POSITIVE FEEDBACK AND ANGIOGENESIS IN TUMOR-GROWTH CONTROL

In vivo tumor growth data from experiments performed in our laboratory suggest that basic fibroblast growth factor (bFGF) and vascular endot helial growth factor (VEGF) are angiogenic signals emerging from an up -regulated genetic message in the proliferating rim of a solid tumor i n response to tumor-wide hypoxia. If these signals are generated in re sponse to unfavorable environmental conditions, i.e. a decrease in oxy gen tension, then the tumor may play an active role in manipulating it s own environment. We have idealized this type of adaptive behavior in our mathematical model via a parameter which represents the carrying capacity of the host for the tumor. If that model parameter is held co nstant, then environmental control is limited to tumor shape and mitog enic signal processing. However, if we assume that the response of the local stroma to these signals is an increase in the host's ability to support an ever larger tumor, then our models describe a positive fee dback control system. In this paper, we generalize our previous result s to a model including a carrying capacity which depends on the size o f the proliferating compartment in the tumor. Specific functional form s for the carrying capacity are discussed. Stability criteria of the s ystem and steady state conditions for these candidate functions are an alyzed. The dynamics needed to generate stable tumor growth, including countervailing negative feedback signals, are discussed in detail wit h respect to both their mathematical and biological properties. (C) 19 97 Society for Mathematical Biology.