title: Elastic free energy drives the shape of prevascular solid tumors.
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 cancer 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.
authors: Department of New Materials and Biosystems, Max Planck Institute for Intelligent Systems, Stuttgart, Germany.
authors: K L
authors: KL
authors: Mills
authors: Department of New Materials and Biosystems, Max Planck Institute for Intelligent Systems, Stuttgart, Germany; Reutlingen University, Reutlingen, Germany.
authors: Ralf
authors: R
authors: Kemkemer
authors: Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, United States of America.
authors: Shiva
authors: S
authors: Rudraraju
authors: Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, United States of America; Department of Mathematics, University of Michigan, Ann Arbor, Michigan, United States of America.
authors: Krishna
authors: K
authors: Garikipati
mesh_terms: D000465:Algorithms; D045744:Cell Line, Tumor; D004548:Elasticity; D006801:Humans; D008962:Models, Theoretical; D009369:Neoplasms / Q000473:pathology*; D013314:Stress, Mechanical; D047368:Tumor Burden