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, d_f, 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, d_f 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 d_f are derived. The characteristic common to these is that each defines the flexure dose as a multiple of the ratio α/β 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 (α/β) {precedes above single-line equals sign} d_f {precedes above single-line equals sign} 0.15 (α/β). Estimates of the region of flexure are presented for a variety of normal and neoplastic tissues.