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10 mm, screw-shaped) and Locatorattachment systems (Zest Anchors, Escondido, CA, USA;diameter: 3.85 mm, length: 3.85 mm) were chosen as over-denture retainers for this biomechanical analysis. The three-dimensional geometries of the edentulous mandible andprosthetic components were modelled in SolidWorks 2008(SolidWorks Corporation, Ve ´ lizy-Villacoublay, France).The geometries of the mandible, overdenture, implant andattachment systems were then meshed using Abaqus 6.8(Simulia Corporation, Ve ´ lizy-Villacoublay, France). Four 3D FEmodels of an edentulous mandible supporting an implantoverdenture were designed (Fig. 1), each with differentnumbers of implants in the anterior area of mandible betweenthe mental foramina. All implants were vertically positionedand well distributed in the interforaminal region, at least6 mm mesial to the mental foramen, as follows: Model A, a single implant was located in the midline of thejaw. Model B, the overdenture was retained by two implants20 mm apart. Model C, the overdenture was retained by three implantswith the central one in the midline of the jaw and other twoa distance of 18 mm to either side. Model D, the overdenture was retained by four implants12 mm apart.The models were meshed with 3D four-node tetrahedronelements. The total numbers of elements and nodes are listedin Table 1. A refined mesh was generated in the interforaminalregion to faithfully reproduce the complex strain distributionobserved in peri-implant bone.2.2. Material propertiesThe edentulous jaw was composed of a 2-mm constantcortical bone layer around a cancellous bone core, covered by a2-mm thick mucosa. The Locator attachment system wascomposed of three parts: abutment, nylon replacement male and titanium cap. The abutment and cap were made ofTi6Al4V titanium alloy, as was the implant. The materialproperties of the cortical and cancellous bone, mucosa andprosthetic components were determined from valuesobtained from the literature (Table 2). All materials wereassumed to be isotropic, homogeneous and linearly elastic.2.3. Contact management and loading conditionsImplants were considered totally osseointegrated. Therefore,a mechanically perfect interface was presumed to existbetween implant and bone. However, the interface betweenthe overdenture and the mucosa was not fixed when function-ing. Instead, the overdenture was able to rotate and slide on themucosa in different directions. To simulate this displacement,we assumed that sliding friction existed between the over-denture and mucosa. The coefficient of sliding friction betweenthe overdenture and mucosa was set to be 0.334 in accordancewith previous experiments carried out by our team.27The models were constrained at the nodes on the mesial anddistal bone in all degrees of freedom. Three types of load wereapplied to the overdenture in each model to simulate functionalloading, namely 100 N vertical and inclined loads on the left firstmolar and 100 N vertical load on the lower incisors. To facilitatediscussion, the three loading conditions have been abbreviatedas VM, IM and VI for vertical load on the left first molar, inclinedload on the left first molar and vertical load on the lowerincisors, respectively. IM refers to a 45-8 angled force buccolin-gually applied at the centre of the left first molar.3. Results3.1. Strain distribution in peri-implant cortical boneMaximum equivalent strains in the cortical bone aroundimplant under three types of load for each model is shown inTable 3. Strain distributions in the peri-implant cortical boneof each model under three loading conditions are illustrated inFigs. 2–5. Under all three loading conditions, the maximumstrain values were below 2500 me in all models. In models A, Cand D, the peak strain values in the cortical bone showed anincreasing trend as the number of implants increased, and theTable 1 – Total number of elements and nodes.Elements NodesModel A 115,100 7080Model B 200,741 50,233Model C 273,726 67,399Model D 404,019 96,916Table 2 – Material properties.Young’smodulus (MPa)Poisson’sratioReferenceTi-6Al-4V 103,400 0.35 Sertgo ¨z andGu ¨ vener23Cortical bone 13,700 0.3 Barbier et al.24Cancellous bone