Mathematical Methods For Cancer Evolution

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Mathematical Methods For Cancer Evolution

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Author : Takashi Suzuki
language : en
Publisher: Springer
Release Date : 2017-06-13

Mathematical Methods For Cancer Evolution written by Takashi Suzuki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-13 with Mathematics categories.

The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology. Cancer cells and their growth via several stages are of particular interest. To describe these events, multi-scale models are applied, involving continuously distributed environment variables and several components related to particles. Hybrid simulations are also carried out, using discretization of environment variables and the Monte Carlo method for the principal particle variables. Rigorous mathematical foundations are the bases of these tools.The monograph is composed of four chapters. The first three chapters are concerned with modeling, while the last one is devoted to mathematical analysis. The first chapter deals with molecular dynamics occurring at the early stage of cancer invasion. A pathway network model based on a biological scenario is constructed, and then its mathematical structures are determined. In the second chapter mathematical modeling is introduced, overviewing several biological insights, using partial differential equations. Transport and gradient are the main factors, and several models are introduced including the Keller‒Segel systems. The third chapter treats the method of averaging to model the movement of particles, based on mean field theories, employing deterministic and stochastic approaches. Then appropriate parameters for stochastic simulations are examined. The segment model is finally proposed as an application. In the fourth chapter, thermodynamic features of these models and how these structures are applied in mathematical analysis are examined, that is, negative chemotaxis, parabolic systems with non-local term accounting for chemical reactions, mass-conservative reaction-diffusion systems, and competitive systems of chemotaxis. The monograph concludes with the method of the weak scaling limit applied to the Smoluchowski‒Poisson equation.

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

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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.

Handbook Of Cancer Models With Applications

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Author : W. Y. Tan
language : en
Publisher: World Scientific
Release Date : 2008

Handbook Of Cancer Models With Applications written by W. Y. Tan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Political Science categories.

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.

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.

Advanced Mathematical Methods In Biosciences And Applications

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Author : Faina Berezovskaya
language : en
Publisher: Springer Nature
Release Date : 2019-09-19

Advanced Mathematical Methods In Biosciences And Applications written by Faina Berezovskaya and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-19 with Mathematics categories.

Featuring contributions from experts in mathematical biology and biomedical research, this edited volume covers a diverse set of topics on mathematical methods and applications in the biosciences. Topics focus on advanced mathematical methods, with chapters on the mathematical analysis of the quasispecies model, Arnold’s weak resonance equation, bifurcation analysis, and the Tonnelier-Gerstner model. Special emphasis is placed on applications such as natural selection, population heterogeneity, polyvariant ontogeny in plants, cancer dynamics, and analytical solutions for traveling pulses and wave trains in neural models. A survey on quasiperiodic topology is also presented in this book. Carefully peer-reviewed, this volume is suitable for students interested in interdisciplinary research. Researchers in applied mathematics and the biosciences will find this book an important resource on the latest developments in the field. In keeping with the STEAM-H series, the editors hope to inspire interdisciplinary understanding and collaboration.

Cancer Modelling And Simulation

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Author : Luigi Preziosi
language : en
Publisher: CRC Press
Release Date : 2003-06-18

Cancer Modelling And Simulation written by Luigi Preziosi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-18 with Mathematics categories.

Understanding how cancer tumours develop and spread is vital for finding treatments and cures. Cancer Modelling and Simulation demonstrates how mathematical modelling and computer simulation techniques are used to discover and gain insight into the dynamics of tumour development and growth. It highlights the benefits of tumour modelling, such as discovering optimal tumour therapy schedules, identifying the most promising candidates for further clinical investigation, and reducing the number of animal experiments. By examining the analytical, mathematical, and biological aspects of tumour growth and modelling, the book provides a common language and knowledge for professionals in several disciplines.

Multiscale Cancer Modeling

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Author : Thomas S. Deisboeck
language : en
Publisher: CRC Press
Release Date : 2010-12-08

Multiscale Cancer Modeling written by Thomas S. Deisboeck and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-08 with Mathematics categories.

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

Cancer Evolution

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Author : Charles Swanton
language : en
Publisher: Perspectives Cshl
Release Date : 2017

Cancer Evolution written by Charles Swanton and has been published by Perspectives Cshl this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Medical categories.

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.

Chemotaxis Reaction Network Mathematics For Self Organization

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Author : Takashi Suzuki
language : en
Publisher: World Scientific
Release Date : 2018-07-27

Chemotaxis Reaction Network Mathematics For Self Organization written by Takashi Suzuki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-27 with Science categories.

This monograph is devoted to recent mathematical theories on the bottom up self-organization observed in closed and isolated thermo-dynamical systems. Its main features include: