Elastic free energy drives the shape of prevascular solid tumors

TL;DR

This study demonstrates that the shape of prevascular solid tumors is driven by the minimization of elastic free energy, with tumors adopting ellipsoidal forms in stiffer environments to reduce system energy.

Contribution

It introduces a mechanical model showing elastic free energy minimization as a key factor in tumor shape determination, supported by in vitro experiments and nonlinear elasticity computations.

Findings

Tumors grow as ellipsoids in stiffer hydrogels.

Ellipsoidal shape minimizes elastic free energy.

Tumor shape depends on hydrogel stiffness.

Abstract

It is well established that the mechanical environment influences cell functions in health and disease. Here, we address how the mechanical environment influences tumor growth, in particular, the shape of solid tumors. In an in vitro tumor model, which isolates mechanical interactions between tumor cells and a hydrogel, we find that tumors grow as ellipsoids, resembling the same, oft-reported observation of in vivo tumors. Specifically, an oblate ellipsoidal tumor shape robustly occurs when the tumors grow in hydrogels that are stiffer than the tumors, but when they grow in more compliant hydrogels they remain closer to spherical in shape. Using large scale, nonlinear elasticity computations we show that the oblate ellipsoidal shape minimizes the elastic free energy of the tumor-hydrogel system. Having eliminated a number of other candidate explanations, we hypothesize that minimization of the elastic free energy is the reason for predominance of the experimentally observed ellipsoidal shape. This result may hold significance for explaining the shape progression of early solid tumors in vivo and is an important step in understanding the processes underlying solid tumor growth.