Hong et al.

Int Chin J Dent 2003; 3: 111-114.

Finite element analysis of the stress variations on the root canal wall ofpulpless tooth by different root canal preparations
Jin Hong, DDS,a Wenwei Xia, DDS,a Yaqin Zhu, DDS,a Xiaoyi Wang, DDS,a andHuanguo Xiong, PhDb
aNinth People’s Hospital, Shanghai Second Medical University, and bFaculty of
Mechanical Engineering, Shanghai Second Industrial University, Shanghai, P. R.
China

Purpose: To analyze the stress variations of the root canal wall of pulpless tooth by different root canalpreparations (RCPs).
Materials and Methods: A finite element model was set up for the mandibular first molar with standard
root shape and treated as control. Routine root canal preparation (R-RCP) and root canal preparation by
step-back technique (RCP-SBT) were modeled. The study was performed under the loading at the top of
the molar occlusal rest in vertical and oblique 45-degree orientations. The maximum von Mises stresses
were calculated in each part of the tooth, the wall of mesial-buccal, mesial-lingual, and distal root canal.
Results: Compared with the control model, R-RCP model and RCP-SBT model showed that the maximum
von Mises stress have no significant changes in each part of the tooth except in the amalgam layer, whichbecame a little larger. There are also no larger changes on the wall of mesial-buccal, mesial-lingual, anddistal root canal.
Conclusion: R-RCP and RCP-SBT will not affect greatly the root and dentin in biomechanics.
(Int Chin J Dent 2003; 3: 111-114.)
Clinical Significance: The results of the current study demonstrate that R-RCP and RCP-SBT are satisfied
techniques for tooth.
Key Words: finite element analysis, root canal preparation, step-back technique.

Introduction
Routine root canal preparation (R-RCP) and root canal preparation by step-back technique (RCP-SBT)
are often used in dental clinic treatment.1,2 However, their effects to the dentin were not reported yet.
Finite element analysis (FEA)3,4 is, therefore, utilized in this work as an important tool to evaluate theseeffects and the dentin and root canal biomechanical characteristics of different RCPs.

Materials and Methods
A first molar of mandible was modeled using FEA, 3-D mesh by Super-SAP 6.0 (Fig. 1). It had the111

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Int Chin J Dent 2003; 3: 111-114.

standard root shape and was treated as the control. The mesial root canal is round-shaped and the distalroot canal is oval-shaped. Marrow cavity was filled with zinc phosphate cement. The molar occlusal
center part was filled with amalgam layer. R-RCP and RCP-SBT were modeled as the shape in Figs. 2 and3. Root canals were filled with gutta-percha.

1

12a2b2cFig. 1. The three dimensional finite-element model of the mandibular first molar.
Fig. 2. Root canal appearances of three models; (a) original model, (b) routine root canalpreparation, and (c) root canal preparation by step-back technique.

Fig. 3.
Three root canal appearances of mesial-buccal
root canal; (a) original model, (b) routine root
canal preparation, and (c) root canal preparation
by step-back technique.
abc

Load Conditions and Boundary Conditions
A nodal force (Load) of 100 N is applied on the top of the molar occlusal rest in vertical and oblique
45-degree orientations. The nodes over the free edges of the root part in the mandible were constrained inthe x-, y-, and z-directional rigid movement.
Material Properties
The corresponding material properties were shown in Table 1.
Table 1. Material properties.
Material
EnamelDentinAmalgam layer
Zinc phosphate cement
Gutta-percha

Young’s modulus (MPa)41,40018,60013,72022,4000.69

112

Poisson’s ratio
0.30
0.32
0.33
0.25
0.45

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Int Chin J Dent 2003; 3: 111-114.

Finite Element Mesh
The finite element model was created using Element Topology: Quad4; and Global edge length: 0.5 mm;
but at the interface between the root canal and dentin, Global edge length is about 0.1 mm. Global edge
lengths were determined by pilot test.
Table 2. The maximum von Mises stress in different part of the tooth (MPa).
Original model
VerticalObliqueload
load
100.92106.69
40.92
43.46
26.31
30.50

Position
Amalgam layer (Enamel)
Amalgam layer (Dentin)
Zinc phosphate cement(Marrow cavity top)
Zinc phosphate cement(Marrow cavity)
Zinc phosphate cement(Root canal top)
Root canal top 1/3
Root canal middle 1/3
Root canal bottom 1/3

R-RCP model
VerticalObliqueload
load
131.67140.91
78.24
78.90
22.50
28.21

RCP-SBT model
VerticalObliqueload
load
131.67140.97
78.24
78.90
22.50
28.21

29.20

49.24

18.54

30.47

18.53

30.47

30.49

50.49

20.19

36.62

22.91

39.24

12.12
1.23
0.09

18.24
1.24
0.12

10.10
0.92
0.05

13.02
1.35
0.06

10.20
1.40
0.11

16.62
1.53
0.13

Table 3. The maximum stress of the wall of mesial-buccal root canal (MPa).
Original model
Position
Root canal top
Root canal top 1/3
Root canal middle 1/3
Root canal bottom 1/3

Vertical load

Oblique load

29.20
12.23
0.85
0.10

43.58
18.24
0.96
0.11

R-RCP model
VerticalObliqueload
load
18.19
20.25
7.16
10.92
0.30
0.32
0.07
0.08

RCP-SBT model
VerticalObliqueload
load
17.34
20.82
10.20
13.25
1.02
1.03
0.09
0.11

Table 4. The maximum stress of the wall of mesial-lingual root canal (MPa).
Original model
Position
Root canal top
Root canal top 1/3
Root canal middle 1/3
Root canal bottom 1/3

Vertical load

Oblique load

8.98
10.67
0.25
0.03

10.48
10.60
0.56
0.03

R-RCP model
VerticalObliqueload
load
8.34
10.35
3.35
5.72
0.34
0.38
0.02
0.04

RCP-SBT model
VerticalOblique
load
load
8.89
9.78
3.17
4.73
0.52
0.63
0.02
0.05

Table 5. The maximum stress of the wall of distal root canal (MPa).
Original model
Position
Root canal top
Root canal top 1/3
Root canal middle 1/3
Root canal bottom 1/3

Vertical load

Oblique load

17.89
9.15
0.55
0.07

27.15
11.71
0.61
0.09

113

R-RCP model
VerticalObliqueload
load
12.63
16.01
6.52
9.22
0.69
0.92
0.02
0.05

RCP-SBT model
VerticalOblique
load
load
12.23
18.58
6.88
9.85
0.69
0.94
0.02
0.05

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Int Chin J Dent 2003; 3: 111-114.

Results
The results of maximum von Mises stress distribution in the different part of the tooth and root canals
were shown in Tables 2 to 5.

Discussion
Effects of the Loading Directions
The maximum von Mises stress in the wall of root canal is affected by the loading directions. Table 2shows that, for the vertical load conditions, the absolute stress became lower from the crown part to the rootpart. However, there is a second maximum stress at the top of root canal. Compared with the control,
R-RCP model and RCP-SBT model showed that the maximum von Mises stress have no significant
changes in each part of the tooth except in the amalgam layer, which became a little larger. For the oblique
load conditions, the stress trend is the similar as the vertical load conditions. The absolute stress became alittle higher in the oblique load conditions.
Stress Distribution in the Wall of Root Canals
Table 3 to 5 show that, under vertical and oblique loading conditions, the absolute stress in R-RCP
model and RCP-SBT model was lower than that in the control model. The absolute stress became lower
from the root canal top to bottom. The absolute stress also became a little higher in the oblique loadconditions.

Conclusion
It can be concluded that both R-RCP and RCP-SBT will not affect greatly the root and dentin inbiomechanics. It demonstrated that R-RCP and RCP-SBT are satisfied techniques for tooth.

References
1. Archer R, Reader A. An in vitro evaluation of ultrasonic after step-back preparation in mandibular molar. J Endodon
1992; 18: 549-52.
2. Haidet J, Reader A. An in vitro comparison of the step-back technique via a step-back/ultrasonic technique in humanmandibular molar. J Endodon 1989; 15: 195-9.
3. Geng JP, Tan KBC, Liu GR. Applications of finite element analysis in implant dentistry, a review of literatures. J
Prosthet Dent 2001; 85: 585-98.
4. Patra AK, DePaolo JM, D'Souza KS, DeTolla D, Meenaghan MA. Guidelines for analysis and redesign of dentalimplants. Impl Dent 1998; 7: 355-68.

Reprint request to:
Dr. Jin Hong
Ninth People’s Hospital, Shanghai Second Medical University,Shanghai, 200011,P. R. China
Tel: +86-21-53078098 Email: hj1221@online.sh.cn
Received on May 10, 2003. Revised on October 12, 2003. Accepted on November 11, 2003.
Copyright ©2003 by the Editorial Council of the International Chinese Journal of Dentistry.

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