Tumor growth in vivo and as multicellular spheroids compared by mathematical models

Miljenko Marušic, Željko Bajzer, Stanimir Vuk-Pavlovic, James P. Freyer

Research output: Contribution to journalArticle

77 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)617-631
Number of pages15
JournalBulletin of Mathematical Biology
Volume56
Issue number4
DOIs
StatePublished - Jul 1994

Fingerprint

Cellular Spheroids
Tumor Growth
tumor
Tumors
Theoretical Models
mathematical models
Mathematical Model
Mathematical models
neoplasms
Cell
Volume Growth
Growth
Neoplasms
cell lines
cells
logit analysis
qualitative analysis
Qualitative Methods
Least Square Fitting
Cells

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)

Cite this

Tumor growth in vivo and as multicellular spheroids compared by mathematical models. / Marušic, Miljenko; Bajzer, Željko; Vuk-Pavlovic, Stanimir; Freyer, James P.

In: Bulletin of Mathematical Biology, Vol. 56, No. 4, 07.1994, p. 617-631.

Research output: Contribution to journalArticle

Marušic, Miljenko ; Bajzer, Željko ; Vuk-Pavlovic, Stanimir ; Freyer, James P. / Tumor growth in vivo and as multicellular spheroids compared by mathematical models. In: Bulletin of Mathematical Biology. 1994 ; Vol. 56, No. 4. pp. 617-631.
@article{1d911a82dddf4dd08cb3f42bdfa7b449,
title = "Tumor growth in 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.",
author = "Miljenko Marušic and Željko Bajzer and Stanimir Vuk-Pavlovic and Freyer, {James P.}",
year = "1994",
month = "7",
doi = "10.1007/BF02460714",
language = "English (US)",
volume = "56",
pages = "617--631",
journal = "Bulletin of Mathematical Biology",
issn = "0092-8240",
publisher = "Springer New York",
number = "4",

}

TY - JOUR

T1 - Tumor growth in vivo and as multicellular spheroids compared by mathematical models

AU - Marušic, Miljenko

AU - Bajzer, Željko

AU - Vuk-Pavlovic, Stanimir

AU - Freyer, James P.

PY - 1994/7

Y1 - 1994/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0028467454&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028467454&partnerID=8YFLogxK

U2 - 10.1007/BF02460714

DO - 10.1007/BF02460714

M3 - Article

C2 - 8054889

AN - SCOPUS:0028467454

VL - 56

SP - 617

EP - 631

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

SN - 0092-8240

IS - 4

ER -