Multifractal spectrum and lacunarity as measures of complexity of osseointegration
- 242 Downloads
The goal of this study is to contribute to a better quantitative description of the early stages of osseointegration, by application of fractal, multifractal, and lacunarity analysis.
Materials and methods
Fractal, multifractal, and lacunarity analysis are performed on scanning electron microscopy (SEM) images of titanium implants that were first subjected to different treatment combinations of i) sand blasting, ii) acid etching, and iii) exposition to calcium phosphate, and were then submersed in a simulated body fluid (SBF) for 30 days. All the three numerical techniques are applied to the implant SEM images before and after SBF immersion, in order to provide a comprehensive set of common quantitative descriptors.
It is found that implants subjected to different physicochemical treatments before submersion in SBF exhibit a rather similar level of complexity, while the great variety of crystal forms after SBF submersion reveals rather different quantitative measures (reflecting complexity), for different treatments. In particular, it is found that acid treatment, in most combinations with the other considered treatments, leads to a higher fractal dimension (more uniform distribution of crystals), lower lacunarity (lesser variation in gap sizes), and narrowing of the multifractal spectrum (smaller fluctuations on different scales).
The current quantitative description has shown the capacity to capture the main features of complex images of implant surfaces, for several different treatments. Such quantitative description should provide a fundamental tool for future large scale systematic studies, considering the large variety of possible implant treatments and their combinations.
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.
KeywordsDental implants Osseointegration Fractal dimension Multifractal spectrum Lacunarity
This work is supported by research grants from CNPq, CAPES and FACEPE (Brazilian research agencies), and MINCYT (Argentinean Ministry of Science, Technology and Productive Innovation).
Compliance with ethical standards
Conflict of interest
The authors declare that they have no competing interests.
- 11.dos Santos LCB, Carvalho AAT, Leao JC, Duarte-Neto PJ, Stosic T, Stosic B (2015) Fractal measure and microscopic modeling of osseointegration. Int J Prosthodont Restor Dent; accepted for publicationGoogle Scholar
- 12.Perotti V, Aprile G, Degidi M, Piatelli A, Lezzi G (2011) Fractal analysis: a novel method to assess roughness organization of implant surface topography. Int J Prosthodont Restor Dent 31:633–639Google Scholar
- 13.Lezzi G, Aprile G, Tripodi D, Scarano A, Piatelli A, Perotti V (2012) Implant surface topographies analyzed using fractal dimension. Implant Dent 20:131–138Google Scholar
- 15.Mandelbrot BB (1982) The fractal geomeytry of nature. Freeman, San FranciscoGoogle Scholar
- 21.L. Seuront, Fractals and multifractals in ecology and aquatic science, Taylor & Francis 2009, 400pGoogle Scholar
- 22.Lovejoy S, Schertzer D (2007) Scale, scaling and multifractals in geophysics: twenty years on. Nonlinear dynamics in Geosciences, Ed. A.A. Tsonis, J. Elsner, Springer, 311-337Google Scholar