Mathematical Analysis of Complex Cellular Activity PDF Download
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Author: Richard Bertram
Publisher: Springer
ISBN: 3319181149
Category : Mathematics
Languages : en
Pages : 120
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Book Description
This book contains two review articles on mathematical physiology that deal with closely related topics but were written and can be read independently. The first article reviews the basic theory of calcium oscillations (common to almost all cell types), including spatio-temporal behaviors such as waves. The second article uses, and expands on, much of this basic theory to show how the interaction of cytosolic calcium oscillators with membrane ion channels can result in highly complex patterns of electrical spiking. Through these examples one can see clearly how multiple oscillatory processes interact within a cell, and how mathematical methods can be used to understand such interactions better. The two reviews provide excellent examples of how mathematics and physiology can learn from each other, and work jointly towards a better understanding of complex cellular processes. Review 1: Richard Bertram, Joel Tabak, Wondimu Teka, Theodore Vo, Martin Wechselberger: Geometric Singular Perturbation Analysis of Bursting Oscillations in Pituitary Cells Review 2: Vivien Kirk, James Sneyd: Nonlinear Dynamics of Calcium
Author: Richard Bertram
Publisher: Springer
ISBN: 3319181149
Category : Mathematics
Languages : en
Pages : 120
Get Book Here
Book Description
This book contains two review articles on mathematical physiology that deal with closely related topics but were written and can be read independently. The first article reviews the basic theory of calcium oscillations (common to almost all cell types), including spatio-temporal behaviors such as waves. The second article uses, and expands on, much of this basic theory to show how the interaction of cytosolic calcium oscillators with membrane ion channels can result in highly complex patterns of electrical spiking. Through these examples one can see clearly how multiple oscillatory processes interact within a cell, and how mathematical methods can be used to understand such interactions better. The two reviews provide excellent examples of how mathematics and physiology can learn from each other, and work jointly towards a better understanding of complex cellular processes. Review 1: Richard Bertram, Joel Tabak, Wondimu Teka, Theodore Vo, Martin Wechselberger: Geometric Singular Perturbation Analysis of Bursting Oscillations in Pituitary Cells Review 2: Vivien Kirk, James Sneyd: Nonlinear Dynamics of Calcium
Author: Viktor Vladimirovich Ivanov
Publisher: Elsevier Science Limited
ISBN: 0444527141
Category : Computers
Languages : en
Pages : 333
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Book Description
The book contains five main parts: Introduction: Evolutionary System and Development Modelling; Part I: A Survey of MM of CAO (cell associated objects); Part II: MM (mathematical models) of Development; Part III: Introduction to Applications; Appendix: Mathematics of Development. The part I gives the reader a survey of hundreds results in the field of the cell and cell associated objects modelling, which are not easy accessible. The original four parts of the book have no analogy in the literature, except the previous book of the first author 'Model Development and Optimization', KAP, 1999, and the book 'Mathematical Modeling in Economics, Ecology and the Environment', KAP, 1999, by N. Hritonenko, Yu. Yatsenko (Yu. Yatsenko is a pupil of the first author of the cell book). The present book is different from the previous mainly by much more profound investigation of such a complicated object as the cell and by much more detailed description of applications to modelling AIDS, cancers, and life longevity. Key features: - Inlet novel class of non-linear mathematical models based on the general theory of evolutionary systems and their development . - Introducing and proving fundamental properties of evolutionary systems on optimal distribution of their various resources on their internal and external functions. - Proof of effective applicability of that class of models to complicated objects such as the cell and the immune network . - Detailed modelling complicated processes such as the cell cycle, protein folding, immune network response, etc. - Detailed analysis of applications to modelling AIDS, cancers, and life longevity. - Introducing and grounding the respective numerical algorithms and software. - Detailed analysis of hundreds of scientific works in the field of mathematical modelling of the cell and cell associated objects. Key features: - Inlet novel class of non-linear mathematical models based on the general theory of evolutionary systems and their development . - Introducing and proving fundamental properties of evolutionary systems on optimal distribution of their various resources on their internal and external functions. - Proof of effective applicability of that class of models to complicated objects such as the cell and the immune network . - Detailed modelling complicated processes such as the cell cycle, protein folding, immune network response, etc. - Detailed analysis of applications to modelling AIDS, cancers, and life longevity. - Introducing and grounding the respective numerical algorithms and software. - Detailed analysis of hundreds of scientific works in the field of mathematical modelling of the cell and cell associated objects.
Author: Lee A. Segel
Publisher: CUP Archive
ISBN: 9780521229258
Category : Mathematics
Languages : en
Pages : 776
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Book Description
Interest in theoretical biology is rapidly growing and this 1981 book attempts to make the theory more accessible to experimentalists. Its primary purpose is to demonstrate to experimental molecular and cellular biologists the possible usefulness of mathematical models. Biologists with a basic command of calculus should be able to learn from the book what assumptions are implied by various types of equations, to understand in broad outline a number of major theoretical concepts, and to be aware of some of the difficulties connected with analytical and numerical solutions of mathematical problems. Thus they should be able to appreciate the significance of theoretical papers in their fields and to communicate usefully with theoreticians in the course of their work.
Author: Michael R. Hamblin
Publisher: Academic Press
ISBN: 0128187921
Category : Technology & Engineering
Languages : en
Pages : 352
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Book Description
Biomedical Applications of Microfluidic Devices introduces the subject of microfluidics and covers the basic principles of design and synthesis of actual microchannels. The book then explores how the devices are coupled to signal read-outs and calibrated, including applications of microfluidics in areas such as tissue engineering, organ-on-a-chip devices, pathogen identification, and drug/gene delivery. This book covers high-impact fields (microarrays, organ-on-a-chip, pathogen detection, cancer research, drug delivery systems, gene delivery, and tissue engineering) and shows how microfluidics is playing a key role in these areas, which are big drivers in biomedical engineering research. This book addresses the fundamental concepts and fabrication methods of microfluidic systems for those who want to start working in the area or who want to learn about the latest advances being made. The subjects covered are also an asset to companies working in this field that need to understand the current state-of-the-art. The book is ideal for courses on microfluidics, biosensors, drug targeting, and BioMEMs, and as a reference for PhD students. The book covers the emerging and most promising areas of biomedical applications of microfluidic devices in a single place and offers a vision of the future. Covers basic principles and design of microfluidics devices Explores biomedical applications to areas such as tissue engineering, organ-on-a-chip, pathogen identification, and drug and gene delivery Includes chemical applications in organic and inorganic chemistry Serves as an ideal text for courses on microfluidics, biosensors, drug targeting, and BioMEMs, as well as a reference for PhD students
Author: Nicola Bellomo
Publisher: World Scientific
ISBN: 9814460974
Category : Mathematics
Languages : en
Pages : 227
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Book Description
This monograph has the ambitious aim of developing a mathematical theory of complex biological systems with special attention to the phenomena of ageing, degeneration and repair of biological tissues under individual self-repair actions that may have good potential in medical therapy.The approach to mathematically modeling biological systems needs to tackle the additional difficulties generated by the peculiarities of living matter. These include the lack of invariance principles, abilities to express strategies for individual fitness, heterogeneous behaviors, competition up to proliferative and/or destructive actions, mutations, learning ability, evolution and many others.Applied mathematicians in the field of living systems, especially biological systems, will appreciate the special class of integro-differential equations offered here for modeling at the molecular, cellular and tissue scales. A unique perspective is also presented with a number of case studies in biological modeling.
Author: Avner Friedman
Publisher: Springer Science & Business Media
ISBN: 9783540291626
Category : Mathematics
Languages : en
Pages : 260
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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: PhD, Guanyu Wang
Publisher: CRC Press
ISBN: 146657223X
Category : Mathematics
Languages : en
Pages : 222
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Book Description
A complex disease involves many etiological and risk factors operating at multiple levels-molecular, cellular, organismal, and environmental. The incidence of such diseases as cancer, obesity, and diabetes are increasing in occurrence, urging us to think fundamentally and use a broader perspective to identify their connection and revolutionize trea
Author: Carlo Bianca
Publisher: World Scientific
ISBN: 9814340537
Category : Mathematics
Languages : en
Pages : 227
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Book Description
This monograph has the ambitious aim of developing a mathematical theory of complex biological systems with special attention to the phenomena of ageing, degeneration and repair of biological tissues under individual self-repair actions that may have good potential in medical therapy. The approach to mathematically modeling biological systems needs to tackle the additional difficulties generated by the peculiarities of living matter. These include the lack of invariance principles, abilities to express strategies for individual fitness, heterogeneous behaviors, competition up to proliferative and/or destructive actions, mutations, learning ability, evolution and many others. Applied mathematicians in the field of living systems, especially biological systems, will appreciate the special class of integro-differential equations offered here for modeling at the molecular, celular and tissue scales. A unique perspective is also presented with a number of case studies in biological modeling.
Author: Christopher P. Fall
Publisher: Springer Science & Business Media
ISBN: 0387224599
Category : Science
Languages : en
Pages : 484
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Book Description
This textbook provides an introduction to dynamic modeling in molecular cell biology, taking a computational and intuitive approach. Detailed illustrations, examples, and exercises are included throughout the text. Appendices containing mathematical and computational techniques are provided as a reference tool.
Author: Amina Eladdadi
Publisher: Springer
ISBN: 1493917935
Category : Mathematics
Languages : en
Pages : 282
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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.
