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Conservation Laws in Cancer Modeling

  • Antonio FasanoEmail author
  • Alessandro Bertuzzi
  • Carmela Sinisgalli
Chapter
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)

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.

Keywords

Conservation laws Cancer modeling Tumor cords Tumor spheroids Multicomponent tumors 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Antonio Fasano
    • 1
    • 2
    Email author
  • Alessandro Bertuzzi
    • 2
  • Carmela Sinisgalli
    • 2
  1. 1.Dipartimento di Matematica “U. Dini”Universita’ di FirenzeFirenzeItaly
  2. 2.Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti” - CNRRomaItaly

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