Dental Materials Journal 2012; 31(2): 297–308

INTRODUCTION

Mechanical modeling evaluations compared different prosthetic designs and treatment planning concepts1). These studies require an accurate simulation of the functional differences between different supporting tissues. The accurate replication of the loading capacities of tissues is important. A non-linear response to loading differences between soft and hard tissues has been previously reported2,3). While mechanical modeling has shown basic qualitative differences and relationships, computer modeling can more effectively demonstrate a quantified assessment of complex modeling differences4,5). The computer based three dimensional (3D) modeling behavior of non-linear soft tissue systems has not been previously reported.

The finite element method (FEM) has developed as a technique for structural analysis. Technical and software improvements have allowed higher resolution accuracies. The FEM depends upon the setting of “constants” for the construction of analysis objects and structural models. These constants require the mathematical valuation setting of analysis limits of modeled oral prosthetics and supporting tissues. The mathematic property values comprising the analysis model component tissue model parts upon which a test model is based, incorporates previously known values. Previous studies have utilized a single material constant for each tissue type resulting in a single linear relationship evaluation.

The residual ridge mucosa and periodontal ligament has been reported to demonstrate non-linear properties based upon human subject measurements6-9). Previous finite element studies and mechanical modeling methods

have demonstrated the basic linear relationships and modeling of different prosthetic treatments involving hard and soft tissue support10-12). A non-linear simulation of soft tissue behavior requires a continuous adjustment of the study material model constant.

Prior finite element evaluations have shown different applications of dental prosthesis designs with specialized attachments11,12). These studies have demonstrated the significance of design geometry for modeled prostheses using a selection of fixed material constants for each supporting tissue or hardware structure. The dependence upon fixed material constant values for the residual ridge mucosa and periodontal ligaments limits the simulation potential and loading range accuracy. This limitation increases simulation error between the actual human subject measurement and the calculated values used during a heavier loading range testing.

Initial finite element non-linear evaluations and testing of creep properties have been shown with two-dimensional base model designs13-15). The modeling detail was nodally limited in earliest 3D finite element models. However, significant improvements in CT data achieved a higher refined detail. Despite the improvements in 3D modeling detail, the application of non-linear definition capable 3D model evaluations has not been previously shown16).

The purpose of this study was to demonstrate the methodology of non-linear evaluation and simulation of differential displacement of simulated human residual ridge mucosa and periodontal ligament supporting different prosthodontic treatments using a 3D modeling finite element analysis.

Three-dimensional finite element stress analysis: The technique and methodology of non-linear property simulation and soft tissue loading behavior for different partial denture designsRyo KANBARA1, Yoshinori NAKAMURA1, Kent T. OCHIAI2, Tatsushi KAWAI3 and Yoshinobu TANAKA1

1Department of Removable Prosthodontics, School of Dentistry, Aichi-Gakuin University, 2-11 Suemori-dori, Chikusa-ku, Nagoya 464-8651, Japan 2Dental Science Center-DEN, University of Southern California, 925 West 34th Street, Los Angeles, California, 90089-0641, USA 3Department of Dental Materials Science, School of Dentistry, Aichi-Gakuin University, 1-100 Kusumoto-cho, Chikusa-ku, Nagoya 464-8650, JapanCorresponding author, Ryo KANBARA; E-mail: ryo1221@dpc.agu.ac.jp

The purpose of this study was to develop and report upon a methodology for a non-linear capacity 3D modeling finite element analysis evaluating the loading behavior of different partial denture designs. A 3D finite element model using human CT data was constructed. An original material constant conversion program was implemented in the data simulation of non-linear tissue behavior. The finite element method material properties of residual ridge mucosa were found to have seven material constants and six conversion points of stress values. Periodontal tissues were found to have three constants, and two conversion points. Three magnetic attachment partial denture designs with different bracing elements were evaluated. Technical procedures for finite element model simulation of nonlinear tissue behavior properties evaluating the oral behavior of prosthetic device designs are reported for prosthodontic testing. The use of horizontal cross-arch bracing positively impacts upon the comparative stability of the partial denture designs tested.

Keywords: Finite element stress analysis, Non-linear soft tissue behavior, Residual ridge mucosa, Periodontal ligament

Received Jul 29, 2011: Accepted Dec 20, 2011doi:10.4012/dmj.2011-165 JOI JST.JSTAGE/dmj/2011-165

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The non-linear modeling technique will be utilized to evaluate different partial denture designs. The partial dentures studied evaluate specific horizontal bracing connector designs with magnetic attachment retained mandibular partial dentures. The present paper reports fabrication procedures and analysis methods for the FEM material property design for residual ridge mucosa and periodontal ligament17-20).

MATERIALS AND METHODS

Finite element analysis test modelMaster model fabrication: A digitally imaged model of a partially edentulous mandible restored with a distal extension partial denture was constructed using human subject CT data (Mimics, Version 11.0, Materialise, Leuven, Belgium)(Fig. 1). The use of CT data was approved by the Aichi-Gakuin School of Dentistry Research Ethics Committee (No.259). The reference model subject data was then input using computer aided engineering (CAE) pre/post processing software (Patran 2010 windows 64bit, MSC software, Los Angels, USA) for fabrication of the FEM master model. Figure 2 shows FEM model fabrication procedures and testing methods. A high performance computer workstation (PRECISION T7400, DELL, Round Rock, Texas, USA) was used for the study. A patient test model was fabricated using the master model for the dental–alveolar base model, and the soft tissues of the supporting edentulous mucosal tissue ridge and periodontal ligament tissue areas of the abutment teeth were then separately replicated. Residual ridge mucosa was defined from CT data as the area between the cortical bone surface and the mucosal base of the denture. The periodontal ligament was defined by a 0.2 mm peri-radicular space surrounding the inter-osseous supported abutment teeth roots. The FEM mandibular model fabricated thus consisted of

supporting residual ridge mucosa, supporting teeth, and mandibular alveolar osseous bone structures.

Prosthesis test model design: A Kennedy class II mandibular distal extension partial denture using extracoronal magnetic attachment was digitally designed and fabricated11,21). The restorative design restored prosthetic dentition to the lower left, first and second molars. The canine and premolars were designated as supporting abutments and splinted using a fixed partial denture restoration retaining a distal extracoronal keeper attachment. Three partial dentures with different bracing support were designated for comparison. The test designs included: a lingual bracing arm, a rest seat arm bracing, and a cross arch bracing arm design (Fig. 3).

Fig. 2 Flow chart of FEM digital model fabrication procedures.

Fig. 1 Master model.

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The testing of different prosthesis designs required that the different denture test prostheses together with their respective fixed abutment areas be digitally replaced for each design testing condition as needed on the mandibular model as shown in Fig. 3.

Soft tissue behavior modeling: Software programming and material constant conversion pointsThe measured applied load displacement values of human subject residual ridge mucosa and mandibular canine (periodontal ligament) have been previously reported. These reports describe vertical displacement of the residual mucosa at the loading site, and displacement

of the periodontal ligament in the apical direction during loading of the mandibular canine (Fig. 4). The residual ridge mucosa6) and mandibular canine7) displacement values were integrated into the mandibular soft tissue model. Non-linear behavior soft tissue displacement requires continued mathematic adjustments.

A material constant conversion program was developed to analyze and simulate the non-linear displacement measurements of residual ridge mucosa and periodontal ligament abutment tissue for simulation of known loading response measurement values found for human subjects. The specialized programming was run as a user subroutine13) with a general purpose

Fig. 3 Prosthesis test model design (distal extracoronal keeper attachment). (a) Lingual bracing arm design, (b) Rest seat arm bracing design, (c) Cross-arch bracing arm design

Fig. 4 Actual soft tissue displacement to load measurement values. (a) residual ridge mucosa6), (b) mandibular canine (periodontal ligament)7)

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nonlinear structure analysis solver program (Marc 2008, MSC software, Los Angels, USA) to reflect the program analysis. A compiler software program was used to facilitate data access (Visual Fortran compiler, Version 10.1, Intel, Santa Clara, USA) (Fig. 5).

The definitions of input criteria to the material conversion programming were input as follows. The residual ridge mucosa and periodontal ligament elements were defined as orthotropic materials, and their element number designations were entered into the programming calculations. The respective set of von Mises stress values were input for each of the specified element components. The von Mises stress values define limits of stress values where the material constants values are reflected non-linearly for the differing component structures. The program proportionally changed the material constants with changes in given stress values at these points for each structural level. The material constants of the residual ridge mucosa and periodontal ligament were automatically altered when the setup stress values exceed each of the designated von Mises stress value reflection points.

The application of material constant conversion pointsThe material constants and their conversion points are critical determinants for non-linear simulation and representations of residual ridge mucosa and periodontal ligament tissue behaviors. The specified application of determined conversion points and material constants results in a close simulation to known tissue behavior values (Table 1).

Each structure was evaluated using these differential soft tissue displacement levels and values. The basic non-linear differences between residual ridge mucosa and periodontal ligament are partially represented by the number of mathematic displacements. Residual ridge mucosa required seven separate displacements and periodontal ligament required three displacements (Fig. 6).

These loading conditions were set as close to the referenced experimental condition as possible for each actual known component measurement shown for human subjects. A complete constraint was applied to the mandibular plane. Programming methodology of displacement levels and corresponding load conditions are shown for the main loading displacement levels.1. Initial displacement points and analysis definitions(a) First displacement definitionsFigures 7 and 8 show the analysis condition of the residual ridge mucosa and the periodontal ligament. The 0.06 kgf load was applied to 60 mm2 loading range, and a 100 gf load was applied on the crown of a mandibular canine in the tooth axial direction. The first displacements of the residual ridge mucosa and the periodontal ligament in the actual measurement are shown in Figs. 6(a) and (b). The first displacement of the residual ridge mucosa under 0.06 kgf load application was 82.5 µm, and that of the periodontal ligament under 100 gf load application was 10 µm. Material properties (Young’s modulus E and Poisson’s ratio γ) were determined so that those values were close to the actual measurements in humans. The von Mises stress value of the element under this condition was separately calculated.2. Further displacement analysis and definitionsThe secondary displacements of the residual ridge mucosa and the mandibular canine in the actual measurement shown in Fig. 6 were 125.0 µm under 0.3

Fig. 5 Programming methodology, material constant conversion computer programming and analysis.

Table 1 Material properties and conversion point of stress value

Residual Ridge Mucosa Periodontal Ligament

Young’s Modulus (MPa) Poisson’s Ratio

Conversion point of Stress Value (MPa)

Young’s Modulus (MPa) Poisson’s Ratio

Conversion point of Stress Value (MPa)

1st 0.150 0.300 1st 0.070 0.2500.002114 0.002584

2nd 0.700 0.350 2nd 0.180 0.3000.006044 0.005648

3rd 3.000 0.350 3rd 0.200 0.3500.024457

4th 3.900 0.3500.038255

5th 4.600 0.4500.055987

6th 11.000 0.4700.056688

7th 16.500 0.490

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kgf load application, and 16.1 µm under 300 gf load application (see Table 1).

Following the initial displacment, the secondary displacement value programming automatically uses the first displacement von Mises stress value as the material constant conversion point first to secondary displacement when the initial conversion point values are exceeded. The program change reflection point was automatically set and performed as a user subroutine.

The residual ridge mucosa secondary displacement material constant was determined by the user subroutine to maintain the first displacement until 0.06 kgf load application, and then approaches the actual human measurement under 0.3 kgf load application. This stress value at the material constant was also set as the conversion point from secondary to third displacement.

The mandibular canine secondary displacement material constant was determined by the same analysis using a subroutine in the periodontal ligament, and the stress value was calculated in the same methods.

3. Third displacement and above analysis definitionsThe secondary displacement obtained material constants and stress values were added to the program to simulate the third displacement, and the analysis was performed using a subroutine for all defined structures. The material constant was determined in the same method as reported the secondary displacement simulation, and the stress value at the conversion point was calculated (Table 1).4. Defined displacements and application of material constants In summary, the mathematical programming process was repeated for each displacement level. A total of seven material constants and stress values for the six conversion points were calculated residual ridge mucosa the same process from the first to third displacement was repeated to the seventh displacement. A total of three material constants up to the third displacement and two stress values were calculated for the periodontal ligament. The basic load displacement curves for each of

Fig. 6 Displacement reflection points for actual measurement values (Load to Displacement curve). (a) residual ridge mucosa (1st–7th displacement) (b) mandibular canine (1st–3rd

displacement)

Fig. 7 Analysis condition (residual ridge mucosa). Fig. 8 Analysis condition (periodontal ligament).

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the different tissue modeled components were presented in graphic form (Figs. 9 and 10).

All modeling parameters were calculated and set using a custom programming user sub-routine to differential separate defined displacement points and previously-reported tissue measurements. Non-linear tissue behavior simulation results in residual ridge mucosa having seven defined displacements, and the periodontal ligament having three defined displacements.

Prosthesis design testing and modeling simulation applicationThree different types of bracing support were designated for comparison (Fig. 3). The magnetic attachment retainer design used incorporates non-resilient contact between distal keeper attachment and the prosthetic magnetic retainer. All extracoronal magnetic designs included a slit where a part of denture metal frame was engaged for retention. 1. Load conditionSequential loads were applied to the tested denture

saddle areas (50 N, 100 N, 200 N). 2. Constraint conditionA compete constraint was applied to the inferior border of the mandible in the X, Y, and Z directions.3. Components and mechanical property values Table 2 shows components and mechanical property values of the analysis model. The same material constant was used for a crown, attachment, and metal frame. The material constants of the oral mucosa and periodontal ligament were changed to reflect the analysis, and the initial and secondary displacements were reproduced.

RESULTS

Comparative denture displacement measurements for magnetic partial denture designsDisplacements of the inferior border of denture were measured along the vertical and horizontal axis of movement. Figures 11 and 12 show the linear measurements. The horizontal linear displacement demonstrated greater range variation compared to the

Fig. 9 Load to displacement curve (residual ridge mucosa).

Fig. 10 Load to displacement curve (periodontal ligament).

Table 2 Model components and mechanical property values

Young’s Modulus (MPa) Poisson’s Ratio Young’s

Modulus (MPa) Poisson’s Ratio

Residual Ridge Mucosa 0.150 0.300Residual Ridge Mucosa 0.700 0.350Periodontal Ligament 3.000 0.350

3.900 0.350Cortical Bone 11,760 0.250 4.600 0.450Sponge Bone 1,470 0.300 11.000 0.470Dentin 11,760 0.350 16.500 0.490Metal 94,080 0.300 Periodontal Ligament 0.070 0.250Resin 2,450 0.300 0.180 0.300

0.200 0.350

Depend onthe Stress Value

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vertical displacement. The cross-arch design demonstrated the lowest comparative horizontal movement. Although the vertical displacement comparisons appeared tighter in range valuations, the lingual bracing arm design demonstrated the least vertical movement of the three designs tested. The range of measurements did not appear to change greatly for both vertical and horizontal testing comparisons at three different levels of force application. 1. Lingual bracing armThe lingual bracing arm design demonstrated higher levels of horizontal movement compared to the other designs. The bracing arm design also demonstrated lower levels of vertical displacement compare to the other designs. The range of vertical movement was within about 13% of the other two designs but about 30% higher in the horizontal range of observed movements. 2. Rest seat arm bracingThe rest seat design showed less horizontal movement than the bracing arm but more than the cross arch bracing arm design. The vertical displacement observations were virtually identical to the cross arch arm design in displacement and only slightly higher than the bracing arm design. 3. Cross-arch bracing armThe cross arch arm demonstrated the greatest resistance to horizontal movement based upon vertical force loading to the partial denture.

Comparative Stress distribution evaluations for supporting tissues with different magnetic partial denture designs1. Supporting cortical bone effects Stress distribution to supporting cortical bone was highest for the bracing arm design and lowest for the cross arch arm partial design at all levels of force application to the tested partial dentures. At lower levels of force application, the load transfer is limited to the most proximal abutment alveolar areas, but as force

application increases, the observed stress distribution increases slightly in the buccal side of the splinted abutment connector between the first and second premolars (Fig. 13).(a) Lingual bracing armThe lingual bracing arm design demonstrated higher levels of stress distribution to supporting cortical bone compared to the other designs. The bracing arm design also demonstrated highest stress concentration for the most proximal abutment areas.(b) Rest seat arm bracingThe rest seat design showed less stress distribution than the bracing arm but more than the cross arch bracing arm design. (c) Cross-arch bracing armThe cross arch arm demonstrated the greatest stress relief to supporting cortical bone compared to the other designs.

2. Supporting tooth/dentition effectsEvaluation of the supporting radicular and prepared tooth areas demonstrated stress concentrations to all splinted abutments. The proximal supporting tooth abutment showed similar levels of support for all partial designs tested (Fig. 14).(a) Lingual bracing armThe lingual bracing arm design demonstrated higher levels of stress concentration to the distal area of cuspid abutment compared to the other designs tested.(b) Rest seat arm bracingThe rest seat design demonstrated slightly higher levels of stress concentration to the mesial and buccul area of second premolar abutment compared to the other designs.(c) Cross-arch bracing armThe cross arch arm demonstrated the greatest stress relief to supporting radicular and prepared tooth areas compared to the other designs.

Fig. 11 Vertical denture displacements for three designs of partial denture (vertical axis of movement).

Fig. 12 Horizontal denture displacements for three designs of partial denture (horizontal axis of movement).

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3. Supporting restorative abutment effectsAt lower force application levels, the observed stress distributions appeared similar for all partial designs tested. However, as force application increase, the bracing arm design showed lower relative force transfer to the extracoronal keeper connection to the distal abutment compared to the cross arch arm and mesial rest designs. The cross arch arm partial denture demonstrated highest force load transfer to the magnetic keeper areas compared to the mesial rest and lingual bracing arm designs. The mesial rest partial denture demonstrated slightly higher stress concentration to the mesial connector of the distal proximal abutment (Fig. 15).(a) Lingual bracing armThe lingual bracing arm design demonstrated lower levels of stress concentration to the extracoronal keeper connection to the distal abutment compared to the other designs. However, the bracing arm design demonstrated slightly heigher levels of stress concentration to the connection between cuspid and first premolar compared to the other designs.(b) Rest seat arm bracingThe rest seat design showed slightly less stress concentration than the cross arch bracing arm design but more than the bracing arm design. The rest seat design also showed slightly higher stress concentration

to the connector of the distal proximal abutment.(c) Cross-arch bracing armThe cross arch arm partial denture demonstrated highest force load transfer to the magnetic keeper areas compared to the other designs. However, the cross arch arm partial denture demonstrated slightly lower stress concentration to the connector of the distal proximal abutment.

DISCUSSION

A prior two-dimensional finite element analysis of the residual ridge mucosa and periodontal ligament demonstrated the functional application of a non-linear functional modeling assessment. The complexity of modeling non-linear soft tissue behavior required two-dimensional modeling initially to assess and evaluate non-linear applications to FEM evaluative programs. Simulations and accurate modeling of the complex structures and morphology of the oral cavity require computed adjustment of the mathematic programming for an accurate simulation. The use of CT patient data ensures the modeling accuracy of the physical hard tissue structures simulated. Relating these concepts to prior mechanical modeling investigations assists in the assessment of evaluative contrast to prior held concepts and ideas.

The patient data generated 3D finite element models

Fig. 13 Stress distributions to cortical bone for three designs of partial denture (50 N, 100 N, 200 N).

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demonstrate accuracy in the skeletal and dental anatomic details as well as providing for realistic prosthetic design applications. Denture base mucosa and abutment tissue behavior details have been reported in mechanical studies of partial dentures22). The accurate and uniform application of these soft tissue definitions and structures permits idealized evaluative comparison to various known prosthetic materials and the design permutations. Although it has been reported that residual ridge mucosa and periodontal ligament independently demonstrates complex behavior, the independent mathematically identified differential tissue reflection point method results in an accurate computer modeling simulation.

The use of defined displacements related to differential load applications to residual ridge mucosa and periodontal ligament tissues required a material constant conversion program that changed the material constants at different stress value conversion points in order to more appropriately and accurately simulate non-linear soft tissue behavior found under supporting oral soft tissues using the FEM.

The methodology of programming and analysis was specifically described for the development of the programming subroutine used with the analysis solver in addition to a conventional calculation routine. This new programming subroutine technique enabled the

uniquely reported finite element analysis simulation of residual ridge mucosa and periodontal ligament displacements to be realistically non-linear in manner that approaches actual measurement values found in humans.

The deformations and physical displacement of loaded oral tissues is thought to be determined by the hydraulic movements of blood and lymph. The lateral hydraulic fluid movements have been reported to be a main determinant for tissue deformations, and are the foundational supports and determinants of movement for prosthetically loaded tissues6,23,24). Although the calculations and component definitions of each of the structure tissues evaluated in this study did not independently separate the lateral components of hydraulic fluid movement mechanics in this study, the estimation maintained overall prior reported measured tissue movement levels under load. In this study, the overall soft tissue displacements of residual ridge mucosa and the periodontal ligaments are evaluated as a sum of the displacement of each defined tissue including both the different soft tissues and constituent fluids.

The mathematic programming accommodation for the non-linear soft tissue behavior simulation is determined by a balance between two important constants: Young’s modulus and Poisson’s ratio. Young’s modulus is a constant that defines amount of a vertical

Fig. 14 Stress distributions of tooth/dentition for three designs of partial denture (50 N, 100 N, 200 N).

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strain of elastic material. The Poisson’s ratio is a constant that defines the ratio of the amount of a vertical strain and the amount of a horizontal strain. These constants are important to the calculation of material properties. The user program of this study automatically changed the material constant at increased physical loads and the defined reflection points or known displacement values of tissue. An increase in the lateral strain of the residual ridge mucosa is larger than vertical strain with increasing loads due to the lateral hydraulic movement of tissue fluid. Therefore, the Poisson’s ratio was considered to be increased. The material constant in the program was set so that the Poisson’s ratio increased with increasing loads to account for this physical phenomena.

The material constant of the periodontal ligament was set so that the Poisson’s ratio increased with increasing loads. Due to the complex structure of the periodontal ligament, the model was fabricated around the root using pentahedron element with 0.2 mm dual structure. The residual ridge mucosa properties affect the behavior of mandibular canine since the tooth is in contact with the oral mucosa in the experimental model. To minimize the influence, the material constant of the periodontal ligament was determined after the material constants of the oral mucosa for each load was fixed on the experimental model.

The confirmation of these settings was confirmed by the measurement and analysis of the test model load-displacement curve. Confirmation of the present study using load-displacement curve confirmation validates the use of automaticchanges for material constants, and demonstrates that appropriate individual displacements for loads applied on the residual ridge mucosa and mandibular canine, measurements were used. The displacements at each load using the user subroutine modified developed program, plotted this load-displacement curve confirmation.

Analysis of confirmation curves permitted programming evaluation of displacement values. The analysis results were obtained by analyzing the displacement using a user subroutine (Figs. 9 and 10). Properties of the residual ridge mucosa were confirmed for simulation by converting 7 material constants. The displacement of the residual ridge mucosa is influenced by the material constant set in the analysis due to the finite element calculation method. We increased the number of converting material constants to obtain the results that were mathematically similar to actual measures found for residual ridge mucosa displacement properties.

Three material constants were used for the analysis of the periodontal ligament. The first period simulated an initial rapid displacement followed by slower second

Fig. 15 Stress distributions of restorative abutments for three designs of partial denture (50 N, 100 N, 200 N).

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and third displacements. These results approached close to previously known periodontal ligament tissue properties found.

The stress-strain curves of the residual ridge mucosa and periodontal ligament were plotted from the calculation history of each structural element at a maximum load to confirm the validity of the program that automatically changes material constants. The confirmation results demonstrated non-linear increasing strain with increased stress. These findings suggest the functionality of the automatic change to the material constants, and close simulation of tissue model behaviors approaching those of the human model.

Evaluation of three different partial denture designs, using a uniform retention design and minor changes to the bracing minor connector design, demonstrated significant recordable changes attributed to each of the designs tests. The use of the FEM modeling method permits a careful individualized component by component evaluation not previously possible by prior physical modeling methods or techniques.

Quantitative evaluation of the physical displacements of the different partial denture designs tested resulted in a demonstration of data significance for movement in the horizontal versus the vertical planes. Conventional partial denture designs have traditionally reported upon the benefit of cross-arch stabilization versus localized minor connector features for partial dentures24-26). The FEM evaluative method permitted a quantifiable evaluation of the proportional relevance of localized versus cross-arch application of horizontal bracing features.

The qualitative evaluation stress concentrations was facilitated by the individual component by component evaluation of the alveolar support, tooth abutment and restorative abutments. The use of such stress distribution data may result in extrapolations of clinical recommendations for tooth restoration and preparation designs, as well as prosthetic abutment and partial denture design feature selection.

CONCLUSION

A non-linear property was mathematically introduced into an analysis programming software for the simulation of non-linear soft tissue behavior under simulated loading of residual ridge mucosa and periodontal ligament with different prosthetic device designs. The programming methodology is described and used for the finite element evaluation of human oral soft tissue mechanical dynamics testing. The validities and attributes of the analysis results and the use of a material constant conversion program were confirmed. The following conclusions were obtained.

1. The behaviors of the residual ridge mucosa and periodontal ligament approximate actual measurements reported in humans. A non-linear property to simulate soft-tissue behavior was successfully introduced into a finite element model. Accurate simulation of human subject

tissue function under prosthetic loading is demonstrated.

2. The introduction of the material non-linear properties to the individual model component tissues, residual ridge mucosa and periodontal ligament tissues, enabled the application of load conditions not previously possible in the linear analysis finite element models.

3. Three designs of partial denture designs retained with magnetic retention attachments were evaluated. The cross arch arm design demonstrated good horizontal bracing stability. All designs of partial dentures demonstrated relative stability and retention of design.

The FEM method described provides for the non-linear simulation of supporting soft tissue properties of greater detail and modeling accuracy.

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