2. Materials and methods
2.1 Finite element modeling
2.1.1 Imaging processing
The posterior mandible (distal of the 2nd premolar to the mesial of the 2nd molar) was taken out from a human dry skull and, frontal sections of computer tomography (CT) images (1 mm interval between images) were obtained. From each CT image (Fig 6a), material boundaries were delineated by an in-house imaging program. This program employs various thresholds in CT number and searches for maximum gradient values of the CT number, which can be used to detect the boundary pixels between different materials (Chang 1990). A depth first search algorithm is then used to find the nearest boundary pixels to re-number the pixels and construct the contour of each material (Fig 6b). The stack of these contours are then put into ANSYS (Swanson Analysis Inc., Huston, PA, USA) to generate a three-dimensional solid model of the mandible.
A resin crown of the implant was duplicated from the first molar, which was then scanned by CT. The same procedure mentioned above was then used to create a three-dimensional solid model of the crown.
2.1.2 Solid model processing and the element type
All implant models were cylindrical with the length of 11.5mm. The detail components of abutment were omitted. The solid models of the posterior mandible, the crown, and the implant were arranged by surgical allocation. After all models were combined by overlap of the Boolean operation, 10-node tetrahedral p-elements (ANSYS solid 148) were used to construct the finite element models.
2.1.3 Anisotropic materials properties
The material properties of the cortical and trabecular bone of the six models were applied as transversely isotropic and linearly elastic (O’Mahony 2001). For cortical bone the buccolingual plane was elastic isotropic along the axis of mesiodistal
isotropic along the axis of inferosuperior direction. The materials of the implant and prosthetic crown were assumed to be isotropic and linearly elastic (Sertgoz 1996;
Ciftci 2000). All material properties are listed in Table 1.
2.1.4 Loading condition and boundary condition
The loading condition was distinguished into two loading modes for evaluation.
The vertical loading mode is vertical forces at central fossas, and the oblique loading mode is oblique forces at functional buccal cusps with 45 degree of lingual inclination.
The magnitude of each force was 100 Newton and was applied at each prostheses unit.
The boundary condition was constrained at the bottom surface of the mandibular bone in all directions. In this study, the region of interest was near the ridge of the mandibular, hence the interference caused by the boundary constraint did not existed.
The bone-implant interface and crown-implant interface were rigidly bonded in all models.
2.1.5 The convergence criteria
All models reached convergence based on the changes of global strain energy less than 5%. The p-element method in ANSYS was used for the convergence tests and the p-value was set to be between 2 (the initial value) and 8 until the convergence was achieved. Most models got converged at p = 4.
2.1.6 The description and dimensions of models
To investigate the effects of crown splinting and various molar implant supports, three implant support conditions (standard implant, wide implant, and two implants) combined with two crown states (splinted and non-splinted crown) were modeled. In total, six finite element models constructed with 10-node tetrahedral p-element (ANSYS solid 148), were generated. To label these models, two sets of symbols were used. The first set of the symbol indicates the splint factor: ‘Spl’ for splinted and
‘nSpl’ for non-splinted. The second set of the symbol represents the implant’s configurations, i.e., S for standard implant (3.75mm in diameter), W for wide implant (5 mm in diameter) and T for two implants (3.75mm in diameter). Table 2 summarizes the notations of these six models. The finite element models of Spl-S, Spl-T and nSpl-W are shown in Fig 7. In these six models, the mandible segment was approximately 32mm mesiodistally, 12 mm buccolingually at the premolar site, and 15 mm buccolingually at the molar site.
In addition, the solid models included a posterior mandible, a splinted crown and three implants (3.75mm in diameter) were arranged along surgical allocation of three kinds of placements (Model In-line, Model B-offset and Model L-offset) as shown in
Fig 8 and Fig 9. Model In-line was defined as insetting implants along a straight line.
Model B-offset and Model L-offset were defined as insetting implants to interlace buccal and lingual offset placements. In these three models, the mandible segment was approximately 38 mm mesiodistally, 11 mm buccolingually at the premolar site, and 16.7 mm buccolingually at the molar site.
2.2 Experimental strain gauge verification (ESGV)
The acrylic resin (Tempron, GC, Kasugai, Japan), a posterior mandibular sample was duplicated from the same mandibular cadaver used in the FE modeling. The splinted second premolar and first molar crown (crown type of Model Spl-S) was also replicated with another acrylic resin (Luxatemp, DMG, Hamburg, Germany). The material properties of these two resins were measured by the uni-axial compressive test on cube specimens which were plastered with bi-axial strain gauges. The Young’s modulus was calculated from the slope of the stress-strain curve within the elastic region. The Poisson’s ratios were obtained from the quotient of the transverse (εt) and axial (εa) strains, that is, ν = εt /εa. These material properties are listed in Table 3 and were used in the validation FE model.
Two stainless steel cylinders (diameter 3.75mm, length 12mm), mimicking the implants, were embedded in the mandibular model with the splinted crown. Two single-axis strain gauges (KFG-1-120-C1-11L1M2R, KYOWA, Tokyo, Japan) were cemented on the lingual side of mandibular model near the implant with cyano-acrylate cement (CC-33A, KYOWA, Tokyo, Japan) (Fig 23), oriented toward the directions of the minimal principal strain obtained from the validation FE model.
In order to evaluate various loading effects, a clamping jig was designed with an adjustable screw-system so that the vertical load could be transferred into an oblique load on the implant/mandible construct (Fig 10). On the premolar crown and the molar crown, a force was applied either at the center fossa with vertical direction or at the buccal cusp with 45 degree buccal inclination, hence in total there were four loading conditions (Fig 11). For each of these four loading cases, two force magnitudes, 100N and 200N, were applied. The strain values were recorded through the data acquisition system (instruNet Hardware, GW instruments, Inc , MA, USA).
Each measurement was repeated three times.
The FE model “Spl-S” was used as the validation FE model for the experimental validation. Therefore, the material properties, loading and boundary conditions of the validation FE model were re-assigned based on the experimental setup. The surface nodes on the lingual mandible near the implant, corresponded to the measured areas
the comparison with principal strains measured in experimental model.
Table 1 Material properties of the finite element models Material
The vectors of x, y and z indicate the buccolingual, infero-superior and mesiodistal direction, respectively.
Fig 6 (a) The CT image of mandible and crown (b) The contours of crown, cortical bone and trabecular bone.
(a) (b)
Table 2 Design parameters of dental implant and prostheses on posterior partial edentulous (2nd premolar and 1st molar) restoration.
Model Layouts of implants Types of prostheses
Spl-S Splinting prosthetic crowns
nSpl-S Non-splinting prosthetic crowns
Spl-T Splinting prosthetic crowns
nSpl-T Non-splinting prosthetic crowns
Spl-W
Splinting prosthetic crowns nSpl-W
Non-splinting prosthetic crowns
(a) (b) (c)
Fig 7 Illustrations of (a) Model Spl-S, the splinted crown were supported by one standard implants at the 1st molar site and one standard implant at the 2nd premolar site. The oblique loads (100N each) were applied on the buccal functional cusps. (b) Model Spl-T, the splinted crown were supported by two standard implants at the 1st molar site and one standard implant at the 2nd premolar site. (c) Model nSpl-W, the non-splinted crowns were supported by one wide implant at the 1st molar site and
3.75 mm
2nd Premolar 1st molar
6.25 mm
5.0 mm
Fig 9 (a) The iso-view and (b) the buccaolingual section of the on-line mode of 3D FE model of the implant-supported posterior prostheses.
Fig 8 The placement designs of the ISPP; the distance of offset was set as 1.2mm.
Because of the anatomic limitation about the buccolingual width of mandible on premolar site, the mesial-distal implant position was not shifted in all three models.
Table 3 Young’s Modulus and Poisson’s ratio of each material of the experimental model was assigned to the validation finite element model.
Material Young’s modulus E (MPa)
Poisson’s ratio ν
Resin (temporon) 2979 0.4
Resin (Luxa temp) 6880 0.4
Steel (ASTM-A242) 200000 0.3
Fig 10 (a) The experimental model was fixed by the aluminum clamping jig with 45 degree of lingual inclination. (b) The self-development of load apply machine.
Fig 11 The strain gauges were attached on the lingual side of the experimental mandibular mold. The resistors of each strain gauge were set along the direction of minimum principle strains obtained from the FE model. Arrows indicated the four loading points (dimples) located on the central fossa and functional cusps.
3. Results
Table 4 shows the minimum (compressive) principal strains in the experimental model and the validation FE model under the four loading conditions. The experimentally measured compressive strains were doubled when the loading increased from 100N to 200N which indicated a linear status of this model. In general, the experimental strains were higher than the simulated strains and the differences were 10% to 50%. However, comparing within all loadings, the experimental and simulated results did show a consistent relationship. This indicated a high correlation between the experimental and the finite element approaches (r2=0.97).
On the results of splinted or non-splinted crowns with standard, wide and two implants
Fig 12 shows the von Mises stress distributions on the cortical bone of the six FE models. High stresses were located at the alveolar crest around the implants, which matched the clinical observations of crestal bone loss (Rangert 1995). In addition, no stress was concentrated at the space between the two implants of two-implant models (Models Spl-T and nSpl-T).
The peak von Mises stresses on the cortical bone around each implant of the six models are shown in Fig 13. With the splinted prosthesis, the peak stresses of bone at the first molar region decreased by 29% in Model Spl-T and 31% in Model Spl-W, respectively, as compared to Model Spl-S. Likewise, with non-splinted prosthetic crowns, the peak stresses of bone at the first molar region were reduced by 37% in Model nSpl-T and 35% in Model nSpl-W, respectively, as compared to Model nSpl-S.
However, the peak stress difference between the wide implant and two implants, for both splinted and non-splinted groups, were not significant.
As for the splinting effect, with a standard implant under molar crown, the differences of peak bone stresses between Model Spl-S and Model nSpl-S were not significant at both premolar and molar regions. However, in two-implant models, the peak stress at premolar region for splinted crown (Model Spl-T) was decreased by 25% as comparing with non-splinted crown (Model nSpl-T). In the wide implant models, the peak stress at premolar region was decreased by 36% as comparing Model Spl-W with Model nSpl-W. This demonstrated that the splinted factor is vital only if the support of the implant at the first molar region is stronger than that at the premolar region.
On the results of in-line, buccal offset and lingual offset placements
To present the simulated results more clearly, the three implants were labeled as implant #1, #2 and #3 from mesial to distal directions, that is for implants placed into
premolar, first molar and second molar regions respectively. For each implant, the peak maximum principal (tensile) stress, the potential fracture index for metal, is located on the implant neck for all three models under both vertical and oblique loading modes. The oblique loading increased the implant stress by at lease 5 times than that of the vertical loading as listed in Table 5. Compared with the In-line placement, only the implant #2 of the L-offset placement under the vertical loading presented a slight peak stress increasing of 1.4%. All the other implants of the buccal and lingual offset placements demonstrated a peak stress decreasing up to 17% and 22% under the vertical and oblique loadings respectively. The largest peak tensile stress among the three implants occurred in implant #1 and the offset placements could provide a 7% of peak stress reduction as compared with the In-line placement on this implant.
The peak von-Mises stress values of cortical and trabecular bones around each implant are shown in Table 6. The peak stresses in cortical bone occurred in the crestal cortex area, and for the trabecular bone the peak stresses occurred near the apex of the implant. Comparing with the In-line placement, under vertical loading, the peak stress of cortical bone was increased by 19% around implant #2 of B-offset placement and by 5.9% around implant #3 of L-offset placement. However, in L-offset placement the peak stress of cortical bone was decreased by 13% around implant #1. The peak stress of trabecular bone around implant #2 was increased by 30% in B-offset placement and by 66% in L-offset placement. In contrast, the peak stress of trabecular bone around implant #1 was decreased by 22% in B-offset placement and by 14% in L-offset placement.
Under oblique loading, the peak stress at cortical bone was increased by 16%
around implant #2 of B-offset placement and by 5.1% around implant #3 of L-offset placement as compared to the In-line placement. However, in the L-offset placement the cortex peak stress was decreased by 9.9% around both implant #1 and #2. In the B-offset placement, the peak stresses of trabecular bone around each implant presented only minor changes. In the L-offset placement, the peak stresses of trabecular bone raised by 14% and 49% around implant #1 and #2 respectively and diminished by 15% around implant #3.
The stress distributions of crestal cortical bone under vertical loading and oblique loading were displayed in Fig 14 and Fig 15. The stress concentration occurred at crestal cortical bone in all models. In addition, comparing the area of gray strips (high stress region) around each implant in Fig 14 and Fig 15, it showed no difference between in-line and offset placements.
Table 4 The mean microstrains (MS) and standard error (SE) measured form the experimental in-vitro test, which were compared with strains of the validation finite element model.
Load
Fig 12 The von Mises stress distributions on the crest bone for the models with (a) splinted crowns and (b) non-splinted crowns.
(a)
(b)
Table 5 The highest maximum principle stress value (MPa) of each implant
In-line B-offset L-offset Implant
no. V O V O V O
#1 16.9 141.1 16.35 131.6 16.85 131.04
#2 16.5 104 14.44 87.89 16.73 81.06
#3 14.58 82.25 12.16 77.34 12.03 69.09 The symbolisms of V and O are represented the vertical loading
and oblique loading modes respectively.
(a)
(b)
Fig 13 The peak von Mises stress of cortical bone around each implant for (a) the splinted crown and (b) the non-splinted crown. Implant 1 is placed in the 2nd premolar region while Implant 2 and Implant 3 are placed in 1st molar region.
Table 6 The maximum von-Mises stress value (MPa) of cortical and trabecular bone around each implant.
Cortical bone Trabecular bone
In-line B-offset L-offset In-line B-offset L-offset Implant
no.
V O V O V O V O V O V O
#1 16.47 51.06 17.3 49.96 14.41 46.01 1.26 3.56 0.98 3.68 1.09 4.04
#2 20.42 59.31 24.26 68.72 21.07 56.69 1.19 3.71 1.55 3.62 1.98 5.54
#3 27.46 77.56 27.08 76.75 29.07 81.51 1.57 5.19 1.64 5.27 1.36 4.43 The symbolisms of V and O are represented the vertical loading and oblique loading modes
respectively.
Fig 14 The von-Mises stress distribution of the crestal bone of the ISPP along three placement designs under the vertical loading condition.
4. Discussion
The predicted principal strains by the validation FE model had a trend similar to those measured from ESGV among all loadings. The deviations in strain values between the ESGV and the FE simulation may be attributed to the measuring error in material properties, and the loading locations and directions between two approaches.
Besides, the orientation of the strain gauge, which does not align perfectly with the direction of principal strains, may also contribute to the deviations in strain. However, these deviations were proportionally changed in response to the alternation of biomechanical parameters in the models. For a purpose of comparing different implant designs, the FE simulation in this study was, therefore, verified.
The advantage of the present FE models was assured by the computed tomography images. In general, the simulated results of FE modeling depend considerably on the geometric structures of the models. In previous finite element studies, the mandibular model was either simplified as a rectangular configuration (Stegaroiu 1998; Wang 2002) or constructed by digital laser scanner (Ciftci 2000;
Akca 2001). The latter approach provides accurate surface topography but lacks the Fig 15 The von-Mises stress distribution of the crestal bone of the ISPP along three placement designs under the oblique loading condition.
cortical shell information, which may over/under predict stress/strain distribution of bone around the implant. Further, by introducing the anisotropic model (O’Mahony 2001), the characteristic of bone material was better reflected.
The investigation of splinted or non-splinted crowns with standard, wide and two implants
The use of the wide implant or two implants in the molar region can provide the advantage of reducing stress in the surrounding bone as shown in this study. This is because of the increased structural capacity and the enlarged bone-implant contact area offered by these implants. Balshi et al. (1996) indicated that a molar crown supported by a standard size implant can easily introduce large bending moments to bone because the dimension of the crown is usually greater than the diameter of the implant. Therefore, the wide implant or two implants are suggested for placement at the molar region to reduce the possibility of overload, which may lead to implant failure associated with the marginal bone loss (Rangert 1995). However, whether the wide-diameter implant (D 5.0mm) or two implants (D 3.75mm) is preferred for the edentulous molar restoration is still an issue. Based on the outcomes of this study;
differences between these two treatments are not significant. Therefore, with sufficient posterior mandibular bone width (buccal-lingual direction), the wide implant is suggested to reduce the surrounding bone stress due to the simplicity of its surgical procedures. However, according to the report of the Davarpanah et al. (2001), placing the wide implants in narrow posterior ridges can lead to marginal bone loss that may raise the risk of implant failure. Therefore, in the cases of insufficient posterior mandibular bone width, two implants are preferred because the stress reduction by two implants is about the same as that induced by the wide implant.
Further, the narrow distance (2.5 mm in this study) between the two implants of two-implant treatment would not increase the bone stress. Nevertheless, it is necessary to note that, recent clinic reports (Attard 2003, Ivanoff 1999) showed that using wide implants could result in higher failure rates than that of the standard implant. However, the authors pointed out that the failure might be associated with the surface treatment and shape of the implant and patients’ bone quality rather than the usage of wide implants.
Some scientific data suggested that prosthetic crown splinting had biomechanical advantage and could raise the success rate because occlusal force could be shared through splinted crowns, thus, decreasing the peak-stresses (Guichet 2002; Wang 2002). However, there is insufficient quantitative evidence to support this hypothesis.
Wang et al. (2002) had developed simplified FE models to evaluate this splinting effect and demonstrated that splinting the prosthetic crowns could reduce stresses in bone. Similar observations were presented in the study of Guichet et al. (2002) using photoelastic models. However, in their simulations the implant structures were loaded on the premolar only. When loading is applied to a single crown and, by splinting the crowns, the loading would redistribute itself through the implant under the unloaded crown, and then the peak stress of bone is decreased certainly. In the present research, the bite forces were exerted at both functional cusps of two crowns to mimic full contacts of normal occlusion. The results of the present study showed that there is no significant difference between Model Spl-S and Model nSpl-S; that is, with standard implants for both premolar and molar, the splinting effect is minimal. Our result
Wang et al. (2002) had developed simplified FE models to evaluate this splinting effect and demonstrated that splinting the prosthetic crowns could reduce stresses in bone. Similar observations were presented in the study of Guichet et al. (2002) using photoelastic models. However, in their simulations the implant structures were loaded on the premolar only. When loading is applied to a single crown and, by splinting the crowns, the loading would redistribute itself through the implant under the unloaded crown, and then the peak stress of bone is decreased certainly. In the present research, the bite forces were exerted at both functional cusps of two crowns to mimic full contacts of normal occlusion. The results of the present study showed that there is no significant difference between Model Spl-S and Model nSpl-S; that is, with standard implants for both premolar and molar, the splinting effect is minimal. Our result