Mathematical Methods For Cancer Evolution PDF Download
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| Author | : Takashi Suzuki |
| Publisher | : Springer |
| Total Pages | : 144 |
| Release | : 2017-06-13 |
| Genre | : Mathematics |
| ISBN | : 9811036713 |
Download Mathematical Methods for Cancer Evolution Book in PDF, ePub and Kindle
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.
| Author | : Pedro Jose Gutiérrez Diez |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 403 |
| Release | : 2012-02-17 |
| Genre | : Medical |
| ISBN | : 146142397X |
Download The Evolution of the Use of Mathematics in Cancer Research Book in PDF, ePub and Kindle
The book will provide an exhaustive and clear explanation of how Statistics, Mathematics and Informatics have been used in cancer research, and seeks to help cancer researchers in achieving their objectives. To do so, state-of-the-art Biostatistics, Biomathematics and Bioinformatics methods will be described and discussed in detail through illustrative and capital examples taken from cancer research work already published. The book will provide a guide for cancer researchers in using Statistics, Mathematics and Informatics, clarifying the contribution of these logical sciences to the study of cancer, thoroughly explaining their procedures and methods, and providing criteria to their appropriate use.
| Author | : Takashi Suzuki |
| Publisher | : Springer Nature |
| Total Pages | : 308 |
| Release | : 2021-08-21 |
| Genre | : Mathematics |
| ISBN | : 9811648662 |
Download Methods of Mathematical Oncology Book in PDF, ePub and Kindle
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.
| Author | : Nicola Bellomo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 481 |
| Release | : 2008-12-10 |
| Genre | : Mathematics |
| ISBN | : 0817647139 |
Download Selected Topics in Cancer Modeling Book in PDF, ePub and Kindle
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.
| Author | : Dominik Wodarz |
| Publisher | : World Scientific |
| Total Pages | : 533 |
| Release | : 2014-04-24 |
| Genre | : Mathematics |
| ISBN | : 9814566381 |
Download Dynamics Of Cancer: Mathematical Foundations Of Oncology Book in PDF, ePub and Kindle
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.
| Author | : Yang Kuang |
| Publisher | : CRC Press |
| Total Pages | : 469 |
| Release | : 2016-04-05 |
| Genre | : Mathematics |
| ISBN | : 1584889918 |
Download Introduction to Mathematical Oncology Book in PDF, ePub and Kindle
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.
| Author | : Takashi Suzuki |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2021 |
| Genre | : |
| ISBN | : 9789811648670 |
Download Methods of Mathematical Oncology Book in PDF, ePub and Kindle
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.
| Author | : Urszula Ledzewicz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 426 |
| Release | : 2012-10-21 |
| Genre | : Mathematics |
| ISBN | : 1461441773 |
Download Mathematical Methods and Models in Biomedicine Book in PDF, ePub and Kindle
Mathematical biomedicine is a rapidly developing interdisciplinary field of research that connects the natural and exact sciences in an attempt to respond to the modeling and simulation challenges raised by biology and medicine. There exist a large number of mathematical methods and procedures that can be brought in to meet these challenges and this book presents a palette of such tools ranging from discrete cellular automata to cell population based models described by ordinary differential equations to nonlinear partial differential equations representing complex time- and space-dependent continuous processes. Both stochastic and deterministic methods are employed to analyze biological phenomena in various temporal and spatial settings. This book illustrates the breadth and depth of research opportunities that exist in the general field of mathematical biomedicine by highlighting some of the fascinating interactions that continue to develop between the mathematical and biomedical sciences. It consists of five parts that can be read independently, but are arranged to give the reader a broader picture of specific research topics and the mathematical tools that are being applied in its modeling and analysis. The main areas covered include immune system modeling, blood vessel dynamics, cancer modeling and treatment, and epidemiology. The chapters address topics that are at the forefront of current biomedical research such as cancer stem cells, immunodominance and viral epitopes, aggressive forms of brain cancer, or gene therapy. The presentations highlight how mathematical modeling can enhance biomedical understanding and will be of interest to both the mathematical and the biomedical communities including researchers already working in the field as well as those who might consider entering it. Much of the material is presented in a way that gives graduate students and young researchers a starting point for their own work.
| Author | : Amina Eladdadi |
| Publisher | : Springer |
| Total Pages | : 282 |
| Release | : 2014-11-06 |
| Genre | : Mathematics |
| ISBN | : 1493917935 |
Download Mathematical Models of Tumor-Immune System Dynamics Book in PDF, ePub and Kindle
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.
| Author | : Yang Kuang |
| Publisher | : CRC Press |
| Total Pages | : 472 |
| Release | : 2018-09-03 |
| Genre | : Mathematics |
| ISBN | : 1315361981 |
Download Introduction to Mathematical Oncology Book in PDF, ePub and Kindle
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.
