Optimal Control For Mathematical Models Of Cancer Therapies

Author : Heinz Schättler,Urszula Ledzewicz
Publisher : Springer
Page : 496 pages
File Size : 45,5 Mb
Release : 2015-09-15
Category : Mathematics
ISBN : 9781493929726

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Optimal Control for Mathematical Models of Cancer Therapies by Heinz Schättler,Urszula Ledzewicz Pdf

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.

Author : Heinz M. Schättler,Urszula Ledzewicz
Publisher : Unknown
Page : 128 pages
File Size : 44,8 Mb
Release : 2015
Category : Cancer
ISBN : 1493929739

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Optimal Control for Mathematical Models of Cancer Therapies by Heinz M. Schättler,Urszula Ledzewicz Pdf

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.

Author : Rory Martin,K. L. Teo
Publisher : World Scientific
Page : 202 pages
File Size : 50,6 Mb
Release : 1994
Category : Medical
ISBN : 9789810214289

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Optimal Control of Drug Administration in Cancer Chemotherapy by Rory Martin,K. L. Teo Pdf

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.

Author : Lalitha R
Publisher : Independent Author
Page : 0 pages
File Size : 46,8 Mb
Release : 2023-03-31
Category : Electronic
ISBN : 1805251961

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A Study On Mathematical Models For The Effect Of Different Therapies And Combination Of Therapies In Cancer Treatments by Lalitha R Pdf

Mathematical modeling is a great tool in the medical field. Mathematical models help to simulate the dynamics of complex systems. Dynamic models typically are represented by differential equations. Mathematical models are used everywhere in cancer research. The number of cancer cells in a tumor is not easy to calculate due to continuous changes in time. So may have to calculate with the help of differential equations easily. Challenge of mathematical modeling is to produce simplest possible model. Many of the researchers developed mathematical models that identify the most effective chemotherapeutic administration regimens using optimization and control techniques. In 1962 L.S. Pontryagin, etal. was developed the model for optimal control. A. Lotka and R. Fisher has been developed the mathematical theory life history evolution in 1970s. Panetta was developed an effective model for heterogeneous tumor and chemotherapeutic drug action in 1996. A.J.Coldman and J.M.Murray was developed the stochastic model of cancer treatment in 2000. L.G. de Pillis, etal. developed the system of ODE for variety of cancers and different treatments in between 2000 to 2013. In recent years so many authors developed them new models based on the above author's research. In recent years most of the people were affected by different types of cancer. Some type of cancer is the curable disease when we detect in early stage. Rare type of cancer is the not fully curable disease but to controls the tumor growth and gives assumption of survival for some years. There are different types of treatments are available according to their stage of the disease. Stages were defined from their tumor size and disease spreading position of their disease. Main treatments of cancers are Surgery, Chemotherapy, Radiation therapy, Immunotherapy, Gene therapy and Hormone therapy. Mathematical modeling of tumor dynamics and treatment responses can be applied to identify better drug administration regimes. Using mathematical model for tumor growth and cancer treatments we can reduce the tumor size. Now everyone must know about types of cancer and correct treatments for that. So select this area and developed the mathematical models for tumor dynamics and combinations of treatments. Collected the breast and colorectal cancer patient's details and fitted to our model then reduced the tumor burden. Also have find that which type of drug combinations are used for colorectal cancer and breast cancer treatments. Here we used Mathematical Tools are Differential Equation, Ordinary Differential Equation (ODE), Formulation of differential equation, Growth model, optimal control, Equilibrium and Stability Analysis in ODE.

Author : João P. Belfo,João M. Lemos
Publisher : Springer Nature
Page : 108 pages
File Size : 53,6 Mb
Release : 2020-06-19
Category : Technology & Engineering
ISBN : 9783030504885

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Optimal Impulsive Control for Cancer Therapy by João P. Belfo,João M. Lemos Pdf

This Springer brief discusses the use of control engineering methods to plan a cancer therapy which tends to reduce tumour size in patients, striking a balance that minimizes the toxic effects of the treatment. The authors address the design and computation of impulsive control therapies, a methodology previously underexplored in the application of control methods to medical modelling. This allows simulation of such discrete events as taking a pill rather than relying on the supply of therapy being continuous and steady. The book begins with an introduction to the topic, before moving onto pharmacokinetic, pharmacodynamical and tumour-growth models and explaining how they describe the relationship between a certain therapy plan and the evolution of cancer. This is placed firmly in the context of work introducing impulsive differential equations. The final chapter summarizes the research presented and suggests future areas of research to encourage readers in taking the subject forward. This book is of interest to biomedical engineers, researchers and students, particularly those with a background in systems and control engineering.

Author : Regina Padmanabhan,Nader Meskin,Ala-Eddin Al Moustafa
Publisher : Springer Nature
Page : 256 pages
File Size : 49,8 Mb
Release : 2020-10-31
Category : Technology & Engineering
ISBN : 9789811586408

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Mathematical Models of Cancer and Different Therapies by Regina Padmanabhan,Nader Meskin,Ala-Eddin Al Moustafa Pdf

This book provides a unified framework for various currently available mathematical models that are used to analyze progression and regression in cancer development, and to predict its dynamics with respect to therapeutic interventions. Accurate and reliable model representations of cancer dynamics are milestones in the field of cancer research. Mathematical modeling approaches are becoming increasingly common in cancer research, as these quantitative approaches can help to validate hypotheses concerning cancer dynamics and thus elucidate the complexly interlaced mechanisms involved. Even though the related conceptual and technical information is growing at an exponential rate, the application of said information and realization of useful healthcare devices are lagging behind. In order to remedy this discrepancy, more interdisciplinary research works and course curricula need to be introduced in academic, industrial, and clinical organizations alike. To that end, this book reformulates most of the existing mathematical models as special cases of a general model, allowing readers to easily get an overall idea of cancer dynamics and its modeling. Moreover, the book will help bridge the gap between biologists and engineers, as it brings together cancer dynamics, the main steps involved in mathematical modeling, and control strategies developed for cancer management. This also allows readers in both medical and engineering fields to compare and contrast all the therapy-based models developed to date using a single source, and to identify unexplored research directions.

Author : Sebastian Aniţa,Viorel Arnăutu,Vincenzo Capasso
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 48,6 Mb
Release : 2011-05-05
Category : Mathematics
ISBN : 9780817680985

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An Introduction to Optimal Control Problems in Life Sciences and Economics by Sebastian Aniţa,Viorel Arnăutu,Vincenzo Capasso Pdf

Combining control theory and modeling, this textbook introduces and builds on methods for simulating and tackling concrete problems in a variety of applied sciences. Emphasizing "learning by doing," the authors focus on examples and applications to real-world problems. An elementary presentation of advanced concepts, proofs to introduce new ideas, and carefully presented MATLAB® programs help foster an understanding of the basics, but also lead the way to new, independent research. With minimal prerequisites and exercises in each chapter, this work serves as an excellent textbook and reference for graduate and advanced undergraduate students, researchers, and practitioners in mathematics, physics, engineering, computer science, as well as biology, biotechnology, economics, and finance.

Author : Amina Eladdadi,Peter Kim,Dann Mallet
Publisher : Springer
Page : 282 pages
File Size : 43,9 Mb
Release : 2014-11-06
Category : Mathematics
ISBN : 9781493917938

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Mathematical Models of Tumor-Immune System Dynamics by Amina Eladdadi,Peter Kim,Dann Mallet Pdf

This collection of papers offers a broad synopsis of state-of-the-art mathematical methods used in modeling the interaction between tumors and the immune system. These papers were presented at the four-day workshop on Mathematical Models of Tumor-Immune System Dynamics held in Sydney, Australia from January 7th to January 10th, 2013. The workshop brought together applied mathematicians, biologists, and clinicians actively working in the field of cancer immunology to share their current research and to increase awareness of the innovative mathematical tools that are applicable to the growing field of cancer immunology. Recent progress in cancer immunology and advances in immunotherapy suggest that the immune system plays a fundamental role in host defense against tumors and could be utilized to prevent or cure cancer. Although theoretical and experimental studies of tumor-immune system dynamics have a long history, there are still many unanswered questions about the mechanisms that govern the interaction between the immune system and a growing tumor. The multidimensional nature of these complex interactions requires a cross-disciplinary approach to capture more realistic dynamics of the essential biology. The papers presented in this volume explore these issues and the results will be of interest to graduate students and researchers in a variety of fields within mathematical and biological sciences.

Author : M Eisen
Publisher : Unknown
Page : 452 pages
File Size : 52,9 Mb
Release : 1979-11-01
Category : Electronic
ISBN : 3642931278

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Mathematical Models in Cell Biology and Cancer Chemotherapy by M Eisen Pdf

Author : Alberto d'Onofrio,Alberto Gandolfi
Publisher : Springer
Page : 336 pages
File Size : 51,7 Mb
Release : 2014-10-16
Category : Mathematics
ISBN : 9781493904587

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Mathematical Oncology 2013 by Alberto d'Onofrio,Alberto Gandolfi Pdf

With chapters on free boundaries, constitutive equations, stochastic dynamics, nonlinear diffusion–consumption, structured populations, and applications of optimal control theory, this volume presents the most significant recent results in the field of mathematical oncology. It highlights the work of world-class research teams, and explores how different researchers approach the same problem in various ways. Tumors are complex entities that present numerous challenges to the mathematical modeler. First and foremost, they grow. Thus their spatial mean field description involves a free boundary problem. Second, their interiors should be modeled as nontrivial porous media using constitutive equations. Third, at the end of anti-cancer therapy, a small number of malignant cells remain, making the post-treatment dynamics inherently stochastic. Fourth, the growth parameters of macroscopic tumors are non-constant, as are the parameters of anti-tumor therapies. Changes in these parameters may induce phenomena that are mathematically equivalent to phase transitions. Fifth, tumor vascular growth is random and self-similar. Finally, the drugs used in chemotherapy diffuse and are taken up by the cells in nonlinear ways. Mathematical Oncology 2013 will appeal to graduate students and researchers in biomathematics, computational and theoretical biology, biophysics, and bioengineering.

Author : T. E. Wheldon
Publisher : CRC Press
Page : 272 pages
File Size : 41,5 Mb
Release : 1988
Category : Art
ISBN : UOM:39015014464666

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Mathematical Models in Cancer Research, by T. E. Wheldon Pdf

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.

Author : Suzanne Lenhart,John T. Workman
Publisher : CRC Press
Page : 272 pages
File Size : 52,9 Mb
Release : 2007-05-07
Category : Mathematics
ISBN : 9781584886402

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Optimal Control Applied to Biological Models by Suzanne Lenhart,John T. Workman Pdf

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 the application of this theory to biological models. Focusing on mathematical concepts, the book first examines the most basic problem for continuous time ordinary differential equations (ODEs) before discussing more complicated problems, such as variations of the initial conditions, imposed bounds on the control, multiple states and controls, linear dependence on the control, and free terminal time. In addition, the authors introduce the optimal control of discrete systems and of partial differential equations (PDEs). Featuring a user-friendly interface, the book contains fourteen interactive sections of various applications, including immunology and epidemic disease models, management decisions in harvesting, and resource allocation models. It also develops the underlying numerical methods of the applications and includes the MATLAB® codes on which the applications are based. Requiring only basic knowledge of multivariable calculus, simple ODEs, and mathematical models, this text shows how to adjust controls in biological systems in order to achieve proper outcomes.

Author : Heinz Schättler,Urszula Ledzewicz
Publisher : Springer Science & Business Media
Page : 652 pages
File Size : 49,5 Mb
Release : 2012-06-26
Category : Mathematics
ISBN : 9781461438342

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Geometric Optimal Control by Heinz Schättler,Urszula Ledzewicz Pdf

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.

Author : M. Eisen
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 53,5 Mb
Release : 2013-03-13
Category : Mathematics
ISBN : 9783642931260

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Mathematical Models in Cell Biology and Cancer Chemotherapy by M. Eisen Pdf

The purpose of this book is to show how mathematics can be applied to improve cancer chemotherapy. Unfortunately, most drugs used in treating cancer kill both normal and abnormal cells. However, more cancer cells than normal cells can be destroyed by the drug because tumor cells usually exhibit different growth kinetics than normal cells. To capitalize on this last fact, cell kinetics must be studied by formulating mathematical models of normal and abnormal cell growth. These models allow the therapeutic and harmful effects of cancer drugs to be simulated quantitatively. The combined cell and drug models can be used to study the effects of different methods of administering drugs. The least harmful method of drug administration, according to a given criterion, can be found by applying optimal control theory. The prerequisites for reading this book are an elementary knowledge of ordinary differential equations, probability, statistics, and linear algebra. In order to make this book self-contained, a chapter on cell biology and a chapter on control theory have been included. Those readers who have had some exposure to biology may prefer to omit Chapter I (Cell Biology) and only use it as a reference when required. However, few biologists have been exposed to control theory. Chapter 7 provides a short, coherent and comprehensible presentation of this subject. The concepts of control theory are necessary for a full understanding of Chapters 8 and 9.

Author : Avner Friedman
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 53,8 Mb
Release : 2005-12-19
Category : Mathematics
ISBN : 3540291628

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Tutorials in Mathematical Biosciences III by Avner Friedman Pdf

This volume introduces some basic mathematical models for cell cycle, proliferation, cancer, and cancer therapy. Chapter 1 gives an overview of the modeling of the cell division cycle. Chapter 2 describes how tumor secretes growth factors to form new blood vessels in its vicinity, which provide it with nutrients it needs in order to grow. Chapter 3 explores the process that enables the tumor to invade the neighboring tissue. Chapter 4 models the interaction between a tumor and the immune system. Chapter 5 is concerned with chemotherapy; it uses concepts from control theory to minimize obstacles arising from drug resistance and from cell cycle dynamics. Finally, Chapter 6 reviews mathematical results for various cancer models.