A new method to calculate the fractal dimension of surfaces: application to human cell proliferation

This paper presents a new method of calculating the fractal dimension of surfaces as well as a correction method which improved the results. To test its efficiency, the algorithms have been applied to stochastic surfaces of mathematical functions with known fractal dimensions and compared with the oscillation and the structure method. Better results have been found. This method, called ANAM, has been used to characterize the roughness of orthopaedic metallic substrates (Ti6A14V alloy) in relation with human osteoblast adhesion. It has then been shown that the fratal dimension parameters correlated statistically with proliferation of cells, corresponding to a lower adhesion on less organized surfaces. The significant correlation observed between fractal dimension parameters and cell adhesion therefore adds a new concept to substratum roughness influence on cell behaviour.