This work presents a comprehensive hybrid computer model simulating the cell population and mass transfer dynamics during tissue growth processes. The model has three major components: (a) a discrete algorithm simulating individual cell activities and cell-cell interactions; (b) transient, three-dimensional partial differential equations (PDE's) describing the convection, diffusion, consumption and, possibly, secretion of nutrients or other important substances in tissue systems; and (c) equations describing how cell behavior is modulated by the local concentration fields.
The hybrid model is first used to study the growth of bioartificial tissues under conditions leading to nutrient depletion. Simulation results indicate that large tissue size, low nutrient diffusivity, high cell uptake rate and low nutrient concentration in the culture media lead to severe transport limitations and have serious adverse effects on the growth rates and the structure of bioartificial tissues. The incorporation of perfusion channels is one of the proposed methods for alleviating diffusional limitations. However, the selection of optimal channel placement and size leads to an interesting optimization problem. Our results indicate the existence of an optimal channel diameter for each set of cell parameters and culture conditions. As diffusional limitations become more severe, larger perfusion channels are needed and the value of the achievable cell density decreases.
Finally, the hybrid model is used to study the acid-mediated growth of solid tumors. With its ability to describe the complex, three-dimensional vasculature of tissues invaded by tumors, our model represents a significant extension of previous two-dimensional studies. In addition to a three-dimensional capillary network generated from literature data, tree-like capillary networks with adjustable overall vascularity are generated using a bifurcating distributive algorithm in order to study the effect of host vascularity on tissue growth. Our simulations produce tumor growth curves similar to those observed clinically. The predicted range of tumor cell acid production rate shows better agreement with experimental values than existing two-dimensional models. Our model can also predict the universal existence of necrotic regions in large tumors.