2. Introduction of Nonlinear Property into Three-Dimensional Finite Element Method

– Part 2 Mechanical Examination of R.P.D. with Extracoronal Attachment –

R. Kanbara, Y. Nakamura, Y. Ohno, T. Iwai, K. Yoshihara, H. Kumano, T. Masuda, Y. Tanaka

Department of Removable Proshodontics, School of Dentistry, Aichi-Gakuin University

Introduction

Extracoronal attachments are often utilized to eliminate visible clasp retainers for purposes of esthetics and improved comfort.  While a bilaterally clasped partial denture is a common design for purposes of cross-arch stability, appropriately designed unilateral partial dentures may be of useful application.  The intraoral dynamics of this denture design may be of significance for study.

The evaluation and realistic simulation of differential function of different of prosthetic designs has been previously reported using the finite element method (FEM). The finite element method (FEM) has traditionally evaluated the linear behavior of various materials.  The incorporation of non-linear formulas and variables has resulted in improved in-vitro simulation of clinical prosthetic load conditions.

The analysis of periodontal ligament and oral mucosa soft tissues has been selected for evaluation and prosthetic load investigation. In the present study, the simulation of the complex behavior of these soft tissues was accomplished using an analysis program simulating the non-linear properties of these soft tissues.

Objective

The purpose of the present study was to introduce nonlinear tissue behavior properties into the periodontal ligament and oral mucosa analysis models for functional investigation of the different prosthetic designs using extracoronal magnetic attachments.

Materials and Methods

1.            Analysis model

  Figure 1 shows the analysis model used in the present study. The model was constructed by Ando using patient CT data and study model¹⁾. An attachment denture design restoring missing mandibular left first and second molars was used. The lower left canine, first and second premolars were restoratively splinted with a fixed partial denture splint incorporating extracoronal magnetic attachments at the distal abutment.

2.            Material non-linear analysis

  A custom analysis program was developed to permit non-linear evaluative capacity to the FEM program used. (Fig. 2)

The new analysis program automatically changes the material constants of the residual ridge and periodontal ligament in order to simulate material non-linear behavior in a three-dimensional finite element analysis model. The behaviors of the residual ridge and periodontal ligament were approximated to reported human tissue property values²⁾. Additional improvements are reported in this present study. Specified reported material non-linear properties were assigned to the residual ridge and periodontal ligament.

  The non-linear tissue modeling capacity results in a test model that may show differential findings in response to a changing test load level. The model behavior response from low to high levels of response would not be accurately representative with linear tissue models of different supporting tissues and structures. The load behaviors of a partial denture, supporting abutments, the attachment behavior under varying load application were investigated.

3.        

2.1       Material non-linear property of the soft tissue

  Non-linear properties of the residual ridge and the previously reported human tissue behavior measurements. (Figures 3).

Using these human tissue values, these measured were subdivided into 7 parts for the residual ridge, and 3 parts for the periodontal ligament. The load-displacement curves of the residual ridge mucosa and periodontal ligament are shown in Figures 4.

Table 1 shows the material constants and stress values for the material constant conversion points.

2.2       Analysis conditions

The analysis model was constructed using CT data input into CAE prepost for converted fabrication of the master finite element model with standard hardware (Patran 2010 windows 64bit, MSC software) (Dell Precision T7400Round Rock, Texas, USA). Modeling analysis conditions were set into tetrahedron and pentahedron elements. The analysis was set for elastic type stress analysis. An analysis software was used for evaluation.(marc 2010 - MSC). A complier was also used as a to introduce the program simulating non-linear soft tissue properties into the analysis. (Intel (R) visual fortran compiler 10.1)

2.2.1    Compone  nts and mechanical properties

Table 2 shows components and mechanical property values that define the material properties.

2.2.2    Boundary conditions

Figure 5 shows load conditions used in the present analysis.

Vertical loads from 5 N to 200 N (equivalent to occlusal force) were applied to the occlusal surfaces of the simulated test partial dentures.

Figure 6 shows constraint and contact conditions used in the present analysis.

A complete constraint was applied to the inferior border of the mandible in the X, Y, and Z directions.

Coulomb’s friction coefficient (μ=0.01) was applied as the contact condition between the mucosal base of the denture and the corresponding residual ridge mucosa, abutment and extracoronal magnetic attachment, and adjacent magnetic attachment retainer and the different test dentures.

Results

1.            Displacements related to different load applications (dentures and abutments)

1.1   Displacement of the anterior part of the denture

Figure 7 shows a change in displacement of the anterior part of the denture related to different load applications. The focal measurement point was the central pit of the lower left first molar of the denture.

1.2   Displacement of the posterior part of the denture

Figure 8 shows a change in displacement of the posterior part of the denture related to different load applications. The focalized measurement point was a posterior margin of the denture base.

1.3   Distal displacement of the abutment (lower left second premolar)

Figure 9 shows a change in distal displacement of the abutment related to different load applications. The focal measurement point was the buccal functional cusp tip of the lower left second premolar.

2.            Displacement of an extracoronal magnetic attachment

Figure 10 shows a vertical displacement of the attachment when the maximum 200 N was applied, and actual strength measurement of an extracoronal attachment with identical designs as previously reported³⁾.

Discussions

1.            Non-linear analysis

A program was developed that automatically changes material constants when the setup stress values exceed the von Mises stress value in order to simulate viscoelastic behavior of the residual ridge mucosa and periodontal ligament (Figures 2, 4). The non-linear tissue modeling technique enables applied prosthetic load evaluations to be more consistent with known reported in vivo conditions. The  defined soft tissue behaviors had not previously been considered for modeling simulation.

2.            Loading condition

When the opposing teeth are healthy, average occlusal force applied to the lower first molars of the partial denture is 14 kg in male and 11 kg in female.(you need a reference for this statement) The average occlusal forces for a  periodontal ligament-borne single-tooth prosthesis, was 23 Kg in male and 17 Kg in female.

The prosthetic denture design of the present study was considered to be periodontal ligament-borne. It is considered that occlusal force applied to the denture base was higher than the reported values of the partial denture. Therefore, the maximum load was set close to the single-tooth denture occlusal value (200 N) assuming the occlusal force applied in the present denture design.

3.            Analysis results

Miyashita⁴⁾ reported that the displacement value of a free-end denture base demonstrated more rapid displacement at lower occlusal forces, and higher resistance to displacement at higher occlusal force loads. The results of the present study (Figures 7 and 8) demonstrated non-linear increasing strain of the posterior margin of the denture base with increased stress. These findings are consistent with those previously reported. Miyashita measured vertical displacements of a denture when the occlusal force up to 8.0 kgf was applied, and reported that vertical displacements range between 110 and 350 μm. The result of the present study was also within this previously reported displacement range.

The distal displacement of the lower left second premolar (Fig 9) demonstrated the material non-linear properties to the periodontal ligament, suggesting that the periodontal ligament of an abutment in the analysis model was non-linearly resistant to the distal displacement. These finding are consistent with reported in vivo findings⁵⁾.

Nakashima et al.³⁾ using a  fabricated an extracoronal magnetic attachment with the identical form as the present analysis study, and reported the strength of an attachment with a  keeper applied load. The report demonstrated an elastic deformation limit of an attachmentwas 140 μm at a 338 N load, followed by permanent deformation when that load level is exceeded. Stress concentrations at an attachment should be minimized since a minimal permanent deformation would significantly impairs the attachmentsfunctionality. The attachment fabrication alloy (Fig. 10) of the present model was Degudent Universal. (Densply Sankin). The displacement at the attachment was investigated for an occlusal force equivalent load simulation (200 N). A displacement of 35.3 μm was observed in the loading direction with a 200 N load application to the denture occlusal surface. Although the material composition of testing model extracoronal attachments values may be slightly different, the attachment’s displacement is considered elastic at the test load equivalent of occlusal force application,  thus suggesting  an acceptable condition for anticipated clinical use.

Something will be happened.

Conclusions

  The non-linear viscoelastic behavior of the residual ridge and periodontal ligament in the analysis model was determined using the finite element method to accurately simulate intraoral mechanical dynamics of a partial denture. The validities of the analysis results and material non-linear analysis were confirmed, and the following conclusions obtained.

1.            The introduction of the material non-linear properties to the residual ridge and periodontal ligament enabled the application of load conditions not previously demonstrated.

2.            The displacement values for abutments and denture demonstrated more rapid displacement at lower load application, and higher resistance to displacement at higher load applications, confirming non-linear behavior.

3.            The elastic displacement of an attachment at occlusal force load equivalents was determined to be acceptable for the prosthetic designs tested.

References

1.               Ando A, Nakamura Y, Kanbara R, Ohno Y and Tanaka Y, Stress Analysis of the Surrounding Tissue of a Extracoronal Attachment using  Three Dimensional Finite Element Method, J J Mag Dent 18(1):32-41, 2009.

2.               Kanbara R, Nakamura Y, Ando A, Kumano H, Masuda T, Sakane M, Ohno Y, Matsukawa R, Takada Y and Tanaka Y, Stress Analysis of an Abutment Tooth with Extracoronal Magnetic Attachment -Introduction of Nonliner Property into Three-Dimensional Finite Element Method-, J J Mag Dent 19(2):44-51, 2010.

3.               Nakashima H, Kumano H, Nakamura Y, Masuda T, Ando A, Miyata T, Hasegawa A, Tanaka Y, Development of the extracoronal attachment "GIGAUSS C 600 EC Keeper Tray", J J Mag Dent 16(2):39-43, 2007.

4.               Miyashita T, Displaceability under localized pressure in the mucous membrane and settling of the denture base caused by biting pressure. Shikwa Gakuho 70(1):38-68,1970.

5.               Ogita K, Measurement of Three-Dimensional Movement of Anterior teeth. J. Japan Prosthodont. Soc. 27(6) : 1210-1233,1983.