The influence of elastic modulus mismatchbetween tooth and post and core restorations onroot fracture

M. Ona1, N. Wakabayashi1, T. Yamazaki2, A. Takaichi1 & Y. Igarashi1

1Department of Removable Partial Prosthodontics, Graduate School, Tokyo Medical and Dental University, Tokyo; and 2School

of Dentistry, Tokyo Medical and Dental University, Tokyo, Japan

Abstract

Ona M, Wakabayashi N, Yamazaki T, Takaichi A, Igar-

ashi Y. The influence of elastic modulus mismatch between

tooth and post and core restorations on root fracture. Interna-

tional Endodontic Journal, 46, 4752, 2013.

Aim To investigate the influence of elastic modulus

mismatch between tooth and post and core restora-

tions on mechanisms of root fracture.

Methodology Three-dimensional mathematical models

of a root filled maxillary premolar tooth with support-

ing periodontium were constructed. The tooth was

restored with a cast NiCr alloy or fibre-reinforced

composite post and core that was bonded or nonbond-

ed to dentine. In the nonbonded simulation, a nonlin-

ear contact analysis was executed to simulate a

friction and a potential sliding phenomenon in the

interface between tooth and post and core. Risks of

root fracture and debonding at the bonded interface

were estimated based on the principal stress of the

root and the shear stress on the interface, respectively.

Results The fracture risk of the bonded cast post

and core was lower than that of the composite post

and core, although the cast restoration exhibited

eight times greater stress than the composite. The risk

of root fracture based on the tensile stress of the tooth

structures was higher with the bonded composite post

and core than that with the cast post and core. These

stresses doubled when the restorations were not

bonded to the tooth structures. The risk of debonding

of the cast post and core based on the shear stress

was approximately twice that of the composite post

and core.

Conclusions The elastic modulus mismatch

appears to be a factor responsible for the debonding of

post and cores from root canals, with the potential to

increase the risk of root fracture indirectly.

Keywords: finite element analysis, fracture, root,

stress.

Received 21 February 2012; accepted 29 May 2012

Introduction

Cast post and core build-ups have long been used to

support fixed restorations in root filled teeth. A 10-

year retrospective study reported a survival rate of

83.0% using cast post and cores (Gomez-Polo et al.

2010). However, in recent years, this conventional

form of restoration has been replaced gradually by

composite cores that incorporate a glass fibre post or

a metallic post. Improved resistance to root fracture

with the composite restoration has been reported

(Naumann et al. 2008, Salameh et al. 2008) as well

as in short-term retrospective clinical studies (Signore

et al. 2011, Zicari et al. 2011) with survival rates of

91.797.2%. The reduced fracture probability was

reportedly attributed to the elastic moduli of compos-

ite and glass fibre that are closer to root dentine in

comparison with cast alloys. However, this argument

is controversial because a metallic restoration with

higher modulus theoretically absorbs a large amount

of stress from the bonded tooth structure, resulting in

Correspondence: Noriyuki Wakabayashi, 1-5-45, Yushima,

Bunkyo, Tokyo 113-8549, Japan (Tel.: +81 3 5803 4935;

fax: +81 3 5803 4946; e-mail: wakabayashi.rpro@tmd.ac.jp).

2012 International Endodontic Journal International Endodontic Journal, 46, 4752, 2013

doi:10.1111/j.1365-2591.2012.02092.x

47

less stress intensity in the root dentine. In fact, some

clinical studies found no improvement in fracture

resistance when using the fibre-reinforced composite

core (Bitter et al. 2008, Vano et al. 2009, Wu et al.

2009).

Mathematical approaches indicated that the loss of

bonding integrity at the interface could increase the

risk of root fracture of teeth restored with a composite

core incorporating a glass fibre post (Santos et al.

2009, 2010). However, the effect of elastic modulus

mismatch between post and cores and tooth structure

on the root fracture mechanism has not been eluci-

dated in relation to the risk of debonding at the inter-

face. Because of this lack of knowledge, clinical

decision making on the post and core material for

root filled teeth is still controversial.

In this study, the overall risk of root fracture and

the probability of debonding at the interface between

tooth and post and core were estimated based on

stress analyses. The purpose of this study was to test

the effect of the elastic modulus mismatch between

tooth and post and core on root fracture under masti-

catory force.

Materials and methods

Finite element (FE) models consisted of a root filled

maxillary second premolar tooth, periodontal liga-

ment and the surrounding alveolar bone. A three-

dimensional intact tooth model was constructed based

on the anatomical image of an adult tooth (Dental

Anatomy & Interactive 3-D Tooth Atlas; Brown &

Herbranson Imaging, Inc, Portola Valley, CA, USA)

(Fig. 1). The pulp chamber was modelled with a sim-

plified oval external cross-section in which the bucco-

palatal depth was twice the mesio-distal width. The

maxillary bone was modelled as a cancellous block

with 2.0-mm-thick cortical bone. Part of the tooth

structures was replaced by post and core and full cov-

erage ceramic crown, with a 1.0-mm ferrule around

the cervical region of the root. Gutta-percha was

inserted into apical third of the root length. A NiCr

alloy cast post or glass fibre post with resin composite

matrix was used for the post and core restoration.

Each model was meshed by approximately 75 000

hexahedral elements determined by preliminary con-

vergence tests (Al-Sukhun et al. 2007) (ANSYS 11.0;

ANSYS Inc., Canonsburg, PA, USA). All materials

were considered homogeneous, linearly elastic and

isotropic, except for the orthotropic glass fibre post

(Table 1; Friedman et al. 1977, Kse et al. 1985,

Farah et al. 1989, Morris 1989, Moroi et al. 1993,

Sano et al. 1994, Lanza et al. 2005). The post and

core was assumed to be perfectly bonded or com-

pletely in contact (nonbonded) to the root. In the

nonbonded simulation, nonlinear contact elements

between tooth and foundation were applied to simu-

late friction and a potential sliding phenomenon, with

a friction coefficient of 0.3. A total axial load of

200 N (Ferrario et al. 2004) was applied to the tip of

the buccal cusp 30 obliquely from palatal to buccal.In each model, the movement of the outer surface of

bone was restricted.

The principal stress distributions in the tooth and

the post and core, and the shear stress distributions

on the interface surfaces, were calculated for all simu-

lations. The magnitudes of the highest maximum

principal stress in the tooth structures (rt) and in thefoundation (rf), and the highest maximum shearstress along the interface surfaces (rshear) were calcu-lated. The fracture risks of the tooth root (Rt) and the

post and core foundation (Rf), and the failure risk of

the interfacial adhesion (Rint) were also calculated

using the following equations (Ona et al. 2011):

(a) (b) (c)

Figure 1 Three-dimensional finite element model of the

maxillary second premolar tooth. (a) Meshed parts of

the tooth model: root (r), post and core foundation (f) and

the crown restoration (c). (b) Assembled premolar model

with increased translucency for visualization. Gutta-percha

(gp) was also modeled in the root canal. (c) The loading and

boundary conditions. The periodontal ligament (pdl) and the

bone block (b) were modeled for support of the tooth struc-

tures. Red arrow indicates an off-axis oblique load on the

inner surface of the buccal cusp. The triangles represent the

fixation at the lower surface of the bone.

Elastic modulus mismatch Ona et al.

2012 International Endodontic JournalInternational Endodontic Journal, 46, 4752, 201348

Rt = rt/flexural strength of root dentine which is104 MPa (Sano et al. 1994), Rf = rf/flexural strengthof the foundation material (790 MPa for the cast

model (Morris 1989) and 55 MPa for the composite

model (Yuzugullu et al. 2008)), and Rint = rshear/Shear bond strength, with a dual-curing resin luting

agent together with a silane-coupling agent, of the

post material to dentine (24.5 MPa for metal (Zhang

& Degrange 2010) and 23.2 MPa for composite

(Scherrer et al. 2010)).

Results

The highest maximum principal tensile stress in the

bonded cast post and core (rf) appeared on the pala-tal side (tension side) of the post half way along its

length (Fig. 2). Even though the rf for the bondedcast alloy was approximately eight times higher than

that of the bonded composite (Table 2), the estimated

risk of the post fracture (Rf) was lower for the alloy

(0.18) than for the composite (0.31). The maximum

stress in the post and core for the nonbonded cast

alloy was slightly lower than the bonded cast alloy,

whilst that of the nonbonded composite doubled com-

pared to the bonded condition. The highest risk was

revealed in the nonbonded composite post and core

(0.67).

The highest maximum principal tensile stress in the

tooth structures (rt) was located at the mesio-buccalcervical region for all the models (Fig. 3). The bonded

composite post and core generated the maximum

principal stress of the root at the cervical region

(32.0 MPa) that was approximately twice as much

that of the bonded cast post and core (15.7 MPa).

These maximum stresses doubled, reaching 61.1 MPa

and 39.2 MPa, respectively, when the post and cores

were not bonded to the tooth structures. The esti-

mated risk of tooth fracture was roughly proportional

to the stress.

The highest maximum shear stress at the interfacial

surface (rshear) of the bonded cast post and core wasconcentrated at the mesial cervical region and the

region near the edge of the post (Fig. 4). The rshear ofthe bonded composite post and core was also concen-

trated at the cervical region but not at the edge of the

post. The shear stress was higher with the bonded

cast alloy (38.3 MPa) than that with the composite

(18.5 MPa), and the failure risk was roughly propor-

tional to the maximum shear stress.

Discussion

The maximum principal stress was considerably lar-

ger in the bonded cast post and core than that in the

bonded fibre-reinforced composite. This was because

the cast alloy post and core, which had a greater

modulus (188 GPa), was likely to receive larger stress

from the root than the composite with a lower modu-

lus (12 GPa). Despite the high stress of the cast

Table 1 Material properties used in the study

Elastic

modulus

(GPa)

Poissons

ratio References

Dentine 14.7* 0.31** *Sano et al. (1994)

**Farah et al.

(1989)

Porcelain 70 0.19 Kse et al. (1985)

Cortical bone 14.7 0.30 Moroi et al. (1993)

Cancellous

bone

4.9 9 101 0.30 Moroi et al. (1993)

Gutta-percha 1.4 9 101 0.49 Friedman et al.(1977)

Periodontal

ligament

6.9 9 103 0.45 Farah et al. (1989)

NiCr alloy 188 0.27 Morris (1989)

Composite

resin

12 0.33 Lanza et al. (2005)

Glass fiber Lanza et al. (2005)

Transverse 9.5 0.27

Longitudinal 37 0.34

Figure 2 The maximum first principal (tensile) stress distri-

butions on the mesial surfaces of the post and core restora-

tions. The post and core was made of cast alloy (left) or

fiber-reinforced composite (right), and perfectly bonded to

tooth structures. Red areas represent the highest stress, as

indicated by the scale bars.

Ona et al. Elastic modulus mismatch

2012 International Endodontic Journal International Endodontic Journal, 46, 4752, 2013 49

restoration, the failure risk was lower with the cast

than that with the composite. This was because of

the higher strength of the alloy in comparison with

the composite. The composite that has a modulus

close to that of the root dentine flexes under loading

in sync with the root, resulting in larger loading

energy or stress transmitted to the root. In other

words, when the post and core foundation was per-

fectly bonded to the root, the elastic modulus mis-

match between the root and the foundation did not

increase the risk of root fracture.

The elastic modulus mismatch, however, was a

strong potential factor that could cause debonding at

the interface. The stiff cast post was unlikely to distort

under loading, which might create larger shear stress

at the interface (rshear) than the relatively flexiblecomposite. As the cast post and core was tilted to the

buccal direction (compression side) under an oblique

load, the high maximum shear stresses appeared at

the cervical and apical interfaces (Fig. 4, left). Once

the debonding occurs, the overall risk of root fracture

can be estimated from the Rint multiplied by Rt of the

nonbonded post and core. According to this estima-

tion, the fracture risk following interfacial failure was

higher with the cast restoration (1.56 9 0.37 =0.58) than that with the composite (0.79 9 0.58 =0.46). The relative comparison of this risk estimation

was not consistent with that based on the bonded

root stress. It is therefore suggested that adhesion of

the post and core restoration to the tooth structures

played a critical role in the fracture initiation of root-

filled teeth.

The likelihood of fracture initiation at the cervical

region of a root filled premolar root (Lustig et al.

2000) was clearly indicated by the areas of stress

concentration in all models. The maximum principal

Table 2 The maximum principal first (tensile) and shear stresses and the fracture risks for each structure. rf; Maximum princi-pal stress in the post and core (MPa), Rf; Fracture risk of the post and core, rt; Maximum principal stress in the tooth (MPa),

Rt; Fracture risk of the tooth, rshear; Maximum shear stress at the interface between the tooth and the restoration (MPa), andRint; Failure risk of the bonded interface

Cast alloy bonded Composite bonded Cast alloy nonbonded Composite nonbonded

rf (Rf) 144.7 (0.18) 17.3 (0.31) 132.4 (0.17) 36.8 (0.67)

rt (Rt) 15.7 (0.15) 32.0 (0.30) 39.2 (0.37) 61.1 (0.58)

rshear (Rint) 38.3 (1.56) 18.5 (0.79)

Figure 3 The maximum first principal (tensile) stress distri-

butions in the cervical root region of the tooth. The cast

(left) or composite (right) post and core was bonded (upper)

or non-bonded (left) to the tooth. The restorations are not

shown in the graphics to highlight the stress distributions of

the root surfaces. Red areas represent the highest tensile

stress, as indicated by the scale bar.

Figure 4 The shear stress distributions on the mesial sur-

faces of the post and core restoration. The post and core was

made of cast (left) or composite (right), and perfectly bonded

to tooth structures. The highest shear stress was indicated as

the maximum (red) or the minimum (blue) stresses depen-

dent on the clockwise and couterclockwise directions.

Elastic modulus mismatch Ona et al.

2012 International Endodontic JournalInternational Endodontic Journal, 46, 4752, 201350

stress was revealed in the mesiobuccal cervical region

where tensile hoop stresses were created as a result

of the impact of the obliquely loaded post, possibly

leading to a vertical root fracture. The relatively thin

mesial root might be another factor for stress concen-

tration. When the post and core is not bonded, the

friction at the contacting interface may result in tilt-

ing movement of the restoration. This contact poten-

tially generates greater pressure on the root surface.

Although the maximum stresses were well below the

flexural strength of root dentine, the potential failure

risk cannot be ignored because repetitive fatigue

loading can cause stress accumulation (Nalla et al.

2004).

Limitations of the study design should be noted.

The failure risk was estimated on the basis of the rel-

ative comparison of the highest maximum stress with

the strength of the materials or the interface. The

method used was the same as that used in the previ-

ous studies, which aimed to assess the effect of inter-

facial failure on the failure of ceramic restorations

(Ona et al. 2011). Although the results serve to clar-

ify the critical elements of material selection for foun-

dation restorations, the limitation of the method

should be considered, especially if the quantitative

assessment of the stresses is to be emphasized. This

study employed two extreme cases of bonding and

nonbonding conditions for interfacial simulation.

However, the perfect boding is not likely to be

obtained, especially in the bonding of composite

matrix reinforced with the fibre post. Bond strength

in deeper areas of the root canal could not be per-

fectly obtained because of inadequate visualization

and difficulties in the application procedure of luting

agents (Zicari et al. 2008). Therefore, the influence of

bonding integrity level and debonding process on the

root fracture should be further investigated. In addi-

tion, the potential failure at the interface between the

composite and the fibre post was not considered.

Future investigation is encouraged to assess the

mechanism of debonding process at multiple inter-

facial sites in relation to the root fracture.

Conclusion

The nonlinear contact stress analysis of this study

indicates that the elastic modulus mismatch between

tooth and post and core restoration appears to be a

factor responsible for the debonding of the restoration,

thereby possibly leading to root fracture indirectly.

The mismatch does not increase the risk of root frac-

ture if the post and core is perfectly bonded to the

tooth structures.

Acknowledgements

This study was supported by a Grant-in-Aid (No:

20592307 to N.W.) for research from the Japan Soci-

ety for Promotion of Science/MEXT. The authors deny

any conflicts of interest to this study.

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