  In this paper, we study a tumor growth model with nutrients. The contact
inhibition for the tumor cells, presented in the model, results in the
evolution of a congested tumor patch. We study the regularity of the tumor
patch as the nutrients' diffusion strength $D$ diminishes. In particular, we
show that for small $D>0$ the boundary of the tumor patch stays in a small
neighborhood of the smooth tumor patch boundary obtained with $D=0$, uniformly
with respect to the Hausdorff distance.
