Tumor growthin vivo and as multicellular spheroids compared by mathematical models
Abstract
In vivo volume growth of two murine tumor cell lines was compared by mathematical modeling to their volume growth as multicellular spheroids. Fourteen deterministic mathematical models were studied. For one cell line, spheroid growth could be described by a model simpler than needed for description of growth in vivo. A model that explicitly included the stimulatory role for cell-cell interactions in regulation of growth was always superior to a model that did not include such a role. The von Bertalanffy model and the logistic model could not fit the data; this result contradicted some previous literature and was found to depend on the applied least squares fitting method. By the use of a particularly designed mathematical method, qualitative differences were discriminated from quantitative differences in growth dynamics of the same cells cultivated in two different three-dimensional systems.
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The standard Gompertz curve could not be distinguished from actual growth curves within the margin of error of the experimental data.
“The authors concluded that the standard Gompertz curve [29], defined as could not be distinguished from the actual growth curves within the margin of error of the experimental data.”
From When the Optimal Is Not the Best: Parameter Estimation in Complex Biological Models (2010) · cites this paper as [13]
Cites
Gompertz, B. (1825) · Philosophical Transactions of the Royal Society of London · doi:10.1098/rstl.1825.0026 · Cited by 3,816 · see citing works
Analysis of growth of multicellular tumour spheroids by mathematical models.
Marušić, M., Bajzer, Ž., Freyer, J. P., & Vuk‐Pavlović, S. (1994) · Cell Proliferation · doi:10.1111/j.1365-2184.1994.tb01407.x · Cited by 203 · see citing works
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Spheroid-based drug screen: Considerations and practical approach
Friedrich, J., Seidel, C., Ebner, R., & Kunz-Schughart, L. A. (2009) · Nature Protocols · doi:10.1038/nprot.2008.226 · Cited by 1,742 · see citing works
A reliable tool to determine cell viability in complex 3-d culture: the acid phosphatase assay
Friedrich, J., Eder, W., Castaneda, J., Doss, M., Huber, E., Ebner, R., & Kunz-Schughart, L. A. (2007) · SLAS DISCOVERY · doi:10.1177/1087057107306839 · Cited by 227 · see citing works
Eissing, T. (2011) · Frontiers in Physiology · doi:10.3389/fphys.2011.00004 · Cited by 204 · see citing works
When the Optimal Is Not the Best: Parameter Estimation in Complex Biological Models
Fernández Slezak, D., Suárez, C., Cecchi, G. A., Marshall, G., & Stolovitzky, G. (2010) · PLoS ONE · doi:10.1371/journal.pone.0013283 · Cited by 57 · see citing works
“We generated synthetic growth data from a Gompertz model that was previously shown [13,14] to follow very closely experimental volume growth data with values of a ~ 7 : 6 , b ~{ 12 and c ~{ 0 : 121 .”
Method
- Authors
- Marušic, M., Bajzer, Ž., Vuk-Pavlovic, S., & Freyer, J. P.
- Affiliations
- Mayo Clinic (US)
- Los Alamos National Laboratory (US)
- Venue
- Bulletin of Mathematical Biology
- Published
- 1994-07
- Volume
- 56
- Issue
- 4
- Pages
- 617-631
- ISSN
- 0092-8240 (ISSN-L)
- 1522-9602
- OpenAlex
- W1965889901
- Cited by
- 99
- References
- 2
- Citations by year
- 2025: 4 · 2024: 1 · 2022: 4 · 2021: 3 · 2020: 6 · 2019: 3 · 2018: 3 · 2017: 3 · 2016: 2 · 2015: 2 · 2014: 7 · 2013: 1 · 2012: 3
- FWCI
- 2.40
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Bulletin of Mathematical Biology (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Institutes of Health (5r29ca045312-04, 5r01ca036535-03)
- National Cancer Institute (CA45312, CA-22585, CA-36535)
- 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 growth, multicellular spheroids, in vivo tumor growth, cell-cell interactions, von Bertalanffy model, logistic growth model, least squares fitting, 3D cell culture, murine tumor cell lines, growth dynamics
- MeSH terms
- Animals, Cell Division, Colonic Neoplasms, Female, Kinetics, Mammary Neoplasms, Experimental, Mathematics, Models, Biological, Time Factors, Tumor Cells, Cultured, Mice
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