A stochastic model to simulate the growth of anchorage dependent cells on flat surfaces

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Abstract
A stochastic model is proposed to simulate the growth of anchorage dependent cells on a flat surface. The model, based on representing the cell shapes on the surface as external irregular polygons with the nuclei distributed as a set of Poisson points (producing a modified Voronoi tessellation of 2 space) and incorporating a distribution function to describe cell division of the perimeter cells of the colony, provides data not only on population dynamics but also on the patterns produced by clusters of cells in the colony. These patterns produced by the model are qualitatively similar to observations reported for some cell cultures. The periods of induction, rapid growth, and decreasing growth asymptoting to zero as confluence is reached are predicted by the model. Quantitative comparison with published experimental data for this is good. The specific growth rate computed for the period of rapid growth predicted by the model is dependent on the distribution function describing the cell division time. As the standard deviation of this increases, the specific growth rate decreases as with a consequent increase in time to achieve confluence. The removal of cells from the colony by shear forces or death is considered in the model. As the probability for removal increases, the cell density at confluence and specific growth rate decrease. The clusters of cells, patterns, in the colony are very sensitive to cell removal. By analyzing these patterns in experiments, an estimate of cell removal can be made. The areas covered by cells on a substrate are fractal patterns. The fractal dimension is always greater than 1 and is a function of the removal probability.