Mathematical models of tumor growth. IV. Effects of a necrotic core.

Two mathematical models for the control of the growth of a tumor by diffusion of mitotic inhibitor are presented. The inhibitor production rate is taken to be uniform in a necrotic core for the first model and in the nonnecrotic region for the second model. Regions of stable and unstable growth are determined, and conclusions are drawn about the limiting peripheral widths of stable tissue growth for both models. Comparisons of the results from the two models indicate that the models are sensitive to the source distributions of inhibitor production.