Modeling Growth of Tumors and Their Spreading Behavior Using Mathematical Functions

  • Bertin Hoffmann
  • Thorsten Frenzel
  • Rüdiger Schmitz
  • Udo Schumacher
  • Gero WedemannEmail author
Part of the Methods in Molecular Biology book series (MIMB, volume 1878)


Computer simulations of the spread of malignant tumor cells in an entire organism provide important insights into the mechanisms of metastatic progression. Key elements for the usefulness of these models are the adequate selection of appropriate mathematical models describing the tumor growth and its parametrization as well as a proper choice of the fractal dimension of the blood vessels in the primary tumor. In addition, survival in the bloodstream and evasion into the connective spaces of the target organ of the future metastasis have to be modeled. Determination of these from experimental models is complicated by systematic and unsystematic experimental errors which are difficult to assess. In this chapter, we demonstrate how to select the best-suited mathematical function to describe tumor growth for experimental xenograft mouse tumor models and how to parametrize them. Common pitfalls and problems are described as well as methods to avoid them.

Key words

Tumor growth Metastatic progression Spreading behavior Mathematical model Parametrization 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Bertin Hoffmann
    • 1
  • Thorsten Frenzel
    • 2
  • Rüdiger Schmitz
    • 2
  • Udo Schumacher
    • 2
  • Gero Wedemann
    • 1
    Email author
  1. 1.Competence Center Bioinformatics, Institute for Applied Computer ScienceUniversity of Applied Sciences StralsundStralsundGermany
  2. 2.Institute for Anatomy and Experimental MorphologyUniversity Cancer Center Hamburg-EppendorfHamburgGermany

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