Finite Element Analysis of Removable Partial Dentures

Experimental procedures were approved by the West China Hospital of Stomatology, Sichuan University (reference number WCHSIRB-D-2018-105). All methods were performed in accordance with the relevant guidelines and regulations in the informed consent. And the informed consent was gotten to publish identifying information including CBCT and oral master model. A 3-dimensional FEA solid model of lower jaw was constructed using clinical CBCT data and master model scanned data from a 53-year-old Chinese patient with bilateral dissociation deletion of Kennedy Class I. Oral examination showed a severely absorbed mandibular bone with 34–37, 31–43, 46, and 47 teeth missing (FDI standard), and no other abnormality was discovered among the remaining teeth. The modeling steps are shown in Fig. 3.Figure 3

The flow chart of modeling.

The mandibular bone was scanned with CBCT (3D Accuitomo scanner, Morita, Kyoto, Japan) at a 0.25-mm-slice thickness and 1-mm scan increment in 401 slice images in DICOM format. The images were imported into the Mimics (Mimics 17.0, Materialise NV) to obtain the mandibular bone model and the remaining teeth models. The output data were then imported to Geomagic Studio (Geomagic Studio12.0, Geomagic Co, USA) for surface reconstruction. The remaining teeth models A (RTMA) and mandibular bone model A (MBMA) were obtained for further use.
The mandibular impression was made by using alginate impression materials, and the master model was made with plaster. The features of oral mucosa were obtained by scanning the master model with a desk scanner (3shape D2000, Denmark), and the obtained data were imported to Geomagic Studio for surface reconstruction. Digitalized master model (DMM) was obtained for further use.
RTMA, MBMA and DMM were aligned in Geomagic Studio by matching three matching points on the remaining teeth surfaces of RTMA and DMM. Boolean operation was first used to remove the exposed part of bone of MBMA to obtain the final mandibular bone model (FMBM). Boolean operation was then used to remove the remaining crowns on the DMM by subtracting it with RTMA, and the final mucosal model (FMM) was obtained. The mucosa thickness was defined with the vertical distance between the mandibular bone surface and the mucosal surface. The 3D oral model obtained with this technique can provide a more accurate geometrical morphology and thickness of mucosa, which is crucial for RPD simulation. The PDL was simulated by adding a 0.2 mm thick shell to the interface area between bone and tooth models, and then the volume shell is subtracted from the bone in order to define the PDL volume as previous studies proposed^{41 (link),42 (link)}. Following the design specifications for RPDs, 4 kinds of RPDs were designed by an experienced prosthodontist as well as technician together by using 3shape Dental System software (Dental system 2017, Denmark). Figure 4 demonstrated the 4 different designs of frameworks, and the designs are as follows:Figure 4

4 Different designs of frameworks.

Framework A: an RPT (Rest-Plate-T bar) clasp set in the canine of left mandibular region; an RPI (Rest-Plate-I bar) clasp set in the second premolar of right mandibular region.
Framework B: an RPT (Rest-Plate-T bar) clasp set in the canine of left mandibular region; an arrow clasp between the premolars of the right mandibular region.
Framework C: an RPT (Rest-Plate-T bar) clasp set in the canine of left mandibular region; an RPL (Rest-Plate-L bar) clasp set in the first premolar of right mandibular region; a back-action clasp in the second premolar of right mandibular region.
Framework D: an Aker clasp in the canine of left mandibular region; a combined clasp between the premolars of right mandibular region.
The FMBM, FMM, RTMA and all the frameworks, denture bases and denture teeth models were then processed by Abaqus/CAE (2016, SIMULIA Co, USA) to convert into a three-dimensional FEA solid model (Fig. 5). The ten-node tetrahedral elements were selected for the models. A convergence study was carried out to determine the optimal size of elements. In Fig. 6, the influence of the size of elements on the maximum Von-Mises stress and maximum displacement of the model is presented. It shown that the stress and displacement were converged as the element size smaller than 0.2 mm. As a result, the size of elements can be located as 0.2 mm.Figure 5

Final components of the model.

Figure 6

Convergence study: Influence of the size of elements on maximum Von-Mises stress and maximum displacement of finite element model.

All materials except the PDL were assumed to be linearly elastic, homogenous and isotropic to simplify the calculations. Table 1 showed the elastic modulus and the Poisson ratio for each material^{43 (link)–45} . As for the PDL, the nonlinear hyper-elastic model was used based on the double linear stress-strain curve of Vollmer’s²⁸ research: when the dependent variable of PDL ɛ < 7.5%, E1 = 0.05 MPa; and when ɛ > 7.5%, E2 = 0.22 MPa. Also, there are several studies used nonlinear parameters with mucosa, previous studies showed that with RPD scenario, the simulation results with linear mucosa parameter were highly correspondence with in vitro test results with sensors^{46 (link)}, indicating linear parameter of mucosa is acceptable under normal occlusal force with RPD scenario. There are also several studies used the same method to investigate the stress and displacement of mucosa with RPD, which can simplify calculation process as well as obtain accurate results^{20 (link),47 (link),48 (link)}.Table 1

Material properties of finite element models.

Material	Elastic Modulus (MPa)	Poisson Ratio
Mucosa	3.45	0.45
Denture Base	2,200	0.31
Cancellous Bone	1,370	0.30
Cortical Bone	13,700	0.30
PDL	Non-linear (see below)	0.45
Tooth Dentin	18,600	0.30
Denture Tooth	1,960	0.30
Co-Cr Alloy	235,000	0.33
Titanium Alloy	11 * 104	0.35
PEEK	4,100	0.4

The tooth was simplified as a uniform dentine material without concerning about the difference between the dentine and the enamel, as the mechanical property of these two materials are proved to be similar in the previous study^{49 (link)}. The PDLs and teeth roots, the denture teeth and denture base were considered as position constraints. The interfaces between the clasps and the remaining teeth were modeled as frictional contacts with appropriate friction coefficients (μ = 0.1), and the friction coefficients between the denture base and mucosa was assumed as μ = 0.01^{43 (link),44} .
To simulate an occlusal force, a vertical load of 120 N was applied to the occlusal surface of both the artificial first molar^{39 (link)}. Although different masticatory activities (e.g. grinding) with various loading patterns may affect the optimization outcome, but the effects of other masticatory activities are less significant compared to the direct biting force because of the magnitudes^{50 (link)}. The following were investigated: the von Mises stress values of the PDLs, mucosa, frameworks, and the displacement of frameworks. Data were exported to SPSS 19.0 (IBM, Chicago, USA) for statistical analysis. One-way ANOVA and the Student-Newman-Keuls q test was used to determine differences among different framework materials and different framework design schemes. For all comparisons, statistical significance was declared if p < 0.05.