Single-Cell-Based Models in Biology and Medicine

  • Alexander R. A. Anderson
  • Mark A. J. Chaplain
  • Katarzyna A. Rejniak

Part of the Mathematics and Biosciences in Interaction book series (MBI)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Hybrid Multiscale Models

  3. The Cellular Potts Model and Its Variants

    1. Front Matter
      Pages 77-77
    2. James A. Glazier, Ariel Balter, Nikodem J. Popławski
      Pages 79-106
    3. Athanasius F. M. Marée, Verônica A. Grieneisen, Paulien Hogeweg
      Pages 107-136
    4. Nicholas J. Savill, Roeland M. H. Merks
      Pages 137-150
    5. Ariel Balter, Roeland M. H. Merks, Nikodem J. Popławski, Maciej Swat, James A. Glazier
      Pages 151-167
  4. Off-lattice Cell Models

  5. Viscoelastic Cell Models

  6. Back Matter
    Pages 325-349

About this book


To adequately describe complex spatio-temporal processes that occur in multi-cellular organisms, a class of models is required that simultaneously takes into account differences between individual cells as well as their ability to communicate and interact with one another and their environment. Single-cell-based models form a framework that allows for the explicit incorporation of different properties of individual cells, but at the same time enables all cells to act together as one collective body. This leads ultimately to more biologically realistic models of heterogeneous tissues and multi-cellular organisms and allows for a better understanding of the principles underlying the complex biological processes occurring during the formation, growth and maintenance of multi-cellular bodies.

The aim of this book is to assemble a collection of different mathematical and computational models and techniques that focus on individual cells, cell processes and cell behaviour, that are also suitable to address problems on the multi-cellular or tissue scale. We would like to focus the level of the book equally to students starting their research in the field of mathematical biology and to scientists already modelling multi-cellular processes. Therefore, our intention is to include in this book a detailed description of each model and an extensive review of suitable biological and medical applications.


Single Cell Model biology cell cell membrane cellular processes environment evolution mathematical biology membrane model modeling morphogenesis simulation tissue

Editors and affiliations

  • Alexander R. A. Anderson
    • 1
  • Mark A. J. Chaplain
    • 1
  • Katarzyna A. Rejniak
    • 1
  1. 1.Division of MathematicsUniversity of DundeeDundeeUK

Bibliographic information