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Methods of Mathematical Oncology

Author: Takashi Suzuki

Publisher: Springer Nature

Published: 2021-08-21

Total Pages: 308

ISBN-13: 9811648662

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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.

Book Synopsis Methods of Mathematical Oncology by : Takashi Suzuki

Download or read book Methods of Mathematical Oncology written by Takashi Suzuki and published by Springer Nature. This book was released on 2021-08-21 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Methods of Mathematical Oncology

Author: Takashi Suzuki

Publisher:

Published: 2021

Total Pages: 0

ISBN-13: 9789811648670

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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.

Book Synopsis Methods of Mathematical Oncology by : Takashi Suzuki

Download or read book Methods of Mathematical Oncology written by Takashi Suzuki and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Mathematical Oncology

Author: Yang Kuang

Publisher: CRC Press

Published: 2018-09-03

Total Pages: 472

ISBN-13: 1315361981

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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.

Book Synopsis Introduction to Mathematical Oncology by : Yang Kuang

Download or read book Introduction to Mathematical Oncology written by Yang Kuang and published by CRC Press. This book was released on 2018-09-03 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Methods for Cancer Evolution

Author: Takashi Suzuki

Publisher: Springer

Published: 2017-06-13

Total Pages: 148

ISBN-13: 9811036713

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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.

Book Synopsis Mathematical Methods for Cancer Evolution by : Takashi Suzuki

Download or read book Mathematical Methods for Cancer Evolution written by Takashi Suzuki and published by Springer. This book was released on 2017-06-13 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Optimal Control for Mathematical Models of Cancer Therapies

Author: Heinz Schättler

Publisher: Springer

Published: 2015-09-15

Total Pages: 511

ISBN-13: 1493929720

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This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments. A number of mathematical models for both classical and novel cancer treatments are presented as optimal control problems with the goal of constructing optimal protocols. The power of geometric methods is illustrated with fully worked out complete global solutions to these mathematically challenging problems. Elaborate constructions of optimal controls and corresponding system responses provide great examples of applications of the tools of geometric optimal control and the outcomes aid the design of simpler, practically realizable suboptimal protocols. The book blends mathematical rigor with practically important topics in an easily readable tutorial style. Graduate students and researchers in science and engineering, particularly biomathematics and more mathematical aspects of biomedical engineering, would find this book particularly useful.

Book Synopsis Optimal Control for Mathematical Models of Cancer Therapies by : Heinz Schättler

Download or read book Optimal Control for Mathematical Models of Cancer Therapies written by Heinz Schättler and published by Springer. This book was released on 2015-09-15 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments. A number of mathematical models for both classical and novel cancer treatments are presented as optimal control problems with the goal of constructing optimal protocols. The power of geometric methods is illustrated with fully worked out complete global solutions to these mathematically challenging problems. Elaborate constructions of optimal controls and corresponding system responses provide great examples of applications of the tools of geometric optimal control and the outcomes aid the design of simpler, practically realizable suboptimal protocols. The book blends mathematical rigor with practically important topics in an easily readable tutorial style. Graduate students and researchers in science and engineering, particularly biomathematics and more mathematical aspects of biomedical engineering, would find this book particularly useful.

Mathematical and Computational Oncology

Author: George Bebis

Publisher: Springer Nature

Published: 2021-12-11

Total Pages: 91

ISBN-13: 3030912418

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This book constitutes the refereed proceedings of the Third International Symposium on Mathematical and Computational Oncology, ISMCO 2021, held in October 2021. Due to COVID-19 pandemic the conference was held virtually. The 3 full papers and 4 short papers presented were carefully reviewed and selected from 20 submissions. The papers are organized in topical sections named: statistical and machine learning methods for cancer research; mathematical modeling for cancer research; spatio-temporal tumor modeling and simulation; general cancer computational biology; mathematical modeling for cancer research; computational methods for anticancer drug development.

Book Synopsis Mathematical and Computational Oncology by : George Bebis

Download or read book Mathematical and Computational Oncology written by George Bebis and published by Springer Nature. This book was released on 2021-12-11 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Symposium on Mathematical and Computational Oncology, ISMCO 2021, held in October 2021. Due to COVID-19 pandemic the conference was held virtually. The 3 full papers and 4 short papers presented were carefully reviewed and selected from 20 submissions. The papers are organized in topical sections named: statistical and machine learning methods for cancer research; mathematical modeling for cancer research; spatio-temporal tumor modeling and simulation; general cancer computational biology; mathematical modeling for cancer research; computational methods for anticancer drug development.

The Evolution of the Use of Mathematics in Cancer Research

Author: Pedro Jose Gutiérrez Diez

Publisher: Springer Science & Business Media

Published: 2012-02-17

Total Pages: 403

ISBN-13: 146142397X

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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.

Book Synopsis The Evolution of the Use of Mathematics in Cancer Research by : Pedro Jose Gutiérrez Diez

Download or read book The Evolution of the Use of Mathematics in Cancer Research written by Pedro Jose Gutiérrez Diez and published by Springer Science & Business Media. This book was released on 2012-02-17 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Oncology 2013

Author: Alberto d'Onofrio

Publisher: Birkhäuser

Published: 2016-09-10

Total Pages: 0

ISBN-13: 9781493948031

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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.

Book Synopsis Mathematical Oncology 2013 by : Alberto d'Onofrio

Download or read book Mathematical Oncology 2013 written by Alberto d'Onofrio and published by Birkhäuser. This book was released on 2016-09-10 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Book Synopsis Dynamics Of Cancer: Mathematical Foundations Of Oncology by : Dominik Wodarz

Download or read book Dynamics Of Cancer: Mathematical Foundations Of Oncology written by Dominik Wodarz and published by World Scientific. This book was released on 2014-04-24 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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

Book Synopsis Multiscale Cancer Modeling by : Thomas S. Deisboeck

Download or read book Multiscale Cancer Modeling written by Thomas S. Deisboeck and published by CRC Press. This book was released on 2010-12-08 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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