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Multi-Hit Kinetics of Tumor Formation, with Special Reference to Experimental Liver and Human Lung Carcinogenesis and Some General Conclusions

Division of Chemical Carcinogenesis, Antoni van Leeuwenhoek-Huis, The Netherlands Cancer Institute, Amsterdam, The Netherlands

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 I(d,t) d^mt^r. 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 [I(d) d^m 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 yielded 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 (I(d) d^m) yields only the number of hits contributed by the carcinogen applied and does not include the background hits. However, when the effect of the carcinogenic dose rate is low or very low, the contribution of background hits to the carcinogenic 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 (m_ex + m_b)n = r, where m_ex and m_b 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 [I(d) d with respect to smoke dose, m_ex = 1; I(t) t⁵ with respect to duration of smoking] are not compatible unless at least one additional background hit (m_b 1) is postulated. This process is an extreme example of the finding that chronic exposure to carcinogen may lead to an incidence rate of cancer that depends far more strongly on duration of exposure than on dose rate.

Finally, the view that the contribution of administered carcinogen to tumor formation in terms of hits decreases as the dose is lowered and may approximate one-hit kinetics has a bearing on the problem of the mode of extrapolation from relatively high doses with known incidence in the animal experiment to the very low doses that correspond to the chosen minimal incidence level that is considered acceptable for the human population.

Received 6/28/76. Accepted 3/ 9/77.