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

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.
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 mean 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.
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.
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.

线性二次（linear-quadratic, LQ）模型针对诸多机理驱动的辐射效应模型而言，是一种简洁且稳健的近似形式。我们认为，该模型在高剂量场景下高估细胞杀伤效应的倾向，源自一项通用假设：辐射诱导损伤（radiogenic lesions）遵循泊松统计（Poisson statistics）分布。
基于这一背景，我们研究了损伤分布过离散的效应——这类情况可能源于对微剂量学（microdosimetric）能量沉积模式、DNA损伤复杂度与修复通路的差异，以及/或细胞辐射应答异质性的考量。这类过离散现象有望降低高剂量下的剂量响应曲线曲率，同时仍能保留LQ模型下、基于单位细胞平均致死损伤数的剂量依赖关系。本研究针对多组受辐照的哺乳动物细胞与酵母菌存活数据集展开分析，所采用的模型包括：带泊松误差的LQ模型、两种自定义负二项（negative binomial, NB）误差分布的LQ模型变体、帕德-线性二次（Padé-linear-quadratic）模型，以及双组分（Two-component）模型。我们通过信息论分析（information-theoretic analysis），对比了所有模型在各数据集上的表现，并基于低/中剂量下的拟合结果，评估了各模型预测高剂量下细胞存活率的能力。
在保留LQ模型平均剂量依赖关系的前提下，仅调整误差分布，即可让NB-LQ模型变体的表现优于标准LQ模型，相较于其他替代模型，往往能更贴合实验数据。
基于负二项误差分布的方法保留了LQ形式化体系的核心机制假设，同时能更精准地估算放射治疗（radiotherapy）中高剂量下的细胞存活率。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——这类效应正是辐射防护（radiation protection）领域的重点关注对象。