摘要：

This monograph is a study of optimal control applied to cancer chemotherapy, the treatment of cancer using drugs that kill cancer cells. The aim is to determine whether current methods for the administration of chemotherapy are optimal, and if alternative regimens should be considered. The research utilizes the mathematical theory of optimal control, an active research area for many mathematicians, scientists, and engineers. It is of multidisciplinary nature, having been applied to areas ranging from engineering to biomedicine. The aim in optimal control is to achieve a given objective at minimum cost. A set of differential equations is used to describe the evolution in time of the process being modelled, and constraints limit the policies that can be used to attain the objective. In this monograph, mathematical models are used to construct optimal drug schedules. These are treatment guidelines specifying which drug to deliver, when, and at what dose. Many current drug schedules have been derived empirically, based upon "rules of thumb". The monograph has been structured so that most of the high-level mathematics is introduced in a special appendix. In this way, a scientist can skip the more subtle aspects of the theory and still understand the biomedical applications that follow. However, the text is self-contained so that a deeper understanding of the mathematics of optimal control can be gained from the mathematical appendix. The mathematical models in this book and the associated computer simulations show that low intensity chemotherapy is a better choice of treatment than high intensity chemotherapy, under certain conditions. Contents: Basic Concepts Optimal Control: Theory and Applications Control Parametrization Technique: A Brief Review Multiple Characteristic Time (MCT) Constraints Minimize the Final Tumour Size Parameter Uncertainty Forced Decrease of Tumour Size Drug Resistance — One Drug Drug Resistance — Two Drugs Summary and Conclusions Readership: Applied mathematicians, scientists in cancer research, optimal control, biomedical engineering, biomathematics and operations research. -->Keywords: Optimal Control; Numerical Solutions; Cancer Chemotherapy; Drug Administration; Mathematical Models of Tumour Growth; Parameter Uncertainty; Maximizing Survival Time; Scheduling of Anti-Cancer Drug; Multiple Drug Chemotherapy; --> Updated review, subj code, msc, website & added keywords on 5/4/2006 Updated subj code & added ebook on 02/04/2008 -->

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