Optimal Control for Mathematical Models of Cancer Therapies: An Application of Geometric Methods (Interdisciplinary Applied Mathematics Book 42)

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. 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. By Heinz Schättler, Urszula Ledzewicz. Front Matter....Pages i-xix Cancer and Tumor Development: Biomedical Background....Pages 1-40 Cell Cycle Specific Cancer Chemotherapy for Homogeneous Tumors....Pages 41-114 Cancer Chemotherapy for Heterogeneous Tumor Cell Populations and Drug Resistance....Pages 115-139 Optimal Control for Problems with a Quadratic Cost Functional on the Therapeutic Agents....Pages 141-170 Optimal Control of Mathematical Models for Antiangiogenic Treatments....Pages 171-235 Robust Suboptimal Treatment Protocols for Antiangiogenic Therapy....Pages 237-274 Combination Therapies with Antiangiogenic Treatments....Pages 275-316 Optimal Control for Mathematical Models of Tumor Immune System Interactions....Pages 317-380 Concluding Remarks....Pages 381-383 Back Matter....Pages 385-496