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).

This book focuses on the analysis of cancer dynamics and the mathematically based synthesis of anticancer therapy. It summarizes the current state-of-the-art in this field and clarifies common misconceptions about mathematical modeling in cancer. Additionally, it encourages closer cooperation between engineers, physicians and mathematicians by showing the clear benefits of this without stating unrealistic goals. Development of therapy protocols is realized from an engineering point of view, such as the search for a solution to a specific control-optimization problem. Since in the case of cancer patients, consecutive measurements providing information about the current state of the disease are not available, the control laws are derived for an open loop structure. Different forms of therapy are incorporated into the models, from chemotherapy and antiangiogenic therapy to immunotherapy and gene therapy, but the class of models introduced is broad enough to incorporate other forms of therapy as well. The book begins with an analysis of cell cycle control, moving on to control effects on cell population and structured models and finally the signaling pathways involved in carcinogenesis and their influence on therapy outcome. It also discusses the incorporation of intracellular processes using signaling pathway models, since the successful treatment of cancer based on analysis of intracellular processes, might soon be a reality. It brings together various aspects of modeling anticancer therapies, which until now have been distributed over a wide range of literature. Written for researchers and graduate students interested in the use of mathematical and engineering tools in biomedicine with special emphasis on applications in cancer diagnosis and treatment, this self-contained book can be easily understood with only a minimal basic knowledge of control and system engineering methods as well as the biology of cancer. Its interdisciplinary character and the authors’ extensive experience in cooperating with clinicians and biologists make it interesting reading for researchers from control and system engineering looking for applications of their knowledge. Systems and molecular biologists as well as clinicians will also find new inspiration for their research.

This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments. A number of mathematical models for both classical and novel cancer treatments are presented as optimal control problems with the goal of constructing optimal protocols. The power of geometric methods is illustrated with fully worked out complete global solutions to these mathematically challenging problems. Elaborate constructions of optimal controls and corresponding system responses provide great examples of applications of the tools of geometric optimal control and the outcomes aid the design of simpler, practically realizable suboptimal protocols. The book blends mathematical rigor with practically important topics in an easily readable tutorial style. Graduate students and researchers in science and engineering, particularly biomathematics and more mathematical aspects of biomedical engineering, would find this book particularly useful.