A cellular automaton model of early tumor growth and invasion.

A hybrid cellular automaton model is described and used to simulate early tumor growth and examine the roles of host tissue vascular density and tumor metabolism in the ability of a small number of monoclonal transformed cells to develop into an invasive tumor. The model incorporates normal cells, tumor cells, necrotic or empty space, and a random network of native microvessels as components of a cellular automaton state vector. Diffusion of glucose and H(+)ions (the latter largely resulting from the tumor's excessive reliance on anaerobic metabolism) to and from the microvessels, and their utilization or production by cells, is modeled through the solution of differential equations. In this way, the cells and microvessels affect the extracellular concentrations of glucose and H(+)which, in turn, affect the evolution of the automaton. Simulations of the model demonstrate that: (i) high tumor H(+)ion production is favorable for tumor growth and invasion; however for every H(+)ion production rate, there exists a range of optimal microvessel densities (leading to a local pH favorable to tumor but not to normal cells) for which growth and invasion is most effective, (ii) at vascular densities below this range, both tumor and normal cells die due to excessively low pH, (iii) for vascular densities above the optimal range the microvessel network is highly efficient at removing acid and therefore the tumor cells lose their advantage over normal cells gained by high local H(+)concentration. While significant spatial gradients of glucose formed, no regions of detrimentally poor glucose perfusion (for either cell type) were observed, regardless of microvessel density. Depending on metabolic phenotype, a variety of tumor morphologies similar to those clinically observed were realized in the simulations. Lastly, a sharp transition (analogous to that of the adenoma-carcinoma sequence) between states of initial tumor confinement and efficient invasiveness was observed when H(+)production reached a critical value.