Complex Far-Field Geometries Determine the Stability of Solid Tumor Growth with Chemotaxis

TL;DR

This study models tumor growth considering complex vascular geometries and chemotaxis, revealing how microenvironment heterogeneity influences morphological stability and instability in solid tumors.

Contribution

We introduce a sharp interface model incorporating complex far-field geometries and chemotaxis to analyze tumor growth stability.

Findings

Vascular heterogeneity induces morphological instabilities.

Nutrient uptake rates and chemotaxis affect tumor stability.

Simulations show diverse tumor morphologies from fingering to compact shapes.

Abstract

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.