Mathematical Modelling as a Tool to Understand Cell Self-renewal and Differentiation

  • Philipp GettoEmail author
  • Anna Marciniak-Czochra
Part of the Methods in Molecular Biology book series (MIMB, volume 1293)


Mathematical modeling is a powerful technique to address key questions and paradigms in a variety of complex biological systems and can provide quantitative insights into cell kinetics, fate determination and development of cell populations. The chapter is devoted to a review of modeling of the dynamics of stem cell-initiated systems using mathematical methods of ordinary differential equations. Some basic concepts and tools for cell population dynamics are summarized and presented as a gentle introduction to non-mathematicians. The models take into account different plausible mechanisms regulating homeostasis. Two mathematical frameworks are proposed reflecting, respectively, a discrete (punctuated by division events) and a continuous character of transitions between differentiation stages. Advantages and constraints of the mathematical approaches are presented on examples of models of blood systems and compared to patients data on healthy hematopoiesis.

Key words

Mathematical model Population dynamics Structured population models Stem cell dynamics Ordinary differential equation 



PG was supported by the German Research Council (DFG) and the Spanish Ministry of Economy and Competitiveness under project MTM 2010-18318. AM-C was supported by the Collaborative Research Center, SFB 873 “Maintenance and Differentiation of Stem Cells in Development and Disease.” The authors would like to thank Thomas Stiehl and Marcel Mohr for help in preparation of figures.


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Copyright information

© Springer Science+Business Media LLC New York 2015

Authors and Affiliations

  1. 1.TU Dresden, Fachrichtung MathematikInstitut für AnalysisDresdenGermany
  2. 2.Basque Center for Applied Mathematics (BCAM)BilbaoSpain
  3. 3.Heidelberg University, Institute of Applied MathematicsInterdisciplinary Center for Scientific Computing and BIOQUANTHeidelbergGermany

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