Modeling mechanical inhomogeneities in small populations of proliferating monolayers and spheroids
- 368 Downloads
Understanding the mechanical behavior of multicellular monolayers and spheroids is fundamental to tissue culture, organism development, and the early stages of tumor growth. Proliferating cells in monolayers and spheroids experience mechanical forces as they grow and divide and local inhomogeneities in the mechanical microenvironment can cause individual cells within the multicellular system to grow and divide at different rates. This differential growth, combined with cell division and reorganization, leads to residual stress. Multiple different modeling approaches have been taken to understand and predict the residual stresses that arise in growing multicellular systems, particularly tumor spheroids. Here, we show that by using a mechanically robust agent-based model constructed with the peridynamic framework, we gain a better understanding of residual stresses in multicellular systems as they grow from a single cell. In particular, we focus on small populations of cells (1–100 s) where population behavior is highly stochastic and prior investigation has been limited. We compare the average strain energy density of cells in monolayers and spheroids using different growth and division rules and find that, on average, cells in spheroids have a higher strain energy density than cells in monolayers. We also find that cells in the interior of a growing spheroid are, on average, in compression. Finally, we demonstrate the importance of accounting for stochastic fluctuations in the mechanical environment, particularly when the cellular response to mechanical cues is nonlinear. The results presented here serve as a starting point for both further investigation with agent-based models, and for the incorporation of major findings from agent-based models into continuum scale models when explicit representation of individual cells is not computationally feasible.
KeywordsPeridynamics Tumor growth Morphogenesis Cell division
Mathematics Subject Classification92C10 74L15
We would like to thank Claudia Vasquez, Andrew Price, Vipul Vachharajani, and Alex Dunn for the stimulating discussions and helpful comments.
Funding This work was supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-114747.
Compliance with ethical standards
Conflicts of interest
The authors declare that they have no conflict of interest.
- Hertwig O (1884) Investigations on the morphology and physiology of the cell: the problem of fertilization and isotropy of the egg, a theory of heredity, vol 3. FischerGoogle Scholar
- Jagiella N, Müller B, Müller M, Vignon-Clementel I, Drasdo D (2016) Inferring growth control mechanisms in growing multi-cellular spheroids of nsclc cells from spatial-temporal image data. PLoS Comput Biol 12(2):1004,412Google Scholar
- Keyomarsi K, Sandoval L, Band V, Pardee A (1991) Synchronization of tumor and normal cells from g1 to multiple cell cycles by lovastatin. Cancer Res 51(13):3602–3609Google Scholar
- Lejeune E, Linder C (2017a) Modeling tumor growth with peridynamics. Biomech Model Mechanobiol 1–17Google Scholar
- Littlewood D (2015) Roadmap for peridynamic software implementation. SAND Report, Sandia National Laboratories, Albuquerque, NM and Livermore, CAGoogle Scholar
- Oterkus S (2015) Peridynamics for the solution of multiphysics problems. PhD thesis, The University of ArizonaGoogle Scholar
- Stylianopoulos T (2017) The solid mechanics of cancer and strategies for improved therapy. J Biomech Eng 139(2):021,004Google Scholar
- Stylianopoulos T, Martin J, Chauhan V, Jain S, Diop-Frimpong B, Bardeesy N, Smith B, Ferrone C, Hornicek F, Boucher Y, Munn L (2012) Causes, consequences, and remedies for growth-induced solid stress in murine and human tumors. Proc Natl Acad Sci 109(38):15101–15108.Google Scholar
- Su Y, Chiang P, Cheng L, Lee C, Swami N, Chou C (2015) High aspect ratio nanoimprinted grooves of poly (lactic-co-glycolic acid) control the length and direction of retraction fibers during fibroblast cell division. Biointerphases 10(4):041,008Google Scholar
- Vavourakis V, Wijeratne P, Shipley R, Loizidou M, Stylianopoulos T, Hawkes D (2017) A validated multiscale in-silico model for mechano-sensitive tumour angiogenesis and growth. PLoS Comput Biol 13(1):e1005,259Google Scholar