WIAS Preprint No. 988, (2004)

Experimental and mathematical study of the influence of growth factors and the kinetics of adult human articular chondrocytes


  • Barbero, Andrea
  • Palumberi, Viviana
  • Wagner, Barbara
  • Sader, Robert
  • Grote, Markus J.
  • Martin, Ivan

2010 Mathematics Subject Classification

  • 92D25 92C37


  • chondrocytes, cell expansion, growth kinetics, delay model


This study aimed at determining how kinetic parameters of adult human articular chondrocytes (AHAC) growth are modulated by the growth factor combination underline TGF$beta$1, underline FGF-2, and underline PDGF BB (TFP), recently shown to stimulate AHAC proliferation. AHAC, isolated from cartilage biopsies of three individuals, were cultured in medium without (CTR) or with TFP. For growth curves, AHAC were seeded at 1000 cells/cm$^2$ and cultured for 12 days, with cell numbers measured fluorimetrically in the same wells every 12 hours. For microcolony tests, AHAC were seeded at 2.5 cells/cm$^2$ and cultured for 6 days, with cell numbers determined for each microcolony by phase contrast microscopy every 8 hours. A mathematical model combining delay and logistic equations was developed to capture the growth kinetic parameters and to enable the description of the complete growth process of the cell culture. As compared to CTR medium, the presence of TFP increased the number of cells/well starting from the fifth day of culture, and a 4-fold larger cell number was reached at confluency. For single microcolonies, TFP reduced the time for the first cell division by 26.6%, the time for subsequent cell divisions (generation time) by 16.8%, and the percentage of quiescent cells by 42.5%. The mathematical model fitted well the experimental data of the growth kinetic. Finally, using both microcolony tests and the mathematical model, we determined that prolonged cell expansion induces an enrichment of AHAC with shorter first division time, but not of those with shorter generation time.

Appeared in

  • J. Cellular Physiology, 204 (2005) pp. 830--838.

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