ORIGINAL RESEARCH ARTICLE

Evaluation of stress and strain distribution in endodontically treated maxillary central incisor with two different post and core systems A 3D Finite element analysis.

Abhinav Agarwal, Patel R.K.V, N. Kalavathy, Prakash Somani

Abstract

Background and objectives: Restoration of endodontically treated teeth is a common problem in restorative dentistry, related to the fractures. Such teeth often require additional support from the root canal by means of a post and core restoration. The present study was carried out to compare the stress & strain distribution patterns in endodontically treated maxillary central incisor restored with two different posts & core materials. Methods: Five three dimensional models were created of a maxillary central incisor with the aid of ANSYS version 10. Each of these model was subjected to standard loading in three directions (Horizontal load - 10N, Vertical load -100N, Oblique load - 50N) and the resultant von mises stresses & strains were evaluated by measuring the distance between the nodes. Results: Maximum Von Mises stress of 408.189 MPa was seen in Model-4 with Prefabricated Light transmitting post and glass ionomer cement core and minimum Von Mises stress of 85 MPa was seen in Model-2 with Prefabricated fiber reinforced post and glass ionomer cement core. Conclusion: Within the limitations of the study it was concluded that Prefabricated Light transmitting post with composite core showed better stress and strain distribution in dentin under all the loading conditions.

Key words: Finite Element Analysis;Nodes;Composite core;glass ionomer core; fiber reinforced post;light transmitting post.

Abhinav Agarwal, Patel R.K.V, N. Kalavathy, Prakash Somani. Evaluation of stress and strain distribution in endodontically treated maxillary central incisor with two different post and core systems A 3D Finite element analysis. International Journal of Prosthetic Dentistry2011:2(2):1-6. 2011 International Journal of Prosthetic Dentistry. Published by Publishing Division, Celesta Software Private Limited. All Rights Reserved.

Received on: 11/11/2010 Accepted on: 11/12/2010


Introduction


Restoration of endodontically treated teeth is a common problem in restorative dentistry.(1-4) Posts are used to retain the core material in posterior teeth, where masticatory loads are essentially compressive.(5) However, when loaded transversally as in case of incisors, the flexural behavior of posts should be carefully evaluated. The magnitude and the angle of incisal load greatly influence the long term success of the restorations involving central incisors.(6)

The prefabricated post and core system is one of the most popular system in endodontically restored teeth. Prefabricated posts have standard dimensions and are made of a variety of metallic and nonmetallic materials.(7, 8) Metal posts possess high strength and good retention. The drawback of such posts is the loss of tooth profile (in the cases where the prefabricated posts are larger than the available tooth structure), higher chances of corrosion and poor esthetics.(9)

Two parameters strongly influences the mechanical behaviour of endodontically treated teeth restored with posts; the characteristics of the interfaces and the rigidity of the materials.6 fiber-reinforced posts were introduced in 1990 to address the concerns of stainless steel and titanium alloys.(10, 11)The Modulus of Elasticity of the fiber post is comparable to the dentin (~20 GPa) and is 5-10 times less rigid than high-modulus metal posts, allowing the post to absorb stress to prevent root fractures.(12) Fiber posts are bonded to the tooth utilizing an etchant, primer, adhesive and resin composite technique. With the post bonded to the tooth, the low modulus of elasticity of the post can afford the fiber post and the tooth to flex together, dissipating any forces placed on the tooth thereby greatly reducing the risk of root fractures.(3) To date there is still no agreement in the literature about which material or technique can optimally restore endodontically treated teeth.(13)

The objective of the study was to evaluate the stress and strain distribution patterns of a sound maxillary central incisor restored with two different posts, two different cores and ceramic crown using finite element analysis.

Methodology

This study was conducted to evaluate the stress and strain distribution when using two different post and core systems. This study utilized finite element (mathematical) models of a single maxillary central incisor of standard dimensions. (Table-1)(9)

Crown

Crown Length

10.5mm

Mesio-Distal width at incisal region

8.5mm

Mesio-Distal width at cervical region

7mm

Facio lingual width at incisal region

7mm

Facio lingual width at cervical region

6mm

Root

Length

13mm

Total tooth length

23.5mm

Concavity of crown at inter proximal (Col area)

3.5 mm(height)

Gutta percha 4mm with a Conical Configuration

4 mm with a conical Configuration

Post Length

9 mm with a parallel side configuration

Core

7mm(tapering configuration of 2- 5 degree)

Periodontal ligament thickness

0.2mm

TABLE 1: (Dimensions of central incisor)15

Finite Element Model: Graphic preprocessing software - ANSYS version 10 was used for creating the geometric representation of a post core restored maxillary central incisor surrounded by normal anatomic structures. This in-vitro model simulated the in-vivo geometry of a maxillary central incisor with dentine, pulp cavity, periodontal ligament, cancellous bone, cortical bone, gutta-percha and the post. However the thickness of the resin luting cement and cementum were eliminated for simplicity in modeling and analysis.

Five three dimensional models were created of a maxillary central incisor with the aid of ANSYS software. All parameters of the individual models remained similar except that a different post and core material was used for each model.

         MODEL 1 was Sound maxillary central incisor.

         MODEL 2 was Maxillary central incisor with prefabricated fiber reinforced post & Glass ionomer cement core.

         MODEL 3 was Maxillary central incisor with prefabricated fiber reinforced post & Composite core.

         MODEL 4 was Maxillary central incisor with prefabricated light transmitting post & glass ionomer cement core.

         MODEL 5 was Maxillary central incisor with prefabricated light transmitting post & composite Core.

Material Properties

All materials used in the model were considered to be homogenous, isotropic and linear elastic. The Poissons ratio () and Youngs modulus (E) of elasticity of the material were incorporated into the model as shown in Table 2.(9, 14, 15)

 

Young's Modulus (GPa)

Poisson's Ratio

Enamel

41.0

0.31

Dentine

18.6

0.31

Periodontal Ligament

68.9

0.45

Cortical Bone

13.7

0.30

Spongy Bone

1.37

0.30

Gingiva

19.6

0.30

All Ceramic Crown

120

0.28

Guttapercha

0.69

0.45

Resin cement ( post)

8.0

0.30

Cement ( crown)

22.4

0.25

Fiber reinforced post

40

.26

Light transmitting post

20

.26

Composite core

12

.30

Glass ionomer core

5.4

.30

Table 2 : Properties of Materials

The finite element model was divided into small elements. Each element was considered to be interconnected at a number of discrete points called nodes. Each model was meshed by elements defined by ten nodes and three degree of freedom in tetrahedral nodes. The displacement of each of these nodes was calculated to determine the maximum Von Mises stresses throughout the structure. The tooth model was surrounded by cancellous bone with 2mm of cortical bone on the outer surface. Thus, this model simulated a clinical situation of a maxillary incisor requiring a post & core restoration. For simplicity in modelling, cement thickness and the dimensions of the cementum were not included in any of the models.

Loading conditions

         Each of these models was subjected to standard loading conditions(6, 16)

         The direction of force application was Horizontal, Vertical and Oblique.

         For Horizontal Loading Load of 10N was applied at a point midway between the cervico-incisal aspect of the crown.

         For Vertical Loading load of 100N was applied at the incisal edge of the crown.

         For Oblique loading load of 50N was applied at a 45 degree angle to the long axis of the tooth.

         In each of the models a standard force was applied and the resultant Maximum Von Mises stresses & strains were evaluated.

Results

In all the five models forces were applied in 3 directions and the resultant maximum Von Mises stresses and strains were observed and tabulated.

Stress and Strain Analysis: In Model 1: Sound maxillary central incisor: The maximum Von Mises stress was observed to be 62 MPa on vertical loading mainly at the incisal edge of the crown structure and the minimum Von Mises stress was observed to be 3.58 MPa on horizontal loading mainly at the mid cervical region between the crown and root structure and middle third of the crown.(Table 3,4) Dentin showed maximum stress value of 11.208 MPa on vertical loading on the proximoincisal part and at the mid cervical region and minimal stress of 1.904 MPa of stress on horizontal loading mainly on the middle third of the crown.(Table 3,4)

In Model 2: Maxillary central incisor with prefabricated fiber reinforced post with Glass ionomer cement core build up

The maximum Von Mises stress was observed to be 404 MPa on vertical loading mainly at the incisal edge of the crown structure and the minimum Von Mises stress was observed to be 85 MPa on horizontal loading mainly seen at the incisal part of the crown. (Table 3,4)

Core showed a maximum stress of 1.204 MPa on horizontal loading in the middle portion of the core and minimum stress of 0.85967MPa on vertical loading seen at the cervical aspect of the core. (Table 3,4) Dentin showed a maximum stress of 511 MPa on vertical loading distributed at the cervical portion of the root dentin and minimum stress of 139.209 MPa on horizontal loading distributed at the cervical portion of the root dentin. (Table 3,4)


 

Model

Post

Core

Dentin stress

Bone Stress

Von Mises

 

 

 

Cancellous

Cortical

 

MODEL-1

Horizontal

 

 

1.904

.9446

13.006

3.58

Vertical

 

 

11.208

4.576

88.653

62

Oblique

 

 

3.628

3.096

40.621

31.957

MODEL-2

Horizontal

2.447

1.204

139.209

5.092

52

85

Vertical

2.759

.8596

511

15.551

159.358

406.474

Oblique

1.242

.957

406.339

8.497

78.9

259

MODEL-3

Horizontal

1.658

2.343

138.612

5.098

52.541

85.509

Vertical

2.362

1.35

609.934

15.616

169.005

404.836

Oblique

1.299

1.359

402.797

8.501

78.894

256.596

MODEL-4

Horizontal

1.692

1.109

139.597

5.096

52.5

85.974

Vertical

1.483

.8736

610

15.53

159.391

408.189

Oblique

.8914

.9450

406

8.507

79.047

258.8

MODEL-5

Horizontal

1.467

1.501

139.081

5.0

52.592

85.57

Vertical

1.207

1.349

509

15.615

158.991

406.694

Oblique

.9325

1.343

402.443

8.512

79.05

256.1

Table 3 Stress values in MPa


 


MODEL

POST()

CORE()

DENTINSTRAIN

BONE STRAIN

VON MISES

 

 

 

CANCELLOUS

CORTICAL

 

MODEL-1

Horizontal

 

 

107

777

.001052

.001297

Vertical

 

 

576

.002532

.004899

.00486

Oblique

 

 

276

.002381

.002974

.003464

MODEL-2

Horizontal

61.2

225

.00832

.003743

.003868

.015413

Vertical

69.0

162

.036041

.011678

.012664

.95274

Oblique

31.1

177

.023884

.006205

.005864

.050389

MODEL-3

Horizontal

58.6

138

.008285

.003747

.003871

.0154

Vertical

59.1

113

.035964

.011651

.012634

.095

Oblique

32.6

113

.023669

.006208

.005863

.050013

MODEL-4

Horizontal

84.6

206

.008349

.003747

.003871

.015454

Vertical

74.2

165

.036017

.011677

.012664

.095219

Oblique

44.6

175

.023862

.006212

.005866

.050317

MODEL-5

Horizontal

73.4

125

.008312

.003751

.003874

.015434

Vertical

60.3

113

.03594

.01165

.012633

.0949

Oblique

46.8

112

.023646

.006215

.005865

.0499

Table 4 Strain Values

 


The post showed a maximum Von Mises stress equivalent of 2.759 MPa on vertical loading mainly concentrated towards the apex of the tooth and minimum stress of 1.242 MPa on oblique loading concentrated toward the middle portion of the post. (Table 3 &4)

In Model 3: Maxillary central incisor with Prefabricated fiber reinforced post with composite core build up.

The maximum Von Mises stress was observed to be 404.84 MPa on vertical loading mainly at the middle third of the crown structure and the minimum Von Mises stress was observed to be 85.509 MPa on horizontal loading mainly seen at the incisal part of the crown. Core showed a maximum stress of 2.343 MPa on horizontal loading in the middle portion of the core and minimum stress of 1.35 MPa on vertical loading seen at the incisal part and near the cervical aspect of the core. Dentin showed a maximum stress of 609.934 MPa on vertical loading distributed at the cervical portion of the root dentin and minimum stress of 138.612 MPa on horizontal loading distributed at the mid cervical portion of the root dentin. The post showed a maximum Von Mises stress equivalent of 2.362 MPa on vertical loading mainly concentrated towards the apex of the tooth and minimum stress of 1.299 MPa on oblique loading concentrated toward the middle portion of the post. (Table 3 &4)

In Model 4: Maxillary central incisor with Prefabricated light transmitting post with Glass ionomer cement core build up

The maximum Von Mises stress was observed to be 408 MPa on vertical loading mainly at the incisal part of the crown structure and the minimum Von Mises stress was observed to be 85.974 MPa on horizontal loading mainly seen at the incisal part of the crown. Core showed a maximum stress of 1.109 MPa on horizontal loading in the middle portion of the core and minimum stress of 0.8736 MPa on vertical loading seen near the base of the core. Dentin showed a maximum stress of 610 MPa on vertical loading distributed at the cervical portion of the root dentin and minimum of 139.597 MPa on horizontal loading distributed at the cervical portion of the root dentin. The post showed a maximum Van Mises stress equivalent of 1.692 MPa on horizontal loading mainly concentrated at coronal portion and minimum stress of 0.8914 MPa on oblique loading concentrated toward the middle portion of the post. (Table 3,4)

In Model 5: Maxillary Central Incisor with prefabricated light transmitting post with composite core build up.

The maximum Von Mises stress was observed to be 406 MPa on vertical loading mainly at the incisal part of the crown structure and the minimum Von Mises stress was observed to be 85.57 MPa on horizontal loading mainly seen at the incisal part of the crown. Core showed a maximum stress of 1.501 MPa on horizontal loading in the middle portion of the core and minimum stress of 1.343 MPa on oblique loading seen near the base of the core. Dentin showed a maximum stress of 509 MPa on vertical loading distributed at the cervical portion of the root dentin and minimum of 139.081 MPa on horizontal loading distributed at the cervical portion of the root dentin. The post showed a maximum Von Mises stress equivalent of 1.467 MPa on horizontal loading mainly concentrated at coronal portion and minimum stress of 0.9325 MPa on oblique loading concentrated toward the middle portion of the post. (Table 3,4)

Discussion

Now a days prefabricated fiber reinforced posts are most commonly used to restore the endodontically treated tooth.(17)These posts have modulus of elasticity close to dentin and are less rigid as compared to the different type of posts used in the past.(18) Because of low modulus of elasticity the fiber post and the tooth can flex together, dissipating any forces placed on the tooth thereby greatly reducing the risk of root fractures.(6, 17)Recently a light emitting post has been introduced which has certain advantages over routine fiber reinforced posts like radiopacity, low modulus of elasticity and enhanced mechanical properties. Radiopacity helps in better conduction of curing light for the use of dual curing resin cements and low modulus helps in better distribution of forces within the tooth structure. In literature very few studies has been done with different types of fiber posts. Similarly several dental materials have been used for core build up procedures. R.E. Jordan stated that improvement in composites and the development of enamel-dentin bonding systems have simulated trends towards more conservative procedures. New formulations of glass ionomer cements have resulted in an increasing range of applications for such materials notably for cermet materials which can be used as an alternative core build up material. A.D.Wilson investigated that the development of resin modified glass ionomer cements have created new choices in the selection of materials. The ability of glass ionomers and glass cermets to adhere to both enamel and dentin and to release fluoride with anticariogenic effect, encourages many clinicians to select such materials in core build up procedures.(19)

According to a study done by Roberto Sorrentio et al, Stress concentrates where non homogenous material distributions are present just like interfaces. Interfaces of materials with different moduli of elasticity represent the weak link of restorative systems, as the toughness/stiffness mismatch influences the stress distribution. In the oral environment, restorative systems are subjected to fatigue stress, namely the repeated application of lower loads than the yield strength of the restorative materials. Nevertheless, such a cycling load application might produce microcracks causing the failure of the restorative systems. Such micro cracks nucleate at locations of highest stress and lowest local strength. Systems investigated either in static and fatigue loading conditions show underposable highest stress concentrations areas and similar fatigue patterns.(6)

According to the results of the present study, the mechanical properties of the post and core material influenced both the position of the concentration areas and the level of stress and strain along the dentin/post/core interfaces.

Conclusion

1) Von Mises stresses & strains were concentrated more in the cervical region of dentin.

2) Von Mises stresses & strains were minimal with Prefabricated light transmitting post and composite core build up.

3) Prefabricated light transmitting post is a better choice for restoring an endodontically treated anterior tooth than Prefabricated fiber reinforced post.

4) Composite core build up material could be a better choice than glass ionomer cement core as composite core build up material showed better stress & strain distribution with different types of loading.

Authors Affiliation: Dr. Abhinav Agarwal, M.D.S., Senior Lecturer, Department of Prosthodontics, Pacific Dental College and Hospital, Debari, Udaipur, 2. Dr. Patel R.K.V, Senior Lecturer, Department of Prosthodontics, Sri Rajiv Gandhi college of dental sciences and hospital,Cholanagar, RT Nagar post, Bangalore, 3. Dr. N. Kalavathy, M.D.S., Professor and Head Department of Prosthodontics, D.A.P.M.R.V. Dental college, Bangalore, 4. Dr. Prakash Somani, M.D.S., Senior Lecturer, Department of Prosthodontics, Pacific dental College and hospital, Debari, Udaipur, India.

Acknowledgement: Department of Prosthodontics, Pacific Dental College and Hospital, Debari, Udaipur, India.

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Address for correspondence

Dr. Abhinav Agarwal, M.D.S.

Senior Lecturer

Pacific Dental College and Hospital,

Debari, Udaipur- 313024

E-mail: drabhi_17@yahoo.co.in


 

Source of Support: Nil, Conflict of interest: None Declared

 

 

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