Fenwick J D
Joint Department of Physics, Institute of Cancer Research and the Royal Marsden NHS Trust, Surrey, UK.
Phys Med Biol. 1998 Aug;43(8):2159-78. doi: 10.1088/0031-9155/43/8/012.
A closed-form formula describing the tumour control probability (tcp) of a heterogeneous collection of tumours has been obtained by analytically averaging the homogeneous double-exponential tcp formula over inter-tumour distributions of clonogen radiosensitivity, density and repopulation rate, tumour volume and dose. The formula can be straightforwardly and relatively quickly fitted to clinical data, yielding radiobiological parameter values for use in tcp modelling. The formula was fitted to published tcp data which catalogued tumour control records grouped by dose and tumour volume, and treatment duration. Fitted parameter values, confidence intervals and goodness-of-fit statistics were determined. The sets of parameter values obtained are unique only to within a scaling factor. The formula provides non-rejectable fits to data which grouped tcp by dose and volume when radiosensitivity parameters take values close to laboratory estimates, the fitted volume dependence parameter, however, taking rather high values. Good fits are obtainable with the intuitively reasonable volume parameter value of one, but with radiosensitivity values around one-third of their laboratory estimates. Non-rejectable fits to data which grouped tcp by dose and treatment duration may be obtained with radiosensitivity and repopulation rate parameters lying close to laboratory estimates.
通过对克隆原放射敏感性、密度和再增殖率、肿瘤体积和剂量的肿瘤间分布，对均匀双指数肿瘤控制概率（tcp）公式进行解析平均，得到了一个描述异质性肿瘤集合体肿瘤控制概率（tcp）的封闭形式公式。该公式可以直接且相对快速地拟合临床数据，得出用于tcp建模的放射生物学参数值。该公式被拟合到已发表的tcp数据，这些数据按剂量、肿瘤体积和治疗持续时间对肿瘤控制记录进行了编目。确定了拟合参数值、置信区间和拟合优度统计量。所获得的参数值集仅在比例因子范围内是唯一的。当放射敏感性参数取值接近实验室估计值时，该公式对按剂量和体积分组的tcp数据提供了不可拒绝的拟合，然而，拟合的体积依赖性参数取值相当高。当体积参数值为直观合理的1时，可获得良好的拟合，但放射敏感性值约为实验室估计值的三分之一。当放射敏感性和再增殖率参数接近实验室估计值时，可对按剂量和治疗持续时间分组的tcp数据获得不可拒绝的拟合。
