Finite Element Analysis of MOD Prosthetic Restored Premolars

LILIANA SANDU, FLORIN TOPALĂ, SORIN POROJAN

School of Dentistry

“V. Babeş” University of Medicine and Pharmacy 9 Revolutiei 1989 Blv., 300041 Timişoara

ROMANIA lilianasandu@gmail.com

Abstract: Inlays and onlays can be used on premolars requiring a MOD restoration instead posterior composite

resins or amalgam direct restorations and offer a durable alternative. Because it is known that MOD restorations may increase the susceptibility to fracture, it is important to ensure optimal performance in

selection of the adequate preparation design to reduce stresses in teeth structures and also in the restorations.

However, inlays and onlays do not restore the original strength of tooth tissues. The aim of the study was to

determine, using finite element analysis, the optimal shapes of metal and ceramics MOD restorations in

premolars in order to minimize the potentially damaging effects of stress on teeth structures and restorations.

The study was performed on an upper first premolar, using a finite element analysis. 3D models of maxillary

first premolars, prepared for MOD inlays and onlays with different tapers were generated. The mesh structure

of the solid 3D model was created using the computational simulation of Ansys finite element analysis

software. An occlusal load of 200 N was conducted, and stresses occurring in the metal and ceramics inlays,

onlays and teeth structures were calculated. In the MOD onlays recorded maximal stresses were higher than in the MOD inlays in the most cases. In the ceramics restorations the stresses were higher than in

the cast metal. Regarding the prosthetic restorations material, in the ceramics inlays and onlays the stress

values were higher. MOD inlays transferred more functional stress to the teeth structures compared to the MOD

onlays.

Key-Words: premolar, MOD cavity design, cast metal restoration, inlay, onlay, 3D model, stress analysis.

1 Introduction Inlays and onlays can be used on premolars

requiring a MOD restoration instead posterior

composite resins or amalgam direct restorations and

offer a durable alternative. Because it is known that

MOD restorations may increase the susceptibility to

fracture, it is important to ensure optimal

performance in selection of the adequate preparation

design to reduce stresses in teeth structures and also

in the restorations.

Inlays restore central cavities in teeth.

Onlays restore one or more cusps and may

completely cover the occlusal surfaces, resulting in

a favorable distribution of stresses in teeth and a

decreased risk of fractures. However, preparation

for onlays requires additional tooth reduction relative to inlay restorations [1, 2].

Because it is known that MOD inlays may increase

the susceptibility to fracture, it is important to

ensure optimal performance in selection of the

adequate preparation design to reduce stresses in

teeth structures and also in the restorations [1].

Large restorations have been considered the

principal factors to predispose a tooth to fracture,

and adequate preparation guidelines are important.

Irrespective of the cavity preparation design,

preparations weaken teeth. To reduce loss of tooth

tissue and to improve biomechanical results, inlay

and onlays restorations are good treatment choices

for extensive cavities in posterior teeth [3, 4].

Cast metal inlays and onlays can prove to be

extremely long-lived restorations because of the

excellent mechanical properties of the gold alloys.

Ceramic inlays are primarily composed of leucite-

reinforced ceramics. The disadvantages of ceramic

are its hardness, which is greater than enamel, low

fracture resistance, and low fatigue strength. The

primary causes of failure of ceramic inlays are

cohesive bulk fractures and marginal deficiencies. Ceramic inlays maintain better anatomic form of the

surface and exhibit better marginal integrity, as well

as stabilize the weakened cusps better than

composite resin inlays [5-12]. However, inlays and

onlays do not restore the original strength of tooth

tissues. Previous studies on strength of MOD prosthetic restored teeth could not resolve which

restoration material provides greater strength and

marginal integrity [13,14].

Mathematical Methods and Techniques in Engineering and Environmental Science

ISBN: 978-1-61804-046-6 402

Finite element analysis (FEA) has been widely

employed in many researches to investigate the

impact and effect of dental materials and restorative

techniques on stress distribution. FEA is deemed as

an effective tool to evaluate the biomechanical

characteristics of these dental restorative materials

and systems, whereby the results carry significant

clinical implications [15,16].

Modern design and valuation in order to obtain an

adequate strength involves numerical simulations.

2 Purpose The aim of the study was to determine, using finite

element analysis, the optimal shapes of metal and

ceramics MOD restorations in premolars in order to

minimize the potentially damaging effects of stress

on teeth structures and restorations.

3 Materials and Method Detailed three-dimensional models are required to

better understand the mechanical behavior of teeth structures and prosthetic dental restorations. The

first step of the study was to achieve 3D models in

order to design and analyze teeth, metal and

ceramics MOD inlays and onlays.

The study was performed on an upper first

premolar, using a finite element analysis. Surfaces

were modeled according with anatomical

dimensions. The nonparametric modeling software

(Blender 2.57b) was used in order to obtain the

shape of root, enamel, dentin and pulp structures

(Fig. 1).

Fig. 1. Premolar surfaces modelled according to the

anatomical dimensions.

The collected data were used to construct three

dimensional models using Rhinoceros (McNeel

North America) NURBS (Nonuniform Rational B-

Splines) modeling program. These points were used

to extrapolate the shape of the object, a process

called reconstruction (Fig. 2). Reconstruction

involves finding and connecting adjacent points in

order to create continuous surfaces. Nonuniform

rational B-spline (NURBS) is a mathematical model

commonly used in computer aided design,

manufacturing and engineering.

Fig. 2. Volume of the premolar.

3D models of maxillary first premolars, prepared for

MOD inlays and onlays with different tapers

(between 0 and 10 degree from the cavity base to

the surface) were generated (Fig. 3). In the onlay

cavity, cusps were reduced and included in the

preparation. Inlay and onlay cavities designs were

created using literature data.

a

b

Fig. 3. Volume of the prepared premolar and the

restoration: a. inlay, b. onlay.

The mesh structure of the solid 3D model was

created using the computational simulation of Ansys

finite element analysis software (Fig. 4).

Mathematical Methods and Techniques in Engineering and Environmental Science

ISBN: 978-1-61804-046-6 403

a

b

Fig. 4. Mesh structure of the restored premolar:

a. with inlay, b. with onlay.

An occlusal load of 200 N was conducted, and

stresses occurring in the inlays, onlays and teeth

structures were calculated. It was applied in 5

points: to the mesial and distal marginal ridge, and

buccal cusp (3 points). At each selected loading point, a load of 40 N was applied perpendicular to

the surface in that point.

In making the finite element models, the

characteristics of a tooth structures, gold alloy and

ceramics used for the restorations were entered into

the computer program (Table 1).

Table 1. Elastic properties of the isotropic

materials. Material/component Elastic

modulus [GPa]

Poisson’s

ratio

Dentin 18.6 0.32

Enamel 84.1 0.33

Gold 70 0.30

Ceramics 204 0.31

3 Results and Discussions For all cavity designs and restoration type, stresses

in the restoration, enamel, and dentin were

evaluated separately (Fig. 5).

a

b

c

Fig. 5. Von Mises equivalent stress values for: a.

restoration, b. enamel, c. dentin (on – onlay, in –

inlay, me – cast metal, cer - ceramics).

In the onlays recorded maximal stresses were higher

than in the inlays in the most cases. In the ceramics

restorations the stresses were higher than in the cast

metal.

Stresses in the enamel were approximately 10 times

lower in the teeth prepared for onlays, compared to

the teeth prepared for inlays. Between the values for

ceramics and cast metal restorations there were no

significant differences.

In the dentin maximal stresses were also similar for

ceramics and cast metal restorations, for the same

preparation design. Depending on the taper, they

were higher for inlays or onlays, in the most cases

for inlays.

Mathematical Methods and Techniques in Engineering and Environmental Science

ISBN: 978-1-61804-046-6 404

For teeth restored with cast metal inlays stresses

were higher in enamel than for those restored with

ceramic inlays. Regarding the restorations, in the

ceramic inlays the stress values were higher. In the

dentin the stresses were more than 10 times lower

for both type of inlays (Fig. 6, 7).

Fig. 6. Von Mises equivalent stress values for cast

metal inlay.

Fig. 7. Von Mises equivalent stress values for

ceramic inlay.

Regarding the stresses in the onlay restored teeth

values in enamel and dentin were about 15 times

lower than in the restorations with no significant

differences between the two structures. In the

ceramic onlays stresses were higher than in the cast

metal (Fig. 8, 9).

Fig. 8. Von Mises equivalent stress values for cast

metal onlay.

Fig. 9. Von Mises equivalent stress values for

ceramic onlay.

The highest stress values were exhibited in the

restoration in the most cases.

Occlusal load on an MOD restored tooth produces

stress surrounding the contact areas in the

restorations and in the enamel (Fig. 10). In the

enamel stresses are located around the contact areas

for inlays prepared teeth and distributed in the

functional cusp and around the buccal cervical area

for the onlays prepared teeth. For onlays restored

teeth the variations for different tapers were smaller

than for inlays restored teeth.

Fig. 10. Von Mises equivalent stress in the ceramic

inlay restored premolar.

Regarding the distribution of stresses in dentin, they

are located in the cervical areas, around the teeth for

all cases (Fig. 11, 12).

Fig. 11. Von Mises equivalent stress in the dentin of

ceramic inlay restored premolar.

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ISBN: 978-1-61804-046-6 405

Fig. 12. Von Mises equivalent stress in the dentin of

ceramic onlay restored premolar.

4 Conclusion Within the limitations of this study, the following

conclusions were drawn:

1. In the MOD onlays recorded maximal stresses

were higher than in the MOD inlays in the most

cases. In the ceramics restorations the stresses

were higher than in the cast metal.

2. Regarding the prosthetic restorations material,

in the ceramics inlays and onlays the stress

values were higher.

3. MOD inlays transferred more functional stress

to the teeth structures compared to the MOD

onlays.

4. The taper of the preparations had no significant

influence on the stress values for all the studied

cases.

4 Acknowledgements This work was supported by CNCSIS-UEFISCSU,

project number PN II-RU TE_217/2010.

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Mathematical Methods and Techniques in Engineering and Environmental Science

ISBN: 978-1-61804-046-6 406