Branching Process Models of Cancer

Branching Process Models of Cancer

Author: Richard Durrett

Publisher: Springer

Published: 2015-06-20

Total Pages: 73

ISBN-13: 3319160656

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This volume develops results on continuous time branching processes and applies them to study rate of tumor growth, extending classic work on the Luria-Delbruck distribution. As a consequence, the author calculate the probability that mutations that confer resistance to treatment are present at detection and quantify the extent of tumor heterogeneity. As applications, the author evaluate ovarian cancer screening strategies and give rigorous proofs for results of Heano and Michor concerning tumor metastasis. These notes should be accessible to students who are familiar with Poisson processes and continuous time Markov chains. Richard Durrett is a mathematics professor at Duke University, USA. He is the author of 8 books, over 200 journal articles, and has supervised more than 40 Ph.D students. Most of his current research concerns the applications of probability to biology: ecology, genetics and most recently cancer.


Branching Processes in Biology

Branching Processes in Biology

Author: Marek Kimmel

Publisher: Springer Science & Business Media

Published: 2006-05-26

Total Pages: 242

ISBN-13: 0387216391

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This book introduces biological examples of Branching Processes from molecular and cellular biology as well as from the fields of human evolution and medicine and discusses them in the context of the relevant mathematics. It provides a useful introduction to how the modeling can be done and for what types of problems branching processes can be used.


Cancer Evolution

Cancer Evolution

Author: Charles Swanton

Publisher: Perspectives Cshl

Published: 2017

Total Pages: 350

ISBN-13: 9781621821434

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Tumor progression is driven by mutations that confer growth advantages to different subpopulations of cancer cells. As a tumor grows, these subpopulations expand, accumulate new mutations, and are subjected to selective pressures from the environment, including anticancer interventions. This process, termed clonal evolution, can lead to the emergence of therapy-resistant tumors and poses a major challenge for cancer eradication efforts. Written and edited by experts in the field, this collection from Cold Spring Harbor Perspectives in Medicine examines cancer progression as an evolutionary process and explores how this way of looking at cancer may lead to more effective strategies for managing and treating it. The contributors review efforts to characterize the subclonal architecture and dynamics of tumors, understand the roles of chromosomal instability, driver mutations, and mutation order, and determine how cancer cells respond to selective pressures imposed by anticancer agents, immune cells, and other components of the tumor microenvironment. They compare cancer evolution to organismal evolution and describe how ecological theories and mathematical models are being used to understand the complex dynamics between a tumor and its microenvironment during cancer progression. The authors also discuss improved methods to monitor tumor evolution (e.g., liquid biopsies) and the development of more effective strategies for managing and treating cancers (e.g., immunotherapies). This volume will therefore serve as a vital reference for all cancer biologists as well as anyone seeking to improve clinical outcomes for patients with cancer.


The Physics of Cancer

The Physics of Cancer

Author: Caterina A. M. La Porta

Publisher: Cambridge University Press

Published: 2017-04-20

Total Pages: 187

ISBN-13: 1108150330

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Recent years have witnessed an increasing number of theoretical and experimental contributions to cancer research from different fields of physics, from biomechanics and soft-condensed matter physics to the statistical mechanics of complex systems. Reviewing these contributions and providing a sophisticated overview of the topic, this is the first book devoted to the emerging interdisciplinary field of cancer physics. Systematically integrating approaches from physics and biology, it includes topics such as cancer initiation and progression, metastasis, angiogenesis, cancer stem cells, tumor immunology, cancer cell mechanics and migration. Biological hallmarks of cancer are presented in an intuitive yet comprehensive way, providing graduate-level students and researchers in physics with a thorough introduction to this important subject. The impact of the physical mechanisms of cancer are explained through analytical and computational models, making this an essential reference for cancer biologists interested in cutting-edge quantitative tools and approaches coming from physics.


Workshop on Branching Processes and Their Applications

Workshop on Branching Processes and Their Applications

Author: Miguel González

Publisher: Springer Science & Business Media

Published: 2010-03-02

Total Pages: 304

ISBN-13: 3642111564

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One of the charms of mathematics is the contrast between its generality and its applicability to concrete, even everyday, problems. Branching processes are typical in this. Their niche of mathematics is the abstract pattern of reproduction, sets of individuals changing size and composition through their members reproducing; in other words, what Plato might have called the pure idea behind demography, population biology, cell kinetics, molecular replication, or nuclear ?ssion, had he known these scienti?c ?elds. Even in the performance of algorithms for sorting and classi?cation there is an inkling of the same pattern. In special cases, general properties of the abstract ideal then interact with the physical or biological or whatever properties at hand. But the population, or bran- ing, pattern is strong; it tends to dominate, and here lies the reason for the extreme usefulness of branching processes in diverse applications. Branching is a clean and beautiful mathematical pattern, with an intellectually challenging intrinsic structure, and it pervades the phenomena it underlies.


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.


Holland-Frei Cancer Medicine

Holland-Frei Cancer Medicine

Author: Robert C. Bast, Jr.

Publisher: John Wiley & Sons

Published: 2017-03-10

Total Pages: 2004

ISBN-13: 111900084X

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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


Multiscale Cancer Modeling

Multiscale Cancer Modeling

Author: Thomas S. Deisboeck

Publisher: CRC Press

Published: 2010-12-08

Total Pages: 492

ISBN-13: 1439814422

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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


Essentials of Glycobiology

Essentials of Glycobiology

Author: Ajit Varki

Publisher: CSHL Press

Published: 1999

Total Pages: 694

ISBN-13: 9780879696818

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Sugar chains (glycans) are often attached to proteins and lipids and have multiple roles in the organization and function of all organisms. "Essentials of Glycobiology" describes their biogenesis and function and offers a useful gateway to the understanding of glycans.


Branching Processes

Branching Processes

Author: Patsy Haccou

Publisher: Cambridge University Press

Published: 2005-05-19

Total Pages: 342

ISBN-13: 9780521832205

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This book covers the mathematical idea of branching processes, and tailors it for a biological audience.