A graphical method to simplify the application of the linear-quadratic dose–effect equation to fractionated radiotherapy

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Abstract
The linear-quadratic (LQ) dose-effect equation has been shown to be capable of providing a number of new insights into clinical radiotherapy. However, even in the most straightforward application of the formalism, i.e. to fractionated radiotherapy, the level of mathematics required to solve the associated equations could be a significant barrier to the wider application of the LQ method. In this paper it is shown that a wide range of problems arising in fractionated radiotherapy are capable of being analyzed with the aid of one basic graph. It is further demonstrated that the extrapolated response dose, which forms the conceptual fulcrum of the LQ method, is an additive quantity, and that the analysis of treatments involving several component parts can be simplified by using this property. The main features of these simplifications are demonstrated using some representative worked examples.