In silico estimates of the free energy rates in growing tumor spheroids
Open accessAbstract
The physics of solid tumor growth can be considered at three distinct size scales: the tumor scale, the cell-extracellular matrix (ECM) scale and the sub-cellular scale. In this paper we consider the tumor scale in the interest of eventually developing a system-level understanding of the progression of cancer. At this scale, cell populations and chemical species are best treated as concentration fields that vary with time and space. The cells have chemo-mechanical interactions with each other and with the ECM, consume glucose and oxygen that are transported through the tumor, and create chemical by-products. We present a continuum mathematical model for the biochemical dynamics and mechanics that govern tumor growth. The biochemical dynamics and mechanics also engender free energy changes that serve as universal measures for comparison of these processes. Within our mathematical framework we therefore consider the free energy inequality, which arises from the first and second laws of thermodynamics. With the model we compute preliminary estimates of the free energy rates of a growing tumor in its pre-vascular stage by using currently available data from single cells and multicellular tumor spheroids.
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Scratch assays have been miniaturized and mechanized, making them compatible with high-throughput screening.
“Scratch assays have been miniaturized and mechanized, making them compatible with high-throughput screening45,46.”
From Inference of weak-form partial differential equations describing migration and proliferation mechanisms in wound healing experiments on cancer cells (2025) · cites this paper as [45]
The Experimental methods section (pp. 8–9) describes growing and imaging tumor spheroids in hydrogels, not scratch assays. Searches for miniaturized or mechanized scratch assays and high-throughput wound-healing screening found no passage in our copy addressing the claim. (LLM, conf=0.76)
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Biomechanics and biophysics of cancer cells☆
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Cancer cells compress intratumour vessels
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Research works printed but not linked: 3
- Chang S F, Chang C A, Lee D-Y, Lee P-L, Yeh Y-M, Yeh C-R, Cheng C-K, Chien S, Chen J J 2008 Tumor cell cycle arrest induced by shear stress: Roles of integrins and Smad Proc. Nat. Acad. Sci. 105 3927-32.
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Srivastava, S., Kinnunen, P. C., Wang, Z., Ho, K. K. Y., Humphries, B. A., Chen, S., Linderman, J. J., Luker, G. D., Luker, K. E., & Garikipati, K. (2025) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1013607 · Cited by 5 · see citing works
“The treatment of cell migration via continuum PDEs is well established in biophysics [45– 47], as is the role of cell arrangement in determining aspects of the progression of cancers [48].”
Self-citation
- Authors
- Narayanan, H., Verner, S. N., Mills, K. L., Kemkemer, R., & Garikipati, K.
- Affiliations
- Simula Research Laboratory (NO)
- University of Michigan (US)
- Max Planck Society (DE)
- Corresponding author
- Garikipati, K
- Venue
- Journal of Physics: Condensed Matter
- Publisher
- IOP Publishing
- Published
- 2010-04-26
- Volume
- 22
- Issue
- 19
- Pages
- 194122
- ISSN
- 0953-8984 (ISSN-L)
- 1361-648X
- OpenAlex
- W2004423354
- Cited by
- 31
- References
- 4
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 3 · 2021: 1 · 2020: 3 · 2019: 1 · 2018: 1 · 2017: 1 · 2016: 1 · 2015: 2 · 2014: 4 · 2013: 4 · 2012: 3
- FWCI
- 4.11
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Physics Condensed Matter (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Max Planck Institute for Plasma Physics (submittedVersion)
- Max Planck Digital Library (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Mathematics › Modeling and Simulation › Mathematical Biology Tumor Growth
- Health Sciences › Medicine › Oncology › Cancer Cells and Metastasis
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Cell Biology › Cellular Mechanics and Interactions
- Keywords
- tumor growth, tumor spheroids, continuum model, extracellular matrix, tumor progression
- MeSH terms
- Animals, Computer Simulation, Energy Metabolism, Humans, Models, Biological, Tumor Cells, Cultured, Spheroids, Cellular, Cell Proliferation
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