SVIBOR - Papers quoted in CC - project code: 1-01-254
### MINISTRY OF SCIENCE AND TECHNOLOGY

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## SVIBOR - Collecting Data on Projects in Croatia

### 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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