Stavreva N, Stavrev P, Warkentin B, Fallone B G
Department of Medical Physics, Cross Cancer Institute, Edmonton, Alberta, Canada.
Phys Med Biol. 2002 Oct 21;47(20):3591-604. doi: 10.1088/0031-9155/47/20/303.
This paper presents a complete set of formulae for the position (D50) and the normalized slope (gamma50) of the dose-response relationship based on the most commonly used radiobiological models for tumours as well as for normal tissues. The functional subunit response models (critical element and critical volume) are used in the derivation of the formulae for the normal tissue. Binomial statistics are used to describe the tumour control probability, the functional subunit response as well as the normal tissue complication probability. The formulae are derived for the single hit and linear quadratic models of cell kill in terms of the number of fractions and dose per fraction. It is shown that the functional subunit models predict very steep, almost step-like, normal tissue individual dose-response relationships. Furthermore, the formulae for the normalized gradient depend on the cellular parameters alpha and beta when written in terms of number of fractions, but not when written in terms of dose per fraction.
本文基于肿瘤及正常组织最常用的放射生物学模型，给出了一套完整的剂量-反应关系位置（D50）和归一化斜率（gamma50）公式。正常组织公式推导中使用了功能亚单位反应模型（关键元件和关键体积）。二项式统计用于描述肿瘤控制概率、功能亚单位反应以及正常组织并发症概率。根据分次次数和每次分次剂量，推导了细胞杀灭的单次打击和线性二次模型的公式。结果表明，功能亚单位模型预测正常组织个体剂量-反应关系非常陡峭，几乎呈阶梯状。此外，归一化梯度公式用分次次数表示时取决于细胞参数α和β，而用每次分次剂量表示时则不然。
