The application of the linear-quadratic dose-effect equation to fractionated and protracted radiotherapy

Abstract

The linear-quadratic (LQ) dose-effect formalism is currently providing new perspectives into the ways in which alterations in the dose per fraction in conventional radiotherapy may be used to bring about improved results with respect to early or late normal tissue reactions. In this paper, using a model initially developed by Roesch, the LQ equations are explored further in terms of dose-rate rather than dose. By the incorporation of one other parameter, mu, which relates to the rate of repair of sub-lethal radiation damage, a more general formalism is obtained. In particular, equations are derived which can be used to examine the relative effectiveness of different treatment regimes, including those involving decaying sources. Such equations are of wider applicability than other LQ derivations which relate only to dose-response relationships. The extended equations, which are fully consistent with the existing LQ method, are also shown to lead directly to other independently established, relationships for protracted irradiation. The nature of the link between high and low dose-rate treatments is discussed, and some worked examples provide indications of how the new equations may be used to assess further the potential clinical benefits of low dose-rate treatments and permanent implants.

The impact of uncertainties associated with MammoSite brachytherapy on the dose distribution in the breast

“…The surviving fraction was calculated using the following relations: ( 20 , 22 , 24 ) $S=e^{-\{\alpha D(1+Gd/\alpha /\beta )\}-\gamma T}$ ${(B{E}_{ff}D)}_i=D_i[1+G{d}_i/\alpha /\beta ]$ …”

Evaluation of the interfractional biological effective dose (BED) variation in MammoSite high dose rate brachytherapy

“…The cell survival (S) fraction from the total dose of “D” delivered in the number of fractions of “n” with fractional dose of “d” is known as following equation based on the linear‐quadratic (LQ) model: ( 3 , 4 ) $\mathrm{S}=\text{exp}[-\alpha \text{nd}-\beta {\text{nd}}^2]=\text{exp}\left[-\alpha \text{nd}\left(1+\frac{\mathrm{normald}}{\alpha /\beta }\right)\right]$ …”

Pulse Frequency in Pulsed Brachytherapy Based on Tissue Repair Kinetics

“…RE was calculated using the equations given below, based on the linear quadratic model for conditions of incomplete, monoexponential repair (22)(23)(24)(25) for continuous irradiation with dose rate Ḋ :…”