Accounting for overdispersion of lethal lesions in the linear quadratic model improves performance at both high and low radiation doses

<b>Purpose:</b> The linear-quadratic (LQ) model represents a simple and robust approximation for many mechanistically-motivated models of radiation effects. We believe its tendency to overestimate cell killing at high doses derives from the usual assumption that radiogenic lesions are distributed according to Poisson statistics. <b>Materials and methods:</b> In that context, we investigated the effects of overdispersed lesion distributions, such as might occur from considerations of microdosimetric energy deposition patterns, differences in DNA damage complexities and repair pathways, and/or heterogeneity of cell responses to radiation. Such overdispersion has the potential to reduce dose response curvature at high doses, while still retaining LQ dose dependence in terms of the number of <i>mean</i> lethal lesions per cell. Here we analyze several irradiated mammalian cell and yeast survival data sets, using the LQ model with Poisson errors, two LQ model variants with customized negative binomial (NB) error distributions, the Padé-linear-quadratic, and Two-component models. We compared the performances of all models on each data set by information-theoretic analysis, and assessed the ability of each to predict survival at high doses, based on fits to low/intermediate doses. <b>Results:</b> Changing the error distribution, while keeping the LQ dose dependence for the mean, enables the NB LQ model variants to outperform the standard LQ model, often providing better fits to experimental data than alternative models. <b>Conclusions:</b> The NB error distribution approach maintains the core mechanistic assumptions of the LQ formalism, while providing superior estimates of cell survival following high doses used in radiotherapy. Importantly, it could also be useful in improving the predictions of low dose/dose rate effects that are of major concern to the field of radiation protection.

<b>研究背景：</b> 线性二次模型（linear-quadratic, LQ）是众多基于机制的辐射效应模型的简洁且稳健的近似形式。我们认为，该模型在高剂量下高估细胞杀伤效应的倾向，源于其默认辐射诱导损伤遵循泊松统计分布的假设。
<b>材料与方法：</b> 基于上述背景，我们探究了过度分散损伤分布的影响——这类分布可能源于微剂量学能量沉积模式、DNA损伤复杂性与修复通路的差异，以及/或细胞辐射响应的异质性。此类过度分散现象可降低高剂量下的剂量响应曲线曲率，同时仍能保留单位细胞<i>平均</i>致死损伤数量对应的LQ剂量依赖关系。本研究分析了多组受辐照的哺乳动物细胞与酵母菌存活数据集，分别采用带泊松误差的LQ模型、两种定制负二项分布（negative binomial, NB）误差分布的LQ模型变体、帕德-线性二次模型以及双组分模型。我们通过信息论分析比较了所有模型在各数据集上的拟合性能，并基于低/中剂量的拟合结果评估了各模型预测高剂量下细胞存活情况的能力。
<b>研究结果：</b> 在保持平均剂量依赖关系符合LQ模型框架的前提下，更改误差分布可使基于负二项分布的LQ模型变体的表现优于标准LQ模型，相较于其他替代模型，通常能更精准地拟合实验数据。
<b>研究结论：</b> 负二项误差分布方法保留了LQ形式体系的核心机制假设，同时针对放射治疗中使用的高剂量场景，能更准确地估算细胞存活情况。值得注意的是，该方法还有助于改善低剂量/剂量率效应的预测结果——这正是辐射防护领域重点关注的研究方向。