title: Peri-implantitis: a complex condition with non-linear characteristics.
abstract: OBJECTIVE
  To cluster peri-implantitis patients and explore non-linear patterns in peri-implant bone levels.
  
  
  METHODS
  Clinical and radiographic variables were retrieved from 94 implant-treated patients (340 implants, mean 7.1 ± 4.1 years in function). Kernel probability density estimations on patient mean peri-implant bone levels were used to identify patient clusters. Inter-relationships of all variables were evaluated by principal component analysis; a k-nearest neighbours method was performed for supervised prediction of implant bone levels at the patient level. Self-similar patterns of mean bone level per implant from different jaw bone sites were examined and their associated fractal dimensions were estimated.
  
  
  RESULTS
  Two clusters of implant-treated patients were identified, one at patient mean bone levels of 1.7 mm and another at 4.0 mm. Five of thirteen available variables (number of teeth, age, gender, periodontitis severity, years of implant service), were predictive for peri-implant bone levels. A high jaw bone fractal dimension was associated with less severe peri-implantitis.
  
  
  CONCLUSIONS
  Non-linearity of peri-implantitis was evidenced by finding different peri-implant bone levels between two main clusters of implant-treated patients and among six different jaw bone sites. The patient mean peri-implant bone levels were predicted from five variables and confirmed complexity for peri-implantitis.
authors.affiliation: Center for Research and Applications of Nonlinear Systems, Department of Mathematics, University of Patras, Patras, Greece.
authors.forename: Georgios
authors.initials: G
authors.lastname: Papantonopoulos
authors.affiliation: Technological Educational Institute of Epirus Department of Accounting and Finance, Preveza, Greece.
authors.forename: Christos
authors.initials: C
authors.lastname: Gogos
authors.affiliation: Computer Systems Laboratory, Department of Electrical and Computer Engineering, University of Patras, Patras, Greece.
authors.forename: Efthymios
authors.initials: E
authors.lastname: Housos
authors.affiliation: Laboratory of Nonlinear Systems and Applied Analysis, Department of Mathematics, University of Patras, Patras, Greece.
authors.forename: Tassos
authors.initials: T
authors.lastname: Bountis
authors.affiliation: Department of Periodontology, Academic Center for Dentistry Amsterdam (ACTA), University of Amsterdam and VU University, Amsterdam, The Netherlands.
authors.forename: Bruno G
authors.initials: BG
authors.lastname: Loos
keywords: complex disease; computational biology; data mining; dental implant; non-linearity; peri-implantitis; statistical learning theory