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Modeling Spatial Effects in Carcinogenesis: Stochastic and Deterministic Reaction-Diffusion Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Conservation Laws in Cancer Modeling

Authors : Antonio Fasano, Alessandro Bertuzzi, Carmela Sinisgalli

Published in: Mathematical Oncology 2013

Publisher: Springer New York

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Abstract

We review mathematical models of tumor growth based on conservation laws in the full system of cells and interstitial liquid. First we deal with tumor cords evolving in axisymmetric geometry, where cells motion is simply passive and compatible with the saturation condition. The model is characterized by the presence of free boundaries with constraints driving the free boundary conditions, which in our opinion are particularly important, especially in the presence of treatments. Then a tumor spheroid is considered in the framework of the so-called two-fluid scheme. In a multicellular spheroid, on the appearance of a fully degraded necrotic core, the analysis of mechanical stresses becomes necessary to determine the motion via momentum balance, requiring the specification of the constitutive law for the “cell fluid.” We have chosen a Bingham-type law that presents considerable difficulties because of the presence of a yield stress, particularly with reference to the determination of an asymptotic configuration. Finally, we report some recent PDE-based models addressing complex processes in multicomponent tumors, more oriented to clinical practice.

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previous chapter Modeling Spatial Effects in Carcinogenesis: Stochastic and Deterministic Reaction-Diffusion
next chapter Avascular Tumor Growth Modelling: Physical Insights to Skin Cancer
Footnotes
1
Some authors adopt the extreme view point that proliferation takes place only at the tumor surface because of contact inhibition (e.g., [17]) and then migrate, driven by the surface curvature. Here we stick to the experimental observation that in the tumors we are talking about proliferation occurs in the tumor mass, whenever enough oxygen is available.
 
2
Here we neglect osmotic pressure.
 
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Metadata
Title
Conservation Laws in Cancer Modeling
Authors
Antonio Fasano
Alessandro Bertuzzi
Carmela Sinisgalli
Copyright Year
2014
Publisher
Springer New York
Book
Mathematical Oncology 2013

Print ISBN: 978-1-4939-0457-0

Electronic ISBN: 978-1-4939-0458-7

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-1-4939-0458-7_2

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