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Purpose: To modify existing linear-quadratic (LQ) equations in order to take account of relative biological effectiveness (RBE) using the concept of biologically effective dose (BED). Methods and Materials: Clinically useful forms of the LQ model have been modified to incorporate RBE effects in such a way as to allow comparison between high- and low-LET (linear energy transfer) radiations in terms of similar biological dose units. The new parameter in the formulation is RBE(M), the intrinsic (or maximum) RBE at zero dose. The principal assumption (following Kellerer and Rossi; ref. 1) is that high-LET radiation modifies the α-coefficient of damage while leaving the β- coefficient unaltered. Results: The equations allow a quantitative estimation of how the apparent RBE will change with changes in dose/fraction or dose- rate and of how the magnitude and rate of change is governed by the low-LET α/β ratio of the irradiated tissue. The modifications are applicable to all types of radiotherapy (fractionated, continuous low dose-rate, therapy with decaying sources, etc.). In cases where the normal tissue RBE(M) is greater than that for the tumor, the revised formulation helps explain why there will be situations where therapeutic index will be adversely affected by use of high-LET radiation. Such clinical advantages as have been observed are more likely to result from favorable geometrical sparing of critical normal tissues and/or the fact that slowly growing tumors may have α/β values more typical of late-responding normal tissues. Conclusions: The incorporation of RBE into existing LQ methodology allows quantitative assessment of clinical applications of high-LET radiations via an examination of the associated BEDs. On the basis of such assessments high-LET radiations are shown to confer few advantages.

Original publication




Journal article


International Journal of Radiation Oncology Biology Physics

Publication Date





639 - 645