Journal of Mathematical Biology

, Volume 63, Issue 4, pp 757–777 | Cite as

Dynamic formation of oriented patches in chondrocyte cell cultures

  • Marcus J. GroteEmail author
  • Viviana Palumberi
  • Barbara Wagner
  • Andrea Barbero
  • Ivan Martin


Growth factors have a significant impact not only on the growth dynamics but also on the phenotype of chondrocytes (Barbero et al. in J. Cell. Phys. 204:830–838, 2005). In particular, as chondrocytes approach confluence, the cells tend to align and form coherent patches. Starting from a mathematical model for fibroblast populations at equilibrium (Mogilner et al. in Physica D 89:346–367, 1996), a dynamic continuum model with logistic growth is developed. Both linear stability analysis and numerical solutions of the time-dependent nonlinear integro-partial differential equation are used to identify the key parameters that lead to pattern formation in the model. The numerical results are compared quantitatively to experimental data by extracting statistical information on orientation, density and patch size through Gabor filters.


Cell alignment Pattern formation Stability Integro-partial differential equations Image processing 

Mathematics Subject Classification (2000)

92C17 92D25 92-08 65M06 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Marcus J. Grote
    • 1
    Email author
  • Viviana Palumberi
    • 1
  • Barbara Wagner
    • 2
  • Andrea Barbero
    • 3
  • Ivan Martin
    • 3
  1. 1.Institute of MathematicsBaselSwitzerland
  2. 2.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany
  3. 3.Department of BiomedicineUniversity HospitalBaselSwitzerland

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