## 2 Materials and Methods
### Data Collection  
The peri-implant marginal radiographic bone loss (MBL) was determined at TB (baseline) and at latest follow-up examination TF (final) by taking linear measurements (DB-SWIN, DURR DENTAL(r)) from the most mesial and distal point of each implant platform to the crestal bone on each intraoral periapical radiograph positioned on a Rinn angularo using a long-cone parallel technique. Characterization of the peri-implantitis defect morphology was classified on radiographs as follows: Class I: infra-osseous defect, Class II: supra-crestal /horizontal defect, and Class III: combined defect [25]. Our collected radiographic data were analysed as a percentage rate at implant and patient levels. Our study was conducted in accordance with the Helsinki declaration of studies on humans. Before participation, each patient was given a detailed description of the procedure and was required to sign an informed consent form. Once the diagnosis of peri-implantitis had been made, all patients received a de novo personalized oral hygiene instruction to change hygiene, and behavioural and professional prophylactic supragingival cleaning (Figure 1). Non-surgical therapy phase consisted in sub-gingival debridement of the peri-implant pocket using specific titanium ultrasonic device (Implant Protect, Satelec Acteon(r) Merignac, France) 4 to 6 weeks before the surgical procedure. If necessary, modification of the prosthesis design was made until it was satisfactory. When possible, screw-retained prostheses were removed to improve access to the contaminated surfaces and repositioned at the end of the surgery, allowing non-submerged healing of all the treated implants. All surgical procedures were performed under local anaesthesia (Articadent Dentsply-Sirona(r) Charlotte, NC, USA 4% articaine with 1/100,000 adrenalaine) by the same surgeon (AB). Intrasulcular incisions were made using a microsurgical blade (MJK Instrument(r), Marseille, France) and extended one tooth on both sides of the treated implant(s). When necessary, vertical releasing incisions were made to allow better direct access to the peri-implant defect. Full-thickness flaps were raised, and granulation tissue and hard depositswere removed using titanium curettes (IMEDIMPLM, Hu-Friedy(r), Chicago, IL, USA) and an ultrasonic titanium device (Implant Protect, Satelec Acteon(r)). All the contaminated implant surface accessible to the burs was treated by implantoplasty with a tungsten carbide bur (red H379 and white H379 UF, biconvex and conical form, implantoplasty kit, Komet(r) Paris, France), using abundant sterile saline solution irrigation with a red contra-angle. Mechanical decontamination was completed using titanium NiTbrushes (ICT Micro and ICT Nano, [PERSON](r) Gyeonggi-do, South Korea) and airflow with glycine powder (Air-N-Go(r) PERIO Acteon(r) Merignac, France) [26; 27]. Chemical decontamination was carried out with 2 min rinses of chlorhexiidine (0.12%) [28; 29]. After these decontamination procedures, the surgical sites were profusely irrigated with sterile saline solution to remove residual titanium particles (Figure 2). Figure 1: Therapeutic flow-chart. Depending on the defect morphology, the surgical design/approach was chosen among three different modalities (Figures 3-5) before beginning the surgical procedure. Figure 4: Implantoplasty for reconstructive treatment of peri-implantitis. Figure 3: Implantoplasty for non-osseous treatment of peri-implantitis. Figure 2: Surgical steps for decontamination of implant surface affected by peri-implantitis. All the infra-osseous defects were filled with xenograft (Symbios Xenograft, Dentsply-Sirona(r) Charlotte, NC, USA) or alloplastic (Symbios Biphasic, Dentsply-Sirona(r)), when the patient refused the animal origin's graft and when it was necessary to stabilize bone-filling materials, covered by a resorbable membrane (Creos Xenoprotect, Nobel Biocare(r) Kloten, Switzerland or Ossix Plus, Datum Dental(r) Lod, Israel).