Tucker S L, Taylor J M
Department of Biomathematics, University of Texas, M.D. Anderson Cancer Center, Houston 77030, USA.
Int J Radiat Biol. 1996 Nov;70(5):539-53. doi: 10.1080/095530096144743.
The standard mechanistic model for the probability of tumour cure (the "Poisson model') is based on the assumption that the number of surviving clonogens at the end of treatment follows a Poisson distribution from tumour to tumour. This assumption is not correct, however, if proliferation of tumour clonogens occurs during treatment, as would be expected in general during a fractionated course of radiotherapy. In the present study, the possible magnitude of the error in the Poisson model was investigated for tumours treated with either conventional fractionation or split-course therapy. An example is presented in which the Poisson model has an absolute error of nearly 100%, predicting a cure rate of 0% when in fact the cure rate was close to 100%. The largest errors in the Poisson model found in this study were for very small tumours (approximately 100 clonogens), but for larger tumours (> or = 10(6) clonogens), the Poisson model may still be highly inaccurate, predicting a cure rate that differs from the actual cure rate by as much as 40%. Three new tumour-cure models are proposed (the GS, PS, and GS+ models), and their accuracy is also investigated. Two of these (the GS and PS models) are better than the Poisson model for the clinically relevant cases tested here. The third model, the GS+ model, consistently produced the most accurate estimate of the tumour cure rate, but has more limited use than the GS and PS models because it is more highly parametrized. It is demonstrated here that no tumour-cure model based on the effective clonogen doubling time will be perfectly accurate in all cases, since the cure rate depends on the details of the cell kinetics contributing to the effective doubling time.
肿瘤治愈概率的标准机制模型（“泊松模型”）基于这样一个假设，即治疗结束时存活的克隆源性细胞数量在不同肿瘤之间遵循泊松分布。然而，如果在治疗期间肿瘤克隆源性细胞发生增殖，而这在分次放射治疗过程中通常是可以预期的，那么这个假设就是不正确的。在本研究中，针对采用传统分割放疗或分段疗程治疗的肿瘤，研究了泊松模型中误差的可能大小。给出了一个例子，其中泊松模型的绝对误差接近100%，预测治愈率为0%，而实际上治愈率接近100%。本研究中发现泊松模型最大的误差出现在非常小的肿瘤（约100个克隆源性细胞）中，但对于较大的肿瘤（≥10⁶个克隆源性细胞），泊松模型可能仍然高度不准确，预测的治愈率与实际治愈率相差高达40%。提出了三种新的肿瘤治愈模型（GS、PS和GS+模型），并对其准确性进行了研究。其中两种模型（GS和PS模型）在此处测试的临床相关病例中比泊松模型更好。第三种模型GS+模型始终能最准确地估计肿瘤治愈率，但由于其参数化程度更高，其用途比GS和PS模型更有限。此处证明，基于有效克隆源性细胞倍增时间的肿瘤治愈模型在所有情况下都不会完全准确，因为治愈率取决于对有效倍增时间有贡献的细胞动力学细节。
