Cancer cells have the characteristic of being able to infinitely increase in the number. Although this characteristic may be true in a cultured cell environment, cancer cells cannot increase in the number infinitely in vivo because of the limitations of nutrition and space. To simulate the multiplication pattern of a cancer cell that increases in the number within the body, the Verhulst population model was used. This population model can be explained as follows. Although multiplication will continue if there is sufficient nutrition, once nutrition becomes insufficient, the growth rate will decline and eventually reach a convergence value.
The number of cells at time t, S ( t ), is determined as follows.

 

 

The number of cells at time t is S ( t ). The convergence value is N , w is a constant for setting the number of cells at day 0 equal 1 (100%), t w is the doubling time, and ρ is the compensation constant. Using this function, we computed the number of cancer cells that would occur in glandular tissue as they increased in number. Simulation of the 2-dimensional form of multiplication was done using a Voronoi diagram ( Fig. 2 ).

 

Fig. 2

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