Brenner D J, Hlatky L R, Hahnfeldt P J, Huang Y, Sachs R K
Center for Radiological Research, Columbia University, New York, New York 10032, USA.
Radiat Res. 1998 Jul;150(1):83-91.
One of the fundamental tools in radiation biology is a formalism describing time-dose relationships. For example, there is a need for reliable predictions of radiotherapeutic isoeffect doses when the temporal exposure pattern is changed. The most commonly used tool is now the linear-quadratic (LQ) formalism, which describes fractionation and dose-protraction effects through a particular functional form, the generalized Lea-Catcheside time factor, G. We investigate the relationship of the LQ formalism to those describing other commonly discussed radiobiological models in terms of their predicted time-dose relationships. We show that a broad range of radiobiological models are described by formalisms in which a perturbation calculation produces the standard LQ relationship for dose fractionation/protraction, including the same generalized time factor, G. This approximate equivalence holds not only for the formalisms describing binary misrepair models, which are conceptually similar to LQ, but also for formalisms describing models embodying a very different explanation for time-dose effects, namely saturation of repair capacity. In terms of applications to radiotherapy, we show that a typical saturable repair formalism predicts practically the same dependences for protraction effects as does the LQ formalism, at clinically relevant doses per fraction. For low-dose-rate exposure, the same equivalence between predictions holds for early-responding end points such as tumor control, but less so for late-responding end points. Overall, use of the LQ formalism to predict dose-time relationships is a notably robust procedure, depending less than previously thought on knowledge of detailed biophysical mechanisms, since various conceptually different biophysical models lead, in a reasonable approximation, to the LQ relationship including the standard form of the generalized time factor, G.
辐射生物学的基本工具之一是一种描述时间-剂量关系的形式体系。例如，当时间暴露模式改变时，需要可靠地预测放射治疗的等效效应剂量。目前最常用的工具是线性二次（LQ）形式体系，它通过一种特定的函数形式，即广义的 Lea-Catcheside 时间因子 G，来描述分次照射和剂量延长效应。我们根据预测的时间-剂量关系，研究了 LQ 形式体系与描述其他常见放射生物学模型的形式体系之间的关系。我们表明，广泛的放射生物学模型可以用这样的形式体系来描述，即通过微扰计算得出剂量分次/延长的标准 LQ 关系，包括相同的广义时间因子 G。这种近似等效性不仅适用于描述二元错配修复模型的形式体系，这些模型在概念上与 LQ 相似，也适用于描述对时间-剂量效应有非常不同解释的模型的形式体系，即修复能力的饱和。在放射治疗的应用方面，我们表明，在临床相关的分次剂量下，典型的可饱和修复形式体系预测的延长效应依赖性与 LQ 形式体系几乎相同。对于低剂量率照射，在诸如肿瘤控制等早期反应终点方面，预测之间同样存在等效性，但在晚期反应终点方面则不太明显。总体而言，使用 LQ 形式体系来预测剂量-时间关系是一个特别稳健的过程，对详细生物物理机制知识的依赖程度比以前认为的要小，因为各种概念上不同的生物物理模型在合理近似下会导致包括广义时间因子 G 的标准形式的 LQ 关系。
