Cell Kinetic Modelling and the Chemotherapy of Cancer

Reproduction or proliferation is the most characteristic feature of life. Higher living organisms are composed of millions of cells, which are organized into tissues and organs. But only cells, those atoms of life, and organisms are endowed with the capacity of proliferation. It is inconceivable that a liver could produce a second liver, but the liver cells are capable of proliferating and therefore the liver can regenerate itself after partial resection, a fact already told by Greek mythology.

Although the basic models of population growth apply to cells as well as to animals and men, the methods used to determine kinetic parameters are quite different in the two areas. In demography and partly in population biology the parameters (e. g. mean life span) are obtained by observations on a certain number of individuals at several stages of their life or during their whole life. But it is impossible to pick up any individual cell in vivo and perform subsequent observations on it. This difficulty in the study of cells however is compensated for by the possibility of observing at any given time a great number of cells and of performing experiments. Observing a great number of cells allows the determination of certain phase indices, and then the relative duration of these phases can be calculated with appropriate formulae. More information is supplied by the observation of synchronous instead of asynchronous cell populations. Synchronization can be achieved by special experimental techniques (see the survey by Nias and Fox, 1971) or by selection of a synchronous subpopulation (e. g. by labelling cells in S-phase). Since the phase indices of synchronous cell populations are varying, samples of the population are taken and prepared for inspection at different times during the course of the experiment. If in a study in vivo only one sample can be taken per animal, then the samples have to be taken at different times from different animals which have received the same treatment. Each sample reflects the state of the population at the time when it was taken, and thus it is possible to draw curves of the observable quantities over time. In the analysis of these curves mathematics are very helpful.

It is a well-established fact that the cytotoxicity of radiation and of most anticancer drugs depends on cell kinetic parameters (Sinclair 1967, Mendelsohn 1975, Valeriote and v. Putten 1975, Bhuyan 1977). This has suggested the idea of exploiting kinetic differences between neoplastic and sensitive normal tissues in order to achieve selective cell kill, i. e. killing a great fraction of tumor cells while sparing the normal cells of the renewal tissues (bone marrow, epithelium of the small intestine, skin). Indeed, cell kinetics are a corner-stone of many theoretical concepts in the treatment of cancer by radiation or cytotoxic drugs (Frei et al. 1969, Skipper and Perry 1970, Skipper 1971, Clarkson 1974, Klein and Lennartz 1974, Southwest Oncology Group 1974, Withers 1975, Valeriote and Edelstein 1977, Gerecke 1979, Swan 1980, Smets 1983). Some attempts to design therapy schedules on a rational basis with cell kinetic concepts have failed in practice and consequently the optimism of the period about 1970 has been displaced by skepticism (v. Putten, 1974) about the benefit of cell kinetics for therapy. But recently this approach has become favored again. There has been a careful palpating of the possibilities and limits of cytokinetic theory in clinical practice (Langen 1980) and the conviction that early failures should be attributed to the lack of data rather than to a presumed inconsistency of cell kinetic theory (Pallavicini et al. 1982).