Medical Radiation Physics, Stockholm University, Sweden.
Phys Med Biol. 2011 Dec 7;56(23):7585-600. doi: 10.1088/0031-9155/56/23/016.
Theoretical modelling of tumour control probability (TCP) with respect to non-uniformity in the dose to the tumour, alternate fractionation schemes and tumour kinetics is a very useful tool for assessment of the influence of changes in dosimetric or radiobiological factors on the outcome of the treatment. Various attempts have been made to also include effects from non-uniform dose to the tumour volume, but the problem has not been fully solved and many factors were totally neglected or not accurately taken into account. This paper presents derivations of analytical expressions of TCP for macroscopic inter-cell dose variations and for random inter-fractional variations in average tumour dose, based on binomial statistics for the TCP and the well-known linear quadratic model for the cell survival. Numerical calculations have been performed to validate the analytical expressions. An analysis of the influence of the deterministic and stochastic heterogeneity in dose delivery on the TCP was performed. The precision requirements in dose delivery are discussed briefly with the support of the presented results. The main finding of this paper is that it is primarily the shape of the cell survival curve that governs how the response is affected by macroscopic dose variations. The analytical expressions for TCP accounting for heterogeneity in dose can quite well describe the TCP for varying dose from cell to cell and random dose in each fraction. An increased TCP is seen when a large number of fractions are used and the variations in dose to the cells are rather high for tissues with low α/β.
关于肿瘤剂量不均匀、交替分割方案和肿瘤动力学对肿瘤控制概率（TCP）的理论建模，是评估剂量学或放射生物学因素变化对治疗结果影响的非常有用的工具。已经进行了各种尝试来包括肿瘤体积不均匀剂量的影响，但该问题尚未完全解决，许多因素被完全忽略或没有准确考虑。本文基于 TCP 的二项式统计和细胞存活的著名线性二次模型，为宏观细胞间剂量变化和随机分次间平均肿瘤剂量变化推导了 TCP 的解析表达式。进行了数值计算以验证解析表达式。分析了剂量传递中的确定性和随机性异质性对 TCP 的影响。本文的主要发现是，主要是细胞存活曲线的形状决定了剂量变化如何影响反应。考虑剂量异质性的 TCP 解析表达式可以很好地描述细胞间剂量变化和每个分次中随机剂量的 TCP。当使用大量分次并且对于低α/β组织的细胞剂量变化较高时，TCP 会增加。
