Emmelot P, Scherer E
Cancer Res. 1977 Jun;37(6):1702-8.
On the basis of the multi-hit concept of cancer formation, the relationships between tumor incidence and dose and time of administration of carcinogen have been analyzed. Simple mathematics have been used, since the available data, in our opinion, hardly justify more sophisticated formularization. The exponential relationship between the cumulative tumor incidence and the dose and time of administration of carcinogen can be described as l(d,t) approximately dmtr. With use of Druckrey's formula, dtn=k, it was derived that the exponent of time, r, is equal to m-n, in which m is the power of the dose dependency of tumor formation [l(d) approximately dm measured at a fixed time] and n is the autonomous time factor featured in the former formula. The factor m is interpretable in terms of the number of discrete events (hits) required for tumor formation, whereas the factor n is mainly determined by the rate of proliferation of intermediate cell populations participating in the carcinogenic process. Since r and n can be experimentally determined, the formula allows the calculation of the exponent (m) of the dose dependency of tumor formation. Analysis of malignant liver tumor formation in the rat by continuous administration of diethylnitrosamine yeilded m = 7, from which it was concluded that seven hits were instrumental in the induction of these liver-cell tumors. Analysis of the formation of less malignant liver tumors after one pulse exposure to the same carcinogen suggested that the process was initiated by at most two concomitant hits in a liver cell and brought to completion by three spontaneous events (changes). The view was advanced that tumor formation in general may result from hits inflicted by the carcinogen applied and from "background" hits (i.e., spontaneous changes and/or hits by carcinogenic stimuli from the environment or present endogenously) and that the relative contribution of these two types of hits to the end effect may depend on dose level and potency of the carcinogen under consideration. It was pointed out that the direct measurement of the dose-response relation (l(d) approximately dm) yields only the number of hits contributed by the carcinogen applied anose rate is low or very low, the contribution of background process becomes significant, and these hits contribute to the power of time, r, of the incidence-time relation. Under these conditions, the formula m-n=r becomes (mex + mb)n=r, where mex and mb denote the number of hits scored by extrinsic carcinogen and background processes, respectively. It is argued that the epidemiological data on lung cancer caused by smoking [l(d) approximately d with respect to smoke dose, mex= 1; l(t) approximately t5 with respect to duration of smoking] are not compatible unless at least one additional background hit (mb greater than or equal to 1) is postulated...
基于癌症形成的多击概念，分析了肿瘤发生率与致癌物剂量及给药时间之间的关系。由于我们认为现有数据几乎无法证明更复杂的公式化是合理的，所以使用了简单的数学方法。累积肿瘤发生率与致癌物剂量及给药时间之间的指数关系可描述为(l(d,t)\approx d^m t^r)。利用德鲁克雷公式(d^t n = k)，推导得出时间指数(r)等于(m - n)，其中(m)是肿瘤形成剂量依赖性的幂次（在固定时间测量的(l(d)\approx d^m)），(n)是前一公式中的自主时间因子。因子(m)可根据肿瘤形成所需的离散事件（击数）数量来解释，而因子(n)主要由参与致癌过程的中间细胞群体的增殖速率决定。由于(r)和(n)可以通过实验确定，该公式允许计算肿瘤形成剂量依赖性的指数((m))。通过连续给予二乙基亚硝胺分析大鼠恶性肝肿瘤的形成，得出(m = 7)，由此得出七次击数对这些肝细胞肿瘤的诱导起作用。对单次脉冲暴露于相同致癌物后形成的恶性程度较低的肝肿瘤的分析表明，该过程最多由肝细胞中的两次同时击数启动，并由三次自发事件（变化）完成。有人提出，一般来说，肿瘤形成可能是由所施加的致癌物造成的击数以及“背景”击数（即自发变化和/或来自环境或内源性存在的致癌刺激的击数）导致的，并且这两种类型的击数对最终效应的相对贡献可能取决于所考虑的致癌物的剂量水平和效力。有人指出，剂量 - 反应关系(l(d)\approx d^m)的直接测量仅得出所施加的致癌物贡献的击数；当剂量率低或非常低时，背景过程的贡献变得显著，并且这些击数对发生率 - 时间关系的时间幂次(r)有贡献。在这些条件下，公式(m - n = r)变为((m_{ex} + m_b)n = r)，其中(m_{ex})和(m_b)分别表示外部致癌物和背景过程得分的击数。有人认为，关于吸烟导致肺癌的流行病学数据（相对于烟雾剂量(l(d)\approx d)，(m_{ex}=1)；相对于吸烟持续时间(l(t)\approx t^5)）不相符，除非假设至少有一个额外的背景击数（(m_b\geq1)）……
