ArticlePloS one2014
Elastic free energy drives the shape of prevascular solid tumors.
Article in PloS one, 2014. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 12 papers.
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Who cites it
12 citing papers in PubMed.
- Inference of weak-form partial differential equations describing migration and proliferation mechanisms in wound healing experiments on cancer cells.PLoS computational biology · 2025Article
- Linear and nonlinear rheology of liberase-treated breast cancer tumors.Biomaterials science · 2023Article
- Digital twin demonstrates significance of biomechanical growth control in liver regeneration after partial hepatectomy.iScience · 2023Article
- Morphogenesis and cell ordering in confined bacterial biofilms.Proceedings of the National Academy of Sciences of the United States of America · 2021Article
- Understanding the influence of substrate when growing tumorspheres.BMC cancer · 2021Article
- A Coupled Mass Transport and Deformation Theory of Multi-constituent Tumor Growth.Journal of the mechanics and physics of solids · 2020Article
- Subpixel Localization of Isolated Edges and Streaks in Digital Images.Journal of imaging · 2020Article
- A computational framework for the morpho-elastic development of molluskan shells by surface and volume growth.PLoS computational biology · 2019Article
- Quantitative cell-based model predicts mechanical stress response of growing tumor spheroids over various growth conditions and cell lines.PLoS computational biology · 2019Article
- Computer simulations suggest that prostate enlargement due to benign prostatic hyperplasia mechanically impedes prostate cancer growth.Proceedings of the National Academy of Sciences of the United States of America · 2019Article
- Toward Morphologically Relevant Extracellular MatrixFrontiers in physiology · 2018Article
- Tissue-scale, personalized modeling and simulation of prostate cancer growth.Proceedings of the National Academy of Sciences of the United States of America · 2016Article
Corrections and comments
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Authors and funding
4 authors.
Funding
No grant is acknowledged in the PubMed record.
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.
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