Introduction To Mathematical Oncology
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Introduction To Mathematical Oncology
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Author : Yang Kuang
language : en
Publisher: CRC Press
Release Date : 2016-04-05
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 2016-04-05 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.
Introduction To Mathematical Oncology
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Author : Yang Kuang
language : en
Publisher: CRC Press
Release Date : 2016-06-14
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 2016-06-14 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.
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.
Dynamics Of Cancer
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Author : Dominik Wodarz
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2014
Dynamics Of Cancer written by Dominik Wodarz and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 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.
An Introduction To Mathematical Reasoning
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Author : Peter J. Eccles
language : en
Publisher: Cambridge University Press
Release Date : 1997-12-11
An Introduction To Mathematical Reasoning written by Peter J. Eccles and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-11 with Mathematics categories.
ÍNDICE: Part I. Mathematical Statements and Proofs: 1. The language of mathematics; 2. Implications; 3. Proofs; 4. Proof by contradiction; 5. The induction principle; Part II. Sets and Functions: 6. The language of set theory; 7. Quantifiers; 8. Functions; 9. Injections, surjections and bijections; Part III. Numbers and Counting: 10. Counting; 11. Properties of finite sets; 12. Counting functions and subsets; 13. Number systems; 14. Counting infinite sets; Part IV. Arithmetic: 15. The division theorem; 16. The Euclidean algorithm; 17. Consequences of the Euclidean algorithm; 18. Linear diophantine equations; Part V. Modular Arithmetic: 19. Congruences of integers; 20. Linear congruences; 21. Congruence classes and the arithmetic of remainders; 22. Partitions and equivalence relations; Part VI. Prime Numbers: 23. The sequence of prime numbers; 24. Congruence modulo a prime; Solutions to exercises.
Mathematics For Life Science And Medicine
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Author : Yasuhiro Takeuchi
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-25
Mathematics For Life Science And Medicine written by Yasuhiro Takeuchi 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 2007-01-25 with Mathematics categories.
Dynamical systems theory in mathematical biology has attracted much attention from many scientific directions. The purpose of this volume is to present and discuss the many rich properties of the dynamical systems that appear in life science and medicine. The main topics include cancer treatment, dynamics of paroxysmal tachycardia, vector disease model, epidemic diseases and metapopulations, immune systems, pathogen competition and coexistence and the evolution of virulence and the rapid evolution of viruses within a host. Each chapter will serve to introduce students and scholars to the state-of-the-art in an exciting area, to present new results, and to inspire future contributions to mathematical modeling in life science and medicine.
Oxford Textbook Of Oncology
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Author : David J. Kerr
language : en
Publisher: Oxford University Press
Release Date : 2016
Oxford Textbook Of Oncology written by David J. Kerr and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Medical categories.
Written by internationally recognized key opinion leaders in all of the oncology sub-disciplines and covering all aspects of the field, the Oxford Textbook of Oncology, Third Edition reflects current best practice and represents a modern approach to managing the cancer patient. This is a definitive resource for oncologists of all varieties.
Methods And Biostatistics In Oncology
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Author : Raphael L. C. Araújo
language : en
Publisher:
Release Date : 2018
Methods And Biostatistics In Oncology written by Raphael L. C. Araújo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Biometry categories.
This book introduces and discusses the most important aspects of clinical research methods and biostatistics for oncologists, pursuing a tailor-made and practical approach. Evidence-based medicine (EBM) has been in vogue in the last few decades, particularly in rapidly advancing fields such as oncology. This approach has been used to support decision-making processes worldwide, sparking new clinical research and guidelines on clinical and surgical oncology. Clinical oncology research has many peculiarities, including specific study endpoints, a special focus on survival analyses, and a unique perspective on EBM. However, during medical studies and in general practice, these topics are barely taught. Moreover, even when EBM and clinical cancer research are discussed, they are presented in a theoretical fashion, mostly focused on formulas and numbers, rather than on clinical application for a proper literature appraisal. Addressing that gap, this book discusse s more practical aspects of clinical research and biostatistics in oncology, instead of relying only on mathematical formulas and theoretical considerations. Methods and Biostatistics in Oncology will help readers develop the skills they need to understand the use of research on everyday oncology clinical practice for study design and interpretation, as well to demystify the use of EBM in oncology.
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
Mathematical Oncology 2013
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Author : Alberto d'Onofrio
language : en
Publisher: Springer
Release Date : 2014-10-16
Mathematical Oncology 2013 written by Alberto d'Onofrio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-16 with Mathematics categories.
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.