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).

Klappentext

This monograph establishes a necessary link between experimental cancer research and mathematical modelling of cell population and presents a new approach to the old problem of building a rational basis for the design of radio- and chemotherapy of cancer. Rather than embark straightaway on model-building the author gives priority to the determination of action parameters of cytotoxic drugs. A survey of autoradiographic experiments and evaluation methods in cell kinetics is given, and classical formulae in this field are improved or generalized. The cell cycle retarding effect of certain drugs which in the past, raised some controversy, is described in a concise quantitative frame-work. Finally, a mathematical model of cell populations under treatment is tested against data from experiments with cell cycle phase-specific drugs and is applied to the problem of choosing optimal time schedules of chemotherapy. The book will serve as a guide to mathematical cell kinetics for biologists, as well as an introduction to the biomedical environment of the field for mathematicians. A knowledge of matrix algebra, calculus, and ordinary differential equations is expected of the reader, but is not essential for using the results in the design and evaluation of cell kinetic experiments.

Inhalt
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.- 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.