On the relationship between common amplitude surface roughness parameters and surface area: Implications for the study of cell–material interactions

In order to show that surface area is not always a quantity proportional to the surface roughness, we have constructed simple surfaces consisting of boxes of the same height equally spaced, and rms roughness and surface area have been computed. We have shown how we can get examples of surface configurations for which an increment in the surface roughness corresponds to a decrease in the surface area, although this is observed only for surfaces having similar rms roughness. We have also shown that even in the more intuitive situations where an increase in the surface roughness leads to an increase in the surface area, this increase is not necessarily equivalent. Analogous conclusions have been found when roughness was evaluated through the average roughness. These results could be interesting when analyzing interfacial phenomena such as cell adhesion, especially from a microscopic point of view, where the exact contact area between interacting phases governs these phenomena, and an exact-as-possible approximation to its real value is desirable. Also, the results of this paper could be of interest in various biomedical applications where the modulation of material surface-by-surface roughness may play a significant role. It can be concluded that care should be taken when using roughness parameters as estimators or indicators of the contact area between phases, since the relationship is not always simple.