An incompletely understood question in the field of biomaterials is how eucaryotic cells adhere on material surfaces. The adhesion of cells on materials is generally studied after some hours. Because this evaluation after some hours cannot let us presume about the future of the cells on the material, we have developed a culture model that does allow study in the long term of an elaborate cell/material interface closer to the in vivo situation. For that, we used a progressive trypsin-based detachment method. Here we report on the mathematical modeling of long-term human primary osteoblastic cell adhesion on metallic substrates, which allows us to quantify the real adhesion simultaneously by taking into account the effect of cell proliferation. A time-dependent adhesion index t(d) is proposed, which varies with culture time t according to the power law: t(d)(t) = at(b), a being independent of b. The exponent b is equal to 0.5 +/- 0.03 and is independent of the substrate's characteristics, meaning that the long-term adhesion increases proportionally to the square root of culture time. On the contrary, the parameter a significantly depends on the material's nature, the surface's topography, and the surface chemistry of the substrate and is sufficient to characterize cell adhesion. From this relationship, we suggest that a diffusion-based process related to the kinetic of formation of extracellular matrix should be involved in long-term adhesion on materials.
(c) 2005 Wiley Periodicals, Inc.