Biomechanical Evaluation of Subcrestal
Placement of Dental Implants: In Vitro
and Numerical Analyses
Chun-Ming Chu,* Jui-Ting Hsu,* Lih-Jyh Fuh,* and Heng-Li Huang*
Background: This study investigates the effect of depth of insertion in subcrestal cortical bone (SB) and thickness of connected cortical bone (CB) for a subcrestal implant place-ment on bone stress and strain using statistical analyses combined with experimental strain-gauge tests and numerical finite element (FE) simulations.
Methods: Three experimental, artificial jawbone models and 72 FE models were prepared for evaluation of bone strain and stress around various equicrestal and subcrestal implants. For in vitro tests, rosette strain gauges were used with a data ac-quisition system to measure bone strain on the bucco-lingual side. The maximum von Mises stresses in the bone were statis-tically analyzed by analysis of variance for FE models.
Results: The experimental bone strains reduced signifi-cantly (22% to 49%) as the thickness of CB increased. FE anal-yses indicated that the suggested CB thickness for efficiently minimizing bone stress was 0.5 to 2.5 mm. The results for the depth of SB were not absolute because obvious stress re-ductions only presented at a certain range of depth (0.6 to 1.2 mm).
Conclusion: Within the limitations of this study, increasing the thickness of CB and maintaining the depth of SB within a limited range can provide the benefit of decreasing the stress and strain in surrounding bone for subcrestally placed im-plants.J Periodontol 2011;82:302-310.
KEY WORDS
Biomechanics; dental implants; dental stress analysis; finite element analysis; implants, experimental; in vitro.
D
ental implants have been applied in dentistry for over 30 years, since the introduction of osseo-integration by Bra˚nemark et al.1 For two-piece implant systems, the implant placement provides the advantage of primary wound closure of soft tissue over the implant, which allows the connection at the interface between implant and bone (osseointegration) to be achieved without disturbing bone growth. After osseointegration, abutment and pros-thetic components are then placed in the implant to perform the occlusal func-tion. However, in this kind of implant surgery, typically 1 to 1.5 mm of peri-implant bone loss occurs during healing and after the first year of implant place-ment.2,3Studies have indicated that many possible factors affect peri-implant bone loss, including reformation of the biologic width,4,5the presence of a microgapbe-tween implant and abutment in two-stage implants,6,7implant overloading,8-10and
peri-implantitis.11,12
Certain implant designs have been proposed for preserving the level of the marginal bone around implants, such as platform switching13 and subcrestal
placement.14-17 A conical abutment (or Morse-taper connection) has been intro-duced as one type of platform-switching design, which means that connecting a reduced-diameter abutment to an implant can result in a circumferential horizontal mismatch around the implant shoulder. It has been proposed to reduce the loss of
* School of Dentistry, China Medical University and Hospital, Taichung, Taiwan.
crestal bone height because the inflammatory cell infil-trate moves inwardly at the implant–abutment gap and away from crestal bone to prevent bone loss.13In addition, an implant with a conical abutment recently has been considered with the treatment of subcrestal placement and in some animal studies has been found to have a positive impact on crestal bone preservation.14-17
The use of subcrestal place-ment of two-stage implants has been found to have a small amount of additional bone loss14 and can even have a positive impact on crestal bone preservation.15 Pontes et al.16,17 indicated that deeper implant inser-tion does not jeopardize the peri-implant ridge height and soft tissue. Welander et al.18,19demonstrated that
osseointegration might oc-cur at or above the level of the implant–abutment junc-tion when implant compo-nents with suitable surface characteristics are subcres-tally placed. In addition, Barros et al.20 showed that the subcrestal placement of a contiguous Morse-taper connection with platform switching was more capable of preserving the interim-plant crestal bone. Because the subcrestal implant place-ment changes the traditional design of the connection (equi-crestal placement) between implant and bone, the stress and strain distribution from the implant to the bone might be influenced when occlusal loading occurs. However, the biomechanical effect of subcrestal implant placement with conical abut-ment on bone stress and strain is still a controversial issue and remains to be investigated.
The aim of this study is to elucidate the effects of subcrestal implant place-ment for various insertion depths and different cortical bone thickness on stress and strain performances of surrounding bone using in vitro experiments and three-dimensional finite element (FE) analyses. MATERIALS AND METHODS
In Vitro Experiments
Three experimental bone models were prepared. In Model 1 (2-mm-thick cortex) and Model 2 (3-mm-thick Figure 1.
A) Schematic of the equicrestal models. Model 1 (right) and Model 2 (left) with 2- and 3-mm thickness of cortical bone, respectively. B) Schematic of the subcrestal models. Compared to the equicrestal models, another 1-mm-thick cortical shell was fixed on the top surface as Model 3 with a total 3-mm thickness of cortical bone. C) Application of 45-degree lingual lateral force to the top of the implant.
cortex), the implants were placed at the level of the crest cortical bone (equicrestal implant placements) (Fig. 1A). Therefore, 2- and 3-mm-thick commercially available synthetic cortical shells†were prepared for attachment to the trabecular bone specimen‡to simu-late jaw bone. After drilling appropriate holes, 3.5 · 11 mm of the commercially available implants§were
in-serted and Morse-taper abutmentsiwere used for
con-nection to the implant. To measure the strain of bone around the implant, rectangular rosette strain gauges¶
(1 mm in length and 1.5 mm in width) were attached to
the buccal and lingual sides of the crestal region of cor-tical shell around the implant by using cyanoacrylate ce-ment#(Fig. 1).
For subcrestal placement, 2 mm of cortical thickness of bone model were prepared as Model 1, and then an addi-tional 1-mm-thick cortical shell was attached on the top of the bone model to create a 1-mm subcrestal bone thick-ness for Model 3 (Fig. 1B). For all models, cyanoacrylate cement** was used to bind the surfaces of implant and bone model to simulate a bonded (osseointegration) in-terface. The dimensions of the bone block were 20 · 30 · 40 mm in the bucco-lingual, me-sio-distal, and apical-coronal directions, respectively.
A customized jig was de-signed with an adjustable screwing device so that a 45-degree lingual oblique force could be applied in the experiments. Each loading procedure involved applying a force of 170 N21to the
con-ical abutment using a univer-sal testing machine†† with a head speed of 1 mm per min-ute (Fig. 1C). Strain-gauge signal process22 related to the three independent strains ea, eb, and ecmeasured by the three gauges comprising the rosette strain gauge was sent to the data acquisition sys-tem‡‡ and analyzed by the
associated software.§§ Each
measurement was repeated three times. The maximum (emax) and minimum (emin) principal strains were obtained as follows:
Figure 2.
A) Cross-sectional view of the solid model, showing its detailed dimensions. B) FE mesh model.
† Model 3401, Pacific Research Laboratory, Vashon Island, WA. ‡ Model 1522-05, Pacific Research Laboratory.
§ ANKYLOS Plus Implant A11 implant system, DENTSPLY Friadent, Mannheim, Germany.
i ANKYLOS 3102-1050, DENTSPLY Friadent. ¶ KFG-1-120-D17-11L3M3S, Kyowa, Tokyo, Japan. # CC-33A, Kyowa.
** CC-33A, Kyowa.
†† JSV-H1000, Japan Instrumentation System, Nara, Japan. ‡‡ CompackDAQ, National Instruments, Austin, TX. §§ LabVIEW SignalExpress, National Instruments.
emax= 1=2ðea+ ecÞ + 1=2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½ðea- ecÞ2 + ð2eb- ea- ecÞ 2 q ð1Þ emin= 1=2ðea+ ecÞ -1=2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½ðea- ecÞ2 + ð2eb- ea- ecÞ 2 q ð2Þ Statistical Analyses
One-way analysis of variance (ANOVA) and Duncan multiple comparisons were used to assess differences in the peak values of principal strains between the models. All analyses were performed using a statisti-cal package of commercial softwareiiwith an a value of 0.05.
FE Analysis
Computer-aided design (CAD) software¶¶was used
to construct a model of the bone block based on a cross-section image of the human mandible in the molar region (Fig. 2A).23 The trabecular core was surrounded by the cortical shell. The cortical shell was divided into two parts: subcrestal cortical bone (SB) and connected cortical bone (CB). The SB was on top of the part of the crestal bone that did not touch the implant surface, and the CB was the remain-ing part of the cortex that was connected to the implant surface. Nine depths of SB were simulated, from 0 (equicrestal) to 1.6 mm, and eight thicknesses of CB were simulated, from 0.5 to 4 mm (Table 1 and Fig. 2A). Therefore, a total of 72 FE models were created for the analyses.
A screw-type of root-form implant (5 · 14 mm) was constructed using CAD software. After obtaining all of the models by applying Boolean operations to the variables, the corresponding solid models were ex-ported in the IGES format to the commercial FE soft-ware## to generate the FE models using 10-node tetrahedral h-elements.*** The interfacial condition between the implant and CB was set as bonded to sim-ulate ideal osseointegration. The contact condition between the abutment and implant was set with a frictional coefficient (m) of 0.3.24The implant and
abutment were modeled as titanium with homoge-neous and isotropic elastic properties. The cortical bone and trabecular bone were considered to be an-isotropic (i.e., with properties varying in different directions) (Table 2).25,26 The mesial and distal
surfaces of the bone models were constrained as the boundary conditions. The loading condition was applied on the top surface of the abutment. A 170-N oblique force was applied at 45 degrees to the long axis of the implant. Based on the convergence testing process27 for appropriate results, the element size was 0.2 mm for the upper part of cortical bone and 0.5 mm else-where in the model (Fig. 2B).
ANOVA was performed to determine how the depths of SB and the thickness of CB influenced the
maximum von Mises stresses in bone. Probability values of <0.05 were considered to be significant. The correlation coefficients (R2) and regressions
were used to determine the relationship between bone stress and various types of SB and CB.
RESULTS
In Vitro Experiments
The mean – SD values of the maximum (emax) and minimum (emin) principal strains on the buccal and lin-gual sides are shown in Figure 3. The peak values of bone strains are the minimum principal strains of bone at the buccal side around an implant (Buccal_emin), and those peak strains were all significant in ANOVA (P <0.001) and Duncan multiple comparisons among three models (Fig. 3). The peak value of bone strain was 48% lower in Model 2 (with a thicker cortical bone) than in Model 1 (-2012 – 114), and 38% lower in Model 3 (with 1-mm-thick subcrestal bone) than in Model 1. Table 1.
SB and CB Variables in FE Models
SB (mm) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 CB (mm) 0.5 1 1.5 2 2.5 3 3.5 4 — SB indicates the depth of cortical bone that did not touch the implant surface. CB is the distance of the remaining part of the cortex that was connected to the implant surface.
Table 2.
Material Properties in the FE Analyses
Material Young Modulus E (MPa) Poisson Ratio n Shear Modulus G (MPa) Cortical bone Ex 19,400 nxy 0.390 Gxy 5,700 nyz 0.300 Ey 12,600 nxz 0.390 Gyz 4,850 nyx 0.253 Ez 12,600 nzy 0.300 Gxz 5,700 nzx 0.253 Trabecular bone Ex 1,148 nxy 0.055 Gxy 68 nyz 0.010 Ey 210 nxz 0.322 Gyz 68 nyx 0.010 Ez 1,148 nzy 0.055 Gxz 434 nzx 0.322 Titanium 110,000 0.30
The subscripts indicate thex, y, and z axes represent the mesial-distal, superior-inferior, and buccal-lingual directions, respectively.
ii Version 9.1, SAS Institute, Cary, NC.
¶¶ SolidWorks 2008, SolidWorks Corporation, Concord, MA. ## ANSYS Workbench 10.0, Swanson Analysis, Huston, PA. *** ANSYS solid 187, Swanson Analysis.
FE Analyses
Both thickness of CB and depth of SB significantly (P <0.0001) affected the bone stress. The maximum von Mises stresses of bone in the 72 FE models are
listed in Table 3. The mean values of bone stresses in the models containing various depths of SB but with the same thickness of CB (bottom row in Table 3) indicate that the stresses reduced as the thick-ness of CB increased, but the rate of the stress reduction gradu-ally declined. The regression equa-tion between the stress and the thickness of CB was approxi-mately quadratic, with a strong correlation (R = 0.84) (Fig. 4A).
The mean stresses of bone in the models containing various thickness of CB but with the same depths of SB (right column in Ta-ble 3) indicate that the bone stress reduced as the depth of SB in-creased. However, no correlation between them was apparent when the depth of SB was <0.6 mm. The regression equation between the stress and the depth of SB was ap-proximately linear, but with a weak correlation (R = 0.37) (Fig. 4B). DISCUSSION
There are few surgical techniques that have been developed to Figure 3.
Mean values (error bars indicate SDs) of the maximum (tensile) and minimum (compressive) principal strains on the buccal and lingual sides of the four experimental models. ANOVA analysis shows the significant difference (P <0.001) in the peak strains (the minimum principal strains) of bone. Asterisks demonstrate significant differences in Duncan multiple range test among the three models.
Table 3.
Maximum von Mises Stresses (MPa) of Bone in the Models and SD in SB and CB Models
With the Same Variable Values
Measurement CB0.5 CB1.0 CB1.5 CB2.0 CB2.5 CB3.0 CB3.5 CB4.0 CB Mean SD SB0 112.4 68.7 56 45.6 40.6 38.4 36.6 35.9 54.3 26 SB0.2 97.4 80.4 56.7 46.3 42.1 41 38.1 38.4 55.1 22.2 SB0.4 97.2 72.3 52.7 46.4 43.2 40.8 41.5 40 54.2 20.4 SB0.6 70.2 64.1 46.1 41.3 36.4 35.5 32.1 31.6 44.7 14.7 SB0.8 73.6 53.7 37.8 34.5 31.1 30.2 28.3 28.4 39.7 16.1 SB1.0 66.5 55.2 49.6 44.1 39.3 36.1 34.7 33.6 44.9 11.6 SB1.2 58.3 46.3 43.8 36.3 32.2 30.6 31.4 32.3 38.9 9.8 SB1.4 60.1 45.8 37.2 35.9 34 31.8 30.6 29.4 38.1 10.3 SB1.6 57.9 48.3 35.1 33.3 35.1 33.6 32.3 29.2 38.1 9.8 SB Mean 77.1 59.4 46.1 40.4 37.1 35.3 34 33.2 SD 20.1 12.5 8.2 5.4 4.4 4.1 4.1 4.2
The numbers after CB and SB represent the amount of CB and SB (e.g., ‘‘CB2’’ means that the model has 2 mm of CB attached to the implant surface). As the increase of CB the bone stress is reduced, and the rate of the stress reduction is gradually declined. In addition, the bone stresses decrease as the SB increases over a certain depth (0.6 mm).
preserve peri-implant bone.28For example, bone
re-sorption is thought to be lower for a subcrestal place-ment of implant than for a traditional (equicrestal) placement of implant,20 but few researchers29have
investigated subcrestal placement of implant or the underlying biomechanical mechanisms. The present study might be the first to have investigated the biomechanical performances of various subcrestal placements of implants by using experimental strain-gauge measurements and nonlinear FE sim-ulations30,31 with statistical analyses. In the experi-mental tests, the strains were measured locally by sensors (i.e., strain gauges) attached at selected lo-cations. The strain gauges were placed on bone near the implant, and hence they were unable to
measure the peak value of the bone strain when this occurred within the bone. However, in the FE simulation, the peak values of the strain within bone were easily determined. Nevertheless, an FE approach produces an approximate solution rather than an exact one, and hence the combined tech-niques of experimental measure-ments and FE simulations as used in the present study might facilitate the understanding of biomechan-ical mechanisms related to sub-crestal implant placement.
The thickness of CB affects bone stresses and strains in both equicrestal and subcrestal im-plants. In the experimental tests, bone strain was lower in the model with 3-mm-thick CB (Model 2) than in the model with 2-mm-thick CB (Model 1). In the FE analyses, the thickness of CB also played a major role in stress reduction, es-pecially as it increased from 0.5 to 2.5 mm. These findings are con-sistent with previous studies indi-cating that thicker cortical bone reduces stress concentrations around implants.32,33However,
in-creasing the CB thickness above 2.5 mm in the models (to 3 and 4 mm) had less effect on stress re-duction; compared with 0.5-mm-thick CB (77.1 MPa), the mean stress decreased by 52% for 2.5-mm-thick CB (37.1 MPa), but only by 5% more for 4-mm-thick CB (decrease of 57%; 33.2 MPa). These findings indicate that the bone stress and strain do not reduce linearly as CB increases, with a limited range of CB thickness (<2.5 mm) being sufficient to provide a superior out-come in terms of decreasing the bone stress and strain around the implant.
The subcrestal placement of the implant into the cortical bone (SB) resulted in a length of bone that was not in contact with the implant. The experimental tests of the effects of the SB length showed that the bone strain was lower in the subcrestal implant (Model 3) than in the equicrestal implant (Model 1). Likewise, in the FE simulation the bone stresses decreased as the SB increased over a certain depth (0.6 mm). How-ever, why the bone stress did not reduce with in-creasing depth for SB >0.6 mm remains unclear Figure 4.
Scatterplot of maximum von Mises bone stress versus models with various thickness of CB (A) and depths of SB (B). Black line indicates the quadratic regression equation for all data points.
and hence requires further investigation. Neverthe-less, this study indicates that results of increasing the depth of SB to decrease the bone stress for a sub-crestal implant are not absolute, with only SB depths larger than a certain value seeming to decrease the bone stress. Therefore, with an evaluation of cortical bone thickness by radiograph or cone-beam com-puted tomography when the total cortical thickness is £2.5 mm, CB thickness should be primarily con-sidered, and equicrestal implant placement is recom-mended rather than subcrestal implant placement from a biomechanics viewpoint. However, for cortical thickness >2.5 mm, a moderate subcrestal implant placement (e.g., 0.6 mm) might be a suggestion for implants to further reduce the bone stress.
Another advantage of a subcrestal implant gen-erally observed in this study is that the peak stress, which might result in bone loss, is distant from the crestal region. Placing an implant subcrestally and using a Morse-taper abutment for the connection (platform switching) can transfer the high-stress area to the subcrestal region and make
it narrower, thereby avoiding the stress concentration at the crestal bone around the implant as is usually found in equicrestal im-plants (Fig. 5). Our findings might help to explain the clinical find-ing of Weng et al.15 that the use
of a subcrestally placed implant with a Morse-taper connection seemed to avoid a large ‘‘dish-shaped’’ bone defect (resorption). This might be beneficial to reduce the risk of bone loss caused by overloading around implants. However, some factors (e.g., in-flammation within the surround-ing tissues, reformation of the biologic width, presence of a microgap between implant and abutment, and peri-implantitis) also affect peri-implant bone loss and were not investigated in this study. This requires further in-vestigation.
One limitation of this study is the simplified geometry of the bone model in the experimental tests. Even though the strength of a bone block is similar to that of jaw bone, the strain patterns might vary with the bone ge-ometry. In addition, although the material properties of the FE mandibular model were assumed
to be anisotropic, the consideration of the inhomo-geneous properties is still needed in future studies. Another limitation was the use of a static occlusal force in the experiments and FE simulations. Al-though oblique loading has been suggested to repre-sent a realistic occlusal load,34chewing movement, especially with dynamic loading simulations, needs to be considered in future investigations.
CONCLUSIONS
Within the limitations of this study, the following conclusions can be drawn. First, increasing the thick-ness of CB reduces bone stress and strain in both equicrestal and subcrestal placement of implants. However, bone stress and strain do not decrease lin-early with increasing CB thickness; only at a certain range of CB thickness (<2.5 mm) can significant reduction occur in the bone stress and strain around the implant. Second, for the results of the subcrestal implant, only at certain depths of SB (0.6 to 1.2 mm)
Figure 5.
von Mises stress distributions in the cortical bone in the equicrestal implant model CB1.5/SB0 (A) and the subcrestal implant model CB1.5/SB0.4 (B). A 45-degree of oblique force (170 N) was applied on the top of the implant and dark blue to red colors represent stress values from lower to higher. The result shows that subcrestal implant placement has a smaller area of high (red) bone stresses than equicrestal implant placement.
is there a benefit to decreasing the surrounding bone stress and strain.
ACKNOWLEDGMENTS
This research was supported by the National Science Council (NSC 98-2320-B-039-005-MY3), a govern-ment-funded organization in Taiwan. The authors thank Ms. Kuan-Ting Chen, China Medical University Biostatistics Center, for her help in statistical ana-lyses. The authors report no conflicts of interest re-lated to this study.
REFERENCES
1. Bra˚nemark PI, Adell R, Breine U, Hansson BO, Lindstro¨m J, Ohlsson A. Intra-osseous anchorage of dental pros-theses. I. Experimental studies.Scand J Plast Reconstr Surg 1969;3:81-100.
2. Adell R, Lekholm U, Rockler B, Bra˚nemark PI. A 15-year study of osseointegrated implants in the treatment of the edentulous jaw.Int J Oral Surg 1981;10:387-416. 3. Jemt T, Lekholm U, Gro¨ndahl K. 3-year followup study of early single implant restorations ad modum Bra˚nemark.Int J Periodontics Restorative Dent 1990; 10(5):340-349.
4. Berglundh T, Lindhe J. Dimension of the periimplant mucosa. Biological width revisited. J Clin Periodontol 1996;23:971-973.
5. Tarnow DP, Cho SC, Wallace SS. The effect of inter-implant distance on the height of inter-inter-implant bone crest.J Periodontol 2000;71:546-549.
6. Ericsson I, Persson LG, Berglundh T, Marinello CP, Lindhe J, Klinge B. Different types of inflammatory reactions in peri-implant soft tissues.J Clin Periodon-tol 1995;22:255-261.
7. Hermann JS, Schoolfield JD, Schenk RK, Buser D, Cochran DL. Influence of the size of the microgap on crestal bone changes around titanium implants. A histometric evaluation of unloaded non-submerged implants in the canine mandible. J Periodontol 2001; 72:1372-1383.
8. Miyata T, Kobayashi Y, Araki H, Ohto T, Shin K. The influence of controlled occlusal overload on peri-implant tissue. Part 4: A histologic study in monkeys. Int J Oral Maxillofac Implants 2002;17:384-390. 9. Isidor F. Influence of forces on peri-implant bone.Clin
Oral Implants Res 2006;17(Suppl. 2):8-18.
10. Heckmann SM, Linke JJ, Graef F, Foitzik CH, Wichmann MG, Weber HP. Stress and inflammation as a detri-mental combination for peri-implant bone loss.J Dent Res 2006;85:711-716.
11. Nociti FH Jr., Cesco De Toledo R, Machado MA, Stefani CM, Line SR, Goncxalves RB. Clinical and microbiological evaluation of ligature-induced peri-implantitis and periodontitis in dogs. Clin Oral Im-plants Res 2001;12:295-300.
12. Zitzmann NU, Berglundh T, Ericsson I, Lindhe J. Spontaneous progression of experimentally induced periimplantitis.J Clin Periodontol 2004;31:845-849. 13. Lazzara RJ, Porter SS. Platform switching: A new
concept in implant dentistry for controlling postrestor-ative crestal bone levels.Int J Periodontics Restorative Dent 2006;26(1):9-17.
14. Todescan FF, Pustiglioni FE, Imbronito AV, Albrektsson T, Gioso M. Influence of the microgap in the
peri-implant hard and soft tissues: A histomorphometric study in dogs.Int J Oral Maxillofac Implants 2002;17: 467-472.
15. Weng D, Nagata MJ, Bell M, Bosco AF, de Melo LG, Richter EJ. Influence of microgap location and configuration on the periimplant bone mor-phology in submerged implants. An experimental study in dogs. Clin Oral Implants Res 2008;19: 1141-1147.
16. Pontes AE, Ribeiro FS, Iezzi G, Piattelli A, Cirelli JA, Marcantonio E Jr. Biologic width changes around loaded implants inserted in different levels in relation to crestal bone: Histometric evaluation in canine man-dible.Clin Oral Implants Res 2008;19:483-490. 17. Pontes AE, Ribeiro FS, da Silva VC, et al. Clinical and
radiographic changes around dental implants inserted in different levels in relation to the crestal bone, under different restoration protocols, in the dog model. J Periodontol 2008;79:486-494.
18. Welander M, Abrahamsson I, Berglundh T. Subcrestal placement of two-part implants. Clin Oral Implants Res 2009;20:226-231.
19. Welander M, Abrahamsson I, Berglundh T. Place-ment of two-part implants in sites with different buccal and lingual bone heights.J Periodontol 2009; 80:324-329.
20. Barros RR, Novaes AB Jr., Muglia VA, Iezzi G, Piattelli A. Influence of interimplant distances and placement depth on peri-implant bone remodeling of adjacent and immediately loaded Morse cone connection im-plants: A histomorphometric study in dogs. Clin Oral Implants Res 2010;21:371-378.
21. Kawaguchi T, Kawata T, Kuriyagawa T, Sasaki K. In vivo 3-dimensional measurement of the force ex-erted on a tooth during clenching.J Biomech 2007; 40:244-251.
22. Hoffmann K. An Introduction to Measurements Using Strain Gages. Darmstadt, Germany: Hottinger Baladwin Messtechnik; 1989:1-257.
23. Eraslan O, Inan O. The effect of thread design on stress distribution in a solid screw implant: A 3D finite element analysis. Clin Oral Investig 2010.14:411-416.
24. Alkan I, Sertgo¨z A, Ekici B. Influence of occlusal forces on stress distribution in preloaded dental implant screws.J Prosthet Dent 2004;91:319-325.
25. O’Mahony AM, Williams JL, Spencer P. Anisotropic elasticity of cortical and cancellous bone in the poste-rior mandible increases peri-implant stress and strain under oblique loading.Clin Oral Implants Res 2001;12: 648-657.
26. Huang HL, Chang CH, Hsu JT, Fallgatter AM, Ko CC. Comparison of implant body designs and threaded designs of dental implants: A 3-dimensional finite element analysis. Int J Oral Maxillofac Implants 2007; 22:551-562.
27. Huang HL, Hsu JT, Fuh LJ, Tu MG, Ko CC, Shen YW. Bone stress and interfacial sliding analysis of implant designs on an immediately loaded maxillary implant: A non-linear finite element study. J Dent 2008;36: 409-417.
28. Hermann F, Lerner H, Palti A. Factors influencing the preservation of the periimplant marginal bone.Implant Dent 2007;16:165-175.
29. 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.
30. Hsu JT, Fuh LJ, Lin DJ, Shen YW, Huang HL. Bone strain and interfacial sliding analyses of platform switching and implant diameter on an immediately loaded implant: Experimental and three-dimensional finite element analyses.J Periodontol 2009;80:1125-1132.
31. Eser A, Akcxa K, Eckert S, Cehreli MC. Nonlinear finite element analysis versus ex vivo strain gauge mea-surements on immediately loaded implants.Int J Oral Maxillofac Implants 2009;24:439-446.
32. Holmes DC, Loftus JT. Influence of bone quality on stress distribution for endosseous implants. J Oral Implantol 1997;23:104-111.
33. 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.
34. Geng JP, Tan KB, Liu GR. Application of finite element analysis in implant dentistry: A review of the literature. J Prosthet Dent 2001;85:585-598.
Correspondence: Professor Heng-Li Huang, School of Den-tistry, China Medical University and Hospital, 91 Hsueh-Shih Road, 404 Taichung, Taiwan. Fax: 1-886-4-22014043; e-mail: hlhuang@mail.cmu.edu.tw.
Submitted January 25, 2010; accepted for publication August 5, 2010.
