Novel fractal characteristic of atomic force microscopy images

Fractal dimension (D_F) is one of the important parameters in the description of object's properties in different fields including biology and medicine. The present paper is focused on the application of the fractal dimension (the box counting dimension) in the analysis of the properties of cell surface on the base of its images obtained by atomic force microscopy (AFM). Fractal dimension of digital 3D AFM images depends on interpoint distances determined by the scanning step in the XY-plane and Z-scale factor t. We have studied the dependence of D_F of AFM images on the Z-scale factor (D_F=φ(t)) with purpose to reveal the features of the dependence and its usefulness in the analysis of the maps of surface properties. Using the model digital surfaces such as the plane, sinusoidal surfaces and "hilly" surface, we revealed that the sizes and spatial frequency of surface structural elements determined the basic features of the dependence (the parameters of peaks on the curve D_F=φ(t)) and the element of chance in the localization of the structural elements on the surface had no significant influence on the dependence. Our findings demonstrate that the dependence of the fractal dimension on the Z-scale factor characterizes the structure of the AFM images more comprehensively than the roughness R_a and fractal dimension D_F evaluated at a certain t. The dependence D_F=φ(t) can be considered as a novel characteristic of AFM images. On analyzing the AFM images (lateral force maps) of glutaraldehyde-fixed adhered human fibroblasts and A549 human lung epithelial cells we found the significant difference in the dependences D_F=φ(t) for different cell types that could be related to the difference of structural and mechanical surface properties of the studied cells.