Mathematical Methods for Cancer Evolution - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mathematical Methods for Cancer Evolution write by Takashi Suzuki. This book was released on 2017-06-13. Mathematical Methods for Cancer Evolution available 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.
The Evolution of the Use of Mathematics in Cancer Research
The Evolution of the Use of Mathematics in Cancer Research - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Evolution of the Use of Mathematics in Cancer Research write by Pedro Jose Gutiérrez Diez. This book was released on 2012-02-17. The Evolution of the Use of Mathematics in Cancer Research available 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.
Selected Topics in Cancer Modeling
Selected Topics in Cancer Modeling - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Selected Topics in Cancer Modeling write by Nicola Bellomo. This book was released on 2008-12-10. Selected Topics in Cancer Modeling available 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.
Methods of Mathematical Oncology
Methods of Mathematical Oncology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Methods of Mathematical Oncology write by Takashi Suzuki. This book was released on 2021-08-21. Methods of Mathematical Oncology available 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.
Dynamics Of Cancer: Mathematical Foundations Of Oncology
Dynamics Of Cancer: Mathematical Foundations Of Oncology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Dynamics Of Cancer: Mathematical Foundations Of Oncology write by Dominik Wodarz. This book was released on 2014-04-24. Dynamics Of Cancer: Mathematical Foundations Of Oncology available 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.
