WIAS Preprint No. 1557, (2010)

Dynamic formation of oriented patches in chondrocyte cell cultures


  • Grote, Marcus
  • Palumberi, Viviana
  • Wagner, Barbara
  • Barbero, Andrea
  • Martin, Ivan

2010 Mathematics Subject Classification

  • 35R09 92C17 35B36 35B35


  • cell alignment, pattern formation, stability, integro-partial differential equations, image processing


Growth factors have a significant impact not only on the growth dynamics but also on the phenotype of chondrocytes (Barbero et al. , J. Cell. Phys. 204, pp. 830-838, 2005). In particular, as chondrocyte populations approach confluence, the cells tend to align and form coherent patches. Starting from a mathematical model for fibroblast populations at equilibrium (Mogilner et al., Physica D 89, pp. 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.

Appeared in

  • J. Math. Biol., 63 (2011) pp. 757--777.

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