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The Mathematics And Mechanics Of Biological Growth
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Book Synopsis The Mathematics and Mechanics of Biological Growth by : Alain Goriely
Download or read book The Mathematics and Mechanics of Biological Growth written by Alain Goriely and published by Springer. This book was released on 2017-05-29 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a general mathematical theory for biological growth. It provides both a conceptual and a technical foundation for the understanding and analysis of problems arising in biology and physiology. The theory and methods are illustrated on a wide range of examples and applications. A process of extreme complexity, growth plays a fundamental role in many biological processes and is considered to be the hallmark of life itself. Its description has been one of the fundamental problems of life sciences, but until recently, it has not attracted much attention from mathematicians, physicists, and engineers. The author herein presents the first major technical monograph on the problem of growth since D’Arcy Wentworth Thompson’s 1917 book On Growth and Form. The emphasis of the book is on the proper mathematical formulation of growth kinematics and mechanics. Accordingly, the discussion proceeds in order of complexity and the book is divided into five parts. First, a general introduction on the problem of growth from a historical perspective is given. Then, basic concepts are introduced within the context of growth in filamentary structures. These ideas are then generalized to surfaces and membranes and eventually to the general case of volumetric growth. The book concludes with a discussion of open problems and outstanding challenges. Thoughtfully written and richly illustrated to be accessible to readers of varying interests and background, the text will appeal to life scientists, biophysicists, biomedical engineers, and applied mathematicians alike.
Book Synopsis Morpho-elasticity by : Alain Goriely
Download or read book Morpho-elasticity written by Alain Goriely and published by Springer. This book was released on 2016-05-06 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Growth plays a fundamental role in many biological processes and is considered to be the hallmark of life itself. It is a process of extreme complexity and its description has been one of the fundamental problems of life sciences. However, until recently, it has not attracted much attention from mathematicians, physicists, and mechanicians. The goal of this monograph is to present the state of knowledge in the mechanics of growth, to provide a rigorous foundation and, to offer a set of mathematical tools for the analysis of specific problems arising in biology accessible to mathematicians, physicists, and biologists. Simple examples, applications and building discussions are included. The emphasis of the book is on the kinematics and mechanics of growth. Accordingly, the three first parts of the book are: Growth of curves and lamentary structure, Growth of surfaces, membranes, and shells, and Volumetric growth.
Book Synopsis Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities by : Rebecca Sanft
Download or read book Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities written by Rebecca Sanft and published by Academic Press. This book was released on 2020-03-30 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring Mathematical Modeling in Biology through Case Studies and Experimental Activities provides supporting materials for courses taken by students majoring in mathematics, computer science or in the life sciences. The book's cases and lab exercises focus on hypothesis testing and model development in the context of real data. The supporting mathematical, coding and biological background permit readers to explore a problem, understand assumptions, and the meaning of their results. The experiential components provide hands-on learning both in the lab and on the computer. As a beginning text in modeling, readers will learn to value the approach and apply competencies in other settings. Included case studies focus on building a model to solve a particular biological problem from concept and translation into a mathematical form, to validating the parameters, testing the quality of the model and finally interpreting the outcome in biological terms. The book also shows how particular mathematical approaches are adapted to a variety of problems at multiple biological scales. Finally, the labs bring the biological problems and the practical issues of collecting data to actually test the model and/or adapting the mathematics to the data that can be collected. Presents a single volume on mathematics and biological examples, with data and wet lab experiences suitable for non-experts Contains three real-world biological case studies and one wet lab for application of the mathematical models Includes R code templates throughout the text, which are also available through an online repository, along with the necessary data files to complete all projects and labs
Book Synopsis Biological Growth and Spread by : W. Jäger
Download or read book Biological Growth and Spread written by W. Jäger and published by Springer Science & Business Media. This book was released on 2013-03-12 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Models in Biology by : Leah Edelstein-Keshet
Download or read book Mathematical Models in Biology written by Leah Edelstein-Keshet and published by SIAM. This book was released on 1988-01-01 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.
Book Synopsis Mathematical Modeling of Biological Systems, Volume II by : Andreas Deutsch
Download or read book Mathematical Modeling of Biological Systems, Volume II written by Andreas Deutsch and published by Springer Science & Business Media. This book was released on 2007-10-12 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume II of this two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. Highlighted throughout are mathematical and computational apporaches to examine central problems in the life sciences, ranging from the organization principles of individual cells to the dynamics of large populations. The chapters are thematically organized into the following main areas: epidemiology, evolution and ecology, immunology, neural systems and the brain, and innovative mathematical methods and education. The work will be an excellent reference text for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics.
Book Synopsis Mechanics of Biological Tissue by : Gerhard A. Holzapfel
Download or read book Mechanics of Biological Tissue written by Gerhard A. Holzapfel and published by Springer Science & Business Media. This book was released on 2006-06-03 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mechanics of biological tissues is a multidisciplinary and rapidly expanding area of research. This book points to important directions combining mechanical sciences with the new developments in biology. It delivers articles on mechanics of tissues at the molecular, cellular, tissue and organ levels.
Book Synopsis On Growth and Form by : D'Arcy Wentworth Thompson
Download or read book On Growth and Form written by D'Arcy Wentworth Thompson and published by DigiCat. This book was released on 2022-11-21 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: On Growth and Form is a scholarly work by D'Arcy Wentworth Thompson. Thompson was a Scottish biologist, mathematician, classics scholar and a pioneer of mathematical biology. Excerpt: "Of the chemistry of his day and generation, Kant declared that it was "a science, but not science,"—"eine Wissenschaft, aber nicht Wissenschaft"; for that the criterion of physical science lay in its relation to mathematics. And a hundred years later Du Bois Reymond, profound student of the many sciences on which physiology is based, recalled and reiterated the old saying, declaring that chemistry would only reach the rank of science, in the high and strict sense, when it should be found possible to explain chemical reactions in the light of their causal relation to the velocities, tensions and conditions of equilibrium of the component molecules; that, in short, the chemistry of the future must deal with molecular mechanics, by the methods and in the strict language of mathematics, as the astronomy of Newton and Laplace dealt with the stars in their courses. We know how great a step has been made towards this distant and once hopeless goal, as Kant defined it, since van't Hoff laid the firm foundations of a mathematical chemistry, and earned his proud epitaph, Physicam chemiae adiunxit."
Book Synopsis Mathematical Modeling of Biological Systems, Volume I by : Andreas Deutsch
Download or read book Mathematical Modeling of Biological Systems, Volume I written by Andreas Deutsch and published by Springer Science & Business Media. This book was released on 2007-06-15 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume I of this two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. The chapters are thematically organized into the following main areas: cellular biophysics, regulatory networks, developmental biology, biomedical applications, data analysis and model validation. The work will be an excellent reference text for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics.
Book Synopsis Biology and Mathematics by : Roger Buis
Download or read book Biology and Mathematics written by Roger Buis and published by John Wiley & Sons. This book was released on 2019-12-12 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: To formalize the dynamics of living things is to search for invariants in a system that contains an irreducible aspect of “fuzziness”, because biological processes are characterized by their large statistical variability, and strong dependence on temporal and environmental factors. What is essential is the identification of what remains stable in a “living being” that is highly fluctuating. The use of mathematics is not limited to the use of calculating tools to simulate and predict results. It also allows us to adopt a way of thinking that is founded on concepts and hypotheses, leading to their discussion and validation. Instruments of mathematical intelligibility and coherence have gradually “fashioned” the view we now have of biological systems. Teaching and research, fundamental or applied, are now dependent on this new order known as Integrative Biology or Systems Biology.
Book Synopsis Parabolic Equations in Biology by : Benoît Perthame
Download or read book Parabolic Equations in Biology written by Benoît Perthame and published by Springer. This book was released on 2015-09-09 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.
Book Synopsis Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes by : Miguel Cerrolaza
Download or read book Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes written by Miguel Cerrolaza and published by Academic Press. This book was released on 2017-12-28 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes covers new and exciting modeling methods to help bioengineers tackle problems for which the Finite Element Method is not appropriate. The book covers a wide range of important subjects in the field of numerical methods applied to biomechanics, including bone biomechanics, tissue and cell mechanics, 3D printing, computer assisted surgery and fluid dynamics. Modeling strategies, technology and approaches are continuously evolving as the knowledge of biological processes increases. Both theory and applications are covered, making this an ideal book for researchers, students and R&D professionals. Provides non-conventional analysis methods for modeling Covers the Discrete Element Method (DEM), Particle Methods (PM), MessLess and MeshFree Methods (MLMF), Agent-Based Methods (ABM), Lattice-Boltzmann Methods (LBM) and Boundary Integral Methods (BIM) Includes contributions from several world renowned experts in their fields Compares pros and cons of each method to help you decide which method is most applicable to solving specific problems
Book Synopsis New Trends in the Physics and Mechanics of Biological Systems by : Martine Ben Amar
Download or read book New Trends in the Physics and Mechanics of Biological Systems written by Martine Ben Amar and published by OUP Oxford. This book was released on 2011-05-26 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: In July 2009, many experts in the mathematical modelling of biological sciences gathered in Les Houches for a 4-week summer school on the mechanics and physics of biological systems. The goal of the school was to present to students and researchers an integrated view of new trends and challenges in physical and mathematical aspects of biomechanics. While the scope for such a topic is very wide, we focused on problems where solid and fluid mechanics play a central role. The school covered both the general mathematical theory of mechanical biology in the context of continuum mechanics but also the specific modelling of particular systems in the biology of the cell, plants, microbes, and in physiology. These lecture notes are organised (as was the school) around five different main topics all connected by the common theme of continuum modelling for biological systems: Bio-fluidics, Bio-gels, Bio-mechanics, Bio-membranes, and Morphogenesis. These notes are not meant as a journal review of the topic but rather as a gentle tutorial introduction to the readers who want to understand the basic problematic in modelling biological systems from a mechanics perspective.
Book Synopsis Mathematical Biology II by : James D. Murray
Download or read book Mathematical Biology II written by James D. Murray and published by Springer Science & Business Media. This book was released on 2011-02-15 with total page 834 pages. Available in PDF, EPUB and Kindle. Book excerpt: This richly illustrated third edition provides a thorough training in practical mathematical biology and shows how exciting mathematical challenges can arise from a genuinely interdisciplinary involvement with the biosciences. It has been extensively updated and extended to cover much of the growth of mathematical biology. From the reviews: ""This book, a classical text in mathematical biology, cleverly combines mathematical tools with subject area sciences."--SHORT BOOK REVIEWS
Book Synopsis Mathematical Concepts and Methods in Modern Biology by : Raina Robeva
Download or read book Mathematical Concepts and Methods in Modern Biology written by Raina Robeva and published by Academic Press. This book was released on 2013-02-26 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Concepts and Methods in Modern Biology offers a quantitative framework for analyzing, predicting, and modulating the behavior of complex biological systems. The book presents important mathematical concepts, methods and tools in the context of essential questions raised in modern biology. Designed around the principles of project-based learning and problem-solving, the book considers biological topics such as neuronal networks, plant population growth, metabolic pathways, and phylogenetic tree reconstruction. The mathematical modeling tools brought to bear on these topics include Boolean and ordinary differential equations, projection matrices, agent-based modeling and several algebraic approaches. Heavy computation in some of the examples is eased by the use of freely available open-source software. Features self-contained chapters with real biological research examples using freely available computational tools Spans several mathematical techniques at basic to advanced levels Offers broad perspective on the uses of algebraic geometry/polynomial algebra in molecular systems biology
Book Synopsis Mathematical Biology by : James D. Murray
Download or read book Mathematical Biology written by James D. Murray and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics has always benefited from its involvement with developing sciences. Each successive interaction revitalises and enhances the field. Biomedical science is clearly the premier science of the foreseeable future. For the continuing health of their subject mathematicians must become involved with biology. With the example of how mathematics has benefited from and influenced physics, it is clear that if mathematicians do not become involved in the biosciences they will simply not be a part of what are likely to be the most important and exciting scientific discoveries of all time. Mathematical biology is a fast growing, well recognised, albeit not clearly defined, subject and is, to my mind, the most exciting modern application of mathematics. The increasing use of mathematics in biology is inevitable as biol ogy becomes more quantitative. The complexity of the biological sciences makes interdisciplinary involvement essential. For the mathematician, biology opens up new and exciting branches while for the biologist mathematical modelling offers another research tool commmensurate with a new powerful laboratory technique but only if used appropriately and its limitations recognised. However, the use of esoteric mathematics arrogantly applied to biological problems by mathemati cians who know little about the real biology, together with unsubstantiated claims as to how important such theories are, does little to promote the interdisciplinary involvement which is so essential. Mathematical biology research, to be useful and interesting, must be relevant biologically.
Book Synopsis Continuum Modeling in Mechanobiology by : Larry A. Taber
Download or read book Continuum Modeling in Mechanobiology written by Larry A. Taber and published by Springer Nature. This book was released on 2020-06-15 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines key theoretical tools that are currently used to develop mathematical models as an aid in understanding the biological response of cells and tissues to mechanical stimuli. Problems in growth and remodeling, tissue and organ development, and functional adaptation are all covered. Chapters on tensor analysis and nonlinear elasticity provide the necessary background for understanding the engineering theories that are currently used to solve challenges in mechanobiology. This is an ideal book for biomechanical engineers who work on problems in mechanobiology and tissue engineering.
