Bone Stress Analysis of Various Angulations of Mesiodistal Implants With Splinted Crowns in the...

Implant-supported fixed partial dental prosthesesare being established as a treatment option for par-

tially edentulous patients. More than one implant is

used to support most restorations, and the meanimplant failure rate for partially edentulous fixed par-tial dentures was 6% in both the maxilla andmandible (range, 1.9% to 12.5%).1

There are many factors influencing the successrate of implants supporting fixed partial dentures.2

Stegaroiu et al3 used three-dimensional (3D) finiteelement (FE) analysis to assess the bone stress aroundimplants and found that the bone stress was highlyaffected by cantilevers. Gunne et al4 emphasized thatthe geometry of the prosthesis and the types ofimplants placed affect the distribution of bone stress;moreover, high stress was evident on extreme can-tilever extensions under vertical loading.

In clinics, especially for an implant-supported fixedpartial prosthesis, restoring an implant can be challeng-ing because the implant is often found to be tiltingafter placement; however, few studies have investi-gated the effects of implant tilting. Tuncelli et al5

demonstrated that tilted implants had advantages overstandard implants because they could resist the harm-ful effects of horizontal loading. Akca and Iplikcioglu6

Bone Stress Analysis of Various Angulations ofMesiodistal Implants with Splinted Crowns in the Posterior Mandible: A Three-Dimensional

Finite Element StudyTing-Hsun Lan, DDS, MDS1/Chin-Yun Pan, DDS, MDS2/Huey-Er Lee, DDS, MS, PhD3/

Heng-Li Huang, MS, PhD4/Chau-Hsiang Wang, DDS, MDS, PhD5

Purpose: Ideally, implants for dental prostheses should be placed parallel to each other. However,anatomic limitations sometimes make nonparallel implants necessary. The purpose of this study was todetermine the bone stresses on implants tilted at various angles and to determine what arrangementsmight carry a higher risk of failure. Materials and Methods: Three-dimensional finite element modelswere constructed using the mean values measured for the Asian mandible in the first and second molarareas. Eight implants were divided into three tilting types: parallel implants (P1PP, P2MM, and P3DD), con-vergent implant apices (C1PD and C2MP), and divergent implant apices (D1DP, D2DM, and D3PM). A bitingload of 200 N was applied vertically and obliquely on the occlusal central fossa of the splinted crowns.The main effects of each level of the three investigated factors (loading type, relationship of implantapices, and distal tilting of one or both implants) in terms of the stress values were computed for allmodels. Results: The loading type was the main factor affecting the stress in bone when comparingimplant apices and distal tilting of the implant body. When loading was combined with distal tilting, thestress values were significantly increased, especially in models P3DD and C1PD. Conclusion: The loadingtype is the main factor affecting the stress distribution for different implantation arrangement. More-over, placement of the implants with distal tilting should be avoided in the posterior mandible. INT J ORALMAXILLOFAC IMPLANTS 2010;25:763–770

Key words: convergent implant apices, divergent implant apices, finite element analysis, implant axis,implant loading

The International Journal of Oral & Maxillofacial Implants 763

1Clinical Instructor, Department of Prosthodontics, Kaohsiung Med-ical University Hospital, Kaohsiung Medical University, Kaohsiung,Taiwan; Head, Department of Dentistry, Antai Medical Care Coop-eration, Antai Tian-Sheng Memorial Hospital, Pingtung, Taiwan.2Clinical Instructor, Department of Orthodontics, Kaohsiung Med-ical University Hospital, Kaohsiung Medical University, Kaohsi-ung, Taiwan.3Professor and Dean, Department of Prosthodontics, KaohsiungMedical University Hospital and School of Dentistry, KaohsiungMedical University, Kaohsiung, Taiwan.4Associate Professor, Biomechanics Laboratory, School of Den-tistry, China Medical University and Hospital, Taichung, Taiwan.5Associate Professor, Department of Prosthodontics, KaohsiungMedical University Hospital and School of Dentistry, KaohsiungMedical University, Kaohsiung, Taiwan.

Correspondence to: Dr Chau-Hsiang Wang, Department ofProsthodontics, Kaohsiung Medical University Hospital, 100 Tz-You 1st Road, Kaohsiung 80756, Taiwan. Fax: +886-7-3157024.Email: [email protected]

© 2009 BY QUINTESSENCE PUBLISHING CO, INC. PRINTING OF THIS DOCUMENT IS RESTRICTED TO PERSONAL USE ONLY. NO PART OF THIS ARTICLE MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM WITHOUT WRITTEN PERMISSION FROM THE PUBLISHER.

evaluated the effects of buccolingual implant angula-tion in the posterior mandible and concluded that buc-colingual angulation of implants might be beneficial inreducing areas of high bone stress in the presence ofrisk factors such as bruxism.

Krekmanov et al7 found no significant differencebetween tilted and nontilted implants in the poste-rior mandible with an implant-supported partialprostheses. Moreover, Satoh et al8 indicated thatthere was a biomechanical rationale for placingimplants with mesial tilting similar to that of naturalteeth. Clinical limitations also mean that nonparallelimplants are occasionally necessary.

A previous study9 suggests that not all implantbody tilting with splinted crowns leads to stress con-centrations. However, that study did not clarify whichfactors affect bone stress, and the amount of loadingwas not sufficient to simulate the clinical situation.Therefore, the hypothesis of the present study wasthat convergent implant apices or implant body dis-tal tilting will lead to greater stress concentration. Thisstudy applied 3D FE analysis to investigate the effectsof various types of mesiodistal implant tilting (includ-ing convergence and divergence of the implantapices) on the bone stresses around implants.

MATERIALS AND METHODS

A bone block from the canine to the posterior borderof the mandible was created in ANSYS (SwansonAnalysis) based on the mean values of the corticalthickness in a database of Asian mandibles (Fig 1).10

Cylindric implants with a length of 11 mm and adiameter of 5 mm were placed into the bone modelin the center of the residual ridge. Two implantsembedded at the sites of the first and second molarswere each restored with a splinted all-ceramic crown.The crown dimensions were 10 mm mesiodistally, 7 mm buccolingually, and 8 mm apicocoronally. Thecenters of the two implants were separated by 10 mm.

The materials used in the models (Table 1) wereassumed to be isotropic, homogeneous, and linearlyelastic. A 3D FE mesh comprising 136,237 elementsand 198,097 nodes was constructed from 10-nodetetrahedral elements.

The eight models (Table 2) created in this studywere divided into three implant apex conditions: par-allel implants (P), convergent implant apices (C), anddivergent implant apices (D). Then, implant tilting wasrepresented: 15 degrees of mesial tilting (M), 15degrees of distal tilting (D), or no tilting (P). Therefore,in the same occlusal plane (Table 2), the eight modelswere designated as follows:

• P1PP: Both implants were placed vertically and par-allel to each other.

• P2MM: Both implants were tilted mesially and paral-lel to each other.

• P3DD: Both implants were tilted distally and parallelto each other.

• C1PD: One implant was placed vertically and theother was tilted distally.

• C2MP: One implant was tilted mesially and theother was placed vertically.

• D1DP: One implant was tilted distally and the otherwas placed vertically.

• D2DM: One implant was tilted distally and the otherwas tilted mesially.

• D3PM: One implant was placed vertically and theother was tilted mesially.

All models were constrained in all directions at thenodes on the mesial and distal borders of the bonesurface. A bite force of 200 N11,12 was applied to thecentral fossa of each prosthetic construction in thefollowing five directions: vertically and at 45 degreesfrom buccal to lingual, lingual to buccal, mesial to dis-tal, and distal to mesial (Table 2). The convergence ofthe FE model was tested in model P1PP with verticalloading to verify that the mesh density was sufficientto produce reliable data.

764 Volume 25, Number 4, 2010

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Fig 1 A bone block from the canine to the posterior border of themandible with different mean cortical bone thickness around theteeth, as created in ANSYS.

Table 1 Properties of the Materials Modeled

Young’s Young’s Material modulus (MPa) Poisson ratio

Cortical bone 13,700 0.3Cancellous bone 1,850 0.3Titanium-aluminum-vanadium 117,000 0.35Ceramic crown 69,000 0.28


There are no explicit guidelines or even sugges-tions in the literature regarding the kind of stressesthat should be used in FE calculations; principalstresses and von Mises stresses are used equallyoften. This study focused on the stresses in bone. Thevon Mises stress is defined as the beginning of defor-mation for ductile material such as metallic implants,and principal stresses can distinguish between tensileand compressive stresses. Furthermore, the minimum

principal stress represents the most negative stress,typically the peak compressive stress. Therefore, eval-uation of these peak compressive stress values couldprovide valuable information for understanding thebone resorption that leads to loss of osseointegrationin dental implant systems. To reduce the complexityof the results, the main effect of each of the threeinvestigated factors (loading type, implant apices con-dition, and tilting of the implant body) on the


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Table 2 Detailed Loading Conditions, Configurations of Implant Apices, and Distal Tilting of Second Molar Implants

Loading types/contact positions Implant apices Implant distal tilting? Sequence no.

1. Vertical: Uniform multiple axial contacts on the central fossa of the molars (200 N)Parallel No 1Parallel No 2Parallel Yes 3Converging Yes 4Converging No 5Diverging Yes 6Diverging Yes 7Diverging No 8

2. B–L: Uniform multiple oblique contacts on the central fossa of molars (200 N) Parallel No 9Parallel No 10Parallel Yes 11Converging Yes 12Converging No 13Diverging Yes 14Diverging Yes 15Diverging No 16

3. L–B: Uniform multiple oblique contacts on the central fossa of molars (200 N)Parallel No 17Parallel No 18Parallel Yes 19Converging Yes 20Converging No 21Diverging Yes 22Diverging Yes 23Diverging No 24

4. M–D: Uniform multiple oblique contacts on the central fossa of molars (200 N)Parallel No 25Parallel No 26Parallel Yes 27Converging Yes 28Converging No 29Diverging Yes 30Diverging Yes 31Diverging No 32

5. D–M: Uniform multiple oblique contacts on the central fossa of molars (200 N)Parallel No 33Parallel No 34Parallel Yes 35Converging Yes 36Converging No 37Diverging Yes 38Diverging Yes 39Diverging No 40

Vertical = vertically applied to central fossa; B–L = applied to central fossa at 45 degrees from buccal to lingual; L–B = applied to central fossa at 45 degreesfrom lingual to buccal; M–D = applied to central fossa at 45 degrees from mesial to distal; D–M = applied to central fossa at 45 degrees from distal to mesial.

Mesial Distal

Mesial Distal

Mesial Distal

Lingual Buccal

Lingual Buccal


mechanical response (stress) was computed based onstatistical methods.13,14 In addition, the data from sim-ulated results were analyzed using a general linearmodel analysis of variance with the Sigmastat statisti-cal package (Jandel). The analysis gave the percent-age contribution that each investigated factor madeto the sum of squares and could determine the fac-tors that minimize stress in the implant-bone system.

RESULTS

The minimum principal stress values for the five load-ing types of the three implant apex conditions arelisted in Table 3. Comparisons of the peak stresses (%)relative to model P1PP are listed in Table 4. To determinethe relative importance of the investigated factors andtheir interactions, analyses of variance were used andare shown in Table 5. The results showed that the load-ing type significantly (P < .05) determined the magni-tude of the stress values, and the percentagecontributions were 77.15% for the bone. Comparisonof the eight implantation designs for loadings in thedifferent directions (Table 3, Fig 2) indicated that theminimum principal bone stress was higher with

oblique loading than with vertical loading. The factor ofimplant apex condition, implant body distal tilting, andthe interaction of loading type and implant apex con-dition did not significantly influence the bone stressvalues (P > .05). However, the interaction between load-ing type and implant body distal tilting or not wasfound to be a significant factor affecting the stressvalue in bone (P < .05), accounting for 10.04% of thestresses in the system.

The percentage peak stresses relative to modelP1PP are listed in Table 4. Under vertical loading (Fig 3),the bone stress was lower in models with divergentimplant apices than in model P1PP (by 12% in modelD2DM, 14% in model D1DP, and 6% in model D3PM),whereas it was higher in models with convergentimplant apices (by 88% in model C1PD and 83% inmodel C2MP) and parallel implants (by 81% in modelP2MM and 73% in model P3DD).

Comparison of the eight models with obliqueloading (Table 3, Fig 2) revealed that the bone stresswas higher for buccal to lingual loading than formesial to distal loading. With loading in the buccal tolingual direction (Table 4, Fig 4), the bone stress var-ied in models with divergent implant apices relativeto model P1PP (7% lower in model D3PM, 10% higher


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Table 3 Peak Minimum Principal Stresses (MPa)in the Cortical Bone for Different MesiodistalImplant Tilting Models

VerticalOblique (45-deg) loading

Model loading B to L L to B M to D D to M

P1PP 20.8 81.3 67.3 50.7 50.0P2MM 37.7 94.2 84.1 40.4 75.2P3DD 35.9 94.5 100.6 77.1 36.8C1PD 39.1 100.6 107.6 81.6 48.1C2MP 38.1 94.7 75.3 53.7 78.7D1DP 23.7 89.4 76.9 51.7 32.1D2DM 18.3 84.5 81.4 38.9 34.9D3PM 22.1 75.8 64.6 40.5 45.0

B = buccal; L = lingual; M = mesial; D = distal; P = parallel implants; C = convergent implant apexes; D = divergent implant apexes; P = perpendicular to occlusal plane; M = mesial tilting; D = distal tilting.

Table 4 Peak Minimum Principal Stress (%) Relative to Model P1PP

VerticalOblique loading

Model loading B to L L to B M to D D to M

P1PP 0 0 0 0 0P2MM 81 16 25 –20 50P3DD 73 16 50 52 –26C1PD 88 24 60 61 –4C2MP 83 17 12 6 57D1DP 14 10 14 2 –36D2DM –12 4 21 –23 –30D3PM 6 –7 –4 –20 –10

B = buccal; L = lingual; M = mesial; D = distal; P = parallel implants; C = convergent implant apexes; D = divergent implant apexes; P = perpendicular to occlusal plane; M = mesial tilting; D = distal tilting.

Table 5 Statistical Findings of Maximum Stress with Respect to Bone

Source DF SS MS %TSS P

Loading type 4 18,455.56 4,613.90 77.15 .049Implant apices 2 2,440.42 1,220.21 10.20 .162Implant body distal tilting 1 387.70 387.70 1.62 .454Loading type � implant apices 8 186.94 23.37 0.78 .949Loading type � implant body distal tilting 4 2,401.77 600.44 10.04 .001Implant apices � implant body distal tilting 2 47.81 23.90 0.01 .200Total 21 23,920.20 100.00

DF = degrees of freedom; SS = sum of squares; MS = mean square; TSS = total sum of squares.


in model D1DP, and 4% higher in model D2DM),whereas it was higher in models with convergentimplant apices (by 24% in model C1PD and 17% inmodel C2MP) and parallel implants (by 16% in modelsP2MM and P3DD).

With loading in the lingual to buccal direction (Table4, Fig 5), the bone stress varied in models with diver-gent implant apices relative to model P1PP (4% lower inmodel D3PM, 14% higher in model D1DP, and 21%higher in model D2DM), whereas it was higher in modelswith convergent implant apices (by 60% in model C1PDand 12% in model C2MP) and parallel implants (by 25%in model P2MM and 50% in model P3DD).

Comparison of the eight models for loading in themesial to distal direction (Table 4, Fig 6) revealed thatthe bone stress was highest in model C1PD and low-est in model D2DM. The bone stress varied in modelswith divergent implant apices relative to model P1PP(20% lower in model D3PM, 23% lower in model D2DM,and 2% higher in model D1DP), whereas it was higherin models with convergent implant apices (by 61% inmodel C1PD and 6% in model C2MP) and in modelswith parallel implants (by 20% in model P2MM and52% in model P3DD).

Comparison of the eight models for loading in thedistal to mesial direction (Table 4, Fig 7) revealed


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120

100

80

60

40

20

0

Peak

bon

e st

ress

(MPa

)

Vertical Oblique B to L Oblique L to B Oblique M to D Oblique D to M

P1PP

P2MM

P3DD

C1PD

C2MP

D1DP

D2DM

D3PM

Fig 2 Comparison of the peakminimum principal stresses inbone among the eight models forloadings in f ive directions.Oblique loading was always at a45-degree angle. B = buccal; L =lingual; M = mesial; D = distal.

Fig 3 Distribution of cortical bone stresses with vertical load-ing. The peak bone stress was highest in model C1PD (middle row,left) and lowest in model D2DM (bottom row, center).

P1PP P2MM P3DD

C1PD C2MP

D1DP D2DM D3PM

–20.795–19.327–17.858–16.390–14.922–13.454–11.985–10.517–9.049–7.581–6.112–4.644–3.176–1.708–.2391.229

Fig 4 Distribution of cortical bone stresses with oblique loadingin the buccal to lingual direction. The peak bone stress was high-est in model C1PD (middle row, left) and lowest in model D3PM(bottom row, right).

P1PP P2MM P3DD

C1PD C2MP

D1DP D2DM D3PM

–81.318–75.217–69.116–63.014–56.913–50.812–44.711–38.610–32.508–26.407–20.306–14.205–8.104–2.0024.09910.2


that the bone stress was highest in model C2MP andlowest in model D1DP. The bone stress was lower inmodels with divergent implant apices than in modelP1PP (by 10% in model D3PM, 30% in model D2DM, and36% in model D1DP), whereas it was varied in modelswith convergent implant apices (57% higher in modelC2MP and 4% lower in model C1PD) and parallelimplants (26% lower in model P3DD and 50% higherin model P2MM).

DISCUSSION

Overloading has been considered a possible reasonfor the loss of osseointegration. Many studies havefocused on preventing bone resorption, especially inthe crestal cortical bone.15–17 Moreover, it was foundthat the stress distribution in implant models wasinfluenced by the thickness of cortical bone.18,19

However, it is difficult to determine the thickness ofcortical bone using a surface scanner.6 A 2008 study9


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Fig 5 Distribution of cortical bone stresses with oblique loadingin the lingual to buccal direction. The peak bone stress was high-est in model C1PD (middle row, left) and lowest in model D3PM(bottom row, right).

Fig 6 Distribution of cortical bone stresses with oblique loadingin the mesial to distal direction. The peak bone stress was high-est in model C1PD (middle row, left) and lowest in model D2DM(bottom row, center).

Fig 7 Distribution of cortical bone stresses with oblique loadingin the distal to mesial direction. The peak bone stress was high-est in model C2MP (middle row, center) and lowest in model D1DP(bottom row, left).

P1PP P2MM P3DD

C1PD C2MP

D1DP D2DM D3PM

–67.260–61.705–56.149–50.594–45.039–39.483–33.928–28.373–22.817–17.262–11.707–6.151–.5964.95910.51516.070

P1PP P2MM P3DD

C1PD C2MP

D1DP D2DM D3PM

–50.720–46.930–43.140–39.349–35.559–31.769–27.979–24.189–20.398–16.608–12.818–9.028–5.238–1.4472.3436.133

P1PP P2MM P3DD

C1PD C2MP

D1DP D2DM D3PM

–50.009–46.246–42.482–38.719–34.956–31.192–27.429–23.666–19.902–16.139–12.376–8.612–4.849–1.0862.6786.441


found that the use of the mean measured dimen-sions of Asian mandibles with different cortical bonethicknesses could mimic asymmetric bone modelsand be differentiated from the results of other stud-ies.6,8 While the use of tomographic slices could be aneasy method for building an accurate model of themandible, individual variations must be considered.When focusing on bone stresses in a bone model, useof the average morphologic data of Asian mandiblescould help provide more accurate results.

Although the relationship of the implant apices wasnot found to influence the stress values in bone signifi-cantly (P > .05), distal tilting of the implant body com-bined with loading type did have a significantinfluence (P < .05). The study of Krekmanov et al7

revealed no significant difference between tilted andnontilted implants for rehabilitating atrophied edentu-lous arches with endosseous implants in the posteriorareas. A 2D finite element analysis of Zampelis et al20

showed that distal tilting of implants splinted by a fixedrestoration did not increase the bone stress comparedto normally placed vertical implants. In the presentstudy, using a 3D asymmetric model of the mandibleand statistical13,14 analysis, the risk of distal tilting wasevident, especially in model C1PD. There were two rea-sons for this: (1) the convergent implant apices areinconsistent with the morphology of the normallydivergent molar roots and (2) the distally tilted implantconflicts with Monson or Spee curvatures among theposterior teeth of natural dental arches.21

The maximum bone stress was lower in modelswith divergent implant apices (D1DP and especiallyD2DM and D3PM) than in standard parallel placement(model P1PP). The bone stress relative to model P1PPwas lower in model D2DM under vertical loading andlower in model D3PM under various oblique loadings.This difference was attributable to two factors: (1) thedivergent implant apices followed the usual mor-phology of the divergent molar roots and (2) thetilted implant either followed (D3PM and D2DM) orconflicted (D2DM) with Monson or Spee curvaturesamong the posterior teeth of natural dental arches.Satoh et al8 reported results similar to those seen formodel D3PM. In addition, with regard to the presenceof the second premolar, there is a risk that implantplacement will damage or destroy the neighboringroot in modelD2DM.

For the parallel implant groups (P1PP, P2MM, andP3DD), the bone stress was highest in models P2MM

and P3DD, especially with vertical loading, in contrastto model P1PP. In addition, comparing models P1PP,D1DP, and C2MP, the bone stress was lowest in modelP1PP. Therefore, the authors do not recommend usingan implant with mesial or distal tilting in the firstmolar area in the posterior mandible.

In the clinical situation, the risks of destroying theneighboring root and bone destruction from prema-ture contact and overloading as a result of bruxismcannot be ignored. To decrease the bone stressescaused by oblique loading, an ideal treatment planmight instead use a better implant arrangement (P1PP,D3PM), a shorter occlusal table of the prosthesis,and/or a lower crown-to-implant ratio. In addition, anexternal-hexagon connection22–24 between implantand abutment is at greater risk of screw deformationor fracture when implant tilting occurs. Impressionmaking for prostheses is also more difficult withgreater implant tilting. Therefore, a cone-beam com-puted tomographic scan and computer-assisted plan-ning of implant placement are considered state of theart and are recommended for patients with risk fac-tors. However, during surgery, the radiographic datashould be rechecked if a surgical limitation occurs,such as a mouth-opening limitation or a nonadapt-able surgical kit. In this study, these results do not con-tradict the rules for standard parallel implants in themandibular posterior area, since, when existing riskfactors such as bruxism are considered, an implantprosthesis replacing molars should avoid distal tilting.

CONCLUSION

Within the limitations of this study, the following con-clusions for implant placement with splinted crownscan be drawn:

1. Loading type (vertical or oblique) is the main fac-tor significantly affecting stress distribution inalveolar bone (P < .05).

2. The relationship of the implant apices (parallel,convergent, or divergent) does not significantlyinfluence bone stress (P > .05).

3. From a purely mechanical viewpoint, implant bod-ies that are tilted distally in the posterior mandibleshould be avoided.

4. A conventional implant arrangement (P1PP) orslight mesial tilting of the second molar (D3PM) aresuggested for applications over the posteriormandible.

ACKNOWLEDGMENTS

This work was supported by a grant from the National ScienceCouncil of Taiwan (NSC 92-2320-B-037-032). The authors wouldlike to thank Dr Hong-Po Chang for his help with the preparation ofthe manuscript.


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