Properties of Tumor Spheroid Growth Exhibited by Simple Mathematical Models
Open accessAbstract
Solid tumors, whether in vitro or in vivo, are not an undifferentiated mass of cells. They include necrotic regions, regions of cells that are in a quiescent state (either slowly growing or not growing at all), and regions where cells proliferate rapidly. The decision of a cell to become quiescent or proliferating is thought to depend on both nutrient and oxygen availability and on the presence of tumor necrosis factor, a substance produced by necrotic cells that somehow inhibits the further growth of the tumor. Several different models have been suggested for the basic growth rate of in vitro tumor spheroids, and several different mechanisms are possible by which tumor necrosis factor might halt growth. The models predict the trajectory of growth for a virtual tumor, including proportions of the various components during its time evolution. In this paper we look at a range of hypotheses about basic rates tumor growth and the role of tumor necrotic factor, and determine what possible tumor growth patterns follow from each of twenty-five reasonable models. Proliferating, quiescent and necrotic cells are included, along with tumor necrosis factor as a potential inhibitor of growth in the proliferating pool and two way exchange between the quiescent and proliferating pools. We show that a range of observed qualitative properties of in vitro tumor spheroids at equilibrium are exhibited by one particular simple mathematical model, and discuss implications of this model for tumor growth.
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The occurrence of the zone of senescence supports the suggestion that necrotic cells arise as quiescent cells die.
“The occurrence of this zone of senescence lends support to the suggestion that necrotic cells arising as quiescent cells die as noted by previous studies [51].”
From Direct Measurements of Oxygen Gradients in Spheroid Culture System Using Electron Parametric Resonance Oximetry (2016) · cites this paper as [51]
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- Authors
- Wallace, D. I., & Guo, X.
- Affiliations
- Dartmouth College (US)
- Corresponding author
- Wallace, Dorothy I.
- ORCID
- Wallace, Dorothy I.
- Venue
- Frontiers in Oncology
- Publisher
- Frontiers Media SA
- Published
- 2013
- Volume
- 3
- Pages
- 51-51
- ISSN
- 2234-943X (ISSN-L)
- PMC
- PMC3598098
- OpenAlex
- W1982782313
- Cited by
- 77
- References
- 1
- Citations by year
- 2026: 5 · 2025: 5 · 2024: 2 · 2023: 5 · 2022: 6 · 2021: 18 · 2020: 4 · 2019: 7 · 2018: 8 · 2017: 4 · 2016: 5 · 2015: 5 · 2014: 2 · 2013: 1
- FWCI
- 4.51
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- cc-by
- Locations
- Frontiers in Oncology (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Topics
- Physical Sciences › Mathematics › Modeling and Simulation › Mathematical Biology Tumor Growth
- Health Sciences › Medicine › Oncology › Cancer Cells and Metastasis
- Health Sciences › Medicine › Public Health, Environmental and Occupational Health › Mathematical and Theoretical Epidemiology and Ecology Models
- Keywords
- tumor spheroids, solid tumor growth, TNF-α, quiescent cells, cell proliferation, growth inhibition
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