Advertisement
Journal of Prosthetic Dentistry

Implant-bone load transfer mechanisms in complete-arch prostheses supported by four implants: A three-dimensional finite element approach

      Statement of problem

      Complete-arch restorations supported by fewer than 5 dental implants can induce unbalanced load transfer and tissue overloading, leading to excessive bone resorption and possible clinical failure. This is primarily affected by the cantilever length, the implant design and positioning, and the morphology and properties of the bone.

      Purpose

      The purpose of this study was to compare 2 different restorative techniques for complete-arch rehabilitations supported by 4 implants. The primary purpose was to highlight the possible risks of excessive stress and unbalanced load transfer mechanisms and to identify the main biomechanical factors affecting loading transmission.

      Material and methods

      Three-dimensional (3D) numerical models of edentulous maxillae and mandibles restored with 2 techniques using 4 implants were generated from computed tomography (CT) images and analyzed with linear elastic finite-element simulations with 3 different static loads. The first technique used 2 vertical mesial implants and 2 tilted distal implants (at a 30 degree angle), and the second used vertical implants that fulfilled platform switching concepts. Bone-muscle interactions and temporomandibular joints were included in the mandibular model. Complete implant osseous integration was assumed and different posthealing crestal bone geometries were modeled. Stress measures (revealing risks of tissue overloading) and a performance index (highlighting the main features of the loading partition mechanisms) were introduced and computed to compare the 2 techniques.

      Results

      Dissimilar load transfer mechanisms of the 2 restorative approaches when applied in mandibular and maxillary models were modeled. Prostheses supported by distally tilted implants exhibited a more effective and uniform loading partition than all vertical implants, except in the simulated maxilla under a frontal load. Tilted distal implants reduced compressive states at distal bone-implant interfaces but, depending on bone morphology and loading type, could induce high tensile stresses at distal crests. Overloading risks on mesial periimplant bone decreased when the efficient preservation of the crestal bone through platform switching strategies was modeled.

      Conclusions

      Numerical simulations highlighted that the cantilever length, the implant design and positioning, and the bone's mechanical properties and morphology can affect both load transmission mechanisms and bone overloading risks in complete-arch restorations supported by 4 implants. Distally tilted implants induced better loading transmission than vertical implants, although the levels of computed stress were physiologically acceptable in both situations.
      Clinical Implications
      Within the limitations of this study, the biomechanical rationale for using tilted distal implants to reduce cantilever mechanisms was that, generally, they contributed to favorable load transmission and a low risk of compressive overloads.
      Currently, the complete-arch rehabilitation of edentulous jaws is achieved by threaded endosseous implants, and many protocols and guidelines are available to those in clinical practice.
      • Ganeles J
      • Rosenberg MM
      • Holt RL
      • Reichmann LH
      Immediate loading of implants with fixed restorations in the completely edentulous mandible: report of 27 patients from private practice.
      • Bocklage R
      Rehabilitation of the edentulous maxilla and mandible with fixed implant-supported restorations applying immediate functional loading: A treatment concept.
      Each technique is characterized by a specific healing period, and the success rate is influenced by patient-dependent morphological and biological conditions.
      • Drago CJ
      Rates of osseointegration of dental implants with regard to anatomical location.
      Poor bone quality and quantity in the molar regions, especially in edentulous individuals, means that complete-arch restorations generally require dental implants to be placed in the anterior region, often resulting in long cantilevered prostheses. The use of long posterior cantilevers can be directly related to the possible overloading of the periimplant regions.
      • Shackleton JL
      • Carr L
      • Slabbert JC
      • Becker PJ
      Survival of fixed implant-supported prostheses related to cantilever lengths.
      • White SN
      • Caputo AA
      • Anderkvist T
      Effect of cantilever length on stress transfer by implant-supported prostheses.
      • Sertgöz A
      • Güvener S
      Finite element analysis of the effect of cantilever and implant length on stress distribution in an implant-supported fixed prosthesis.
      Therefore, high stress concentrations at bone-implant interfaces may produce physiologically inadmissible strains which then activate biological bone resorption.
      • Irving JT
      Factors concerning bone loss associated with periodontal disease.
      • Carter DR
      • Van Der Meulen MC
      • Beaupré GS
      Mechanical factors in bone growth and development.
      • Guo XE
      Mechanical properties of cortical and cancellous bone tissue.
      Consequently, depending on implant geometry and placement,
      • Baggi L
      • Cappelloni I
      • Di Girolamo M
      • Maceri F
      • Vairo G
      The influence of implant diameter and length on stress distribution of osseointegrated implants related to crestal bone geometry: a three-dimensional finite element analysis.
      periimplant bone weakening/loss and cratering can occur, leading to possible implant failure.
      • Roos-Jansåker AM
      • Lindahl C
      • Renvert H
      • Renvert S
      Nine- to fourteen-year follow-up of implant treatment. Part I: implant loss and associations to various factors.
      • Romeo E
      • Chiapasco M
      • Ghisolfi M
      • Vogel G
      Long-term clinical effectiveness of oral implants in the treatment of partial edentulism. Seven-year life table analysis of a prospective study with ITI dental implants system used for single-tooth restorations.
      • Eckert SE
      • Wollan PC
      Retrospective review of 1170 endosseous implants placed in partially edentulous jaws.
      • Lekholm U
      • Gunne J
      • Henry P
      • Higuchi K
      • Lindén U
      • Bergström C
      • et al.
      Survival of the Brånemark implant in partially edentulous jaws: a 10-year prospective multicenter study.
      Clinical evidence suggests that the cratering phenomena can be limited when platform switching strategies are applied.
      • López-Marí L
      • Calvo-Guirado JL
      • Martín-Castellote B
      • Gomez-Moreno G
      • López-Marí M
      Implant platform switching concept: An updated review.
      • Lazzara RJ
      • Porter SS
      Platform switching: A new concept in implant dentistry for controlling postrestorative crestal bone levels.
      • Maeda Y
      • Miura J
      • Taki I
      • Sogo M
      Biomechanical analysis on platform switching: is there any biomechanical rationale?.
      Recently, restorative systems using tilted distal implants have been proposed
      • Krekmanov L
      • Kahn M
      • Rangert B
      • Lindström H
      Tilting of posterior mandibular and maxillary implants for improved prosthesis support.
      • Aparicio C
      • Perales P
      • Rangert B
      Tilted implants as an alternative to maxillary sinus grafting: a clinical, radiologic, and periotest study.
      • Calandriello R
      • Tomatis M
      Simplified treatment of the atrophic posterior maxilla via immediate/early function and tilted implants: A prospective 1-year clinical study.
      • Capelli M
      • Zuffetti F
      • Del Fabbro M
      • Testori T
      Immediate rehabilitation of the completely edentulous jaw with fixed prostheses supported by either upright or tilted implants: a multicenter clinical study.
      • Testori T
      • Del Fabbro M
      • Capelli M
      • Zuffetti F
      • Francetti L
      • Weinstein RL
      Immediate occlusal loading and tilted implants for the rehabilitation of the atrophic edentulous maxilla: 1-year interim result of a multicenter prospective study.
      • Del Fabbro M
      • Bellini CM
      • Romeo D
      • Francetti L
      Tilted implants for the rehabilitation of edentulous jaws: A systematic review.
      to reduce the posterior cantilever.
      Currently, 2 of the most commonly used systems for complete-arch immediate loading rehabilitation of edentulous jaws are based on the All-on-4 (Nobel Biocare AB, Göteborg, Sweden) and SynCone (Dentsply Friadent, Mannheim, Germany) concepts.
      • Ferreira EJ
      • Kuabara MR
      • Gulinelli JL
      “All-on-four” concept and immediate loading for simultaneous rehabilitation of the atrophic maxilla and mandible with conventional and zygomatic implants.
      • Romanos GE
      Present status of immediate loading of oral implants.
      • Eccellente T
      • Piombino M
      • Piattelli A
      • Perrotti V
      • Iezzi G
      A new treatment concept for immediate loading of implants inserted in the edentulous mandible.
      Both systems use threaded implants placed in the anterior region and allow the rehabilitation of 12 to 14 teeth per arch. The All-on-4 protocol is based on 2 vertical mesial implants and 2 tilted distal implants, distally angled with respect to the vertical direction of between 30 and 45 degrees. In this treatment, implants are crestally positioned, and significant cratering effects generally occur. When the SynCone protocol is applied, implants are all vertical and are designed and positioned following platform switching concepts. Accordingly, a significant reduction of crestal bone loss is expected, but when implants are placed in the anterior region, a longer posterior cantilever is generally needed for complete-arch rehabilitations. The clinical effectiveness and reliability of these techniques have been examined in a number of recent studies showing the results of both in vivo and follow-up analyses.
      • Ferreira EJ
      • Kuabara MR
      • Gulinelli JL
      “All-on-four” concept and immediate loading for simultaneous rehabilitation of the atrophic maxilla and mandible with conventional and zygomatic implants.
      • Khatami AH
      • Smith CR
      “All-on-Four” immediate function concept and clinical report of treatment of an edentulous mandible with a fixed complete denture and milled titanium framework.
      • Maló P
      • Rangert B
      • Nobre M
      All-on-4 immediate-function concept with Brånemark System implants for completely edentulous maxillae: a 1-year retrospective clinical study.
      • Degidi M
      • Piattelli A
      A 7-year follow-up of 93 immediately loaded titanium dental implants.
      • Portmann M
      • Glauser R
      Report of a case receiving full-arch rehabilitation in both jaws using immediate implant loading protocols: a 1-year resonance frequency analysis follow-up.
      • Pomares C
      A retrospective study of edentulous patients rehabilitated according to the ‘all-on-four’ or the ‘all-on-six’ immediate function concept using flapless computer-guided implant surgery.
      Nevertheless, the in vivo assessment of stress and strain distributions in the bone is difficult in clinical practice.
      • Clelland NL
      • Gilat A
      • McGlumphy EA
      • Brantley WA
      A photoelastic and strain gauge analysis of angled abutments for an implant system.
      • Begg T
      • Geerts GA
      • Gryzagoridis J
      Stress patterns around distal angled implants in the all-on-four concept configuration.
      Therefore, a numeric approach able to evaluate stresses and strains induced in the periimplant regions could facilitate the control of those design parameters that affect load transfer and overloading risk, thereby optimizing the durability and effectiveness of the rehabilitation.
      Recently, finite element approaches have been used successfully in prosthetic dentistry to analyze the influence of mechanical and biological factors,
      • Baggi L
      • Cappelloni I
      • Di Girolamo M
      • Maceri F
      • Vairo G
      The influence of implant diameter and length on stress distribution of osseointegrated implants related to crestal bone geometry: a three-dimensional finite element analysis.
      • Baggi L
      • Cappelloni I
      • Maceri F
      • Vairo G
      Stress-based performance evaluation of osseointegrated dental implants.
      • Van Staden RC
      • Guan H
      • Loo YC
      Application of the finite element method in dental implant research.
      • Petrie CS
      • Williams JL
      Comparative evaluation of implant designs: influence of diameter, length, and taper on strains in the alveolar crest. A three-dimensional finite-element analysis.
      • Chun HJ
      • Shin HS
      • Han CH
      • Lee SH
      Influence of implant abutment type on stress distribution in bone under various loading conditions using finite element analysis.
      • Kitagawa T
      • Tanimoto Y
      • Nemoto K
      • Aida M
      Influence of cortical bone quality on stress distribution in bone around dental implant.
      and to improve many clinical treatments. Numerical studies have analyzed some effects of tilted implants and the influence of the posterior cantilever length.
      • Bevilacqua M
      • Tealdo T
      • Menini M
      • Pera F
      • Mossolov A
      • Drago C
      • et al.
      Three-dimensional finite element analysis of load transmission using different implant inclinations and cantilever lengths.
      • Bevilacqua M
      • Tealdo T
      • Menini M
      • Pera F
      • Mossolov A
      • Drago C
      • et al.
      The influence of cantilever length and implant inclination on stress distribution in maxillary implant-supported fixed dentures.
      Moreover, examples of All-on-4 applications have been simulated through simplified numerical models.
      • Bellini CM
      • Romeo D
      • Galbusera F
      • Agliardi E
      • Pietrabissa R
      • Zampelis A
      • et al.
      A finite element analysis of tilted versus non-tilted implant configurations in the edentulous maxilla.
      • Zampelis A
      • Rangert B
      • Heijl L
      Tilting of splinted implants for improved prosthodontic support: a two-dimensional finite element analysis.
      • Bonnet AS
      • Postaire M
      • Lipinski P
      Biomechanical study of mandible bone supporting a four-implant retained bridge: finite element analysis of the influence of bone anisotropy and foodstuff position.
      • Silva CG
      • Mendonça JA
      • Randazzo Lopez LR
      • Landre Jr, J
      Stress patterns on implants in prostheses supported by four or six implants: a three-dimensional finite element analysis.
      However, some biomechanical aspects related to cantilever and tilted implants are not completely understood.
      In this study, stress-based performances of complete-arch restorations supported by 4 implant using All-on-4 and SynCone concepts were investigated by means of a three-dimensional (3D) finite element (FE) approach. A numeric method able to analyze 3D patient-based models of restored jaws was developed and applied to compare the 2 techniques when used in edentulous jaws (both maxilla and mandible). The load transmission mechanisms and the risks of bone overloading were evaluated by using linear elastic static simulations that accounted for different posthealing crestal bone morphologies.

      Material and Methods

      Two different approaches to the rehabilitation of completely edentulous arches with endosseous implants placed in the anterior region were analyzed and compared. The first (denoted as A4) was based on the All-on-4 concept and used 4 NobelSpeedy Groovy implants (Nobel Biocare AB). The second (denoted as SC) applied the SynCone system with 4 Ankylos implants (Dentsply Friadent). The main geometric properties of trapezoidal-threaded implants used for defining numeric models relevant to SC and A4 (Fig. 1) are summarized in Table I. Both systems used 2 central implants (mesial) placed vertically and 2 lateral implants (distal). The distal implants were vertically placed in SC and distally tilted in A4 at a 30 degree angle in the plane orthogonal to the buccolingual direction. In A4 different abutments by Nobel Biocare (Multi-unit Abutments for vertical implants, 30 degree Multi-unit Abutments for tilted implants) were considered, and a fixed connection with the prosthetic bar was modeled. For Ankylos implants (SC) the abutments were modeled in accordance with the platform switching concepts, and the abutment-bar connection was assumed to be achieved by telescopic crowns.
      Figure thumbnail gr1
      Fig. 1Three-dimensional (3D) numerical models of both mandibular and maxillary jaws equipped with rehabilitative devices based on All-on-4 and SynCone concepts (c: cantilever length). Maxillary model was delimited in upper region by 2 planar cutting surfaces separated by nasal cavity. Prosthetic bar was modeled as 3 mm thick, 5 mm deep, and 65.8 mm long. Left: cyan colored regions (inner regions of jaw models) correspond to trabecular bone tissue; yellow colored regions (outer regions) correspond to compact bone.
      Table IMain geometrical parameters defining implants and rehabilitative techniques analyzed in this study (SC: SynCone-based; A4: All-on-4). When necessary, values in square brackets refer to mandibular model and values in round brackets refer to distal implants. Notation refers to Figure 2: l is implant length; d denotes implant maximum diameter; p is average thread pitch; t is average thread depth; L1 denotes distance between mesial implants (CL and CR, Fig. 2); L2 is distance between distal implants (L and R, Fig. 2); c is cantilever length
      l (mm)d (mm)p (mm)t (mm)L1 (mm)L2 (mm)c (mm)
      SC9.53.50.90.4512.0 [16.0]29.0 [31.0]15.0
      A411.5 (15.0)4.00.60.212.0 [16.0]35.0 [38.0]5.0
      Implant models were fitted into the models of complete bone arches, defined by disregarding gingival soft tissues and distinguishing cortical and trabecular bone regions (Fig. 1). In the mandible model, the articular disks of the temporomandibular joints were modeled with 2 thin regions mated with condyles. The maxilla was modeled by considering the maxilla process up to the cortical bone at the anterior-nasal-spine level (Fig. 1). The axes of mesial implants were identically placed in both SC and A4, and implant lengths were chosen such that the in bone depth was approximately 11 mm. Tilted distal implants in A4 were positioned such that their in-bone ends belonged to the vertical axes of the distal implants in SC (Fig. 2). Because of the different bone morphology, distances among implants in the mandible and maxilla were assumed to be different (Table I). The 4-implant-supported prosthetic bar was modeled by considering a pseudo-parabolic middle-line geometry (Fig. 1), and models of bar and abutments were arranged so that the bar-bone distance was 5 mm in all models. In a given jaw, the bar model was the same for the 2 techniques, and a cantilever scheme 5 mm long for A4 and 15 mm for SC was chosen (Table I).
      Figure thumbnail gr2
      Fig. 2Implant positioning in maxillary (on left) and mandibular (on right) models. A, SynCone-based technique using Ankylos implants. B, All-on-4 technique using Nobel Biocare implants (ℓ: implant length; d: implant maximum diameter; p: average thread pitch; t: average thread depth; L1: distance between mesial implants; L2: distance between distal implants; L: left implant; CL: central-left implant; CR: central-right implant; R: right implant).
      To describe the physiological bone structure after a period of healing and function realistically, crestal bone geometries were adapted to match well-established clinical observations of crestal bone loss and remodeling (Fig. 3).
      • Baggi L
      • Cappelloni I
      • Di Girolamo M
      • Maceri F
      • Vairo G
      The influence of implant diameter and length on stress distribution of osseointegrated implants related to crestal bone geometry: a three-dimensional finite element analysis.
      • Degidi M
      • Piattelli A
      • Shibli JA
      • Strocchi R
      • Iezzi G
      Bone formation around a dental implant with a platform switching and another with a TissueCare Connection. A histologic and histomorphometric evaluation in man.
      • Abboud M
      • Koeck B
      • Stark H
      • Wahl G
      • Paillon R
      Immediate loading of single tooth implants in the posterior region.
      • Shin YK
      • Han CH
      • Heo SJ
      • Kim S
      • Chun HJ
      Radiographic evaluation of marginal bone level around implants with different neck designs after 1 year.
      For Nobel Biocare implants a cratering morphology with a mean crestal bone loss of about 45% in thickness was modeled. For Ankylos implants, because of the platform switching configuration and subcrestal positioning, a lower crestal bone loss (about 20% in thickness) and a bone layer apposition 0.3 mm thick were modeled.
      Figure thumbnail gr3
      Fig. 3Geometric modeling of posthealing crestal bone morphology in functioning implants. Comparison between local bone configurations obtained after virtual implant positioning (that is, obtained by merging implant and bone models) and posthealing models (depending on implant shape and placement) used for numerical simulations.
      Models of implants and prosthetic bars were developed by using a parametric computer-aided design (CAD) software (SolidWorks 9; Dassault Systemes, Concord, Mass), whereas 3D jaw models were reconstructed from computed tomography (CT) images by using a commercial tool (Mimics10.1; Materialise Dental NV, Leuven, Belgium) that allowed the identification of the cortical and trabecular bone regions (Fig. 1). Discrete FE meshes were generated by using 10-node quadratic tetrahedral elements with 3 degrees of freedom per node and were analyzed with a commercial code (ANSYS 11.0; ANSYS Inc, Canonsburg, Pa). As a result of a preliminary convergence analysis, the mean value of the mesh size was set to approximately 1 mm from the bone-implant interfaces and to approximately 0.2 mm at the periimplant regions (Fig. 1).
      Materials were assumed to have a linear elastic isotropic behavior (Table II),
      • Baggi L
      • Cappelloni I
      • Di Girolamo M
      • Maceri F
      • Vairo G
      The influence of implant diameter and length on stress distribution of osseointegrated implants related to crestal bone geometry: a three-dimensional finite element analysis.
      • Baggi L
      • Cappelloni I
      • Maceri F
      • Vairo G
      Stress-based performance evaluation of osseointegrated dental implants.
      • Lemon JE
      • Dietsh-Misch F
      Biomaterials for dental implants.
      • Natali AN
      • Hart RT
      • Pavan PG
      • Knets I
      Mechanics of bone tissue.
      • Beek M
      • Koolstra JH
      • Van Ruijven LJ
      • Van Eijden TMGJ
      Three-dimensional finite element analysis of the human temporomandibular joint disc.
      and all material volumes were considered as homogeneous. Mandibular tissues were approximated by a quality-II bone,
      • Lekholm U
      • Zarb GA
      Patient selection and preparation.
      and the maxillary trabecular bone was assumed to be less dense than that of the mandible, resulting in a smaller value of the Young modulus.
      • Natali AN
      • Hart RT
      • Pavan PG
      • Knets I
      Mechanics of bone tissue.
      Table IIElastic constants adopted for 3D finite element analyses (E: Young modulus, v: Poisson ratio)
      MaterialRegionE (GPa)v
      Titanium alloy
      • Baggi L
      • Cappelloni I
      • Maceri F
      • Vairo G
      Stress-based performance evaluation of osseointegrated dental implants.
      • Lemon JE
      • Dietsh-Misch F
      Biomaterials for dental implants.
      Implants114.00.34
      Gold alloy
      • Baggi L
      • Cappelloni I
      • Maceri F
      • Vairo G
      Stress-based performance evaluation of osseointegrated dental implants.
      • Lemon JE
      • Dietsh-Misch F
      Biomaterials for dental implants.
      Prosthetic bar105.00.23
      Cancellous bone
      • Baggi L
      • Cappelloni I
      • Di Girolamo M
      • Maceri F
      • Vairo G
      The influence of implant diameter and length on stress distribution of osseointegrated implants related to crestal bone geometry: a three-dimensional finite element analysis.
      • Natali AN
      • Hart RT
      • Pavan PG
      • Knets I
      Mechanics of bone tissue.
      Mandible1.00.3
      Maxilla0.50.3
      Cortical bone
      • Baggi L
      • Cappelloni I
      • Di Girolamo M
      • Maceri F
      • Vairo G
      The influence of implant diameter and length on stress distribution of osseointegrated implants related to crestal bone geometry: a three-dimensional finite element analysis.
      • Natali AN
      • Hart RT
      • Pavan PG
      • Knets I
      Mechanics of bone tissue.
      Mandible and maxilla13.70.3
      Soft tissue
      • Beek M
      • Koolstra JH
      • Van Ruijven LJ
      • Van Eijden TMGJ
      Three-dimensional finite element analysis of the human temporomandibular joint disc.
      Articular disks (Mandible)0.0060.4
      Displacement functions were assumed to be continuous at all possible interfaces among contiguous volumes, and the complete implant osseous integration was modeled accordingly. Models of the restored jaws were constrained by enforcing zero-displacement conditions for all nodes belonging to the upper surfaces of the articular disks in the mandible and for all nodes belonging to the virtual cutting surfaces in the maxilla (Fig. 1).
      Three different static loads were considered in the FE analyses. The first (Load 1) was a complete-mouth loading, defined as a uniformly distributed intrusive vertical load acting upon the free surface of the prosthetic bar and with a resultant value of 300 N. The second (Load 2) was a cantilever load, defined as a distal concentrated load applied at the end of the right cantilever, and the third (Load 3) was a frontal load, defined as a concentrated load applied at the midspan of the central part of the bar between mesial implants. The forces which defined Loads 2 and 3 consisted of an intrusive vertical component of 250 N and of a horizontal one (along the buccolingual direction) of 100 N. Muscular forces were included only in the mandibular model, accounting for masseter, temporalis, and internal pterygoid muscles.
      • Trainor PG
      • McLachlan KR
      • McCall WD
      Modelling of forces in the human masticatory system with optimization of the angulations of the joint loads.
      Depending on the loading type, the muscle-bone interactions were modeled for each muscle by considering a uniformly distributed load that acted upon the muscle-bone connection surface (Fig. 4, Table III).
      Figure thumbnail gr4
      Fig. 4Mandibular bone surfaces that modeled bone-muscle connection areas considered for muscular force distributions.
      Table IIIComponents of resultant muscular forces acting upon mandibular model, referred to Cartesian frame introduced in Figure 4 and to loading situa­tions under investigation.
      • Trainor PG
      • McLachlan KR
      • McCall WD
      Modelling of forces in the human masticatory system with optimization of the angulations of the joint loads.
      Values in (respectively, not in) parentheses indicate force components acting upon corresponding muscle-bone connection sur­faces at x > 0 (respectively, x < 0)
      MasseterTemporalisPterygoid
      Comp. Loadx (N)y (N)z (N)x (N)y (N)z (N)x (N)y (N)z (N)
      120.0 (−20.0)−31.8 (−31.8)82.8 (82.8)9.7 (−9.7)19.4 (19.4)77.8 (77.8)−20.6 (20.6)−12.5 (−12.5)35.7 (35.7)
      220.0 (−13.2)−31.8 (−21.0)82.8 (54.6)9.7 (−8.2)19.4 (16.3)77.8 (65.3)−20.6 (13.9)−12.5 (−8.4)35.7 (24.1)
      320.9 (−20.9)−33.3 (−33.3)86.6 (86.6)16.8 (−16.8)33.5 (33.5)134.1 (134.1)−19.0 (19.0)−11.4 (−11.4)32.8 (32.8)
      Jaw models treated by using SC and A4 were numerically compared by analyzing stress distributions at the simulated periimplant regions. The von Mises equivalent stress (σVM), often used in numerical dental studies,
      • Baggi L
      • Cappelloni I
      • Di Girolamo M
      • Maceri F
      • Vairo G
      The influence of implant diameter and length on stress distribution of osseointegrated implants related to crestal bone geometry: a three-dimensional finite element analysis.
      • Baggi L
      • Cappelloni I
      • Maceri F
      • Vairo G
      Stress-based performance evaluation of osseointegrated dental implants.
      • Van Staden RC
      • Guan H
      • Loo YC
      Application of the finite element method in dental implant research.
      • Petrie CS
      • Williams JL
      Comparative evaluation of implant designs: influence of diameter, length, and taper on strains in the alveolar crest. A three-dimensional finite-element analysis.
      • Chun HJ
      • Shin HS
      • Han CH
      • Lee SH
      Influence of implant abutment type on stress distribution in bone under various loading conditions using finite element analysis.
      • Kitagawa T
      • Tanimoto Y
      • Nemoto K
      • Aida M
      Influence of cortical bone quality on stress distribution in bone around dental implant.
      • Bevilacqua M
      • Tealdo T
      • Menini M
      • Pera F
      • Mossolov A
      • Drago C
      • et al.
      Three-dimensional finite element analysis of load transmission using different implant inclinations and cantilever lengths.
      • Bevilacqua M
      • Tealdo T
      • Menini M
      • Pera F
      • Mossolov A
      • Drago C
      • et al.
      The influence of cantilever length and implant inclination on stress distribution in maxillary implant-supported fixed dentures.
      • Bellini CM
      • Romeo D
      • Galbusera F
      • Agliardi E
      • Pietrabissa R
      • Zampelis A
      • et al.
      A finite element analysis of tilted versus non-tilted implant configurations in the edentulous maxilla.
      • Zampelis A
      • Rangert B
      • Heijl L
      Tilting of splinted implants for improved prosthodontic support: a two-dimensional finite element analysis.
      • Bonnet AS
      • Postaire M
      • Lipinski P
      Biomechanical study of mandible bone supporting a four-implant retained bridge: finite element analysis of the influence of bone anisotropy and foodstuff position.
      • Silva CG
      • Mendonça JA
      • Randazzo Lopez LR
      • Landre Jr, J
      Stress patterns on implants in prostheses supported by four or six implants: a three-dimensional finite element analysis.
      was used as a global stress indicator to characterize load transfer and partition mechanisms. Since the von Mises stress measure does not allow a distinction between tensile and compressive local stresses, more effective and direct indications of possible overloads were obtained by analyzing principal stress measures.
      • Baggi L
      • Cappelloni I
      • Di Girolamo M
      • Maceri F
      • Vairo G
      The influence of implant diameter and length on stress distribution of osseointegrated implants related to crestal bone geometry: a three-dimensional finite element analysis.
      • Baggi L
      • Cappelloni I
      • Maceri F
      • Vairo G
      Stress-based performance evaluation of osseointegrated dental implants.
      Accordingly, maximum compressive (σC) and maximum tensile (σT) principal stresses were used as local risk measures of bone-implant interfacial physiological failure or of the activation of the resorption process. Therefore, periimplant areas where σVM attains high mean values correspond to implants that transfer a great amount of the load, whereas high local peaks of σC and/or σT denote a possible risk of local overloading. Assuming the ultimate bone strength as a physiological limit, local overloading at cortical bone occurs in compression when σC exceeds 170 to 190 MPa, in tension when σT exceeds 100 to 130 MPa, and at trabecular bone when σT or σC exceeds 5 MPa.
      • Guo XE
      Mechanical properties of cortical and cancellous bone tissue.
      • Baggi L
      • Cappelloni I
      • Di Girolamo M
      • Maceri F
      • Vairo G
      The influence of implant diameter and length on stress distribution of osseointegrated implants related to crestal bone geometry: a three-dimensional finite element analysis.
      • Baggi L
      • Cappelloni I
      • Maceri F
      • Vairo G
      Stress-based performance evaluation of osseointegrated dental implants.
      • Natali AN
      • Hart RT
      • Pavan PG
      • Knets I
      Mechanics of bone tissue.
      FE-based stress solutions were postprocessed by using a custom-made procedure. For each implant, mean and peak values of σVM, σC, and σT were computed at the trabecular (∑t) and compact (∑c) periimplant control regions, defined by considering bone layers of about 1 mm in thickness surrounding the implant.
      To analyze the loading partition mechanisms, a performance index, denoted as the partition ratio P, was introduced. For an assigned load and on a given jaw, the index was defined as P=σ¯VM/σ¯VMmax (where P is a value between 0 and 1), and was computed for each implant and for each rehabilitative technique in both ∑c and ∑t. For a given control region (∑c or ∑t), denotes the mean value of σVM around a given implant in that region and is the maximum value among all values of computed for all implants in both rehabilitative techniques. Thereby, one prosthetic treatment can provide better load transmission than another if the corresponding values of P are more uniformly distributed among implants.

      Results

      Fig. 5, Fig. 6 show the distributions of σVM computed at each periimplant bone region, Figure 7 shows the values of the partition index P, and finally Fig. 8, Fig. 9 depict mean and peak values of σC and σT obtained numerically at the bone-implant interfaces.
      Figure thumbnail gr5
      Fig. 5Mandibular model. Von Mises stress contours (blue: 0; purple: 40 MPa) at each periimplant bone region for different simulated loads and referred to plane containing implant axis and orthogonal to buccolingual direction.
      Figure thumbnail gr6
      Fig. 6Maxillary model. Von Mises stress contours (blue: 0; purple: 40 MPa) at each periimplant bone region for different simulated loads and referred to plane containing implant axis and orthogonal to buccolingual direction.
      Figure thumbnail gr7
      Fig. 7Loading partition index P computed for both SC (SynCone-based, filled symbols) and A4 (All-on-4, unfilled symbols) in mandibular and maxillary models and under different loads (Load 1: complete-mouth loading, dark blue symbols; Load 2: cantilever load, black symbols; Load 3: frontal load, light blue symbols; L: left implant; CL: central-left implant; CR: central-right implant; R: right implant). Values for A, cortical bone in mandibular model; B, trabecular bone in mandibular model; C, cortical bone in maxillary model; D, trabecular bone in maxillary model.
      Figure thumbnail gr8
      Fig. 8Principal stress measures (σC compressive and σT tensile) at cortical bone-implant interfaces for simulated implants in A4 (All-on-4, light blue bars) and SC (SynCone-based, dark blue bars) restorations, in mandibular (on left) and maxillary (on right) models. Average (bars) and peak (lines) values (L: left implant; CL: central-left implant; CR: central-right implant; R: right implant).
      Figure thumbnail gr9
      Fig. 9Principal stress measures (σC compressive and σT tensile) at trabecular bone-implant interfaces for simulated implants in A4 (All-on-4, light blue bars) and SC (SynCone-based, dark blue bars) restorations in mandibular (on left) and maxillary (on right) models. Average (bars) and peak (lines) values (L: left implant; CL: central-left implant; CR: central-right implant; R: right implant).
      Numerical simulations highlighted that stress concentration areas were located at the cortical bone around the implant necks and that Load 2 was the most severe, producing the highest values of all stress measures at the right periimplant interfaces. Except in the simulated maxilla under Load 3, A4 produced patterns of σVM more homogeneous and with smaller values than SC. This was confirmed by analyzing the values of the partition index P. In the mandibular model, the greatest differences in P values were experienced at the right implant in the case of Load 2 (PA4 was smaller than PSC by about 18% in ∑c and 60% in ∑t) and at the distal implants for Loads 1 and 3 (PA4 was smaller than PSC by about 15% to 22% in ∑c and about 30% in ∑t). In the maxillary model and for Load 2, the greatest differences in P values were again at the right implant (PA4 was smaller than PSC by about 56% in ∑c and 51% in ∑t), whereas a different behavior with the mandibular model was computed for Loads 1 and 3. For the maxillary model under Load 1, distal implants in SC transferred the greatest amount of the load (mesial PSC was smaller than distal PSC by about 70% to 80%), whereas in A4 the load was more uniformly distributed, with a slightly greater load transferred by the mesial implants (distal PA4 was smaller than mesial PA4 by about 5% to 10% in ∑c and 45% to 50% in ∑t). On the contrary, for the maxillary model under Load 3, A4 performed worse than SC, resulting in higher and less homogeneous P values (the difference between mesial and distal PSC-values was smaller than that in A4 by approximately 50% to 60%, with the highest values of PSC-at the mesial implants-smaller than those of PA4 by about 40% to 50%).
      The principal stress measures computed in ∑c under loads 1 and 3 were greater in the mandibular model than in the maxillary one; these were almost similar for Load 2. The opposite occurred in ∑t. Peaks and mean values of σC computed in A4 under loads 1 and 3 were smaller than those in SC (up to 40 to 50%) in the distal ∑c (both in mandible and maxilla) but produced higher values (up to 90% to 100%) of σC in the maxillary model at mesial ∑t. Furthermore, tilted implants in A4 produced higher peaks and mean values (up to 180% to 200%) of σT in ∑c than SC, especially in the mandibular model. For all the simulated situations and within the limitations of this study, the principal stress measures computed never exceeded the physiological limits introduced for the cortical bone, whereas the strength value in compression for the cancellous bone was slightly exceeded around the mesial implants in the A4-based maxillary model under Load 3 and around the right implant in the SC-based mandibular model under Load 2.

      Discussion

      This numerical study has shown that the 2 complete-arch rehabilitative techniques based on All-on-4 (A4) and SynCone (SC) concepts and involving 4 endosseous implants positioned in the anterior region can exhibit stress-based biomechanical behavior and loading transmission mechanisms that are different in maxillary and mandibular models, primarily as a result of the cantilever length, the implant design concepts and positioning, the patient-dependent morphology, and mechanical properties of bone. In agreement with other studies,
      • Clelland NL
      • Gilat A
      • McGlumphy EA
      • Brantley WA
      A photoelastic and strain gauge analysis of angled abutments for an implant system.
      • Begg T
      • Geerts GA
      • Gryzagoridis J
      Stress patterns around distal angled implants in the all-on-four concept configuration.
      • Baggi L
      • Cappelloni I
      • Maceri F
      • Vairo G
      Stress-based performance evaluation of osseointegrated dental implants.
      • Van Staden RC
      • Guan H
      • Loo YC
      Application of the finite element method in dental implant research.
      • Petrie CS
      • Williams JL
      Comparative evaluation of implant designs: influence of diameter, length, and taper on strains in the alveolar crest. A three-dimensional finite-element analysis.
      • Chun HJ
      • Shin HS
      • Han CH
      • Lee SH
      Influence of implant abutment type on stress distribution in bone under various loading conditions using finite element analysis.
      • Kitagawa T
      • Tanimoto Y
      • Nemoto K
      • Aida M
      Influence of cortical bone quality on stress distribution in bone around dental implant.
      • Bevilacqua M
      • Tealdo T
      • Menini M
      • Pera F
      • Mossolov A
      • Drago C
      • et al.
      Three-dimensional finite element analysis of load transmission using different implant inclinations and cantilever lengths.
      • Bevilacqua M
      • Tealdo T
      • Menini M
      • Pera F
      • Mossolov A
      • Drago C
      • et al.
      The influence of cantilever length and implant inclination on stress distribution in maxillary implant-supported fixed dentures.
      • Bellini CM
      • Romeo D
      • Galbusera F
      • Agliardi E
      • Pietrabissa R
      • Zampelis A
      • et al.
      A finite element analysis of tilted versus non-tilted implant configurations in the edentulous maxilla.
      • Zampelis A
      • Rangert B
      • Heijl L
      Tilting of splinted implants for improved prosthodontic support: a two-dimensional finite element analysis.
      • Bonnet AS
      • Postaire M
      • Lipinski P
      Biomechanical study of mandible bone supporting a four-implant retained bridge: finite element analysis of the influence of bone anisotropy and foodstuff position.
      • Silva CG
      • Mendonça JA
      • Randazzo Lopez LR
      • Landre Jr, J
      Stress patterns on implants in prostheses supported by four or six implants: a three-dimensional finite element analysis.
      proposed 3D FE analyses have suggested that bone overloads can affect cortical bone around the implant necks, mainly in compression. In addition, overloading risk can occur in maxillary trabecular bone around the mesial implants and increases with the depth of the in-bone implant positioning.
      As clinical,
      • Shackleton JL
      • Carr L
      • Slabbert JC
      • Becker PJ
      Survival of fixed implant-supported prostheses related to cantilever lengths.
      • White SN
      • Caputo AA
      • Anderkvist T
      Effect of cantilever length on stress transfer by implant-supported prostheses.
      • Sertgöz A
      • Güvener S
      Finite element analysis of the effect of cantilever and implant length on stress distribution in an implant-supported fixed prosthesis.
      • Krekmanov L
      • Kahn M
      • Rangert B
      • Lindström H
      Tilting of posterior mandibular and maxillary implants for improved prosthesis support.
      • Aparicio C
      • Perales P
      • Rangert B
      Tilted implants as an alternative to maxillary sinus grafting: a clinical, radiologic, and periotest study.
      • Calandriello R
      • Tomatis M
      Simplified treatment of the atrophic posterior maxilla via immediate/early function and tilted implants: A prospective 1-year clinical study.
      • Capelli M
      • Zuffetti F
      • Del Fabbro M
      • Testori T
      Immediate rehabilitation of the completely edentulous jaw with fixed prostheses supported by either upright or tilted implants: a multicenter clinical study.
      • Testori T
      • Del Fabbro M
      • Capelli M
      • Zuffetti F
      • Francetti L
      • Weinstein RL
      Immediate occlusal loading and tilted implants for the rehabilitation of the atrophic edentulous maxilla: 1-year interim result of a multicenter prospective study.
      • Del Fabbro M
      • Bellini CM
      • Romeo D
      • Francetti L
      Tilted implants for the rehabilitation of edentulous jaws: A systematic review.
      • Maló P
      • Rangert B
      • Nobre M
      All-on-4 immediate-function concept with Brånemark System implants for completely edentulous maxillae: a 1-year retrospective clinical study.
      photoelastic,
      • Begg T
      • Geerts GA
      • Gryzagoridis J
      Stress patterns around distal angled implants in the all-on-four concept configuration.
      and numerical
      • Bevilacqua M
      • Tealdo T
      • Menini M
      • Pera F
      • Mossolov A
      • Drago C
      • et al.
      Three-dimensional finite element analysis of load transmission using different implant inclinations and cantilever lengths.
      • Bevilacqua M
      • Tealdo T
      • Menini M
      • Pera F
      • Mossolov A
      • Drago C
      • et al.
      The influence of cantilever length and implant inclination on stress distribution in maxillary implant-supported fixed dentures.
      • Bellini CM
      • Romeo D
      • Galbusera F
      • Agliardi E
      • Pietrabissa R
      • Zampelis A
      • et al.
      A finite element analysis of tilted versus non-tilted implant configurations in the edentulous maxilla.
      • Zampelis A
      • Rangert B
      • Heijl L
      Tilting of splinted implants for improved prosthodontic support: a two-dimensional finite element analysis.
      • Bonnet AS
      • Postaire M
      • Lipinski P
      Biomechanical study of mandible bone supporting a four-implant retained bridge: finite element analysis of the influence of bone anisotropy and foodstuff position.
      • Silva CG
      • Mendonça JA
      • Randazzo Lopez LR
      • Landre Jr, J
      Stress patterns on implants in prostheses supported by four or six implants: a three-dimensional finite element analysis.
      studies have indicated, the present numerical findings also show that using long posterior cantilevers can induce high stress concentrations on bone, especially at the distal periimplant regions. In agreement with the numerical simulations of Bevilacqua et al,
      • Bevilacqua M
      • Tealdo T
      • Menini M
      • Pera F
      • Mossolov A
      • Drago C
      • et al.
      Three-dimensional finite element analysis of load transmission using different implant inclinations and cantilever lengths.
      • Bevilacqua M
      • Tealdo T
      • Menini M
      • Pera F
      • Mossolov A
      • Drago C
      • et al.
      The influence of cantilever length and implant inclination on stress distribution in maxillary implant-supported fixed dentures.
      the present results emphasized that the use of tilted distal implants can be effective in reducing such effects, thereby inducing more favorable load transmission characteristics. Furthermore, as indicated by the numerical results obtained by Maeda et al
      • Maeda Y
      • Miura J
      • Taki I
      • Sogo M
      Biomechanical analysis on platform switching: is there any biomechanical rationale?.
      and Baggi et al,
      • Baggi L
      • Cappelloni I
      • Di Girolamo M
      • Maceri F
      • Vairo G
      The influence of implant diameter and length on stress distribution of osseointegrated implants related to crestal bone geometry: a three-dimensional finite element analysis.
      • Baggi L
      • Cappelloni I
      • Maceri F
      • Vairo G
      Stress-based performance evaluation of osseointegrated dental implants.
      the proposed simulations showed that the stress-based performance and long-term effectiveness of a rehabilitation can be significantly improved if the crestal bone loss is effectively counteracted, especially when cantilever effects are not dominant. The mutual influence of cantilever effects and crestal bone morphology seemed to be primarily affected by the loading type. For complete-mouth loading (Load 1) and cantilever load (Load 2), the cantilever influence prevailed, and the distal tilted implants in A4 (Nobel Biocare implants) produced less risk of compressive overload and more uniform stress distributions than the distal vertical implants in SC (Ankylos). However, because of the preservation of the crestal bone modeled for Ankylos implants in accordance with platform switching concepts, mesial implants exhibited opposite comparative results. When a frontal load (Load 3) was simulated, cantilever mechanisms were not activated, and the effects of platform switching seemed to prevail. As a result, stress distributions computed in A4-based models were more critical than those in SC applications. Differences in stress distributions among maxillary and mandibular models can be mainly related to the different physiologically based modeling assumptions regarding bone quality and morphology.
      In regard to load transfer features, A4-based numerical models (both mandibular and maxillary) allowed the computation of better transmission mechanisms under loads 1 and 2 than SC, resulting in more homogeneous loading partition. Under Load 1 all implants contributed to the load transmission, whereas, in the case of Load 2, at most, the 2 implants on the loading side were involved. Under Load 3 the transfer mechanisms simulated in the maxillary and mandibular models were significantly different, A4 producing better loading partition than SC in the mandible and worse in the maxilla. In agreement with basic statics, this evidence can be justified by observing that Load 3 was transferred by mainly intrusive actions upon the mesial implants and extrusive actions upon the distal implants. When L1 (Fig. 2) decreased (passing from the mandibular to maxillary model), the mesial intrusive forces increased and the distal extrusive ones decreased, thereby modifying the loading partition. When the difference between L2 and L1 (Fig. 2) increased (passing from A4 to SC), the distal extrusive actions further decreased, further contributing to a nonhomogeneous loading partition.
      The numerical results also showed that tilted implants in A4 can induce significant tensile stresses at distal crests, mainly in the mandibular model. When tilted implants transferred mostly extrusive components (Load 3), tensile stresses were computed at the distal side of the tilted implants, whereas when tilted implants transferred intrusive components (loads 1 and 2), tensile stresses were located at the mesial side. Correspondingly, risk of ineffective osseous integration and bone damage (bone is 30% stronger in compression than in tension
      • Guo XE
      Mechanical properties of cortical and cancellous bone tissue.
      ) might arise.
      Contrary to a number of recent numerical approaches,
      • Maeda Y
      • Miura J
      • Taki I
      • Sogo M
      Biomechanical analysis on platform switching: is there any biomechanical rationale?.
      • Baggi L
      • Cappelloni I
      • Maceri F
      • Vairo G
      Stress-based performance evaluation of osseointegrated dental implants.
      • Van Staden RC
      • Guan H
      • Loo YC
      Application of the finite element method in dental implant research.
      • Petrie CS
      • Williams JL
      Comparative evaluation of implant designs: influence of diameter, length, and taper on strains in the alveolar crest. A three-dimensional finite-element analysis.
      • Chun HJ
      • Shin HS
      • Han CH
      • Lee SH
      Influence of implant abutment type on stress distribution in bone under various loading conditions using finite element analysis.
      • Kitagawa T
      • Tanimoto Y
      • Nemoto K
      • Aida M
      Influence of cortical bone quality on stress distribution in bone around dental implant.
      • Bevilacqua M
      • Tealdo T
      • Menini M
      • Pera F
      • Mossolov A
      • Drago C
      • et al.
      Three-dimensional finite element analysis of load transmission using different implant inclinations and cantilever lengths.
      • Bevilacqua M
      • Tealdo T
      • Menini M
      • Pera F
      • Mossolov A
      • Drago C
      • et al.
      The influence of cantilever length and implant inclination on stress distribution in maxillary implant-supported fixed dentures.
      • Bellini CM
      • Romeo D
      • Galbusera F
      • Agliardi E
      • Pietrabissa R
      • Zampelis A
      • et al.
      A finite element analysis of tilted versus non-tilted implant configurations in the edentulous maxilla.
      • Zampelis A
      • Rangert B
      • Heijl L
      Tilting of splinted implants for improved prosthodontic support: a two-dimensional finite element analysis.
      • Bonnet AS
      • Postaire M
      • Lipinski P
      Biomechanical study of mandible bone supporting a four-implant retained bridge: finite element analysis of the influence of bone anisotropy and foodstuff position.
      • Silva CG
      • Mendonça JA
      • Randazzo Lopez LR
      • Landre Jr, J
      Stress patterns on implants in prostheses supported by four or six implants: a three-dimensional finite element analysis.
      the present study accounted for the influence of the posthealing crestal bone morphology in functioning implants, detailed geometrical modeling for maxillary and mandibular jaws, muscle-bone static interactions, and temporomandibular articulation. Nevertheless, some limitations of the modeling assumptions adopted in this study can be found. In detail, the ideal and unrealistic condition of 100% osseous integration was assumed. Stress analyses were performed by simulating static loads and including muscle-jaw interactions and temporomandibular joints through simplified approaches.
      • Beek M
      • Koolstra JH
      • Van Ruijven LJ
      • Van Eijden TMGJ
      Three-dimensional finite element analysis of the human temporomandibular joint disc.
      • Trainor PG
      • McLachlan KR
      • McCall WD
      Modelling of forces in the human masticatory system with optimization of the angulations of the joint loads.
      Bone and articular disks were modeled as dry isotropic linear elastic materials, whose mechanical properties were assumed to be time-independent. The space dependence of bone density and mechanical response were simply described by distinguishing trabecular and cortical homogeneous regions. These assumptions do not completely describe clinical scenarios because of possible osseointegration defects at the periimplant regions, different patient-dependent loading distributions, more complex and time-dependent forces and muscular effects, anisotropic, nonhomogeneous, nonlinear and inelastic response of living tissues, and bone remodeling and spatially graded tissue properties. Nevertheless, in agreement with other numerical studies,
      • Shackleton JL
      • Carr L
      • Slabbert JC
      • Becker PJ
      Survival of fixed implant-supported prostheses related to cantilever lengths.
      • White SN
      • Caputo AA
      • Anderkvist T
      Effect of cantilever length on stress transfer by implant-supported prostheses.
      • Sertgöz A
      • Güvener S
      Finite element analysis of the effect of cantilever and implant length on stress distribution in an implant-supported fixed prosthesis.
      • Baggi L
      • Cappelloni I
      • Di Girolamo M
      • Maceri F
      • Vairo G
      The influence of implant diameter and length on stress distribution of osseointegrated implants related to crestal bone geometry: a three-dimensional finite element analysis.
      • Maeda Y
      • Miura J
      • Taki I
      • Sogo M
      Biomechanical analysis on platform switching: is there any biomechanical rationale?.
      • Baggi L
      • Cappelloni I
      • Maceri F
      • Vairo G
      Stress-based performance evaluation of osseointegrated dental implants.
      • Van Staden RC
      • Guan H
      • Loo YC
      Application of the finite element method in dental implant research.
      • Petrie CS
      • Williams JL
      Comparative evaluation of implant designs: influence of diameter, length, and taper on strains in the alveolar crest. A three-dimensional finite-element analysis.
      • Chun HJ
      • Shin HS
      • Han CH
      • Lee SH
      Influence of implant abutment type on stress distribution in bone under various loading conditions using finite element analysis.
      • Kitagawa T
      • Tanimoto Y
      • Nemoto K
      • Aida M
      Influence of cortical bone quality on stress distribution in bone around dental implant.
      • Bevilacqua M
      • Tealdo T
      • Menini M
      • Pera F
      • Mossolov A
      • Drago C
      • et al.
      Three-dimensional finite element analysis of load transmission using different implant inclinations and cantilever lengths.
      • Bevilacqua M
      • Tealdo T
      • Menini M
      • Pera F
      • Mossolov A
      • Drago C
      • et al.
      The influence of cantilever length and implant inclination on stress distribution in maxillary implant-supported fixed dentures.
      • Bellini CM
      • Romeo D
      • Galbusera F
      • Agliardi E
      • Pietrabissa R
      • Zampelis A
      • et al.
      A finite element analysis of tilted versus non-tilted implant configurations in the edentulous maxilla.
      • Zampelis A
      • Rangert B
      • Heijl L
      Tilting of splinted implants for improved prosthodontic support: a two-dimensional finite element analysis.
      • Bonnet AS
      • Postaire M
      • Lipinski P
      Biomechanical study of mandible bone supporting a four-implant retained bridge: finite element analysis of the influence of bone anisotropy and foodstuff position.
      • Silva CG
      • Mendonça JA
      • Randazzo Lopez LR
      • Landre Jr, J
      Stress patterns on implants in prostheses supported by four or six implants: a three-dimensional finite element analysis.
      • Lemon JE
      • Dietsh-Misch F
      Biomaterials for dental implants.
      • Beek M
      • Koolstra JH
      • Van Ruijven LJ
      • Van Eijden TMGJ
      Three-dimensional finite element analysis of the human temporomandibular joint disc.
      • Trainor PG
      • McLachlan KR
      • McCall WD
      Modelling of forces in the human masticatory system with optimization of the angulations of the joint loads.
      the present assumptions can be accepted, in a computational sense, to deduce significant and clinically useful indications for the comparative stress-based assessment of complete-arch restorations.
      Another possible limitation is that the bar modeling was performed only to allow suitable loading transfer toward the implant-bone coupled system. Moreover, in a given jaw model, the bar was assumed to be the same for both the complete-arch restorative approaches. This could be considered a limitation because clinicians could adopt a shorter cantilever length when using the SC system. Nevertheless, such an assumption allowed for a consistent comparison between the 2 techniques, when for the same number of supporting implants and anterior positioning, the length of the rehabilitated arch (the number of the rehabilitated teeth) was also the same. Finally, the displacement boundary conditions adopted in maxillary models and consisting of fixing the entire virtual cutting surfaces (not including the nasal cavity) (Fig. 1) could seem an excessively rigid constraint. Nevertheless, nodes on these surfaces belong to the cortical bone that extends beyond the maxillary process described. Therefore, because of the mechanical properties of such a region, although lateral implants are relatively close to these computational boundaries, the corresponding periimplant stress distributions should not be significantly affected. This occurrence seems to be confirmed by comparing the present results with those obtained by Bevilacqua et al,
      • Bevilacqua M
      • Tealdo T
      • Menini M
      • Pera F
      • Mossolov A
      • Drago C
      • et al.
      The influence of cantilever length and implant inclination on stress distribution in maxillary implant-supported fixed dentures.
      and, in view of a comparative assessment, such a possible modeling limitation should not influence the main indications obtained in this study.
      To enhance the present FE approach, future studies will be devoted to the modeling of bone as a nonlinear, anisotropic, viscous, and nonhomogeneous regenerative tissue that responds to stress by resorption or regeneration under time-dependent muscular and external loads. Moreover, a more accurate correlation between bone density and its mechanical response should allow a better description of the spatial distribution of the material properties.

      Conclusions

      Within the limitations of this 3D finite element study, numerical simulations on both maxillary and mandibular models have shown that both the complete-arch rehabilitative approaches analyzed may have advantages and disadvantages, primarily because of the mutual coupling between cantilever mechanisms and cratering effects. Distal tilted implants in complete-arch prostheses allow a reduction of compressive stresses at the distal periimplant bone as a result of the reduction of cantilever effects on loading transmission mechanisms. Nevertheless, distally tilted implants can produce higher tensile stresses when compared with distal vertical implants, increasing risks of ineffective crestal osseous integration and bone damage. Platform switching strategies and subcrestal positioning can reduce the risk of bone overloading, especially at the mesial periimplant regions, where possible cantilever mechanisms are generally not dominant.

      References

        • Ganeles J
        • Rosenberg MM
        • Holt RL
        • Reichmann LH
        Immediate loading of implants with fixed restorations in the completely edentulous mandible: report of 27 patients from private practice.
        Int J Oral Max Impl. 2001; 16: 418-426
        • Bocklage R
        Rehabilitation of the edentulous maxilla and mandible with fixed implant-supported restorations applying immediate functional loading: A treatment concept.
        Implant Dent. 2002; 11: 154-158
        • Drago CJ
        Rates of osseointegration of dental implants with regard to anatomical location.
        J Prosthodont. 1992; 1: 29-31
        • Shackleton JL
        • Carr L
        • Slabbert JC
        • Becker PJ
        Survival of fixed implant-supported prostheses related to cantilever lengths.
        J Prosthet Dent. 1994; 71: 23-26
        • White SN
        • Caputo AA
        • Anderkvist T
        Effect of cantilever length on stress transfer by implant-supported prostheses.
        J Prosthet Dent. 1994; 71: 493-499
        • Sertgöz A
        • Güvener S
        Finite element analysis of the effect of cantilever and implant length on stress distribution in an implant-supported fixed prosthesis.
        J Prosthet Dent. 1996; 76: 165-169
        • Irving JT
        Factors concerning bone loss associated with periodontal disease.
        J Dent Res. 1970; 49: 262-267
        • Carter DR
        • Van Der Meulen MC
        • Beaupré GS
        Mechanical factors in bone growth and development.
        Bone. 1996; 18: 5S-10S
        • Guo XE
        Mechanical properties of cortical and cancellous bone tissue.
        in: Cowin SC Bone mechanics handbook. 2nd ed. CRC Press, Boca Raton2001: 10.1-10.23
        • Baggi L
        • Cappelloni I
        • Di Girolamo M
        • Maceri F
        • Vairo G
        The influence of implant diameter and length on stress distribution of osseointegrated implants related to crestal bone geometry: a three-dimensional finite element analysis.
        J Prosthet Dent. 2008; 100: 422-431
        • Roos-Jansåker AM
        • Lindahl C
        • Renvert H
        • Renvert S
        Nine- to fourteen-year follow-up of implant treatment. Part I: implant loss and associations to various factors.
        J Clin Periodontol. 2006; 33: 283-289
        • Romeo E
        • Chiapasco M
        • Ghisolfi M
        • Vogel G
        Long-term clinical effectiveness of oral implants in the treatment of partial edentulism. Seven-year life table analysis of a prospective study with ITI dental implants system used for single-tooth restorations.
        Clin Oral Implants Res. 2002; 13: 133-143
        • Eckert SE
        • Wollan PC
        Retrospective review of 1170 endosseous implants placed in partially edentulous jaws.
        J Prosthet Dent. 1998; 79: 415-421
        • Lekholm U
        • Gunne J
        • Henry P
        • Higuchi K
        • Lindén U
        • Bergström C
        • et al.
        Survival of the Brånemark implant in partially edentulous jaws: a 10-year prospective multicenter study.
        Int J Oral Maxillofac Implants. 1999; 14: 639-645
        • López-Marí L
        • Calvo-Guirado JL
        • Martín-Castellote B
        • Gomez-Moreno G
        • López-Marí M
        Implant platform switching concept: An updated review.
        Med Oral Patol Oral Cir Bucal. 2009; 14: e450-e454
        • Lazzara RJ
        • Porter SS
        Platform switching: A new concept in implant dentistry for controlling postrestorative crestal bone levels.
        Int J Periodontics Restorative Dent. 2006; 26: 9-17
        • Maeda Y
        • Miura J
        • Taki I
        • Sogo M
        Biomechanical analysis on platform switching: is there any biomechanical rationale?.
        Clin Oral Implants Res. 2007; 18: 581-584
        • Krekmanov L
        • Kahn M
        • Rangert B
        • Lindström H
        Tilting of posterior mandibular and maxillary implants for improved prosthesis support.
        Int J Oral Maxillofac Implants. 2000; 15: 405-414
        • Aparicio C
        • Perales P
        • Rangert B
        Tilted implants as an alternative to maxillary sinus grafting: a clinical, radiologic, and periotest study.
        Clin Implant Dent Relat Res. 2001; 3: 39-49
        • Calandriello R
        • Tomatis M
        Simplified treatment of the atrophic posterior maxilla via immediate/early function and tilted implants: A prospective 1-year clinical study.
        Clin Implant Dent Relat Res. 2005; 7: S1-12
        • Capelli M
        • Zuffetti F
        • Del Fabbro M
        • Testori T
        Immediate rehabilitation of the completely edentulous jaw with fixed prostheses supported by either upright or tilted implants: a multicenter clinical study.
        Int J Oral Maxillofac Implants. 2007; 22: 639-644
        • Testori T
        • Del Fabbro M
        • Capelli M
        • Zuffetti F
        • Francetti L
        • Weinstein RL
        Immediate occlusal loading and tilted implants for the rehabilitation of the atrophic edentulous maxilla: 1-year interim result of a multicenter prospective study.
        Clin Oral Implants Res. 2008; 19: 227-232
        • Del Fabbro M
        • Bellini CM
        • Romeo D
        • Francetti L
        Tilted implants for the rehabilitation of edentulous jaws: A systematic review.
        Clin Implant Dent Relat Res. 2010; https://doi.org/10.1111/j.1708-8208.2010.00288.x
        • Ferreira EJ
        • Kuabara MR
        • Gulinelli JL
        “All-on-four” concept and immediate loading for simultaneous rehabilitation of the atrophic maxilla and mandible with conventional and zygomatic implants.
        Br J Oral Maxillofac Surg. 2010; 48: 218-220
        • Romanos GE
        Present status of immediate loading of oral implants.
        J Oral Implantol. 2004; 30: 189-197
        • Eccellente T
        • Piombino M
        • Piattelli A
        • Perrotti V
        • Iezzi G
        A new treatment concept for immediate loading of implants inserted in the edentulous mandible.
        Quintessence Int. 2010; 41: 489-495
        • Khatami AH
        • Smith CR
        “All-on-Four” immediate function concept and clinical report of treatment of an edentulous mandible with a fixed complete denture and milled titanium framework.
        J Prosthodont. 2008; 17: 47-51
        • Maló P
        • Rangert B
        • Nobre M
        All-on-4 immediate-function concept with Brånemark System implants for completely edentulous maxillae: a 1-year retrospective clinical study.
        Clin Oral Implants Res. 2005; 7: S88-S94
        • Degidi M
        • Piattelli A
        A 7-year follow-up of 93 immediately loaded titanium dental implants.
        J Oral Implantol. 2005; 31: 25-31
        • Portmann M
        • Glauser R
        Report of a case receiving full-arch rehabilitation in both jaws using immediate implant loading protocols: a 1-year resonance frequency analysis follow-up.
        Clin Implant Dent Relat Res. 2006; 8: 25-31
        • Pomares C
        A retrospective study of edentulous patients rehabilitated according to the ‘all-on-four’ or the ‘all-on-six’ immediate function concept using flapless computer-guided implant surgery.
        Eur J Oral Implantol. 2010; 3: 155-163
        • Clelland NL
        • Gilat A
        • McGlumphy EA
        • Brantley WA
        A photoelastic and strain gauge analysis of angled abutments for an implant system.
        Int J Oral Maxillofac Implants. 1993; 8: 541-548
        • Begg T
        • Geerts GA
        • Gryzagoridis J
        Stress patterns around distal angled implants in the all-on-four concept configuration.
        Int J Oral Maxillofac Implants. 2009; 24: 663-671
        • Baggi L
        • Cappelloni I
        • Maceri F
        • Vairo G
        Stress-based performance evaluation of osseointegrated dental implants.
        Simul Model Pract Theory. 2008; 16: 971-987
        • Van Staden RC
        • Guan H
        • Loo YC
        Application of the finite element method in dental implant research.
        Comput Methods Biomech Biomed Engin. 2006; 9: 257-270
        • Petrie CS
        • Williams JL
        Comparative evaluation of implant designs: influence of diameter, length, and taper on strains in the alveolar crest. A three-dimensional finite-element analysis.
        Clin Oral Implants Res. 2005; 16: 486-494
        • Chun HJ
        • Shin HS
        • Han CH
        • Lee SH
        Influence of implant abutment type on stress distribution in bone under various loading conditions using finite element analysis.
        Int J Oral Maxillofac Implants. 2006; 21: 195-202
        • Kitagawa T
        • Tanimoto Y
        • Nemoto K
        • Aida M
        Influence of cortical bone quality on stress distribution in bone around dental implant.
        Dent Mater J. 2005; 24: 219-224
        • Bevilacqua M
        • Tealdo T
        • Menini M
        • Pera F
        • Mossolov A
        • Drago C
        • et al.
        Three-dimensional finite element analysis of load transmission using different implant inclinations and cantilever lengths.
        Int J Prosthodont. 2008; 21: 539-542
        • Bevilacqua M
        • Tealdo T
        • Menini M
        • Pera F
        • Mossolov A
        • Drago C
        • et al.
        The influence of cantilever length and implant inclination on stress distribution in maxillary implant-supported fixed dentures.
        J Prosthet Dent. 2011; 105: 5-13
        • Bellini CM
        • Romeo D
        • Galbusera F
        • Agliardi E
        • Pietrabissa R
        • Zampelis A
        • et al.
        A finite element analysis of tilted versus non-tilted implant configurations in the edentulous maxilla.
        Int J Prosthodont. 2009; 22: 155-157
        • Zampelis A
        • Rangert B
        • Heijl L
        Tilting of splinted implants for improved prosthodontic support: a two-dimensional finite element analysis.
        J Prosthet Dent. 2007; 6: S35-S43
        • Bonnet AS
        • Postaire M
        • Lipinski P
        Biomechanical study of mandible bone supporting a four-implant retained bridge: finite element analysis of the influence of bone anisotropy and foodstuff position.
        Med Eng Phys. 2009; 31: 806-815
        • Silva CG
        • Mendonça JA
        • Randazzo Lopez LR
        • Landre Jr, J
        Stress patterns on implants in prostheses supported by four or six implants: a three-dimensional finite element analysis.
        Int J Oral Maxillofac Implants. 2010; 25: 239-246
        • Degidi M
        • Piattelli A
        • Shibli JA
        • Strocchi R
        • Iezzi G
        Bone formation around a dental implant with a platform switching and another with a TissueCare Connection. A histologic and histomorphometric evaluation in man.
        Titanium. 2009; 1: 10-17
        • Abboud M
        • Koeck B
        • Stark H
        • Wahl G
        • Paillon R
        Immediate loading of single tooth implants in the posterior region.
        Int J Oral Maxillofac Implants. 2005; 20: 61-68
        • Shin YK
        • Han CH
        • Heo SJ
        • Kim S
        • Chun HJ
        Radiographic evaluation of marginal bone level around implants with different neck designs after 1 year.
        Int J Oral Maxillofac Implants. 2006; 21: 789-794
        • Lemon JE
        • Dietsh-Misch F
        Biomaterials for dental implants.
        in: Misch CE Contemporary implant dentistry. 3rd ed. Mosby, St. Louis2007: 271-302
        • Natali AN
        • Hart RT
        • Pavan PG
        • Knets I
        Mechanics of bone tissue.
        in: Natali AN Dental biomechanics. Taylor & Francis, London2003: 1-19
        • Beek M
        • Koolstra JH
        • Van Ruijven LJ
        • Van Eijden TMGJ
        Three-dimensional finite element analysis of the human temporomandibular joint disc.
        J Biomech. 2000; 33: 307-316
        • Lekholm U
        • Zarb GA
        Patient selection and preparation.
        in: Brånemark PI Zarb GA Albrektsson T Tissue-integrated prostheses: osseointegration in clinical dentistry. Quintessence, Chicago1985: 199-209
        • Trainor PG
        • McLachlan KR
        • McCall WD
        Modelling of forces in the human masticatory system with optimization of the angulations of the joint loads.
        J Biomech. 1995; 28: 829-843