Chemical-Kinetics Model for the Growth of a Multicellular Tumor Spheroid

We propose a model based on chemical kinetic analysis for the growth of a multicellular tumor spheroid. The growth of avascular tumor cells is simulated by an autocatalytic reaction where the cell itself converts glucose and oxygen into a new cell. Glucose is assumed to be the limiting substrate, and its depletion gives rise to the necrosis of tumor cells. Since the depletion is assumed to be the major cause of the central necrosis, the death of tumor cells is determined by the critical value of the concentration. The concentration profile of glucose inside the tumor is obtained from a reaction-diffusion equation. The characteristic features of the experimental results are demonstrated well in this model.