Conceptual frameworks for mathematical modeling of tumor growth dynamics

Ž Bajzer, M. Marušić, S. Vuk-Pavlović

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

The paper discusses the applicability of some empirical and functional mathematical models of tumor growth to multicell tumor spheroids which are a three-dimensional experimental paradigm of prevascular tumors. A new mathematical model based on receptor-mediated regulation of growth is developed and tested and two additional functional models (autostimulation, competing populations) are analyzed. It is demonstrated that these models, defined by two autonomous differential equations, can describe spontaneous tumor regression. The concept of tumor magnification factor, a quantifier of positive feedback mechanisms, is elaborated.

Original languageEnglish (US)
Pages (from-to)31-46
Number of pages16
JournalMathematical and Computer Modelling
Volume23
Issue number6
StatePublished - 1996

Fingerprint

Tumor Growth
Mathematical Modeling
Tumors
Tumor
Functional Model
Mathematical Model
Positive Feedback
Mathematical models
Quantifiers
Receptor
Regression
Paradigm
Model-based
Differential equation
Differential equations
Three-dimensional
Framework
Mathematical modeling
Conceptual framework
Feedback

Keywords

  • Mathematical models
  • Multicell tumor spheroids
  • Tumor growth
  • Tumor magnification factor
  • Tumor regression

ASJC Scopus subject areas

  • Information Systems and Management
  • Control and Systems Engineering
  • Applied Mathematics
  • Computational Mathematics
  • Modeling and Simulation

Cite this

Bajzer, Ž., Marušić, M., & Vuk-Pavlović, S. (1996). Conceptual frameworks for mathematical modeling of tumor growth dynamics. Mathematical and Computer Modelling, 23(6), 31-46.

Conceptual frameworks for mathematical modeling of tumor growth dynamics. / Bajzer, Ž; Marušić, M.; Vuk-Pavlović, S.

In: Mathematical and Computer Modelling, Vol. 23, No. 6, 1996, p. 31-46.

Research output: Contribution to journalArticle

Bajzer, Ž, Marušić, M & Vuk-Pavlović, S 1996, 'Conceptual frameworks for mathematical modeling of tumor growth dynamics', Mathematical and Computer Modelling, vol. 23, no. 6, pp. 31-46.
Bajzer, Ž ; Marušić, M. ; Vuk-Pavlović, S. / Conceptual frameworks for mathematical modeling of tumor growth dynamics. In: Mathematical and Computer Modelling. 1996 ; Vol. 23, No. 6. pp. 31-46.
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