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.
This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. The emphasis is on the geometric aspects of the theory and on illustrating how these methods can be used to solve optimal control problems. It provides tools and techniques that go well beyond standard procedures and can be used to obtain a full understanding of the global structure of solutions for the underlying problem. The text includes a large number and variety of fully worked out examples that range from the classical problem of minimum surfaces of revolution to cancer treatment for novel therapy approaches. All these examples, in one way or the other, illustrate the power of geometric techniques and methods. The versatile text contains material on different levels ranging from the introductory and elementary to the advanced. Parts of the text can be viewed as a comprehensive textbook for both advanced undergraduate and all level graduate courses on optimal control in both mathematics and engineering departments. The text moves smoothly from the more introductory topics to those parts that are in a monograph style were advanced topics are presented. While the presentation is mathematically rigorous, it is carried out in a tutorial style that makes the text accessible to a wide audience of researchers and students from various fields, including the mathematical sciences and engineering. Heinz Schättler is an Associate Professor at Washington University in St. Louis in the Department of Electrical and Systems Engineering, Urszula Ledzewicz is a Distinguished Research Professor at Southern Illinois University Edwardsville in the Department of Mathematics and Statistics.
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.
Combination Therapy against Multidrug Resistance explores the potential of combination therapy as an efficient strategy to combat multi-drug resistance. Multidrug resistance (MDR) occurs when microorganisms such as bacteria, fungi, viruses, and parasites are excessively exposed to antimicrobial drugs such as antibiotics, antifungals, or antivirals, and in response the microorganism undergoes mutations or develops different resistance mechanisms to combat the drug for its survival. MDR is becoming an increasingly serious problem in both developed and developing nations. Bacterial resistance to antibiotics has developed faster than the production of new antibiotics, making bacterial infections increasingly difficult to treat, and the same is true for a variety of other diseases. Combination therapy proves to be a promising strategy as it offers potential benefits such as a broad spectrum of efficacy, greater potency than the drugs used in monotherapy, improved safety and tolerability, and reduction in the number of resistant organisms. This book considers how combination therapy can be applied in multiple situations, including cancer, HIV, tuberculosis, fungal infections, and more. Combination Therapy Against Multidrug Resistance gathers the most relevant information on the prospects of combination therapy as a strategy to combat multridrug resistance and helping to motivate the industrial sector and government agencies to invest more in research and development of this strategy as a weapon to tackle the multidrug resistance problem. It will be useful to academics and researchers involved in the development of new antimicrobial or antiinfective agents and treatment strtategies to combat multidrug resistance. Clinicians and medical nurses working in the field of infection prevention and control (IPC) will also find the book relevant - Explores strategic methods with investigation of both short- and long-term goals to combat multidrug resistance - Presents a broad scope to understand fully the ways to apply combined therapy to multidrug resistance - Provides an overview of combination therapy, but also includes specific cases such as cancer, tuberculosis, HIV and malaria
Holland-Frei Cancer Medicine, Ninth Edition, offers a balanced view of the most current knowledge of cancer science and clinical oncology practice. This all-new edition is the consummate reference source for medical oncologists, radiation oncologists, internists, surgical oncologists, and others who treat cancer patients. A translational perspective throughout, integrating cancer biology with cancer management providing an in depth understanding of the disease An emphasis on multidisciplinary, research-driven patient care to improve outcomes and optimal use of all appropriate therapies Cutting-edge coverage of personalized cancer care, including molecular diagnostics and therapeutics Concise, readable, clinically relevant text with algorithms, guidelines and insight into the use of both conventional and novel drugs Includes free access to the Wiley Digital Edition providing search across the book, the full reference list with web links, illustrations and photographs, and post-publication updates
Cancer is a complex disease process that spans multiple scales in space and time. Driven by cutting-edge mathematical and computational techniques, in silico biology provides powerful tools to investigate the mechanistic relationships of genes, cells, and tissues. It enables the creation of experimentally testable hypotheses, the integration of dat
This book constitutes the refereed proceedings of the Second International Conference on Evolutionary Multi-Criterion Optimization, EMO 2003, held in Faro, Portugal, in April 2003. The 56 revised full papers presented were carefully reviewed and selected from a total of 100 submissions. The papers are organized in topical sections on objective handling and problem decomposition, algorithm improvements, online adaptation, problem construction, performance analysis and comparison, alternative methods, implementation, and applications.
Cancer research deals with all aspects of malignant transformation, tumour growth and the effects of treatment. Mathematical models enable quantitative representations of the changes affecting cell state and cell number. This book provides a review of the scope of mathematical modelling in cancer research, bringing together for the first time a group of related mathematical topics including multistage carcinogenesis, tumour growth kinetics, growth control, radiotherapy, chemotherapy and biological targeting in cancer treatment. Physicists and mathematicians interested in medical research, biomathematicians, biostatisticians, radiation and medical oncologists and experimental and theoretical biologists will welcome this critical review of mathematical modelling in cancer research. This book will also be of interest to clinicians, basic cancer scientists and physicists working in radiotherapy departments, and to postgraduate students on courses in oncology and subjects.
From economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into t
