Fractal Analysis: A Novel Method to Assess Roughness Organization of Implant Surface Topography

Surface roughness is important for implant osseointegration. It has mostly been assessed by amplitude and height descriptors. Fractal analysis is derived from fractal geometry and is used to describe the organization of objects found in nature, quantifying their shape complexity with a value. Fractal dimension (Df ) is an index of the space-filling properties of an object and can be used as a parameter that describes the organization of surface roughness. The greater the Df value, the more chaotic the surface topography. The aim of this study was to assess the Df of implants with three different surface topographies to evaluate whether a novel method to measure roughness of implant surface topography could be developed. Forty-five disk-shaped samples (10 × 2 mm) with three different surface topographies were analyzed by scanning electron microscopy: group A, machined surface; group B, sandblasted and acid-etched surface; and group C, sandblasted, acid-etched, and neutralized surface. Images at 20,000× and 50,000× magnification were processed for quantitative analysis of Df using the box-counting method. Df values were correlated to the image magnification. At 20,000× magnification, Df for groups A, B, and C was 1.81, 1.67, and 1.59, respectively. At 50,000× magnification, Df was lower for all examined groups; more specifically, Df was 1.77, 1.59, and 1.42 for groups A, B, and C, respectively. Statistically significant differences were found between groups A and C at both magnifications. Df is used widely and successfully as a measurement to characterize anatomical structures and physiologic and pathologic processes. Df not only provides an index of roughness size values, but also a measure of roughness spatial organization; therefore, it could be a promising method to differentiate between rough surfaces capable of supporting osseointegration.