© 2017

The Mathematics and Mechanics of Biological Growth

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

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

  1. 1.Department of MathematicsUniversity of OxfordOxfordUnited Kingdom

Bibliographic information


“Goriely’s book is self-contained and provides sufficient review of the background material necessary to understand the mathematics employed in the study of phenomena he describes. … Overall, the text is well written, richly illustrated, and enjoyable to read, although the monograph is lengthy. I applaud Prof. Goriely on his impressive text.” (Bhargav Karamched, SIAM Review, Vol. 61 (1), March, 2019)

“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)