Jia et al.

Int Chin J Dent 2007; 7: 23-26.

A three-dimensional finite element analysis of a tilted molar as afixed partial denture abutment
Jun Jia, DDS, PhD,a Yuanyuan Duan, DDS,a Shaofeng Zhang, DDS, PhD,a Jipeng Liu,BSc,b Lei Jin, DDS,a and Jianxue Zhou, BSc aabDepartment of Orthodontics, College of Stomatology, The Fourth Military Medical University, Xi’an
Xi’an Institute of Applied Electronic Engineering, Xi’an, P. R. China

Purpose: To evaluate the stress distributions around the tilted molar abutment of a fixed partial denture (FPD)
using finite element analysis.
Materials and Methods: Three-dimensional finite element models of tilted mandibular molar before and after
the restoration of a 3-unit FPD as the abutment were constructed by the combination of the computed
tomographic (CT) scanning technology and Ansys software. A vertical load was applied to the central fossa of
the second molar. The stress distributions were calculated and compared between these models.
Results: The results showed that the introduction of a FPD decreased the stresses on the mesial area of the root
and the adjacent area to the apex of the tilted molar and increased the stress surrounding the second premolar
which is the other abutment of the FPD.
Conclusion: It is concluded that the placement of the FPD modified the stress distribution around the roots ofthe tilted molar abutment and favored the tilted molar. (Int Chin J Dent 2007; 7: 23-26.)
Key Words: fixed partial denture, three-dimensional finite element analysis, tilted abutment.

Introduction
It is frequently found in the clinical practice that the teeth adjacent to the lost teeth tend to tilt if the edentulous
space has not been restored in time which may attribute to the influence of mesial components of occlusal force.1
It is always a dilemma to choose this kind of tilted molar as the fixed partial denture (FPD) abutment or not.
Although in early days, Tylman2 has insisted that it was inappropriate to choose those teeth tilted over 24
degrees as FPD abutments, a number of scholars have made researches about this issue in order to investigate thefurther applications of such teeth.3,4 The introduction of FPD may modify the stress distribution around the tilted
molar abutment because the FPD can share and conduct the occlusal force on the tilted molar to the otherabutments. The CT-based three-dimensional (3D) finite element analysis (FEA) is an accepted theoreticaltechnique used in the investigation of biomechanical problems. It has been proven to be a precise method forevaluating dental restorations and it offers many advantages over other methods. FEA modeling not only cansimulate complex geometric shapes and material properties, but also can simulate various boundary conditions,which are difficult to replicate in experiments.5 Therefore, this study compared the stress distribution of dental
supporting structures of a tilted mandibular molar as an abutment before and after the restoration of three-unit
FPD (mandibular second premolar to second molar) using software of 3D FEA, by this means, in order toascertain further how the placement of a fixed prosthesis modified these stresses and their distribution.

Materials and Methods
Construction of 3D FEA models
The CT scan section images of a donor were obtained on a PQ6000 CT machine (Picker International Inc.,
Cleveland, OH, USA) to provide the data of finite element models. The donor was a male adult with complete
dentition and healthy occlusion. The obtained 38 CT photos which related to the needed teeth were converted
into the BMP files and imported into the software of Amira (Mercury computer systems Inc., Chelmsford, MA,USA). Then the computer model of the exterior rough surface meshing of the second premolar, first and second

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Int Chin J Dent 2007; 7: 23-26.

mandibular molars was procured from Amira Software and exported as IGES files. The model was assigned anorthogonal XYZ coordinate system. UG NX4 Software (UGS Inc., Plano, TX, USA) was utilized to construct
the inner structures and tilting angle and finally compose the final solid mesh of FPD. The models of FPD withand without the surrounding bones were shown in the Fig. 1. In this study, one unrestored model with tilted firstmolar of 30°and second premolar and one model of 3-unit FPD with the second premolar and tilted molar asabutments were created. And the type of the pontic in the model is the modified ridge-lap design which iscommonly used in the clinical practice. The tilting angle was ascertained according to the axis of the midline ofdentition. ANSYS (ANSYS Inc., Canonsburg, PA, USA) finite element solver software was used to mesh,compute and analyze the stresses in each model. The untreated model consisted of 465,300 elements and 80,505
nodes. And the restored model consisted of 603,120 elements and 107,185 nodes.

Fig. 1. Model of FPD having titled molar abutment with and without the surrounding bones.

Material properties and load type
Poisson ratio and the modulus of elasticity of materials are listed in Table 1 which are adopted from theliterature.6-8 The following assumptions were made in order to simplify the calculations. The material of theFPD, the tooth dentine, and the luting cement after setting were assumed to be homogeneous, linearly elastic,and isotropic. The anisotropy of the FPD and the dentin was not taken into account. The lateral and distal
planes and the bottom were assumed to be fixed; no translation or rotation was allowed in any direction.
Table 1.

Mechanical parameters of the related materials.

Materials
DentinCortical bone
Trabecular boneCementum
Alloy

Elastic modulus (MPa)1.35×104
1.45×104
2.15×102
1.38×104
8.46×104

Poisson’s ratio (-)
0.30
0.30
0.30
0.30
0.40

Reference
5 Shimizu et al., 2005
6 Aydin and Tekkaya, 1992
6 Aydin and Tekkaya, 1992
7 Yang et al., 1996
6 Aydin and Tekkaya, 1992

This study set a bite force of 225 N on the central fossa of second molar, which is about the maximum normal
functional bite force of Chinese people.9 The bite force was distributed uniformly on the points of the crown of
the second mandibular molar in contact in occlusion perpendicular to the surface. Loading forces on the models
were static. Analyses of the stress distributions formed on the root and adjacent alveolar bone were undertaken.

Results
The maximum Von mises stress, tensile stress and compressive stress values in the supporting tissues were24

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Int Chin J Dent 2007; 7: 23-26.

listed in the Table 2. Von mises stress is a scalar function of the components of the stress and can express theequal effective stress in the finite element analysis model. And the Von mises stress values in the different areas
were shown in the Fig. 2. From the stress patterns of the unrestored models, it is found that the Von mises stress
was concentrated in the top area of mesial alveolar bone and areas around the apex of mesial and lateral roots.
And the highest stress value was observed in the top area of mesial alveolar bone. The compressive stresses
located mainly in the mesial area of roots with the maximum value appearing in the top area of the mesial
alveolar bone. However, the tensile stresses were concentrated in the lateral areas and the maximum value
appeared in the top area of lateral part. There is a rather small stress distribution with a range of -0.03-0.10 MPa
in the supporting tissues around the second premolar because of the absence of the load on it. For the restoredmodel by a FPD, although the stress distribution of the tilted molar is similar with that of the unrestored one, thestress values decreased for all the areas such as top areas of alveolar ridge, apex area and furcation area. And forthe second premolar, the stresses increased which concentrated in the apex area as compressive stress and thecervix area as tensile stress. From the detailed values in the Table 2, all the three kinds of maximum stressvalues for the restored model were lower than those of unrestored one. And as it is shown in the Fig. 2, themaximum values of Von mises stress appeared in the top area of the mesial alveolar ridge before and after therestoration. And for other areas, the minimum values appeared in the top area of lateral alveolar ridge. However,for all the areas, the Von mises stress values decreased after the introduction of FPD.
Table 2.

Maximum stress values beforeand after the restoration in MPa.
Models

BeforeAfterTensile stressCompressive stress
Von mises stress

5.86-12.08
14.02

2.56
-9.22
9.45

Fig. 2.
Von mises stress values in the different areas before
and after the restoration: 1, top area of mesial
alveolar ridge of second premolar; 2, top area oflateral alveolar ridge of second premolar; 3, apex
area of second premolar; 4, mesial apex area ofsecond molar; 5, lateral apex area of second molar; 6,
furcation area of second molar; 7, top area of mesial
alveolar ridge of second molar; and 8, top area oflateral alveolar ridge of second molar.

Discussion
A mandibular molar that tilts mesially into the edentulous space is a common problem in clinical practice of
fixed prosthodontics. When the separate molar endures the occlusal force itself, the mesial component of theforce can not be conducted to the subjacent teeth and finally counteract in the midline and therefore, that willinduce an unusual strain in the supporting tissues and may lead to the aggressive mesial bone absorption.10 Thenthe dentist must consider this situation and decide the proper treatment. This study adopted the CT-based 3D
FEA method to investigate the stress distribution of the FPD with the tilted molar as abutment. This method has
better geometric similarity than the 2D FEA and it is also more convenient and simpler than the conventionalmethods.
The results proved the hypothesis that the introduction of the FPD can modify the stress distribution aroundthe tilted molar abutment. The data showed that the stress values of tilted molar decreased and the stress of25

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Int Chin J Dent 2007; 7: 23-26.

premolar increased after the restoration. That indicated that the occlusal force was conducted by the FPD to thesecond premolar. This improved the stress distribution of tilted molar by the supporting of the two abutment
teeth after the introduction of fixed prosthesis. And this conducted force can be further shared by the other teeth.
Before the restoration, the stress is highest in the mesial area of the supporting tissues and that will hurt thealveolar tissues and may lead to the bone resorption. The introduction of FPD can make the stress distribution
more stable and protect the periodontal tissue which was consistent with the 2D and photoelastic results reported
by some researches.2,3,11 The restoration can modify the stress distribution but it can not change the pattern ofstress distribution. After the restoration, there is also stress concentration in the mesial area of tilted molar.
However, there are still some limitations in the study. The further study will be carried out for the models withlarger tilting angles because the tilting angle was set as 30 degrees in this study.

Besides, experimental

mechanical method such as photoelastic study should be done to complement and prove the results of finite
element analysis.
Here we present a study of CT-based 3D FEA to investigate the stress distribution of a FPD using a tilted
molar as abutment and compare the stress distribution and values before and after the restoration. It can beconcluded that the restoration of FPD can improve the stress distribution of tilted molar and the occlusal force
can be shared by the other abutment. The stress distribution has become more stable and that will help toprevent the trauma of periodontal tissue and the possible bone absorption after the restoration of FPD. Then thefurther study is also needed to investigate the change of stresses for the molar abutments with different tilting
angles in order to help the decision of clinical treatment.

References
1. Stern N, Revah A, Becker A. The tilted posterior tooth. Part I: Etiology, syndrome, and prevention. J Prosthet Dent 1981; 46:
404-07.
2. Hood JA, Farah JW, Craig RG. Modification of stresses in alveolar bone induced by a tilted molar. J Prosthet Dent 1975; 34:
415-21.
3. Yang HS, Thompson VP. A two-dimensional stress analysis comparing fixed prosthodontic approaches to the tilted molarabutment. Int J Prosthodont 1991; 4: 416-24.
4. Mihram WL, Nemetz H. The tilted molar: a prosthetic and periodontal dilemma. Oral Health 1991; 81: 11-5.
5. Shimizu Y, Usui K, Araki K, Kurosaki N, Takanobu H, Takanashi A. Study of finite element modeling from CT images. Dent
Mater J 2005; 24: 447-55.
6. Aydin AK, Tekkaya AE. Stress induced by different loadings around weak abutments. J Prosthet Dent 1992; 68: 879-84.
7. Yang HS, Chung HJ, Park YJ. Stress analysis of a cantilevered fixed partial denture with normal and reduced bone support. JProsthetic Dent 1996; 76: 424-30.
8. Peters MC, Poort HW, Farah JW, et al. Stress analysis of a tooth restored with a post and core. J Dent Res 1983; 62: 760-63.
9. Xu JW. Modern Oral Prosthodontics. Beijing: Higher Education Press; 2000. p. 88.
10. Sadan A. The tipped mandibular molar as a bridge abutment: Part 2. Pract Periodontics Aesthet Dent 1999; 11: 772.
11. Woo YJ, Chung HG, Jo KH. A photoelastic study of the stress distribution in the surrounding tissues of the abutments of a
fixed partial denture with tilted molar abutments. Taehan Chikkwa Uisa Hyophoe Chi 1989; 27: 49-60.

Correspondence to:
Dr. Jun Jia
Department of Prosthodontics, College of Stomatology, The Fourth Military Medical University
145 Changle Xi Road, Xi’an, 710032, P. R. China
Fax: +86-29-82528818 E-mail: jiajun@fmmu.edu.cn
Received January 12, 2007. Accepted March 9, 2007.
Copyright ©2007 by the International Chinese Journal of Dentistry.

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