Cell Kinetic Modelling and the Chemotherapy of Cancer (Lecture Notes in Biomathematics)

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.