Optimal Control for Mathematical Models of Cancer Therapies

An Application of Geometric Methods

Heinz Schättler, Urszula Ledzewicz (Autoren)

Buch | Softcover

496 Seiten

2016 | Softcover reprint of the original 1st ed. 2015
Springer-Verlag New York Inc.
978-1-4939-4279-4 (ISBN)

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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.

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.

Erscheint lt. Verlag	22.10.2016
Reihe/Serie	Interdisciplinary Applied Mathematics ; 42
Zusatzinfo	85 Illustrations, color; 30 Illustrations, black and white; XIX, 496 p. 115 illus., 85 illus. in color.
Verlagsort	New York
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Medizin / Pharmazie ► Medizinische Fachgebiete ► Onkologie
	Technik ► Elektrotechnik / Energietechnik
Schlagworte	anti-angiogenic treatment • geometric optimal control • Mathematical Models • mathematical models forcancer therapies • optimal control • optimal protocols
ISBN-10	1-4939-4279-4 / 1493942794
ISBN-13	978-1-4939-4279-4 / 9781493942794
Zustand	Neuware