Abstract:
We present a mathematical model for the invasion of healthy tissue by tumour cells.
In particular we focus on the 3D computational simulation and 3D visualization aspects of the problem.
We consider a continuous mathematical model consisting of three PDEs describing the interactions of tumour cells,
the matrix degrading enzymes they produce and the tissue into which they invade.
We examine the effects that both irregular bounded tissue domains as well as heterogeneities within these
tissues will have on tumour invasion.
A powerful Java and OpenGL implementation of the marching cubes volume rendering technique
is used to present the shaded outer surface of a three dimensional tumour in both heterogeneous and irregular domains.
Through transparency blending either density differences within the tumour or different layers i.e. proliferating,
quiescent and necrotic cells can be visualized in three dimensions. Transparency applied to the tissue enables an
exact localization of the tumour within the domain and can be used to examine the interactions between the tissue and the tumour.
Implications of the work for developing a software tool for clinical oncologists are discussed.
Keywords: Avascular Tumour Invasion, Visualization, Simulation, Mathematical Modelling, Marching Cubes, Transparency
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