2. Materials and methods
2.2 Experimental Strain Gauge Verification
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.