Mathematics Development Biology And Tumour Growth
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Mathematics Developmental Biology And Tumour Growth
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Author : Fernando Giráldez
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Mathematics Developmental Biology And Tumour Growth written by Fernando Giráldez and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Developmental biology and tumour growth are two important areas of current research where mathematics increasingly provides powerful new techniques and insights. The unfolding complexity of living structures from egg to embryo gives rise to a number of difficult quantitative problems that are ripe for mathematical models and analysis. Understanding this early development process involves the study of pattern formation, which mathematicians view through the lens of dynamical systems. This book addresses several issues in developmental biology, including Notch signalling pathway integration and mesenchymal compartment formation. Tumour growth is one of the primary challenges of cancer research. Its study requires interdisciplinary approaches involving the close collaboration of mathematicians, biologists and physicians. The summer school addressed angiogenesis, modelling issues arising in radiotherapy, and tumour growth viewed from the individual cell and the relation to a multiphase-fluid flow picture of that process. This book is suitable for researchers, graduate students, and advanced undergraduates interested in mathematical methods of developmental biology or tumour growth.
Introduction To Mathematical Oncology
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Author : Yang Kuang
language : en
Publisher: CRC Press
Release Date : 2018-09-03
Introduction To Mathematical Oncology written by Yang Kuang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Mathematics categories.
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.
Mathematics Development Biology And Tumour Growth
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Author :
language : en
Publisher:
Release Date : 2009
Mathematics Development Biology And Tumour Growth written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Tutorials In Mathematical Biosciences Iii
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Author : Avner Friedman
language : en
Publisher: Springer
Release Date : 2005-11-23
Tutorials In Mathematical Biosciences Iii written by Avner Friedman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-23 with Mathematics categories.
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.
Mathematical Models Of Tumor Immune System Dynamics
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Author : Amina Eladdadi
language : en
Publisher: Springer
Release Date : 2014-11-06
Mathematical Models Of Tumor Immune System Dynamics written by Amina Eladdadi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-06 with Mathematics categories.
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.
Selected Topics In Cancer Modeling
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Author : Nicola Bellomo
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-10
Selected Topics In Cancer Modeling written by Nicola Bellomo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-10 with Mathematics categories.
This collection of selected chapters offers a comprehensive overview of state-of-the-art mathematical methods and tools for modeling and analyzing cancer phenomena. Topics covered include stochastic evolutionary models of cancer initiation and progression, tumor cords and their response to anticancer agents, and immune competition in tumor progression and prevention. The complexity of modeling living matter requires the development of new mathematical methods and ideas. This volume, written by first-rate researchers in the field of mathematical biology, is one of the first steps in that direction.
Mathematical Models In Cell Biology And Cancer Chemotherapy
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Author : M. Eisen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-13
Mathematical Models In Cell Biology And Cancer Chemotherapy written by M. Eisen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-13 with Mathematics categories.
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.
Computational Biology Of Cancer
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Author : Dominik Wodarz
language : en
Publisher: World Scientific
Release Date : 2005
Computational Biology Of Cancer written by Dominik Wodarz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
- Provides an introduction to computational methods in cancer biology - Follows a multi-disciplinary approach
Dynamics Of Cancer Mathematical Foundations Of Oncology
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Author : Dominik Wodarz
language : en
Publisher: World Scientific
Release Date : 2014-04-24
Dynamics Of Cancer Mathematical Foundations Of Oncology written by Dominik Wodarz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-24 with Mathematics categories.
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.
Systems Biology Of Tumor Microenvironment
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Author : Katarzyna A. Rejniak
language : en
Publisher: Springer
Release Date : 2016-10-13
Systems Biology Of Tumor Microenvironment written by Katarzyna A. Rejniak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-13 with Medical categories.
This edited volume discusses the complexity of tumor microenvironments during cancer development, progression and treatment. Each chapter presents a different mathematical model designed to investigate the interactions between tumor cells and the surrounding stroma and stromal cells. The topics covered in this book include the quantitative image analysis of a tumor microenvironment, the microenvironmental barriers in oxygen and drug delivery to tumors, the development of tumor microenvironmental niches and sanctuaries, intravenous transport of the circulating tumor cells, the role of the tumor microenvironment in chemotherapeutic interventions, the interactions between tumor cells, the extracellular matrix, the interstitial fluid, and the immune and stromal cells. Mathematical models discussed here embrace both continuous and agent-based approaches, as well as mathematical frameworks of solid mechanics, fluid dynamics and optimal control theory. The topics in each chapter will be of interest to a biological community wishing to apply the mathematical methods to interpret their experimental data, and to a biomathematical audience interested in exploring how mathematical models can be used to address complex questions in cancer biology.