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Cited by 204Mathematical Biology Tumor GrowthCancer Cells and MetastasisMathematical and Theoretical Epidemiology and Ecology Models

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
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Abstract

We wished to determine the applicability of previously proposed deterministic mathematical models to description of growth of multicellular tumour spheroids. The models were placed into three general classes: empirical, functional and structural. From these classes, 17 models were applied systematically to growth curves of multicellular tumour spheroids used as paradigms of prevascular and microregional tumour growth. The spheroid growth curves were determined with uniquely high density of measurements and high precision. The theoretical growth curves obtained from the models were fitted by the weighted least-squares method to the 15 measured growth curves, each corresponding to a different cell line. The classical growth models such as von Bertalanffy, logistic and Gompertz were considered as nested within more general models. Our results demonstrate that most models fitted the data fairly well and that criteria other than statistical had to be used for final selection. The Gompertz, the autostimulation and the simple spheroid models were the most appropriate for spheroid growth in the empirical, functional and structural classes of models, respectively. We also showed that some models (e.g. logistic, von Bertalanffy) were clearly inadequate. Thus, contrary to the widely held belief, the sigmoid character of a three or more parameter growth function is not sufficient for adequate fits.

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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 [14]

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Authors
Marušić, M., Bajzer, Ž., Freyer, J. P., & Vuk‐Pavlović, S.
Affiliations
  • Mayo Clinic (US)
  • Los Alamos National Laboratory (US)
Corresponding author
Vuk‐Pavlović, S.
ORCID
Marušić, M.
Venue
Cell Proliferation
Publisher
Wiley
Published
1994-02
Volume
27
Issue
2
Pages
73-94
ISSN
  • 0960-7722 (ISSN-L)
  • 1365-2184
DOI
10.1111/j.1365-2184.1994.tb01407.x
OpenAlex
W2099998237
Cited by
203
References
39
Citations by year
2026: 6 · 2025: 5 · 2024: 3 · 2023: 8 · 2022: 4 · 2021: 8 · 2020: 11 · 2019: 4 · 2018: 4 · 2017: 9 · 2016: 8 · 2015: 4 · 2014: 8 · 2013: 10 · 2012: 8
FWCI
4.12
Type
journal article
Language
en
Open access
closed
Licence
onlinelibrary.wiley.com/termsAndConditions#vor (vor, 5203 d)
Locations
  • Cell Proliferation (publishedVersion)
  • PubMed (publishedVersion)
Funders
  • National Institutes of Health (5r29ca045312-04, 5r01ca051150-04)
  • National Cancer Institute (CA45312, CA51150)
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, tumor growth modeling, Gompertz model, von Bertalanffy model, logistic model, model selection, cell lines
MeSH terms
Cell Division, Humans, Models, Biological, Spheroids, Cellular

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