Authors:
- Presents a mathematical theory to quantify and model biological growth processes
- Shows how mechanics and geometry are coupled during growth and how complex forms and morphological patterns may arise due to instabilities
- Illustrated with simple examples and detailed biological applications
- Includes supplementary material: sn.pub/extras
Part of the book series: Interdisciplinary Applied Mathematics (IAM, volume 45)
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Table of contents (17 chapters)
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Front Matter
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Introduction: Where It All Starts
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Front Matter
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Filament Growth: A One-Dimensional Theory
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Front Matter
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Surface Growth: A Two-Dimensional Theory
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Front Matter
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Volumetric Growth: A Three-Dimensional Theory
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Front Matter
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About this book
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.
Reviews
“The book grasps the conceptual and technical aspects underpinning the role of mechanics in the growth of biological tissues. It is the first major modern monograph on the subject, which synthesizes the research activity in this vivid field of the mathematics and mechanics of growth since now more than two decades. … The monograph is overall well-structured and rich in illustrations and will be accessible and appealing to readers with different interest and background, including life scientists … .” (Jean-François Ganghoffer, Journal of Geometry and Symmetry in Physics JGSP, Vol. 49, 2018)
“The book is very informative, it is written in an easy readable and intriguing way. It has a large reference list of 1369 bibliographic descriptions and a carefully prepared index. The book should be helpful for researchers who work in the multidisciplinary fields of theoretical biology, biomechanics, biomedical engineering, biophysics and applied mathematics.” (Svetoslav Markov, zbMATH 1398.92003, 2018)
Authors and Affiliations
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Department of Mathematics, University of Oxford, Oxford, United Kingdom
Alain Goriely
Bibliographic Information
Book Title: The Mathematics and Mechanics of Biological Growth
Authors: Alain Goriely
Series Title: Interdisciplinary Applied Mathematics
DOI: https://doi.org/10.1007/978-0-387-87710-5
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media LLC 2017
Hardcover ISBN: 978-0-387-87709-9Published: 31 May 2017
Softcover ISBN: 978-1-4939-7911-0Published: 27 July 2018
eBook ISBN: 978-0-387-87710-5Published: 29 May 2017
Series ISSN: 0939-6047
Series E-ISSN: 2196-9973
Edition Number: 1
Number of Pages: XXII, 646
Number of Illustrations: 341 b/w illustrations
Topics: Mathematical and Computational Biology, Biological and Medical Physics, Biophysics, Developmental Biology, Cell Physiology, Classical Mechanics