Use of the linear quadratic model in order to accommodate a small reduction in the number of fractions of a standard radiotherapy treatment regime

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Abstract
Use of the linear quadratic model is considered for reduction, by one or two fractions, of the number of fractions in a daily fractionated reference schedule while maintaining a continuous regime. The cases of maintaining late or early tumour reacting tissue are considered with the inclusion of time effects. The reduction of biologically effective dose (BED) to early-tumour type tissue is shown to be overestimated for both cases if time effects are not taken into account. A third option is outlined, which equates the magnitude of the fractional reduction of BED for early-tumour-reacting tissue to the fractional increase in BED for latereacting tissue without accounting for time effects. Using this option, the resulting variations in BED for lateand early-tumour tissue are compared with the accepted tolerances in physical dose delivery and some examples presented. The overestimated prediction of the variation in BED for early-tumour tissue still applies in this option, suggesting that this is the way the linear quadratic model should be applied to such a schedule change.