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Mathematical Medicine and Biology Advance Access published online on March 21, 2005
Mathematical Medicine and Biology, doi:10.1093/imammb/dqi005
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Received December 9, 2003
Revised July 21, 2004
Accepted November 30, 2004

Article

A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion

Alexander R. A. Anderson 1*

1 Division of Mathematics, University of Dundee, Dundee DD1 4HN, UK

* To whom correspondence should be addressed.
Alexander R. A. Anderson, E-mail: anderson{at}maths.dundee.ac.uk


  Abstract

In this paper we present a hybrid mathematical model of the invasion of healthy tissue by a solid tumour. In particular we consider early vascular growth, just after angiogenesis has occurred. We examine how the geometry of the growing tumour is affected by tumour cell heterogeneity caused by genetic mutations. As the tumour grows, mutations occur leading to a heterogeneous tumour cell population with some cells having a greater ability to migrate, proliferate or degrade the surrounding tissue. All of these cell properties are closely controlled by cell-cell and cell-matrix interactions and as such the physical geometry of the whole tumour will be dependent on these individual cell interactions. The hybrid 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 three variables are continuous (i.e. concentrations) and the tumour cells are discrete (i.e. individuals). With this hybrid model we examine how individual-based cell interactions (with one another and the matrix) can affect the tumour shape and discuss which of these interactions is perhaps most crucial in influencing the tumour's final structure.


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