Multi-hit kinetics of tumor formation, with special reference to experimental liver and human lung carcinogenesis and...

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...