A Hybrid Multiscale Model of Solid Tumour Growth and Invasion: Evolution and the Microenvironment

  • Alexander R. A. Anderson
Part of the Mathematics and Biosciences in Interaction book series (MBI)


Cancer is a complex, multiscale process, in which genetic mutations occurring at a subcellular level manifest themselves as functional changes at the cellular and tissue scale. The importance of tumour cell/microenvironment interactions is currently of great interest to both the biological and the modelling communities. In this chapter we present a hybrid discrete-continuum (HDC) mathematical model of tumour invasion that considers the tumour as a collection of many individual cancer cells that interact with and modify the environment through which they grow and migrate. The HDC model we develop focuses on four key variables implicated in the invasion process: tumour cells, host tissue (extracellular matrix), matrix-degradative enzymes and oxygen. The model is considered to be hybrid since the latter 3 variables are continuous (i.e. concentrations) and the tumour cells are discrete (i.e. individuals). We shall examine how individual-based cell interactions (with one another and the microenvironment) can affect the tumour morphology. We will also discuss the evolutionary influence that the microenvironment has upon the tumours genetic makeup. The HDC model focuses on the microscale (individual cell) level to produce computational simulations of tumour at the tissue scale. As we shall discuss, this technique, developed in previous models of nematode migration and angiogenesis, is intrinsically multiscale and can easily incorporate a range of scales i.e. genetic, sub-cellular, cellular and tissue.


Solid Tumour Growth Tissue Scale Individual Cancer Cell Nematode Migration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Alexander R. A. Anderson
    • 1
  1. 1.Division of MathematicsUniversity of DundeeDundeeScotland, UK

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