Oxygen in the Tumor Microenvironment: Mathematical and Numerical Modeling

  • Edoardo MilottiEmail author
  • Thierry Fredrich
  • Roberto Chignola
  • Heiko Rieger
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 1259)


There are many reasons to try to achieve a good grasp of the distribution of oxygen in the tumor microenvironment. The lack of oxygen – hypoxia – is a main actor in the evolution of tumors and in their growth and appears to be just as important in tumor invasion and metastasis. Mathematical models of the distribution of oxygen in tumors which are based on reaction-diffusion equations provide partial but qualitatively significant descriptions of the measured oxygen concentrations in the tumor microenvironment, especially when they incorporate important elements of the blood vessel network such as the blood vessel size and spatial distribution and the pulsation of local pressure due to blood circulation. Here, we review our mathematical and numerical approaches to the distribution of oxygen that yield insights both on the role of the distribution of blood vessel density and size and on the fluctuations of blood pressure.


Tumor hypoxia Microcirculation Tumor angiogenesis Tumor growth Tumor metabolism Tumor hemodynamics Tumor cords Tumor heterogeneity Mathematical modeling Computer modeling Numerical simulations Lattice-free models Cell-based tumor models Radiation therapy Darwinian evolution in tumors 


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Edoardo Milotti
    • 1
    Email author
  • Thierry Fredrich
    • 2
  • Roberto Chignola
    • 3
  • Heiko Rieger
    • 2
  1. 1.Department of PhysicsUniversity of TriesteTriesteItaly
  2. 2.Center for Biophysics & FB Theoretical PhysicsSaarland UniversitySaarbrückenGermany
  3. 3.Department of BiotechnologyUniversity of VeronaVeronaItaly

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