Optimal Control for Mathematical Models of Cancer Therapies

Heinz Schättler is a Professor of Electrical and Systems Engineering at Washington University in St. Louis. He holds a Master's degree in Mathematics from the University of Würzburg in Germany and a Ph.D. in Mathematics from Rutgers University. His main research area is optimal control theory where he has published extensively on applications of methods and tools from optimal control and dynamical systems theory to problems motivated by real life applications. Besides the medical topics that are the focus of this text, these include electric power systems as well as models in economics, physics and electronics. Urszula Ledzewicz is a Distinguished Research Professor in the Department of Mathematics and Statistics at Southern Illinois University Edwardsville. She specialized in optimal control theory at the University of Lodz, Poland, where she received a master’s and doctorate in Applied Mathematics. Her research interests include optimal control and optimization, mathematicalmodeling and analysis of systems in biomedicine with special emphasis on mathematical models for cancer growth and treatments. She has been active in the field as an Associate Editor of numerous scientific journals focused on nonlinear analysis, dynamical systems and mathematical biosciences. The authors also have published the text Geometric Optimal Control – Theory, Methods and Examples (Springer, 2012) and were co-editors for Mathematical Methods and Models in Biomedicine (Springer, 2012).

Cancer and Tumor Development: Biomedical Background.- Cell-Cycle Specific Cancer Chemotherapy for Homogeneous Tumors.- Cancer Chemotherapy for Heterogeneous Tumor Cell Populations and Drug Resistance.- Optimal Control for Problems with a Quadratic Cost Functional on the Therapeutic Agents.- Optimal Control of Mathematical Models for Antiangiogenic Treatments.- Robust Suboptimal Treatment Protocols for Antiangiogenic Therapy.- Combination Therapies with Antiangiogenic Treatments.- Optimal Control for Mathematical Models of Tumor Immune System Interactions.- Concluding Remarks.- Appendices.