Multifractal spectrum and lacunarity as measures of complexity of osseointegration

DANIEL DE SOUZA SANTOS, LEONARDO CAVALCANTI BEZERRA DOS SANTOS, ALESSANDRA DE ALBUQUERQUE TAVARES CARVALHO, JAIR CARNEIRO LEÃO, CLAUDIO DELRIEUX, TATIJANA STOSIC, BORKO STOSIC

CLINICAL ORAL INVESTIGATIONS.

SPRINGER HEIDELBERG

Lugar: HEIDELBERG; Año: 2016 vol. 20 p. 1271 - 1278

1432-6981

Objectives: The goal of thisstudy is to contribute to a better quantitative description of the early stagesof osseointegration, by application of fractal, multifractal and lacunarity analysis.Materials and methods: Fractal, multifractal, and lacunarity analysis are performed on scanning electronmicroscopy (SEM) images of titanium implants that were first subjected todifferent treatment combinations of i) sand blasting, ii) acid etching and iii)exposition to calcium phosphate, and were then submersed in a simulated bodyfluid (SBF) for thirty days. All the three numerical techniques are applied tothe implant SEM images before and after SBF immersion, in order to provide acomprehensive set of common quantitative descriptors.Results: It is foundthat implants subjected to different physicochemical treatments before submersionin SBF exhibit a rather similar level of complexity, while the great variety ofcrystal forms after SBF submersion reveals rather different quantitativemeasures (reflecting complexity), for different treatments. In particular, itis found that acid treatment, in most combinations with the other consideredtreatments, leads to a higher fractal dimension (more uniform distribution ofcrystals), lower lacunarity (lesser variation in gap sizes), and to narrowingthe multifractal spectrum (smaller fluctuations on different scales).Conclusion: The current quantitative description has shown the capacity to capture the main features ofcomplex images of implant surfaces, for several different treatments. Suchquantitative description should provide a fundamental tool for future largescale systematic studies, considering the large variety of possible implanttreatments and their combinations.Clinical relevance: 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 basisfor further systematic experimental studies. Clinical practice should benefitfrom such studies in the long term, by more ready access to implants of higherquality.