During the last 30 years, many chemical compounds that are active against tumors have been discovered or developed. At the same time, new methods of testing drugs for cancer therapy have evolved. nefore 1964, drug testing on animal tumors was directed to observation of the incfease in life span of the host after a single dose. A new approach, in which the effects of multiple doses on the proliferation kinetics of the tumor in vivo as well as of cell lines in vitro are investigated, has been outlined by Skipper and his co-workers in a series of papers beginning in 1964 (Skipper, Schabel and Wilcox, 1964 and 1965). They also investigated the influence of the time schedule in the treatment of experimental tumors. Since the publication of those studies, cell population kinetics cannot be left out of any discussion of the rational basis of chemotherapy. When clinical oncologists began to apply cell kinetic concepts in practice about 15 years ago, the theoretical basis was still very poor, in spite of Skipper's progress, and the lack of re­ levant cytokinetic and pharmacologic data was apparent. Subsequently, much theoretical work has been done and many cell kinetic models have been elaborated (for a review see Eisen, 1977).

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I. Mathematical models of cell populations.- 1. Proliferation and differentiation of cells.- 2. The cell cycle.- 3. The simple model of tumor growth.- 4. The extended model of tumor growth.- 5. Cell age distribution and phase indices.- 6. The general model with distributed cycle time.- 7. The Kendall-Takahashi model.- II. Determination of cell kinetic parameters.- Introduction: Cell kinetic experiments.- 1. Pulse labelling.- 2. Continuous labelling.- 3. Metaphase arrest.- 4. Continuous labelling with metaphase arrest.- 5. Fractions of labelled mitoses (FLM).- 6. Double labelling.- 7. Double labelling and FLM.- 8. Which experiments are to be chosen?.- III. Cell kinetics and cancer therapy.- 1. The surviving fraction after a single dose.- 2. Phase-specific cell kill.- 3. Block of the cell cycle.- 4. Recruitment of resting cells.- 5. A complex mathematical model and computer programs.- 6. Implications for drug testing.- 7. Potential implications for therapy.- 1. Limit theorems for matrix models.- 2. A model with periodic parameters.- 3. Pharmacokinetics and the dose-effect relation.- List of symbols.- References.