Multifractal spectrum and lacunarity as measures of complexity of osseointegration

Abstract

Quantitative description of early stages of osseointegration on titanium implants with different treatments should help develop a better understanding of this phenomenon, in general, and provide basis for further systematic experimental studies. Clinical practice should benefit from such studies in the long term, by more ready access to implants of higher quality.

A “best fit” approach for synergistic surface parameters to guide the design of candidate implant surfaces

“…A combination of FD and lacunarity analyses has been shown to improve the recognition of textures in images from several databases . Indeed, lacunarity and FD have been used to assess the changes in the trabecular bone from dental radiographs to observe healing process following dental implant placement and the structural changes of trabecular bone in osteoporosis . We have added porosity to this synergistic group of parameters.…”

“…Furthermore, importantly, they found no correlation between FD and surface roughness . More recently, de Souza Santos et al employed both FD and lacunarity to monitor change in the surface patterns of blasted and acid etched titanium dental implants after submersion in simulated body fluid (SBF). They concluded that acid treatment and SBF immersion created the most complex and lowest lacunarity surfaces of those studied .…”

“…More recently, de Souza Santos et al employed both FD and lacunarity to monitor change in the surface patterns of blasted and acid etched titanium dental implants after submersion in simulated body fluid (SBF). They concluded that acid treatment and SBF immersion created the most complex and lowest lacunarity surfaces of those studied . However, in neither study did the authors relate the measured parameters to biological performance, although both mentioned a potential relevance to osseointegration.…”

Radiographic texture of the trabecular bone of the proximal phalanx in horses with metacarpophalangeal osteoarthritis

“…FD serves as a potent image texture descriptor, quantifying object complexity, with elevated values signifying more complex structures [ 7 , 12 , 19 , 22 , 37 , 41 ]. However, given that distinct fractal objects may exhibit identical FDs, lacunarity is employed to augment FD, offering insights into image heterogeneity [ 8 , 15 , 38 ] by evaluating the spatial arrangement of voids, hence elucidating the pixel distribution and organization, essentially quantifying space occupancy [ 3 , 15 ]. Homogeneous objects display low lacunarity with consistent gap sizes, whereas heterogeneous entities demonstrate high lacunarity [ 43 ].…”