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.