=Paper= {{Paper |id=Vol-1159/paper1 |storemode=property |title=Mathematical models on cancer progression |pdfUrl=https://ceur-ws.org/Vol-1159/paper1.pdf |volume=Vol-1159 |dblpUrl=https://dblp.org/rec/conf/apn/Beccuti14 }} ==Mathematical models on cancer progression== https://ceur-ws.org/Vol-1159/paper1.pdf 
    Mathematical models on cancer progression

                                        Marco Beccuti

                              Università degli Studi di Torino,
                             Dipartimento di Informatica, Italy
                                    beccuti@di.unito.it



    Abstract. The Cancer Stem Cell (CSC) involvement into tumor progression,
tumor recurrence, and therapy resistance is one of the most studied subject of
current cancer research [10,4,8,6]. Nevertheless, due to the complex dynamics
characterizing the CSC tumor, a comprehensive theory has not been established
yet. To this end, some advises can be obtained combining mathematical modeling
and experimental data [5,9,2,7]. Indeed, mathematical modeling is a powerful
instrument which may drive the comprehension of a biological system, providing
a clear description of its essential dynamics.
    The aim of this talk is hence to show how the CSC tumor growth could be de-
scribed/studied through the application of mathematical models. In details two
different modeling approaches are presented: the former one consists in a mul-
tilevel/multiscale model [1], which details both molecular and cellular aspects.
By means of this framework we were able to reproduce the tumor growth trend
observed in mice, highlighting the strong connection existing between cellular
events and cell population dynamics. We were also able to reproduce molecular
vaccinations, correctly miming the in vivo vaccinations in animals. However, this
detailed approach can engender difficulties in the parameter estimation process
when only few kinetic information is available.
    The second contribution [3] was designed really to address this complexity
issue. We defined a new compartmental mathematical framework only focusing
on the cell subpopulation dynamics. Indeed, the aim of this work was to describe
CSC tumor progression trying to identify its essential mechanisms at population
level. Through a quantitative and qualitative analysis of our model was hence
possible to define rules controlling the breast cancer progression.
    Lastly, we point out that the CSC theory is applicable to several other human
cancers. Therefore, being our two model based on the key dynamics of the CSC
theory, they can be further adapted for the study of many other tumor cases
too.

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M. Heiner (Ed.): BioPPN 2014, a satellite event of PETRI NETS 2014,
CEUR Workshop Proceedings Vol. 1159, 2014.
2                                    M. Beccuti

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                 Proc. BioPPN 2014, a satellite event of PETRI NETS 2014