Acid-mediated tumor invasion: How does vasculature affect the growth characteristics?

We study the growth of an implanted avascular tumor in rats, in two-dimensions, based on a model where the mechanism of invasion is centered on tumor-induced acidification of the micro-environment and consequent death of normal cells. The spatial distribution of the acid density around the tumor is found using mean-field analysis. By assuming that the viability of both normal and tumor cells falls sharply below certain threshold values of the local pH, we determine the conditions for the formation and radius of a necrotic core at the center, as a function of the tumor radius. We show mathematically that the mean micro-vessel density (MVD) plays a pivotal role in determining the growth characteristics of the tumor. When the MVD is sufficiently small, accumulation of excess acid inside the tumor leads to the formation of a necrotic core, which occupies a significant fraction of the total area in large tumors. However, necrosis is reduced when the mean MVD inside the tumor is larger than outside because of the more efficient removal of excess acid. At sufficiently high MVD, necrosis might be absent in the tumor, or confined to small regions mostly devoid of micro-vessels. Quantitative estimates of MVD for these different phases of growth are obtained, and verified using explicit cellular automaton simulations. Recent experimental studies on the correlation between necrosis and MVD support our main conclusions.