Flexure dose: the low-dose limit of effective fractionation

Total radiation dose often can be increased without subsequent increases in the severity of tissue injury by using reduced doses per fraction. The flexure dose, df, is defined as the largest fractional dose for which further fractionation produces no significant change in the total dose required to reach a specified effect level. Thus, df is clinically relevant in that it represents the limit of effective dose fractionation. For those tissues in which injury reflects depletion of a critical proportion of target cells, the flexure dose is a measure of the extent of the initial, nearly linear portion of the dose-survival curve. More generally, the flexure dose is a measure of the extent of the initial, nearly linear portion of a dose-response curve in organized tissue, whatever its relationship to clonogenic target cells might be. Several quantitative expressions for df are derived. The characteristic common to these is that each defines the flexure dose as a multiple of the ratio alpha/beta of the parameters of the linear-quadratic model of cell survival or dose response, where the multiple is a measure of experimental or statistical resolution. These multiples tend to fall within a limited range, thereby defining the "region of flexure" via the inequality 0.05 (alpha/beta) less than or equal to df less than or equal to 0.15 (alpha/beta). Estimates of the region of flexure are presented for a variety of normal and neoplastic tissues.