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Author: Fernando Giráldez Publisher: American Mathematical Soc. ISBN: 0821846639 Category : Mathematics Languages : en Pages : 137
Book Description
Developmental biology and tumour growth are two important areas of current research where mathematics increasingly provides powerful new techniques and insights. The unfolding complexity of living structures from egg to embryo gives rise to a number of difficult quantitative problems that are ripe for mathematical models and analysis. Understanding this early development process involves the study of pattern formation, which mathematicians view through the lens of dynamical systems. This book addresses several issues in developmental biology, including Notch signalling pathway integration and mesenchymal compartment formation. Tumour growth is one of the primary challenges of cancer research. Its study requires interdisciplinary approaches involving the close collaboration of mathematicians, biologists and physicians. The summer school addressed angiogenesis, modelling issues arising in radiotherapy, and tumour growth viewed from the individual cell and the relation to a multiphase-fluid flow picture of that process. This book is suitable for researchers, graduate students, and advanced undergraduates interested in mathematical methods of developmental biology or tumour growth.
Author: Fernando Giráldez Publisher: American Mathematical Soc. ISBN: 0821846639 Category : Mathematics Languages : en Pages : 137
Book Description
Developmental biology and tumour growth are two important areas of current research where mathematics increasingly provides powerful new techniques and insights. The unfolding complexity of living structures from egg to embryo gives rise to a number of difficult quantitative problems that are ripe for mathematical models and analysis. Understanding this early development process involves the study of pattern formation, which mathematicians view through the lens of dynamical systems. This book addresses several issues in developmental biology, including Notch signalling pathway integration and mesenchymal compartment formation. Tumour growth is one of the primary challenges of cancer research. Its study requires interdisciplinary approaches involving the close collaboration of mathematicians, biologists and physicians. The summer school addressed angiogenesis, modelling issues arising in radiotherapy, and tumour growth viewed from the individual cell and the relation to a multiphase-fluid flow picture of that process. This book is suitable for researchers, graduate students, and advanced undergraduates interested in mathematical methods of developmental biology or tumour growth.
Author: Yang Kuang Publisher: CRC Press ISBN: 1315361981 Category : Mathematics Languages : en Pages : 472
Book Description
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: Avner Friedman Publisher: Springer ISBN: 3540324151 Category : Mathematics Languages : en Pages : 254
Book Description
This volume introduces some basic mathematical models for cell cycle, proliferation, cancer, and cancer therapy. Chapter 1 gives an overview of the modeling of the cell division cycle. Chapter 2 describes how tumor secretes growth factors to form new blood vessels in its vicinity, which provide it with nutrients it needs in order to grow. Chapter 3 explores the process that enables the tumor to invade the neighboring tissue. Chapter 4 models the interaction between a tumor and the immune system. Chapter 5 is concerned with chemotherapy; it uses concepts from control theory to minimize obstacles arising from drug resistance and from cell cycle dynamics. Finally, Chapter 6 reviews mathematical results for various cancer models.
Author: Nicola Bellomo Publisher: Springer Science & Business Media ISBN: 0817647139 Category : Mathematics Languages : en Pages : 481
Book Description
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 ISBN: 9814566381 Category : Mathematics Languages : en Pages : 533
Book Description
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: Amina Eladdadi Publisher: Springer ISBN: 1493917935 Category : Mathematics Languages : en Pages : 282
Book Description
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: W. Jäger Publisher: Springer Science & Business Media ISBN: 3642618502 Category : Science Languages : en Pages : 521
Book Description
These Proceedings have been assembled from papers presented at the Conference on Models of Biological Growth and Spread, held at the German Cancer Research Centre Heidelberg and at the Institute of Applied Mathematics of the University of Heidelberg, July 16-21, 1979. The main theme of the conference was the mathematical representation of biolog ical populations with an underlying spatial structure. An important feature of such populations is that they and/or their individual com ponents may interact with each other. Such interactions may be due to external disturbances, internal regulatory factors or a combination of both. Many biological phenomena and processes including embryogenesis, cell growth, chemotaxis, cell adhesion, carcinogenesis, and the spread of an epidemic or of an advantageous gene can be studied in this con text. Thus, problems of particular importance in medicine (human and veterinary), agriculture, ecology, etc. may be taken into consideration and a deeper insight gained by utilizing (more) realistic mathematical models. Since the intrinsic biological mechanisms may differ considerably from each other, a great variety of mathematical approaches, theories and techniques is required. The aims of the conference were (i) To provide an overview of the most important biological aspects. (ii) To survey and analyse possible stochastic and deterministic approaches. (iii) To encourage new research by bringing together mathematicians interested in problems of a biological nature and scientists actively engaged in developing mathematical models in biology.
Author: Fernando Giráldez
Author: Fernando Giráldez
Author: Yang Kuang
Author: Avner Friedman
Author: 
Author: Nicola Bellomo
Author: Dominik Wodarz
Author: Dominik Wodarz
Author: Amina Eladdadi
Author: M Eisen
Author: W. Jäger