Asymmetric Growth of Tumor Spheroids in a Symmetric Environment

Abstract

In this work, we studied the stability of radially symmetric growth in tumor spheroids using a reaction-diffusion model. In this model, nutrient concentration and internal pressure are local variables that implicitly relate the proliferation of cells to the growth of the tumor. The analytical solution of the governing model was presented in an orthonormal spherical harmonic basis. It was shown that the radially symmetric steady-state solution to the growth of tumor spheroids, under symmetric growth conditions, was unstable with respect to small asymmetric perturbations. Such perturbations excited the asymmetric modes of growth, which could grow in time and change the spherical configuration of the tumor. The number of such modes and their rates of growth depended on parameters such as surface tension, external energy and the rate of nutrient consumption. This analysis indicated that the spherical configuration of tumor spheroids, even under experimentally controlled symmetric growth conditions, were naturally unstable. This was confirmed by a comparison between the shapes of in vitro human glioblastoma (hGB) spheroids and the configuration of the first few asymmetric modes predicted by the model.