Numerical analysis and computational simulation of partial differential
equation models in mathematical biology are now an integral part
of the research in this field. Increasingly we are seeing the development of
partial differential equation models in more than one space dimension, and it
is therefore necessary to generate a clear and effective visualisation platform
between the mathematicians and biologists to communicate the results. The
mathematical extension of models to three spatial dimensions from one or two
is often a trivial task, whereas the visualisation of the results is more complicated.
The scope of this paper is to apply the established marching cubes
volume rendering technique to the study of solid tumour growth and invasion,
and present an adaptation of the algorithm to speed up the surface rendering
from numerical simulation data. As a specific example, in this paper we examine
the computational solutions arising from numerical simulation results
of a mathematical model of malignant solid tumour growth and invasion in an
irregular heterogeneous three-dimensional domain, i.e., the female breast. Due
to the different variables that interact with each other, more than one data set
may have to be displayed simultaneously, which can be realized through transparency
blending. The usefulness of the proposed method for visualisation in
a more general context will also be discussed.
Mathematics Subject Classification: 76M27,92B05,92C15,92C50.