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.
Highlights
Tumorigenesis and solid tumor growth are associated with altered mechanics in the tumor’s environment such as increased matrix stiffness and growth-induced mechanical stress [1,2,3,4]
Monitoring displacements in the hydrogel surrounding ellipsoidal tumors using co-embedded fluorescent micro-beads, Cheng and co-workers [7] sought to explain the observed symmetrybreaking that leads to ellipsoidal tumors grown from murine mammary carcinoma cells
By correlating these fields with tumor shape and Caspase-3 activity, the authors concluded that mechanical stress was causing a higher fraction of cell death along the minor axis and driving the tumor to grow in the corresponding ellipsoidal shape
Summary
Tumorigenesis and solid tumor growth are associated with altered mechanics in the tumor’s environment such as increased matrix stiffness and growth-induced mechanical stress [1,2,3,4]. The tumor’s size and morphology may be affected [7,8,9] Both in vivo and in vitro, solid tumors are often described as being ellipsoidal in shape. In a model of the early, prevascular stage of tumor growth, tumor cells are embedded and allowed to grow in a tissue-mechanics-mimicking hydrogel [7,8,9]. In such an environment, tumor shape has been shown to suffer a loss of symmetry from spherical to ellipsoidal for two different tumor cell lines [7,9] (murine mammary carcinoma and rat prostate carcinoma, respectively). Since the hydrogel is biochemically inert to cellular attachment, the effect of the mechanical environment on tumor growth is isolated
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