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Mechanical Responses of Periodontal Ligament under A Realistic Orthodontic Loading
Available online at www.sciencedirect.com
ProcediaProcedia Engineering 00 (2011) 000–000 Engineering 31 (2012) 828 – 833
Procedia Engineering www.elsevier.com/locate/procedia
International Conference on Advances in Computational Modeling and Simulation
Mechanical Responses of Periodontal Ligament under A Realistic Orthodontic Loading Huixiang Huanga*, Wencheng Tanga, Bin Yanb , Bin Wuc a
c
School of Mechanical Engineering, Southeast University, 211189, Nanjing, China b School of Stomatology,Nanjing Medical University,210029,Nanjing,China School of Mechanical and Electronic Engineering,Nanjing Forestry University,210037,Nanjing,China
Abstract The aim of this research was to investigate the initial mechanical responses in periodontal ligament (PDL) under a realistic orthodontic loading for two parallel forces. The finite element (FE) model including maxillary, central incisor and PDL was created based on the computed tomography and reverse engineering. The material behavior of the PDL was considered to be hyperelastic. In order to evaluate the stresses derived from two parallel forces, the comparison with the stresses under simplified concentrated force was made. The results showed that the stress distributions of the PDL calculated by ABAQUS with the two types of loads were similar, but the stress level in the PDL for two parallel forces was a bit higher than that for concentrated force. So the two parallel forces could reflect more accurately the root resorption in actual clinical treatment. The stresses and the strains were concentrated in the areas near the alveolar crest and the root apex in the lingual-buccal PDL.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Kunming University of Science and Technology Keywords: Orthodontic force; Periodontal ligament; Finite element; Hyperelasticity; Stress and strain
1. Introduction Orthodontic forces acting on tooth directly and its supporting apparatus (alveolar bone, periodontal ligament, and root cementum ) indirectly, generate a compound set of mechanical stimuli triggering biologic reactions in associated PDL and alveolar bone, thus inducing teeth to move to more appropriate positions in the jaw[1]. The remodeling occurred in the alveolar bone is the underlying reason for tooth movement, and it is believed that stresses and strains
* Corresponding author. Tel.: +86-15952081723 E-mail address: [email protected].
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2012.01.1108
Huixiang Huang al. / Procedia Engineering 31 (2012) 828 – 833 Huixiang Huang et al./etProcedia Engineering 00 (2011) 000–000
induced in the PDL by orthodontic forces are the proper mechanical signals initiating orthodontic bone remodeling processes[2,3]. So it is essential for clinicians to understand the forces applied to the tooth and the mechanical responses in the PDL, in order to improve the clinical efficiency and outcomes of the treatment, and understand the biomechanical mechanism of orthodontic tooth movement.
Orthodontic force systems result from the deformation of the continuous archwire for fixed orthodontic appliance used in orthodontic treatment and orthodontic tooth movement is the result of biologic reaction to applied orthodontic forces. Despite the optimal force for orthodontic tooth movement is an open question, ideally, an optimal orthodontic force should stimulate rapid tooth movement with minimal biologic trauma of the tooth, PDL, and alveolar bone, and histologically, it is desirable for an optimal force to maintain a stress level in the PDL that initiates a maximal cellular response for bone apposition and resorption, while maintaining the vitality of the local tissues[4]. It was proved that excessive stresses under orthodontic loading can lead to root resorption, and root resorption is a serious iatrogenic problem during orthodontic treatment. So it is necessary to quantitatively determine mechanical responses to orthodontic loads in a realistic orthodontic treatment. Since the FE method was introduced into dental biomechanical research in 1973 [5,6], it has been extensively applied to analyze the stress and strain fields in the tooth support structures[7]. In previous investigations, the forces from archwire acting on bracket were simplified as a concentrated force translated to tooth, but due to the prefabricate radian of archwire, mostly, the contacts between archwire and bracket only arise at the two endpoints of the bracket slot. In other words, the actual orthodontic loading should be considered as a pair of parallel forces rather than a concentrated force. The purpose of this investigation was to study the mechanical responses of PDL under two parallel forces by FE method. The tooth component model incorporating orthodontic appliance including archwire and bracket was established (Fig.1b), then we compared and discussed the stresses of the PDL under two parallel forces and a concentrated force in the light of previous investigations of biologic reactions during orthodontic tooth movement. 2. Material To acquire geometry of the real tooth, CT image-reconstruction technique was used in this investigation, and 3D model of the maxillary central incisor was constructed by the Mimics10.0 software. The data of case was obtained from the orthodontics Division of Jiangsu Province Hospital. The equipment for data sampling is Sensation 16 screw CT machine made in Germany. 3. Methods 3.1. CAD Model The tissues were segmented on the basis of their densities by selecting the value of threshold for the CT image, then the region growth was used to reconstruct the surface of the partial maxillary segment and its central incisor respectively. Finally their point clouds were achieved, and filtering the redundant noise points was conducted to obtain the precise characteristics of the partial maxillary and central incisor. The point clouds after being filtered were imported into the CATIA software, and the triangular grids were generated from the point cloud. And then the smooth processing of the triangular grids had been carried out to preclude the effect of the singularities, which made the grid surfaces approach to the actual geometry of the tooth. In order to acquire the free-form surfaces, the triangular surfaces were split into finite smaller regions, and the free-form surfaces of the partial maxillary and central incisor were closed to yield their solid models. Therefore, the CAD models of central incisor, PDL and maxillary shown in Fig.1a, were received through executing Boolean operation among central incisor solid model, tooth solid model thickened outwards as 0.2mm and partial maxillary solid model.
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Huixiang Huang et al.Engineering / Procedia Engineering 31 (2012) 828 – 833 Huixiang Huang et al./ Procedia 00 (2011) 000–000
(a)
(b)
Fig.1. (a) The CAD models of central incisor, PDL and maxillary, (b) The CAD model of tooth components incorporating orthodontic appliance
Fig.2 Loading and boundary conditions of FE model (F=0.25N)
3.2. CAE Models and Finite Element Analysis To acquire better mesh quality, the CAD models of central incisor, PDL and maxillary were imported into HyperMesh software to generate CAE models. Then the CAE models were input into the ABAQUS software to do finite element analysis. The Young’s modulus of the tooth and alveolar bone is approximately 20000-30000 times that of the PDL, and their deformations are negligible in comparison with that of PDL [8], in order to save the time of calculation, thereby, the central incisor and alveolar bone were postulated for rigid body (The relative error was found to be less than 1%). The element types of the central incisor and the alveolar bone were both used for R3D4, and their models consisted of 10562 and 19806 elements respectively. If the orthodontic forces are maintained for a long time, the stresses and the strains in the PDL will trigger alveolar bone remodeling processes resulting in a permanent change in tooth position[9], and this study was focused on the mechanical responses of the PDL under short-term forces ,associated with initial tooth displacement caused. However, the degree of initial tooth displacement is related to the material properties of the tooth, the alveolar bone and especially PDL. Although the linear elastic model is widely used for the PDL, it is commonly accepted that the PDL component is nonlinear. Moreover, the present investigations have proved that the transient characteristics of the PDL are more suitable for nonlinear constitutive models to describe. The nonlinearity of the PDL, published in former literatures, can be described using the hyperelasticity, the bilinear behavior or the time-dependent viscoelasticity, in addition, several constitutive models have been proposed to characterize the PDL’s hyperelasticity[10,11]. So the hyperelastic property of PDL was taken into consideration in this investigation, and the strain energy potential function for Ogden model can be expressed as
W
N 2 i ai 1 ai ai ( 3) ( J 1) 2i 1 2 3 2 ai i 1 i 1 Di N
(1)
Where W is strain energy function, 1 , 2 and 3 are the principle stretches ,and J is the elastic volume ratio. i is related to the initial shear modulus of the material, a i and Di are the parameters of material.
831
Huixiang Huang al. / Procedia Engineering 31 (2012) 828 – 833 Huixiang Huang et al./etProcedia Engineering 00 (2011) 000–000 1 3 i J i ，123 1
(2)
The data of an unaxial tension test for the PDL in the literature [12] was used for fitting of the third order Ogden model, so the curve fitting and the coefficients were shown in Fig.3 and Table 1. The Poisson’s ratio for the PDL was assumed to be 0.45. The element type for the PDL with a total thickness of 0.2mm was C3D8RH, and the PDL model contained 51589 elements.
Fig.3 Fitting of Ogden model and test data
i 1 2 3
Table 1 Coefficients of the third order Ogden model
i
ai
Di
-24.4237106 15.8966494 8.56953079
1.99994222 3.99994113 -2.00005453
4.87164332 0.00000000 0.00000000
The whole FE model was supported by applying the rigid boundary conditions in all degrees of freedom to all nodes of the alveolar bone as shown in Fig.2. The contact constraint between the central incisor and the PDL was set up with “tie”, as well as that between the alveolar bone and the PDL. In order to evaluate the mechanical responses of the PDL under two parallel forces which is in accordance with realistic loads in orthodontic clinical treatment, the two parallel forces and a concentrated force with the value of 0.5N were applied respectively to the central incisor, and the directions of them were perpendicular to the bracket, as shown in Fig.2. Moreover, the distance of two parallel forces was 3mm for the width of the bracket. 4. Results With these material parameters and boundary conditions, the calculations for nonlinear FE model was performed, then the stresses and their distributions were generated in the PDL, as shown in Fig.4 and Fig.5. The stress distributions of the PDL for the two types of loading conditions were similar, and there were stress concentration areas near the alveolar ridge at the lingual PDL and near the apex at the buccal PDL, whereas the maximal stress appeared at the alveolar ridge of the lingual PDL as shown in Fig.6. The stress levels within the PDL for the two parallel forces were higher than those for the simplified concentrated force, when the total value of each was 0.5N. With the increasing of the value, the
832
Huixiang Huang et al.Engineering / Procedia Engineering 31 (2012) 828 – 833 Huixiang Huang et al./ Procedia 00 (2011) 000–000
differences of the stress levels for them were more pronounced, and vice versa. Therefore, it was easier for the two parallel forces to control and reduce the root resorption. The PDL under two parallel forces with 0.5N undergone both tensile and compressive principal stresses, as shown in Fig.7. The tensile principal stresses were located in the buccal-cervical area and lingual apical area of the PDL, whereas the compressive principal stresses occurred in the opposite areas. The areas of high strain were present at the alveolar crest and root apex in the PDL, as shown in Fig.8. Thus this is in agreement with the result of the present study [13].
Fig.4 Stress in the PDL for two parallel forces
Fig.5 Stress in the PDL for concentrated force
Fig.6 The stresses for the lingual-buccal section of the PDL along the PDL from the apex during the application of the two parallel forces with 0.5N
Fig.7 Principal stresses in the PDL
Fig.8 Principal strains in the PDL
Huixiang Huang al. / Procedia Engineering 31 (2012) 828 – 833 Huixiang Huang et al./etProcedia Engineering 00 (2011) 000–000
5. Conclusion The 3D FE model was established to simulate the mechanical responses of the PDL under the two parallel forces. The new modeling method is more accurate than the traditional method, especially the CAE model, and the loads applied with two parallel force is more realistic than the simplified concentrated force in orthodontic treatment. The result demonstrated that it is more desirable to reduce the occurrence of root resorption by using realistic orthodontic loads. Despite of the difference of the stress levels caused by two type of loading conditions, the distribution of the stresses in the PDL is similar, and the concentrations of stress and strain occur in the alveolar ridge and apex of the lingual-buccal PDL. The accurate mechanical responses of periodontal ligament can be obtained through actual load condition, and they may be used to propose better treatment plans for patients, then the period of treatment can be shortened . References [1] Clarice Field,lonut Ichim,Michael V.Swain,etc. Mechanical responses to orthodontic loading: A 3-dimensional finite element multi-tooth model,Am J Orthod Dentofacial Orthop 2009;135:174-81. [2] Kawarizadeh A, Bourauel C, Jager A. Experimental and numerical determination of initial tooth mobility and material properties of the periodontal ligament in rat molar specimens,Eur J Orthod 2003;25:569-78. [3] Wu Bin, TANG Wencheng, Yan Bin. Study on Stress Distribution in Periodontal ligament of Impacted Tooth Based on Hyperelastic model.IEEE 2009. [4] Krishnan V, Davidovitch Z. Cellular, molecular, and tissue-level reactions to orthodontic force, Am J Orthod Dentofacial Orthop 2006;129: 469,461-32. [5] Thresher R.W.The stress analysis of human teeth. J Biomech 1973;5:443-9. [6] Farah JW. Photo-elastic and finite element stress analysis of a restored axisymmetric first molar. J Biomech 1973;5:551-60. [7] Cattaneo PM, Dalstra M, Melsen B. The finite element method: a tool to study orthodontic tooth movement. J Dent Res 2005;84:428-33. [8] Provatidis CG.A comparative FEM-study of tooth mobility using isotropic and anisotropic models of the periodontal ligament. Med Eng Phy 2000;22:359-70. [9] Ziegler A, Keilig L, Kawarizadeh A, Jager A, Bourauel C. Numerical simulation of the biomechanical behaviour of multirooted teeth. Eur J Orthod 2005;27:333-9. [10] Lihe Qian, Mitsugu Todo, Yasuyuki Morita, Yasuyuki Matsushita, Kiyoshi Koyano. Deformation analysis of the periodontium considering the viscoelasticity of the periodontal ligament. Dental Materials 2009;25:1285-92. [11] Natali AN, Pavan PG, Scarpa C. Numerical analysis of tooth mobility: formulation of a non-linear constitutive law for the periodontal ligament. Dental Materials 2004;20:623-9. [12] Yoshida Noriaki, Koga Yoshiyuki, Peng Chien-Lun, et al. In vivo measurement of the elastic modulus of the human periodontal ligament. Med Eng Phy 2001;23:567-72. [13] Cattaneo PM, Dalstra M, Melsen B. Strains in periodontal ligament and alveolar bone associated with orthodontic tooth movement analyzed by finite element.Orthod Craniofac Res 2009;12:120-8.
833
ProcediaProcedia Engineering 00 (2011) 000–000 Engineering 31 (2012) 828 – 833
Procedia Engineering www.elsevier.com/locate/procedia
International Conference on Advances in Computational Modeling and Simulation
Mechanical Responses of Periodontal Ligament under A Realistic Orthodontic Loading Huixiang Huanga*, Wencheng Tanga, Bin Yanb , Bin Wuc a
c
School of Mechanical Engineering, Southeast University, 211189, Nanjing, China b School of Stomatology,Nanjing Medical University,210029,Nanjing,China School of Mechanical and Electronic Engineering,Nanjing Forestry University,210037,Nanjing,China
Abstract The aim of this research was to investigate the initial mechanical responses in periodontal ligament (PDL) under a realistic orthodontic loading for two parallel forces. The finite element (FE) model including maxillary, central incisor and PDL was created based on the computed tomography and reverse engineering. The material behavior of the PDL was considered to be hyperelastic. In order to evaluate the stresses derived from two parallel forces, the comparison with the stresses under simplified concentrated force was made. The results showed that the stress distributions of the PDL calculated by ABAQUS with the two types of loads were similar, but the stress level in the PDL for two parallel forces was a bit higher than that for concentrated force. So the two parallel forces could reflect more accurately the root resorption in actual clinical treatment. The stresses and the strains were concentrated in the areas near the alveolar crest and the root apex in the lingual-buccal PDL.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Kunming University of Science and Technology Keywords: Orthodontic force; Periodontal ligament; Finite element; Hyperelasticity; Stress and strain
1. Introduction Orthodontic forces acting on tooth directly and its supporting apparatus (alveolar bone, periodontal ligament, and root cementum ) indirectly, generate a compound set of mechanical stimuli triggering biologic reactions in associated PDL and alveolar bone, thus inducing teeth to move to more appropriate positions in the jaw[1]. The remodeling occurred in the alveolar bone is the underlying reason for tooth movement, and it is believed that stresses and strains
* Corresponding author. Tel.: +86-15952081723 E-mail address: [email protected].
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2012.01.1108
Huixiang Huang al. / Procedia Engineering 31 (2012) 828 – 833 Huixiang Huang et al./etProcedia Engineering 00 (2011) 000–000
induced in the PDL by orthodontic forces are the proper mechanical signals initiating orthodontic bone remodeling processes[2,3]. So it is essential for clinicians to understand the forces applied to the tooth and the mechanical responses in the PDL, in order to improve the clinical efficiency and outcomes of the treatment, and understand the biomechanical mechanism of orthodontic tooth movement.
Orthodontic force systems result from the deformation of the continuous archwire for fixed orthodontic appliance used in orthodontic treatment and orthodontic tooth movement is the result of biologic reaction to applied orthodontic forces. Despite the optimal force for orthodontic tooth movement is an open question, ideally, an optimal orthodontic force should stimulate rapid tooth movement with minimal biologic trauma of the tooth, PDL, and alveolar bone, and histologically, it is desirable for an optimal force to maintain a stress level in the PDL that initiates a maximal cellular response for bone apposition and resorption, while maintaining the vitality of the local tissues[4]. It was proved that excessive stresses under orthodontic loading can lead to root resorption, and root resorption is a serious iatrogenic problem during orthodontic treatment. So it is necessary to quantitatively determine mechanical responses to orthodontic loads in a realistic orthodontic treatment. Since the FE method was introduced into dental biomechanical research in 1973 [5,6], it has been extensively applied to analyze the stress and strain fields in the tooth support structures[7]. In previous investigations, the forces from archwire acting on bracket were simplified as a concentrated force translated to tooth, but due to the prefabricate radian of archwire, mostly, the contacts between archwire and bracket only arise at the two endpoints of the bracket slot. In other words, the actual orthodontic loading should be considered as a pair of parallel forces rather than a concentrated force. The purpose of this investigation was to study the mechanical responses of PDL under two parallel forces by FE method. The tooth component model incorporating orthodontic appliance including archwire and bracket was established (Fig.1b), then we compared and discussed the stresses of the PDL under two parallel forces and a concentrated force in the light of previous investigations of biologic reactions during orthodontic tooth movement. 2. Material To acquire geometry of the real tooth, CT image-reconstruction technique was used in this investigation, and 3D model of the maxillary central incisor was constructed by the Mimics10.0 software. The data of case was obtained from the orthodontics Division of Jiangsu Province Hospital. The equipment for data sampling is Sensation 16 screw CT machine made in Germany. 3. Methods 3.1. CAD Model The tissues were segmented on the basis of their densities by selecting the value of threshold for the CT image, then the region growth was used to reconstruct the surface of the partial maxillary segment and its central incisor respectively. Finally their point clouds were achieved, and filtering the redundant noise points was conducted to obtain the precise characteristics of the partial maxillary and central incisor. The point clouds after being filtered were imported into the CATIA software, and the triangular grids were generated from the point cloud. And then the smooth processing of the triangular grids had been carried out to preclude the effect of the singularities, which made the grid surfaces approach to the actual geometry of the tooth. In order to acquire the free-form surfaces, the triangular surfaces were split into finite smaller regions, and the free-form surfaces of the partial maxillary and central incisor were closed to yield their solid models. Therefore, the CAD models of central incisor, PDL and maxillary shown in Fig.1a, were received through executing Boolean operation among central incisor solid model, tooth solid model thickened outwards as 0.2mm and partial maxillary solid model.
829
830
Huixiang Huang et al.Engineering / Procedia Engineering 31 (2012) 828 – 833 Huixiang Huang et al./ Procedia 00 (2011) 000–000
(a)
(b)
Fig.1. (a) The CAD models of central incisor, PDL and maxillary, (b) The CAD model of tooth components incorporating orthodontic appliance
Fig.2 Loading and boundary conditions of FE model (F=0.25N)
3.2. CAE Models and Finite Element Analysis To acquire better mesh quality, the CAD models of central incisor, PDL and maxillary were imported into HyperMesh software to generate CAE models. Then the CAE models were input into the ABAQUS software to do finite element analysis. The Young’s modulus of the tooth and alveolar bone is approximately 20000-30000 times that of the PDL, and their deformations are negligible in comparison with that of PDL [8], in order to save the time of calculation, thereby, the central incisor and alveolar bone were postulated for rigid body (The relative error was found to be less than 1%). The element types of the central incisor and the alveolar bone were both used for R3D4, and their models consisted of 10562 and 19806 elements respectively. If the orthodontic forces are maintained for a long time, the stresses and the strains in the PDL will trigger alveolar bone remodeling processes resulting in a permanent change in tooth position[9], and this study was focused on the mechanical responses of the PDL under short-term forces ,associated with initial tooth displacement caused. However, the degree of initial tooth displacement is related to the material properties of the tooth, the alveolar bone and especially PDL. Although the linear elastic model is widely used for the PDL, it is commonly accepted that the PDL component is nonlinear. Moreover, the present investigations have proved that the transient characteristics of the PDL are more suitable for nonlinear constitutive models to describe. The nonlinearity of the PDL, published in former literatures, can be described using the hyperelasticity, the bilinear behavior or the time-dependent viscoelasticity, in addition, several constitutive models have been proposed to characterize the PDL’s hyperelasticity[10,11]. So the hyperelastic property of PDL was taken into consideration in this investigation, and the strain energy potential function for Ogden model can be expressed as
W
N 2 i ai 1 ai ai ( 3) ( J 1) 2i 1 2 3 2 ai i 1 i 1 Di N
(1)
Where W is strain energy function, 1 , 2 and 3 are the principle stretches ,and J is the elastic volume ratio. i is related to the initial shear modulus of the material, a i and Di are the parameters of material.
831
Huixiang Huang al. / Procedia Engineering 31 (2012) 828 – 833 Huixiang Huang et al./etProcedia Engineering 00 (2011) 000–000 1 3 i J i ，123 1
(2)
The data of an unaxial tension test for the PDL in the literature [12] was used for fitting of the third order Ogden model, so the curve fitting and the coefficients were shown in Fig.3 and Table 1. The Poisson’s ratio for the PDL was assumed to be 0.45. The element type for the PDL with a total thickness of 0.2mm was C3D8RH, and the PDL model contained 51589 elements.
Fig.3 Fitting of Ogden model and test data
i 1 2 3
Table 1 Coefficients of the third order Ogden model
i
ai
Di
-24.4237106 15.8966494 8.56953079
1.99994222 3.99994113 -2.00005453
4.87164332 0.00000000 0.00000000
The whole FE model was supported by applying the rigid boundary conditions in all degrees of freedom to all nodes of the alveolar bone as shown in Fig.2. The contact constraint between the central incisor and the PDL was set up with “tie”, as well as that between the alveolar bone and the PDL. In order to evaluate the mechanical responses of the PDL under two parallel forces which is in accordance with realistic loads in orthodontic clinical treatment, the two parallel forces and a concentrated force with the value of 0.5N were applied respectively to the central incisor, and the directions of them were perpendicular to the bracket, as shown in Fig.2. Moreover, the distance of two parallel forces was 3mm for the width of the bracket. 4. Results With these material parameters and boundary conditions, the calculations for nonlinear FE model was performed, then the stresses and their distributions were generated in the PDL, as shown in Fig.4 and Fig.5. The stress distributions of the PDL for the two types of loading conditions were similar, and there were stress concentration areas near the alveolar ridge at the lingual PDL and near the apex at the buccal PDL, whereas the maximal stress appeared at the alveolar ridge of the lingual PDL as shown in Fig.6. The stress levels within the PDL for the two parallel forces were higher than those for the simplified concentrated force, when the total value of each was 0.5N. With the increasing of the value, the
832
Huixiang Huang et al.Engineering / Procedia Engineering 31 (2012) 828 – 833 Huixiang Huang et al./ Procedia 00 (2011) 000–000
differences of the stress levels for them were more pronounced, and vice versa. Therefore, it was easier for the two parallel forces to control and reduce the root resorption. The PDL under two parallel forces with 0.5N undergone both tensile and compressive principal stresses, as shown in Fig.7. The tensile principal stresses were located in the buccal-cervical area and lingual apical area of the PDL, whereas the compressive principal stresses occurred in the opposite areas. The areas of high strain were present at the alveolar crest and root apex in the PDL, as shown in Fig.8. Thus this is in agreement with the result of the present study [13].
Fig.4 Stress in the PDL for two parallel forces
Fig.5 Stress in the PDL for concentrated force
Fig.6 The stresses for the lingual-buccal section of the PDL along the PDL from the apex during the application of the two parallel forces with 0.5N
Fig.7 Principal stresses in the PDL
Fig.8 Principal strains in the PDL
Huixiang Huang al. / Procedia Engineering 31 (2012) 828 – 833 Huixiang Huang et al./etProcedia Engineering 00 (2011) 000–000
5. Conclusion The 3D FE model was established to simulate the mechanical responses of the PDL under the two parallel forces. The new modeling method is more accurate than the traditional method, especially the CAE model, and the loads applied with two parallel force is more realistic than the simplified concentrated force in orthodontic treatment. The result demonstrated that it is more desirable to reduce the occurrence of root resorption by using realistic orthodontic loads. Despite of the difference of the stress levels caused by two type of loading conditions, the distribution of the stresses in the PDL is similar, and the concentrations of stress and strain occur in the alveolar ridge and apex of the lingual-buccal PDL. The accurate mechanical responses of periodontal ligament can be obtained through actual load condition, and they may be used to propose better treatment plans for patients, then the period of treatment can be shortened . References [1] Clarice Field,lonut Ichim,Michael V.Swain,etc. Mechanical responses to orthodontic loading: A 3-dimensional finite element multi-tooth model,Am J Orthod Dentofacial Orthop 2009;135:174-81. [2] Kawarizadeh A, Bourauel C, Jager A. Experimental and numerical determination of initial tooth mobility and material properties of the periodontal ligament in rat molar specimens,Eur J Orthod 2003;25:569-78. [3] Wu Bin, TANG Wencheng, Yan Bin. Study on Stress Distribution in Periodontal ligament of Impacted Tooth Based on Hyperelastic model.IEEE 2009. [4] Krishnan V, Davidovitch Z. Cellular, molecular, and tissue-level reactions to orthodontic force, Am J Orthod Dentofacial Orthop 2006;129: 469,461-32. [5] Thresher R.W.The stress analysis of human teeth. J Biomech 1973;5:443-9. [6] Farah JW. Photo-elastic and finite element stress analysis of a restored axisymmetric first molar. J Biomech 1973;5:551-60. [7] Cattaneo PM, Dalstra M, Melsen B. The finite element method: a tool to study orthodontic tooth movement. J Dent Res 2005;84:428-33. [8] Provatidis CG.A comparative FEM-study of tooth mobility using isotropic and anisotropic models of the periodontal ligament. Med Eng Phy 2000;22:359-70. [9] Ziegler A, Keilig L, Kawarizadeh A, Jager A, Bourauel C. Numerical simulation of the biomechanical behaviour of multirooted teeth. Eur J Orthod 2005;27:333-9. [10] Lihe Qian, Mitsugu Todo, Yasuyuki Morita, Yasuyuki Matsushita, Kiyoshi Koyano. Deformation analysis of the periodontium considering the viscoelasticity of the periodontal ligament. Dental Materials 2009;25:1285-92. [11] Natali AN, Pavan PG, Scarpa C. Numerical analysis of tooth mobility: formulation of a non-linear constitutive law for the periodontal ligament. Dental Materials 2004;20:623-9. [12] Yoshida Noriaki, Koga Yoshiyuki, Peng Chien-Lun, et al. In vivo measurement of the elastic modulus of the human periodontal ligament. Med Eng Phy 2001;23:567-72. [13] Cattaneo PM, Dalstra M, Melsen B. Strains in periodontal ligament and alveolar bone associated with orthodontic tooth movement analyzed by finite element.Orthod Craniofac Res 2009;12:120-8.
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