  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.
