SVIBOR - Papers quoted in CC - project code: 1-01-254

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Papers quoted in Current Contents on project 1-01-254


Quoted papers: 8
Other papers: 12
Total: 20


Title: Modeling Autostimulation of Growth in Multicellular Tumor Spheroids

Authors:
Marućiš, Miljenko (125056)
Bajzer, Željko
Freyer, J.
Vuk-Pavloviš, Stanimir
Journal: International Journal of Biomedical Computing
Number: 29
Year: 1991
Pages: from 149 to 158
Language: engleski

Title: Modeling Hormone-Dependent Cell-Cell Interactions in Tumor Growth: a Simulation Study

Authors:
Marućiš, Miljenko (125056)
Bajzer, Željko
Vuk-Pavloviš, Stanimir
Journal: Periodicum Biologorum
Number: 93
Year: 1991
Pages: from 649 to 656
Language: engleski

Title: Generalized Two-Parameter Equation of Growth

Authors:
Marućiš, Miljenko (125056)
Bajzer, Željko
Journal: Journal of Mathematical Analysis and Applications
Number: 2
Volume: 179
Year: 1993
Pages: from 446 to 462
Number of references: 24
Language: engleski
Summary: We considered the general growth equation $y'=ayČšĐalphać+byČšĐbetać$ that encompasses the well-known growth equations by Bertalanffy and Verhulst-Pearl (logistic) as special cases. The solutions of this equation for some values of $Đalpha$ and/or $Đbeta$ can be found in the literature. Here we present the general solution, for any real $Đalpha$ and $Đbeta$, and discuss its behavior. We found that the generalized Gompertz growth equation $y'=ayČšĐać+ byČšĐać Đln y$ and its solution could be considered a limiting case of the general growth equation and its solution, respectively. Thus, all three classical growth models (Bertalanffy, logistic and Gompertz) are nested within the general model. This nesting relationship makes it possible to compare statistically the applicability of models to data.

Title: Analysis of Growth of Multicellular Tumor Spheroids by Mathematical Models

Authors:
Marućiš, Miljenko (125056)
Bajzer, Željko
Freyer, J.
Vuk-Pavloviš, Stanimir
Journal: Cell Proliferations
Number: 27
Year: 1994
Pages: from 73 to 94
Language: engleski
Summary: We wished to determine the applicability of previously proposed deterministic mathematical models to description of growth of multicellular tumor spheroids. The models were placed into three general classes: empirical, functional and structural. From these classes, seventeen models were applied systematically to growth curves of multicellular tumor spheroids used as paradigms of prevascular and microregional tumor 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 fifteen measured growth curves, each corresponding to a different cell line. The classical growth models such as 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 then 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.

Title: Tumor Growth in vivo and as Multicellular Spheroids Compared by Mathematical Models

Authors:
Marućiš, Miljenko (125056)
Bajzer, Željko
Vuk-Pavloviš, Stanimir
Freyer, J.
Journal: Bulletin of Mathematical Biology
Number: 56
Year: 1994
Pages: from 617 to 631
Language: engleski
Summary: 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 simpler model than needed for description of growth in vivo. The model that explicitly included the stimulatory role for cell-cell interactions in regulation of growth was always superior to the 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 application of the proper 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.


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