Although each cell in the body has a 3-dimensional cubic structure, epithelial tissue can be considered to be a modified bag made up of a 2-dimensional sheet. In this research, using a dynamic simulation model, we simulated the increase in the number of cancer cells in a 2-dimensional plane. The software used was Mathematica ver. 5.2 and ver. 8.0.4.

Normal tissues and organs show a specific, orderly cell arrangement. In contrast, cancer tissue shows a polygonal pattern of cells with unequal size. This polygonal pattern appears to be determined by the nature of the constituent cells. In this study, to illustrate the growth of cancer cells within normal tissue, I attempted to fit these patterns using Voronoi diagrams.

Here, the appearance of the spread of cancer cells in normal tissue is simulated as a sheet of cells in a polygonal pattern. When the forms of the cancer cells were expressed by Voronoi cell areas, the random form of a cancer tissue was represented very well by Voronoi diagrams.

Voronoi diagrams are used in an area of research in computational geometry. There are a variety of applications of Voronoi diagrams, such as geographic information systems, robotics, and computer graphics. In this research, a Voronoi diagram was applied to cancer tissue and the multiplication pattern of cancer cells. Using this approach, simulations were performed for radiotherapy in which radiation particles hit a target at random. Voronoi diagrams can also be used to simulate normal tissue ( Fig. 1A: glandular tissue, Fig. 1B: squamous epithelial tissue ).

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