Optimal Control for Mathematical Models of Cancer Therapies
Optimal Control for Mathematical Models of Cancer Therapies

Author: Heinz Schättler

Publisher: Springer

Published: 2015-09-15

Total Pages: 511

ISBN-13: 1493929720

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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.

Handbook of Cancer Models with Applications
Handbook of Cancer Models with Applications

Author: W. Y. Tan

Publisher: World Scientific

Published: 2008

Total Pages: 592

ISBN-13: 9812779485

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Composed of contributions from an international team of leading researchers, this book pulls together the most recent research results in the field of cancer modeling to provide readers with the most advanced mathematical models of cancer and their applications.Topics included in the book cover oncogenetic trees, stochastic multistage models of carcinogenesis, effects of ionizing radiation on cell cycle and genomic instability, induction of DNA damage by ionizing radiation and its repair, epigenetic cancer models, bystander effects of radiation, multiple pathway models of human colon cancer, and stochastic models of metastasis. The book also provides some important applications of cancer models to the assessment of cancer risk associated with various hazardous environmental agents, to cancer screening by MRI, and to drug resistance in cancer chemotherapy. An updated statistical design and analysis of xenograft experiments as well as a statistical analysis of cancer occult clinical data are also provided.The book will serve as a useful source of reference for researchers in biomathematics, biostatistics and bioinformatics; for clinical investigators and medical doctors employing quantitative methods to develop procedures for cancer diagnosis, prevention, control and treatment; and for graduate students.

Dynamics Of Cancer: Mathematical Foundations Of Oncology
Dynamics Of Cancer: Mathematical Foundations Of Oncology

Author: Dominik Wodarz

Publisher: World Scientific

Published: 2014-04-24

Total Pages: 533

ISBN-13: 9814566381

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The book aims to provide an introduction to mathematical models that describe the dynamics of tumor growth and the evolution of tumor cells. It can be used as a textbook for advanced undergraduate or graduate courses, and also serves as a reference book for researchers. The book has a strong evolutionary component and reflects the viewpoint that cancer can be understood rationally through a combination of mathematical and biological tools. It can be used both by mathematicians and biologists. Mathematically, the book starts with relatively simple ordinary differential equation models, and subsequently explores more complex stochastic and spatial models. Biologically, the book starts with explorations of the basic dynamics of tumor growth, including competitive interactions among cells, and subsequently moves on to the evolutionary dynamics of cancer cells, including scenarios of cancer initiation, progression, and treatment. The book finishes with a discussion of advanced topics, which describe how some of the mathematical concepts can be used to gain insights into a variety of questions, such as epigenetics, telomeres, gene therapy, and social interactions of cancer cells.

Multiscale Modeling of Cancer
Multiscale Modeling of Cancer

Author: Vittorio Cristini

Publisher: Cambridge University Press

Published: 2010-09-09

Total Pages: 299

ISBN-13: 1139491504

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Mathematical modeling, analysis and simulation are set to play crucial roles in explaining tumor behavior, and the uncontrolled growth of cancer cells over multiple time and spatial scales. This book, the first to integrate state-of-the-art numerical techniques with experimental data, provides an in-depth assessment of tumor cell modeling at multiple scales. The first part of the text presents a detailed biological background with an examination of single-phase and multi-phase continuum tumor modeling, discrete cell modeling, and hybrid continuum-discrete modeling. In the final two chapters, the authors guide the reader through problem-based illustrations and case studies of brain and breast cancer, to demonstrate the future potential of modeling in cancer research. This book has wide interdisciplinary appeal and is a valuable resource for mathematical biologists, biomedical engineers and clinical cancer research communities wishing to understand this emerging field.

Computational Biology Of Cancer: Lecture Notes And Mathematical Modeling
Computational Biology Of Cancer: Lecture Notes And Mathematical Modeling

Author: Dominik Wodarz

Publisher: World Scientific

Published: 2005-01-24

Total Pages: 266

ISBN-13: 9814481874

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The book shows how mathematical and computational models can be used to study cancer biology. It introduces the concept of mathematical modeling and then applies it to a variety of topics in cancer biology. These include aspects of cancer initiation and progression, such as the somatic evolution of cells, genetic instability, and angiogenesis. The book also discusses the use of mathematical models for the analysis of therapeutic approaches such as chemotherapy, immunotherapy, and the use of oncolytic viruses.

Mathematical Models in Cancer Research,
Mathematical Models in Cancer Research,

Author: T. E. Wheldon

Publisher: CRC Press

Published: 1988

Total Pages: 272

ISBN-13:

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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.

Introduction to Mathematical Oncology
Introduction to Mathematical Oncology

Author: Yang Kuang

Publisher: CRC Press

Published: 2016-04-05

Total Pages: 469

ISBN-13: 1584889918

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Introduction to Mathematical Oncology presents biologically well-motivated and mathematically tractable models that facilitate both a deep understanding of cancer biology and better cancer treatment designs. It covers the medical and biological background of the diseases, modeling issues, and existing methods and their limitations. The authors introduce mathematical and programming tools, along with analytical and numerical studies of the models. They also develop new mathematical tools and look to future improvements on dynamical models. After introducing the general theory of medicine and exploring how mathematics can be essential in its understanding, the text describes well-known, practical, and insightful mathematical models of avascular tumor growth and mathematically tractable treatment models based on ordinary differential equations. It continues the topic of avascular tumor growth in the context of partial differential equation models by incorporating the spatial structure and physiological structure, such as cell size. The book then focuses on the recent active multi-scale modeling efforts on prostate cancer growth and treatment dynamics. It also examines more mechanistically formulated models, including cell quota-based population growth models, with applications to real tumors and validation using clinical data. The remainder of the text presents abundant additional historical, biological, and medical background materials for advanced and specific treatment modeling efforts. Extensively classroom-tested in undergraduate and graduate courses, this self-contained book allows instructors to emphasize specific topics relevant to clinical cancer biology and treatment. It can be used in a variety of ways, including a single-semester undergraduate course, a more ambitious graduate course, or a full-year sequence on mathematical oncology.

Geometric Optimal Control
Geometric Optimal Control

Author: Heinz Schättler

Publisher: Springer Science & Business Media

Published: 2012-06-26

Total Pages: 652

ISBN-13: 1461438349

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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.

Mathematical and Computational Oncology
Mathematical and Computational Oncology

Author: George Bebis

Publisher: Springer Nature

Published: 2021-12-11

Total Pages: 91

ISBN-13: 3030912418

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This book constitutes the refereed proceedings of the Third International Symposium on Mathematical and Computational Oncology, ISMCO 2021, held in October 2021. Due to COVID-19 pandemic the conference was held virtually. The 3 full papers and 4 short papers presented were carefully reviewed and selected from 20 submissions. The papers are organized in topical sections named: statistical and machine learning methods for cancer research; mathematical modeling for cancer research; spatio-temporal tumor modeling and simulation; general cancer computational biology; mathematical modeling for cancer research; computational methods for anticancer drug development.

Methods of Mathematical Oncology
Methods of Mathematical Oncology

Author: Takashi Suzuki

Publisher: Springer Nature

Published: 2021-08-21

Total Pages: 308

ISBN-13: 9811648662

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This book presents original papers reflecting topics featured at the international symposium entitled “Fusion of Mathematics and Biology” and organized by the editor of the book. The symposium, held in October 2020 at Osaka University in Japan, was the core event for the final year of the research project entitled “Establishing International Research Networks of Mathematical Oncology.” The project had been carried out since April 2015 as part of the Core-to-Core Program of Japan Society for the Promotion of Science (JSPS). In this book, the editor presents collaborative research from prestigious organizations in France, the UK, and the USA. By utilizing their individual strengths and realizing the fusion of life science and mathematical science, the project achieved a combination of mathematical analysis, verification by biomedical experiments, and statistical analysis of chemical databases. Mathematics is sometimes regarded as a universal language. It is a valuable property that everyone can understand beyond the boundaries of culture, religion, and language. This unifying force of mathematics also applies to the various fields of science. Mathematical oncology has two aspects, i.e., data science and mathematical modeling, and definitely helps in the prediction and control of biological phenomena observed in cancer evolution. The topics addressed in this book represent several methods of applying mathematical modeling to scientific problems in the natural sciences. Furthermore, novel reviews are included that may motivate many mathematicians to become interested in biological research.