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Mathematical Modeling of Tumor Growth Kinetics


Bajzer, Željko; Vuk-Pavlović, Stanimir; Huzak, Miljenko
Mathematical Modeling of Tumor Growth Kinetics // A Survey of Models for Tumor-Immune System Dynamics / Adam, John A ; Bellomo, Nicola (ur.).
Boston: Birkhauser, 1997. str. 89-133


Naslov
Mathematical Modeling of Tumor Growth Kinetics

Autori
Bajzer, Željko ; Vuk-Pavlović, Stanimir ; Huzak, Miljenko

Vrsta, podvrsta i kategorija rada
Poglavlja u knjigama, znanstveni

Knjiga
A Survey of Models for Tumor-Immune System Dynamics

Urednik/ci
Adam, John A ; Bellomo, Nicola

Izdavač
Birkhauser

Grad
Boston

Godina
1997

Raspon stranica
89-133

Sažetak
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 modellers 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekt / tema
037008

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb