title: Multifractal spectrum and lacunarity as measures of complexity of osseointegration.
abstract: OBJECTIVE
  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.
  
  
  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.
  
  
  RESULTS
  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).
  
  
  CONCLUSIONS
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Departamento de Física, Universidade Federal Rural de Pernambuco, Rua Dom Manoel de Medeiros s/n, Dois Irmãos, 52171-900, Recife, PE, Brazil.
authors.forename: Daniel
authors.initials: D
authors.lastname: de Souza Santos
authors.affiliation: Departamento de Clínica e Odontologia Preventiva, Universidade Federal de Pernambuco, Av. Prof. Moraes Rego 1235, 50670-901, Recife, PE, Brazil.
authors.forename: Leonardo Cavalcanti Bezerra
authors.initials: LC
authors.lastname: Dos Santos
authors.affiliation: Departamento de Clínica e Odontologia Preventiva, Universidade Federal de Pernambuco, Av. Prof. Moraes Rego 1235, 50670-901, Recife, PE, Brazil.
authors.forename: Alessandra
authors.initials: A
authors.lastname: de Albuquerque Tavares Carvalho
authors.affiliation: Departamento de Clínica e Odontologia Preventiva, Universidade Federal de Pernambuco, Av. Prof. Moraes Rego 1235, 50670-901, Recife, PE, Brazil.
authors.forename: Jair Carneiro
authors.initials: JC
authors.lastname: Leão
authors.affiliation: Departamento de Ingeniería Eléctrica y de Computadoras, Universidad Nacional del Sur, B8000FWB, Bahía Blanca, Argentina.
authors.forename: Claudio
authors.initials: C
authors.lastname: Delrieux
authors.affiliation: Departamento de Estatística e Informática, Universidade Federal Rural de Pernambuco, Rua Dom Manoel de Medeiros s/n, Dois Irmãos, 52171-900, Recife, PE, Brazil.
authors.forename: Tatijana
authors.initials: T
authors.lastname: Stosic
authors.affiliation: Departamento de Estatística e Informática, Universidade Federal Rural de Pernambuco, Rua Dom Manoel de Medeiros s/n, Dois Irmãos, 52171-900, Recife, PE, Brazil. borko@pq.cnpq.br.
authors.forename: Borko
authors.initials: B
authors.lastname: Stosic
mesh_terms: D000134:Acid Etching, Dental; D002130:Calcium Phosphates / Q000737:chemistry; D003758:Dental Implantation, Endosseous; D015921:Dental Implants; D003775:Dental Polishing / Q000379:methods; D017709:Fractals; D008855:Microscopy, Electron, Scanning; D016348:Osseointegration / Q000502:physiology*; D013499:Surface Properties; D014025:Titanium / Q000737:chemistry
chemical_list: D002130:Calcium Phosphates; D015921:Dental Implants; C020243:calcium phosphate; D014025:Titanium
keywords: Dental implants; Fractal dimension; Lacunarity; Multifractal spectrum; Osseointegration