Book Description
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.
Table of Contents
General Introduction vii
Hybrid Multiscale Models 1
A Hybrid Multiscale Model of Tumour Invasion: Evolution and the Microenvironment 3
Lattice-gas Cellular Automaton Modeling of Developing Cell Systems 29
Two-dimensional Multiscale Model of Cell Motion in a Chemotactic Field 53
The Cellular Potts Model and Its Variants 77
Magnetization to Morphogenesis: A Brief History of the Glazier-Graner-Hogeweg Model 79
The Cellular Potts Model and Biophysical Properties of Cells, Tissues and Morphogenesis 107
The Cellular Potts Model in Biomedicine 137
The Glazier-Graner-Hogeweg Model: Extensions, Future Directions, and Opportunities for Further Study 151
Off-lattice Cell Models 169
Center-based Single-cell Models: An Approach to Multi-cellular Organization Based on a Conceptual Analogy to Colloidal Particles 171
Models with Lattice-free Center-based Cells Interacting with Continuum Environment Variables 197
Modeling Multicellular Structures Using the Subcellular Element Model 221
Viscoelastic Cell Models 241
Cell-based Models of Blood Clotting 243
A 3-D Deformable Ellipsoidal Cell Model with Cell Adhesion and Signaling 271
Modelling the Development of ComplexTissues Using Individual Viscoelastic Cells 301
Addresses 325
Index 329
Colour Figures 335