaction between reoxygenation, repair, and repopulation. Repair of radiation damage was demonstrated for both acutely and chronically hypoxic tumor cells, although severely and chronically hypoxic cells appeared to be less capable of such repair. Reoxygenation was a major factor determining response to fractionated irradiation under normal conditions, occurring rapidly and extensively. In the assays using v = 10, reoxygenation was as complete for radiations given three times per day as for treatment using ti of 1-2 days. Respiration of O2 at 30 psi improved results of treatment for all fractionation schedules studied. Proliferation of surviving cells between treatments given under clamp conditions caused <tex-math>${\rm TCD}_{50}$</tex-math> to increase sharply with prolongation of total overall time of treatment beyond 9 days. However, a precise evaluation of the extent of tumor cell proliferation during the course of irradiation under aerobic or hyperbaric conditions was not possible because the relative roles of concurrent reoxygenation and redistribution could not be quantified.

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