  In this paper, we develop a sharp interface tumor growth model to study the
effect of the tumor microenvironment using a complex far-field geometry that
mimics a heterogeneous distribution of vasculature. Together with different
nutrient uptake rates inside and outside the tumor, this introduces variability
in spatial diffusion gradients. Linear stability analysis suggests that the
uptake rate in the tumor microenvironment, together with chemotaxis, may induce
unstable growth, especially when the nutrient gradients are large. We
investigate the fully nonlinear dynamics using a spectrally accurate boundary
integral method. Our nonlinear simulations reveal that vascular heterogeneity
plays an important role in the development of morphological instabilities that
range from fingering and chain-like morphologies to compact, plate-like shapes
in two-dimensions.
