The Mathematics and Mechanics of Biological Growth

  • Alain Goriely

Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 45)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Introduction: Where It All Starts

    1. Front Matter
      Pages 1-1
    2. Alain Goriely
      Pages 3-26
    3. Alain Goriely
      Pages 27-49
    4. Alain Goriely
      Pages 51-59
  3. Filament Growth: A One-Dimensional Theory

    1. Front Matter
      Pages 61-61
    2. Alain Goriely
      Pages 63-96
    3. Alain Goriely
      Pages 97-123
    4. Alain Goriely
      Pages 125-172
  4. Surface Growth: A Two-Dimensional Theory

    1. Front Matter
      Pages 173-173
    2. Alain Goriely
      Pages 175-205
    3. Alain Goriely
      Pages 207-229
    4. Alain Goriely
      Pages 231-249
    5. Alain Goriely
      Pages 251-258
  5. Volumetric Growth: A Three-Dimensional Theory

    1. Front Matter
      Pages 259-259
    2. Alain Goriely
      Pages 261-344
    3. Alain Goriely
      Pages 345-373
    4. Alain Goriely
      Pages 375-397
    5. Alain Goriely
      Pages 399-429
    6. Alain Goriely
      Pages 431-474
    7. Alain Goriely
      Pages 475-551
  6. Conclusion: Where It Does Not End

    1. Front Matter
      Pages 553-553
    2. Alain Goriely
      Pages 555-580
  7. Back Matter
    Pages 581-646

About this book


This monograph presents a general mechanical 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 is 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.


Biological growth Filament growth Balance laws Volumetric growth Evolution laws Mathematical biology Mechanical biology Morphogenesis Morphoelasticity Physiology

Authors and affiliations

  • Alain Goriely
    • 1
  1. 1.Department of MathematicsUniversity of OxfordOxfordUnited Kingdom

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media LLC 2017
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-87709-9
  • Online ISBN 978-0-387-87710-5
  • Series Print ISSN 0939-6047
  • Series Online ISSN 2196-9973
  • Buy this book on publisher's site