Mathematical Modeling of Tumor Growth Kinetics

  • Ž. Bajzer
  • S. Vuk-Pavlović
  • M. Huzak
Part of the Modeling and Simulation in Science, Engineering, & Technology book series (MSSET)


The overall goal of this survey is to develop and present a coherent and integrated interpretation of mathematical models which describe tumor growth. Rigorous description and quantitative understanding of tumor growth kinetics have been a focus of mathematical modelers for more than five decades. Consequently, many models have been proposed, ranging from conceptually and mathematically simple empirical models to complex “functional” models which include kinetics of the cell cycle, cell-cell interactions, cell age distribution, microenvironmental factors, etc. However, these models have been seldom validated against experimental tumor growth curves, largely because of the relative scarcity of appropriate data. On the other hand, contemporary experimental techniques increase the prospects for obtaining high quality data. With this in mind, we summarize the pertinent deterministic models of tumor growth kinetics with special emphasis on model scrutiny against experimental data. Prominent among these models is the Gompertz model which has been remarkably successful in description of growth curves for various tumors. The biological interpretation of this model, originally developed as an actuarial curve, remains unclear and we summarize the relevant interpretations of this model. Also, we discuss two other similarly simple models, the logistic model and the von Bertalanffy model, and then present models of increasing complexity which include elements of the cell cycle and cell-cell interactions. Within the typical kinetic paradigm, these models are based on systems of ordinary differential equations. However, we also consider models defined by partial differential equations which involve age and time.


Tumor Growth Quiescent Cell Growth Fraction Gompertz Model Tumor Growth Curve 
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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Ž. Bajzer
    • 1
  • S. Vuk-Pavlović
    • 1
  • M. Huzak
    • 2
  1. 1.Mayo Clinic and Mayo FoundationRochesterUSA
  2. 2.University of ZagrebZagrebCroatia

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