Dental Traumatology 2015; 31: 190–195; doi: 10.1111/edt.12159
Stress distribution in delayed replanted teeth splinted with different orthodontic wires: a three-dimensional finite element analysis Fernando Isquierdo de Souza1, Wilson Roberto Poi2, Vanessa Ferreira da Silva2, Ana Paula Martini1, Regis Alexandre da Cunha Melo1, Sonia Regina Panzarini2, Eduardo Passos Rocha1 1
Department of Dental Materials and Prosthodontics, Aracßatuba Dental School, Unesp – Univ Estadual Paulista; 2Department of Surgery and Integrated Clinical, Aracßatuba Dental School, Unesp – Univ Estadual Paulista, Aracßatuba, Brazil
Key words: avulsion; dental trauma; biomechanics; finite element analysis Correspondence to: Fernando Isquierdo de Souza, DDS, MSc Student, Departamento de gicos e Pro tese, Faculdade Materiais Odontolo de Odontologia de Aracßatuba, Unesp, Univ Bonifa cio, 1193 Estadual Paulista, Rua Jose CEP 16015-050, Aracßatuba, SP, Brazil Tel.: +551836363290 Fax: +551836363245 e-mail: [email protected]
Abstract – Aim: The aim was to evaluate the biomechanical behavior of the supporting bony structures of replanted teeth and the periodontal ligament (PDL) of adjacent teeth when orthodontic wires with different mechanical properties are applied, with three-dimensional finite element analysis. Materials and methods: Based on tomographic and microtomographic data, a three-dimensional model of the anterior maxilla with the corresponding teeth (tooth 13–tooth 23) was generated to simulate avulsion and replantation of the tooth 21. The teeth were splinted with orthodontic wire (Ø 0.8 mm) and composite resin. The elastic modulus of the three orthodontic wires used, that is, steel wire (FA), titanium–molybdenum wire (FTM), and nitinol wire (FN) were 200 GPa, 84 GPa, and 52 GPa, respectively. An oblique load (100 N) was applied at an angle of 45° on the incisal edge of the replanted tooth and was analyzed using Ansys Workbench software. The maximum (rmax) and minimum (rmin) principal stresses generated in the PDL, cortical and alveolar bones, and the modified von Mises (rvM) values for the orthodontic wires were obtained. Results: With regard to the cortical bone and PDL, the highest rmin and rmax values for FTM, FN, and FA were checked. With regard to the alveolar bone, rmax and rmin values were highest for FA, followed by FTM and FN. The rvM values of the orthodontic wires followed the order of rigidity of the alloys, that is, FA > FTM > FN. Conclusion: The biomechanical behavior of the analyzed structures with regard to all the three patterns of flexibility was similar.
Accepted 13 November, 2014
Tooth avulsion is a serious injury (1), whose repair can be considered as one of the most complex processes, because it involves periodontal and pulpal damage (2). With an incidence of approximately 16% of all traumatic injuries of the permanent dentition (3, 4), it mainly affects children and adolescent males, aged between 7 and 20 years (5). Although immediate replantation is the treatment of choice (6–8), literature has shown that most avulsed teeth are replanted after a long extra-alveolar time (2, 7, 9). Splinting forms a part of the treatment protocol (10, 11), but differs according to the type of wire used when flexible splints are used in the management of avulsed teeth, the International Association of Dental Traumatology (IADT) recommends that avulsed permanent teeth without concomitant fracture of the alveolar process should be splinted for a period of 4 weeks irrespective of whether the avulsed teeth present an open or a closed apex (11). 190
However, as numerous varieties of orthodontic wires are available in the market for splinting purposes, the precise criterion of what is considered rigid or flexible has not been rigorously established, thus hindering the design of a clinical protocol (5). Although research on dental trauma and the use of different types of splints with varied methodologies (5, 12, 13) is being undertaken, presently, the outcome of different types of splints in the management of replanted avulsed teeth is not yet known (11). Similarly, the biomechanical behavior of bone and periodontal ligament associated with different types of splints has not been studied yet. The intraoral biomechanics is complex (14), which can be simulated using the finite element method (15–18). This method is a powerful tool for troubleshooting stress/strain-related issues and aids in the management of biomaterials and complex structures (19). © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd
Stress distribution in delayed replanted teeth
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f e i d c
b
g a
h
Fig. 1. Solid model in different colors and degrees of transparency illustrating structures such as enamel (a), dentin (b), dental pulp (c), periodontal ligament (d), alveolar bone (e), cortical bone (f), orthodontic wire (g), composite resin plugs (h), and suppressed periodontal ligament (i).
Thus, the purpose of this study was to evaluate using three-dimensional finite element analysis (3D FEA), the biomechanical behavior of the bone that supports the replanted tooth (element 21), and also behavior of the cortical bone, alveolar bone, and the periodontal ligaments of the adjacent splinted teeth, on varying the mechanical properties of the orthodontic wires. The hypothesis was that the biomechanical behavior and stress distribution in the analyzed structures would differ according to the stiffness of the orthodontic wire. Materials and methods
On the basis of the tomographic and micro-tomographic data, a three-dimensional anterior maxillary model with six teeth (canines, central and lateral incisors) was generated using the SOLIDWORKS 2010 program (Dassault Systemes SolidWorks Corp., Concord, MA, USA). The teeth were buccally splinted with orthodontic wires and composite resin, to simulate the splinting of the upper left replanted central incisor. The teeth (including their components, i.e. enamel, dentin, and the pulp), their supporting structures (cortical bone, alveolar bone, and periodontal ligament), composite plugs, and the orthodontic wires were included in the solid model (Fig. 1). These materials were considered isotropic, homogeneous and linearly elastic. The mechanical properties (elastic modulus and
Fig. 2. Model with triangular parabolic mesh of finite element.
Poisson’s ratio) and the stiffness number of the orthodontic wires (Ms) were assigned according to the specific literature (Table 1). Three models were generated: FA, FTM, and FN. FA (control) – Teeth were splinted with composite resin and 0.8-mm-thick orthodontic wire composed of stainless steel alloy. FTM – Teeth were splinted with composite resin and 0.8-mm-thick orthodontic wire composed of titanium–molybdenum alloy (Ti-Mo). FN – Teeth were splinted with composite resin and 0.8-mm-thick orthodontic wire composed of nickel– titanium alloy (Ni-Ti). Subsequently, the periodontal ligament of the upper left central incisor was removed to simulate tooth avulsion and delayed tooth replantation (letter i highlights the detail, Fig. 1). Numerical analysis was performed with finite element software ANSYS Workbench 14.0 (Ansys, Inc., Canonsburg, PA, USA), which determined the areas/regions of interest in the model and generated the finite element mesh (Fig. 2). Triangular parabolic elements of 0.3 mm were used for making the mesh. Refinement was established based on the convergence analysis (6%) (17). Finally, the models had 747 442 nodes and 421 789 elements.
Table 1. Young’s modulus (MPa) and Poisson’s ratio of structure and materials Structure
E (MPa)
v
Ms
References
Cortical bone Medular bone Dentin Enamel PDL CR Stainless steel alloy Ti-Mo alloy Ni-Ti alloy
13 000 1300 18 600 80 000 68.9 16 600 200 000 84 000 52 000
0.3 0.3 0.31 0.3 0.45 0.24 0.3 0.3 0.3
– – – – – – 1.0 0.42 0.26
(20, 21) (21, 22) (17, 21, 23) (17) (17, 23) (24) (25) (25) (25)
E = Young’s Modulus, v = Poisson’s Ratio, Ms = Material-stiffness Number, PDL = Periodontal Ligament, CR = Composite Resin, Ti-Mo = Titanium–molybdenum Alloy, Ni-Ti = Nickel–titanium Alloy. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd
Fig. 3. Model representing load incidence and fixed support.
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FA
FTM
the other structures that were considered to be nonductile, the maximum principal stress values (rmax) and the minimum principal stress values (rmin) were obtained to enable better interpretation of the behavior of the cortical and alveolar bones, and periodontal ligament with regard to the different orthodontic wires used.
FN
σmax (MPa)
20 15 10 5
Results
0 PDL
Cortical bone
Alveolar bone
Graph 1. Values of maximum principal stress (rmax) in bone structures and PDL.
For the mathematical analysis, an oblique load of 100 N was applied at an angle 45° on the incisal edge of 21 in all the three models to simulate food interposition, because the treatment protocol provides that the traumatized tooth remains in infra-occlusion after stabilization. The fixed support was determined along 3 Cartesian axes (x = y = z = 0) to characterize the boundary condition, and the models were fixed on the distal faces (Fig. 3). Considering the fact that metallic alloys are ductile (non-friable), the modified von Mises equivalent stress values (rvM) were obtained for orthodontic wires. For
Cortical bone
The maximum principal stress values (rmax) were highest for the FTM model (18.9 MPa), followed by those for the models FN (18.5 MPa) and FA (18.3 MPa, Graph 1). The rmax distribution maps illustrate the similarity in stress distribution and concentration in the FA and FTM models. In the FN model, pressure concentration occurred slightly lower with respect to the midline of the buccal surface of the structure, in comparison with the other models (Fig. 4). The highest rmax concentration in this structure occurred at the lingual surface of the right canine for all the three models (Fig. 5). With regard to the minimum principal stress values (rmin), the same sequence was observed with higher values for the model FTM ( 10.6 MPa) followed by the models FN ( 10.1 MPa) and FA ( 9.54 MPa,
Fig. 4. Maps of distribution of rmax in bone structures and PDL. Image sequence: C (Cortical Bone), A (Alveolar Bone), P (Periodontal Ligament), respectively. (Left to right sequence: FA – wire composed of stainless steel alloy, FTM – wire composed of titanium–molybdenum alloy, FN – wire composed of nickel– titanium alloy).
Fig. 5. Zoomed images of the region of highest rmax in bone structures and PDL. The gray label indicates the site of minor stress and the red label indicates the site of major stress. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd
Stress distribution in delayed replanted teeth Graph 2). Highest stress concentration occurred at the distolingual surface of the left canine for all the three models.
FA
FTM
193
FN
150
In the alveolar bone, the rmax values were proportional to the stiffness sequence of orthodontic wires used for fixation with higher values for the FA model (5.06 MPa), followed by FTM model (4.27 MPa) and FN model (4.1 MPa, Graph 1). As with the cortical bone, the region of highest stress concentration was the same for all three models, but occurred in the alveolar bone on the apical region of the replanted tooth (Fig. 5). The rmin values were also proportional to the order of stiffness of the wires, with the FA model showing the highest value 25 MPa), followed by FTM model ( 23.7 MPa) and FN model ( 23.2 MPa, Graph 2). The highest stress concentration occurred in the apical region of the replanted tooth in all three models (Fig. 5). The rmax distribution maps show similar images for FA and FN models. The FTM model differs from the others in that the highest concentration of stress occurred in the middle region of the buccal surface of the structure (Fig. 4). Periodontal ligament (PDL)
The rmax values were similar to the sequence of the cortical bone results with highest values for FTM model (5.49 MPa), followed by FN model (5.14 MPa) and FA model (5.06 MPa, Graph 1). Highest stress concentration occurred in the distolingual surface of the left canine in all the three models. The rmin values were highest for FTM model ( 3 MPa), followed by FN ( 2.91 MPa) and FA models ( 2.45 MPa, Graph 2). The region where highest concentration occurred was the distobuccal surface of the left canine in all the models. The rmax distribution maps of the three wires used in the post-traumatic fixation are almost similar (Fig. 4) and differ slightly only in the distal surface of the left canine in the FN model (Fig. 5), where a zoomed image is visualized as a point with lower pressure. Orthodontic wires
The modified von Mises equivalent stress (rvM) values were assigned for the orthodontic wires; wires with
σmin (MPa)
0 –5
PDL
Cortical bone
Alveolar bone
–10 –15 –20 –25 FA
FTM
FN
Graph 2. Values of minimum principal stress (rmin) in bone structures and PDL. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd
σvM (MPa)
Alveolar bone
100 50 0 Ortodontic wires
Graph 3. von Mises equivalent stress (rvM) for orthodontic wires.
greater rigidity were associated with higher stresses (Graph 3). Discussion
According to the treatment guidelines proposed by The International Association of Dental Traumatology for managing avulsed permanent teeth (11), flexible splints should be used to treat delayed teeth replantation. But the concepts of what is ‘flexible’, and the ideal material for achieving such stabilization, are not established. According to Kwan et al. (5), splinting with stainless steel orthodontic wire of 0.4 mm diameter, with the aid of composite resin, could be considered as rigid. In the present study, metal wires of 0.8 mm diameter were used. Burstone (25) established that when orthodontic wires of the same thickness but of different alloy compositions are compared, the wires composed of alloys with lower elastic modulus such as Ti-Mo and Ni-Ti show more flexibility in comparison with the ones composed of alloys with higher elastic modulus. On this basis, stainless steel alloy wire (control) was used to simulate a rigid splint, the titanium– molybdenum alloy wire with intermediate flexibility was used to simulate a semi-rigid splint (58% more flexible than the rigid splint), and nickel–titanium (nitinol) alloy wire (the most flexible of the three alloys tested, and approximately 74% more flexible than the rigid splint) was used to simulate a flexible splint (Table 1). Thus, we tried to establish three patterns of stiffness to simulate stabilization of a delayed replanted tooth. Current literature emphasizes the importance of using a flexible splint for stabilization of injured teeth, because it allows physiological movement, which in turn favors periodontal and pulpal healing (5, 26–29). According to Mazzoleni et al. (30), two biomechanical factors are considered sine qua non for successful treatment: light loads applied on the healing tissue and controlled tooth movement (about 50 um) within the alveolus. Cengiz et al. (29) cite in their paper that the tendency is to assume that greater the rigidity of the splint, lower would be the stresses transferred to the
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traumatized support structures, hence better the healing process. Our results partially contradict this opinion because greater stress concentration occurred in the alveolus of the traumatized tooth when a rigid splint was simulated (FA). Inspite of a large difference in the flexibility of the alloys tested, our results showed no major differences with regard to the biomechanical behavior of the simulated post-traumatic splints, On the contrary, the three models behaved almost similarly, showing a subtle difference in the maps of stress concentration, and in the maximum (rmax) and minimum (rmin) principal stress values. In addition, contrary to what has been postulated in the proposed hypothesis, with regard to the alveolar bone, stresses increased as the flexibility of the wires decreased (FA > FTM > FN). In the other observed structures (cortical bone and periodontal ligament of adjacent teeth), the wire with intermediate flexibility (FTM) transferred higher stresses, followed by the wire with greater flexibility (FN), and the rigid wire (FA). Thus, the proposed hypothesis was partly rejected, because stress did not vary according to the order of stiffness of the orthodontic wires. Longitudinal clinical follow-up studies on tooth replantation show that achieving absolute immobility of the replanted tooth and total reduction of tension between the surfaces of injured tissues is not necessarily required for their healing (28). This implies that ‘controlled’ mobility and induction of stresses or functional tension of a low magnitude favors the healing of injured tissue (29). The results of present study show that even the most rigid splint (FA), whose wire was larger than the ones typically used for this function, displayed some amount of flexibility, that is, transferred some tension to not only the adjacent teeth and their supporting structures (cortical and alveolar bones and periodontal ligament) but also to the traumatized tissues. This stress distribution pattern was similar to that of the more flexible wires used in this simulation. Thus, the results suggest that biomechanical similarity of wires elicits a similar clinical response is expected. However, to validate the results obtained in this simulation, further clinical and longitudinal followup studies are required regarding the management of tooth avulsion and their post-traumatic contentions when splinted with composite resin and orthodontic wires of different flexibilities. However, the present study has some limitations. It analyses static behavior, involves simplified calculations of mathematical functions, is linear in nature, and did not consider modifications in the distribution of stresses and strains on the geometric structures. Conclusion
The finite element analysis of simulation of post-traumatic splints for tooth replantation showed that the biomechanical behavior of the analyzed bone structures and periodontal ligament was similar for all the three patterns of flexibility/three models tested.
Acknowledgements
This study was supported by the S~ ao Paulo State Research Foundation in Brazil (FAPESP # 2008/ 00209-9). Conflict of interest
The authors report no conflict of interests. References 1. Silva EJ, Rollemberg CB, de Souza C-FT, Zaia AA. A multiparametric assay to compare the cytotoxicity of soy milk with different storage media. Dent Traumatol 2013;29:319–22. 2. Soares AJ, Gomes BP, Zaia AA, Ferraz CC, de Souza-Filho FJ. Relationship between clinical-radiographic evaluation and outcome of teeth replantation. Dent Traumatol 2008;24:183–8. 3. Martin MP, Pileggi R. A quantitative analysis of Propolis: a promising new storage media following avulsion. Dent Traumatol 2004;20:85–9. 4. Trope M. Avulsion of permanent teeth: theory to practice. Dent Traumatol 2011;27:281–94. 5. Kwan SC, Johnson JD, Cohenca N. The effect of splint material and thickness on tooth mobility after extraction and replantation using a human cadaveric model. Dent Traumatol 2012;28:277–81. 6. Andreasen JO. A time-related study of periodontal healing and root resorption activity after replantation of mature permanent incisors in monkeys. Swed Dent J 1980;4:101–10. 7. Andreasen JO, Borum MK, Jacobsen HL, Andreasen FM. Replantation of 400 avulsed permanent incisors. 1. Diagnosis of healing complications. Endod Dent Traumatol 1995;11: 51–8. 8. Flores MT, Andersson L, Andreasen JO, Bakland LK, Malmgren B, Barnett F et al. Guidelines for the management of traumatic dental injuries. II. Avulsion of permanent teeth. Dent Traumatol 2007;23:130–6. 9. Panzarini SR, Saad-Neto M, Sonoda CK, Poi WR, Carvalho ACP. Avuls~ oes dentarias em pacientes jovens e adultos na regi~ao de Aracßatuba. Rev Assoc Paul Cir Dent 2003;57:6. 10. Andreasen JO, Andreasen FM. Avulsions. In: Andreasen JO, Andreasen FM, Andersson L, editors. Proceedings of the Textbook and color atlas of traumatic injuries to the teeth. Wiley-Blackwell; 2007. p. 444–88. 11. Andersson L, Andreasen JO, Day P, Heithersay G, Trope M, Diangelis AJ et al. International Association of Dental Traumatology guidelines for the management of traumatic dental injuries: 2. Avulsion of permanent teeth. Dent Traumatol 2012;28:88–96. 12. von Arx T, Filippi A, Lussi A. Comparison of a new dental trauma splint device (TTS) with three commonly used splinting techniques. Dent Traumatol 2001;17:266–74. 13. Berthold C, Thaler A, Petschelt A. Rigidity of commonly used dental trauma splints. Dent Traumatol 2009;25:248–55. 14. Assuncao WG, Barao VA, Tabata LF, Gomes EA, Delben JA, dos Santos PH. Biomechanics studies in dentistry: bioengineering applied in oral implantology. J Craniofac Surg 2009;20:1173–7. 15. Cattaneo PM, Dalstra M, Melsen B. The finite element method: a tool to study orthodontic tooth movement. J Dent Res 2005;84:428–33. 16. Freitas AC Jr, Rocha EP, dos Santos PH, Ko CC, Martin M Jr, de Almeida EO. Mechanics of the maxillary central incisor. Influence of the periodontal ligament represented by beam elements. Comput Methods Biomech Biomed Engin 2010;13:515–21. 17. Rocha EP, Anchieta RB, Freitas AC Jr, De Almeida EO, Cattaneo PM, Chang KC. Mechanical behavior of ceramic © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd
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veneer in zirconia-based restorations: a 3-dimensional finite element analysis using microcomputed tomography data. J Prosthet Dent 2011;105:14–20. Freitas-Junior AC, Rocha EP, Bonfante EA, Almeida EO, Anchieta RB, Martini AP et al. Biomechanical evaluation of internal and external hexagon platform switched implantabutment connections: An in vitro laboratory and threedimensional finite element analysis. Dent Mater 2012;28: e218–28. Qian Y, Zhou X, Yang J. Correlation between cuspal inclination and tooth cracked syndrome: a three-dimensional reconstruction measurement and finite element analysis. Dent Traumatol 2013;29:226–33. Carter DR, Spengler DM. Mechanical properties and composition of cortical bone. Clin Orthop Relat Res 1978;135:192– 217. Su KC, Chuang SF, Ng EY, Chang CH. An investigation of dentinal fluid flow in dental pulp during food mastication: simulation of fluid–structure interaction. Biomech Model Mechanobiol 2013;3:527–35. Brown CJ, Wang CJ, Yettram AL, Procter P. Intramedullary nails with two lag screws. Clin Biomech (Bristol, Avon) 2004;19:519–25. Ko CC, Chu CS, Chung KH, Lee MC. Effects of posts on dentin stress distribution in pulpless teeth. J Prosthet Dent 1992;68:421–7.
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24. Huysmans MC, Van der Varst PG. Finite element analysis of quasistatic and fatigue failure of post and cores. J Dent 1993;21:57–64. 25. Burstone CJ. Variable-modulus orthodontics. Am J Orthod 1981;80:1–16. 26. Ram D, Cohenca N. Therapeutic protocols for avulsed permanent teeth: review and clinical update. Pediatr Dent 2004;26:251– 5. 27. Kinirons MJ, Boyd DH, Gregg TA. Inflammatory and replacement resorption in reimplanted permanent incisor teeth: a study of the characteristics of 84 teeth. Endod Dent Traumatol 1999;15:269–72. 28. Andreasen JO, Andreasen FM, Mejare I, Cvek M. Healing of 400 intra-alveolar root fractures. 2. Effect of treatment factors such as treatment delay, repositioning, splinting type and period and antibiotics. Dent Traumatol 2004;20:203–11. 29. Burcak CS, Stephan AA, Cehreli ZC. Biomechanical effects of splint types on traumatized tooth: a photoelastic stress analysis. Dent Traumatol 2006;22:133–8. 30. Mazzoleni S, Meschia G, Cortesi R, Bressan E, Tomasi C, Ferro R. In vitro comparison of the flexibility of different splint systems used in dental traumatology. Dent Traumatol 2010;26:30–6.
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Stress distribution in delayed replanted teeth splinted with different orthodontic wires: a three-dimensional finite element analysis Fernando Isquierdo de Souza1, Wilson Roberto Poi2, Vanessa Ferreira da Silva2, Ana Paula Martini1, Regis Alexandre da Cunha Melo1, Sonia Regina Panzarini2, Eduardo Passos Rocha1 1
Department of Dental Materials and Prosthodontics, Aracßatuba Dental School, Unesp – Univ Estadual Paulista; 2Department of Surgery and Integrated Clinical, Aracßatuba Dental School, Unesp – Univ Estadual Paulista, Aracßatuba, Brazil
Key words: avulsion; dental trauma; biomechanics; finite element analysis Correspondence to: Fernando Isquierdo de Souza, DDS, MSc Student, Departamento de gicos e Pro tese, Faculdade Materiais Odontolo de Odontologia de Aracßatuba, Unesp, Univ Bonifa cio, 1193 Estadual Paulista, Rua Jose CEP 16015-050, Aracßatuba, SP, Brazil Tel.: +551836363290 Fax: +551836363245 e-mail: [email protected]
Abstract – Aim: The aim was to evaluate the biomechanical behavior of the supporting bony structures of replanted teeth and the periodontal ligament (PDL) of adjacent teeth when orthodontic wires with different mechanical properties are applied, with three-dimensional finite element analysis. Materials and methods: Based on tomographic and microtomographic data, a three-dimensional model of the anterior maxilla with the corresponding teeth (tooth 13–tooth 23) was generated to simulate avulsion and replantation of the tooth 21. The teeth were splinted with orthodontic wire (Ø 0.8 mm) and composite resin. The elastic modulus of the three orthodontic wires used, that is, steel wire (FA), titanium–molybdenum wire (FTM), and nitinol wire (FN) were 200 GPa, 84 GPa, and 52 GPa, respectively. An oblique load (100 N) was applied at an angle of 45° on the incisal edge of the replanted tooth and was analyzed using Ansys Workbench software. The maximum (rmax) and minimum (rmin) principal stresses generated in the PDL, cortical and alveolar bones, and the modified von Mises (rvM) values for the orthodontic wires were obtained. Results: With regard to the cortical bone and PDL, the highest rmin and rmax values for FTM, FN, and FA were checked. With regard to the alveolar bone, rmax and rmin values were highest for FA, followed by FTM and FN. The rvM values of the orthodontic wires followed the order of rigidity of the alloys, that is, FA > FTM > FN. Conclusion: The biomechanical behavior of the analyzed structures with regard to all the three patterns of flexibility was similar.
Accepted 13 November, 2014
Tooth avulsion is a serious injury (1), whose repair can be considered as one of the most complex processes, because it involves periodontal and pulpal damage (2). With an incidence of approximately 16% of all traumatic injuries of the permanent dentition (3, 4), it mainly affects children and adolescent males, aged between 7 and 20 years (5). Although immediate replantation is the treatment of choice (6–8), literature has shown that most avulsed teeth are replanted after a long extra-alveolar time (2, 7, 9). Splinting forms a part of the treatment protocol (10, 11), but differs according to the type of wire used when flexible splints are used in the management of avulsed teeth, the International Association of Dental Traumatology (IADT) recommends that avulsed permanent teeth without concomitant fracture of the alveolar process should be splinted for a period of 4 weeks irrespective of whether the avulsed teeth present an open or a closed apex (11). 190
However, as numerous varieties of orthodontic wires are available in the market for splinting purposes, the precise criterion of what is considered rigid or flexible has not been rigorously established, thus hindering the design of a clinical protocol (5). Although research on dental trauma and the use of different types of splints with varied methodologies (5, 12, 13) is being undertaken, presently, the outcome of different types of splints in the management of replanted avulsed teeth is not yet known (11). Similarly, the biomechanical behavior of bone and periodontal ligament associated with different types of splints has not been studied yet. The intraoral biomechanics is complex (14), which can be simulated using the finite element method (15–18). This method is a powerful tool for troubleshooting stress/strain-related issues and aids in the management of biomaterials and complex structures (19). © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd
Stress distribution in delayed replanted teeth
191
f e i d c
b
g a
h
Fig. 1. Solid model in different colors and degrees of transparency illustrating structures such as enamel (a), dentin (b), dental pulp (c), periodontal ligament (d), alveolar bone (e), cortical bone (f), orthodontic wire (g), composite resin plugs (h), and suppressed periodontal ligament (i).
Thus, the purpose of this study was to evaluate using three-dimensional finite element analysis (3D FEA), the biomechanical behavior of the bone that supports the replanted tooth (element 21), and also behavior of the cortical bone, alveolar bone, and the periodontal ligaments of the adjacent splinted teeth, on varying the mechanical properties of the orthodontic wires. The hypothesis was that the biomechanical behavior and stress distribution in the analyzed structures would differ according to the stiffness of the orthodontic wire. Materials and methods
On the basis of the tomographic and micro-tomographic data, a three-dimensional anterior maxillary model with six teeth (canines, central and lateral incisors) was generated using the SOLIDWORKS 2010 program (Dassault Systemes SolidWorks Corp., Concord, MA, USA). The teeth were buccally splinted with orthodontic wires and composite resin, to simulate the splinting of the upper left replanted central incisor. The teeth (including their components, i.e. enamel, dentin, and the pulp), their supporting structures (cortical bone, alveolar bone, and periodontal ligament), composite plugs, and the orthodontic wires were included in the solid model (Fig. 1). These materials were considered isotropic, homogeneous and linearly elastic. The mechanical properties (elastic modulus and
Fig. 2. Model with triangular parabolic mesh of finite element.
Poisson’s ratio) and the stiffness number of the orthodontic wires (Ms) were assigned according to the specific literature (Table 1). Three models were generated: FA, FTM, and FN. FA (control) – Teeth were splinted with composite resin and 0.8-mm-thick orthodontic wire composed of stainless steel alloy. FTM – Teeth were splinted with composite resin and 0.8-mm-thick orthodontic wire composed of titanium–molybdenum alloy (Ti-Mo). FN – Teeth were splinted with composite resin and 0.8-mm-thick orthodontic wire composed of nickel– titanium alloy (Ni-Ti). Subsequently, the periodontal ligament of the upper left central incisor was removed to simulate tooth avulsion and delayed tooth replantation (letter i highlights the detail, Fig. 1). Numerical analysis was performed with finite element software ANSYS Workbench 14.0 (Ansys, Inc., Canonsburg, PA, USA), which determined the areas/regions of interest in the model and generated the finite element mesh (Fig. 2). Triangular parabolic elements of 0.3 mm were used for making the mesh. Refinement was established based on the convergence analysis (6%) (17). Finally, the models had 747 442 nodes and 421 789 elements.
Table 1. Young’s modulus (MPa) and Poisson’s ratio of structure and materials Structure
E (MPa)
v
Ms
References
Cortical bone Medular bone Dentin Enamel PDL CR Stainless steel alloy Ti-Mo alloy Ni-Ti alloy
13 000 1300 18 600 80 000 68.9 16 600 200 000 84 000 52 000
0.3 0.3 0.31 0.3 0.45 0.24 0.3 0.3 0.3
– – – – – – 1.0 0.42 0.26
(20, 21) (21, 22) (17, 21, 23) (17) (17, 23) (24) (25) (25) (25)
E = Young’s Modulus, v = Poisson’s Ratio, Ms = Material-stiffness Number, PDL = Periodontal Ligament, CR = Composite Resin, Ti-Mo = Titanium–molybdenum Alloy, Ni-Ti = Nickel–titanium Alloy. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd
Fig. 3. Model representing load incidence and fixed support.
Souza et al.
192
FA
FTM
the other structures that were considered to be nonductile, the maximum principal stress values (rmax) and the minimum principal stress values (rmin) were obtained to enable better interpretation of the behavior of the cortical and alveolar bones, and periodontal ligament with regard to the different orthodontic wires used.
FN
σmax (MPa)
20 15 10 5
Results
0 PDL
Cortical bone
Alveolar bone
Graph 1. Values of maximum principal stress (rmax) in bone structures and PDL.
For the mathematical analysis, an oblique load of 100 N was applied at an angle 45° on the incisal edge of 21 in all the three models to simulate food interposition, because the treatment protocol provides that the traumatized tooth remains in infra-occlusion after stabilization. The fixed support was determined along 3 Cartesian axes (x = y = z = 0) to characterize the boundary condition, and the models were fixed on the distal faces (Fig. 3). Considering the fact that metallic alloys are ductile (non-friable), the modified von Mises equivalent stress values (rvM) were obtained for orthodontic wires. For
Cortical bone
The maximum principal stress values (rmax) were highest for the FTM model (18.9 MPa), followed by those for the models FN (18.5 MPa) and FA (18.3 MPa, Graph 1). The rmax distribution maps illustrate the similarity in stress distribution and concentration in the FA and FTM models. In the FN model, pressure concentration occurred slightly lower with respect to the midline of the buccal surface of the structure, in comparison with the other models (Fig. 4). The highest rmax concentration in this structure occurred at the lingual surface of the right canine for all the three models (Fig. 5). With regard to the minimum principal stress values (rmin), the same sequence was observed with higher values for the model FTM ( 10.6 MPa) followed by the models FN ( 10.1 MPa) and FA ( 9.54 MPa,
Fig. 4. Maps of distribution of rmax in bone structures and PDL. Image sequence: C (Cortical Bone), A (Alveolar Bone), P (Periodontal Ligament), respectively. (Left to right sequence: FA – wire composed of stainless steel alloy, FTM – wire composed of titanium–molybdenum alloy, FN – wire composed of nickel– titanium alloy).
Fig. 5. Zoomed images of the region of highest rmax in bone structures and PDL. The gray label indicates the site of minor stress and the red label indicates the site of major stress. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd
Stress distribution in delayed replanted teeth Graph 2). Highest stress concentration occurred at the distolingual surface of the left canine for all the three models.
FA
FTM
193
FN
150
In the alveolar bone, the rmax values were proportional to the stiffness sequence of orthodontic wires used for fixation with higher values for the FA model (5.06 MPa), followed by FTM model (4.27 MPa) and FN model (4.1 MPa, Graph 1). As with the cortical bone, the region of highest stress concentration was the same for all three models, but occurred in the alveolar bone on the apical region of the replanted tooth (Fig. 5). The rmin values were also proportional to the order of stiffness of the wires, with the FA model showing the highest value 25 MPa), followed by FTM model ( 23.7 MPa) and FN model ( 23.2 MPa, Graph 2). The highest stress concentration occurred in the apical region of the replanted tooth in all three models (Fig. 5). The rmax distribution maps show similar images for FA and FN models. The FTM model differs from the others in that the highest concentration of stress occurred in the middle region of the buccal surface of the structure (Fig. 4). Periodontal ligament (PDL)
The rmax values were similar to the sequence of the cortical bone results with highest values for FTM model (5.49 MPa), followed by FN model (5.14 MPa) and FA model (5.06 MPa, Graph 1). Highest stress concentration occurred in the distolingual surface of the left canine in all the three models. The rmin values were highest for FTM model ( 3 MPa), followed by FN ( 2.91 MPa) and FA models ( 2.45 MPa, Graph 2). The region where highest concentration occurred was the distobuccal surface of the left canine in all the models. The rmax distribution maps of the three wires used in the post-traumatic fixation are almost similar (Fig. 4) and differ slightly only in the distal surface of the left canine in the FN model (Fig. 5), where a zoomed image is visualized as a point with lower pressure. Orthodontic wires
The modified von Mises equivalent stress (rvM) values were assigned for the orthodontic wires; wires with
σmin (MPa)
0 –5
PDL
Cortical bone
Alveolar bone
–10 –15 –20 –25 FA
FTM
FN
Graph 2. Values of minimum principal stress (rmin) in bone structures and PDL. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd
σvM (MPa)
Alveolar bone
100 50 0 Ortodontic wires
Graph 3. von Mises equivalent stress (rvM) for orthodontic wires.
greater rigidity were associated with higher stresses (Graph 3). Discussion
According to the treatment guidelines proposed by The International Association of Dental Traumatology for managing avulsed permanent teeth (11), flexible splints should be used to treat delayed teeth replantation. But the concepts of what is ‘flexible’, and the ideal material for achieving such stabilization, are not established. According to Kwan et al. (5), splinting with stainless steel orthodontic wire of 0.4 mm diameter, with the aid of composite resin, could be considered as rigid. In the present study, metal wires of 0.8 mm diameter were used. Burstone (25) established that when orthodontic wires of the same thickness but of different alloy compositions are compared, the wires composed of alloys with lower elastic modulus such as Ti-Mo and Ni-Ti show more flexibility in comparison with the ones composed of alloys with higher elastic modulus. On this basis, stainless steel alloy wire (control) was used to simulate a rigid splint, the titanium– molybdenum alloy wire with intermediate flexibility was used to simulate a semi-rigid splint (58% more flexible than the rigid splint), and nickel–titanium (nitinol) alloy wire (the most flexible of the three alloys tested, and approximately 74% more flexible than the rigid splint) was used to simulate a flexible splint (Table 1). Thus, we tried to establish three patterns of stiffness to simulate stabilization of a delayed replanted tooth. Current literature emphasizes the importance of using a flexible splint for stabilization of injured teeth, because it allows physiological movement, which in turn favors periodontal and pulpal healing (5, 26–29). According to Mazzoleni et al. (30), two biomechanical factors are considered sine qua non for successful treatment: light loads applied on the healing tissue and controlled tooth movement (about 50 um) within the alveolus. Cengiz et al. (29) cite in their paper that the tendency is to assume that greater the rigidity of the splint, lower would be the stresses transferred to the
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traumatized support structures, hence better the healing process. Our results partially contradict this opinion because greater stress concentration occurred in the alveolus of the traumatized tooth when a rigid splint was simulated (FA). Inspite of a large difference in the flexibility of the alloys tested, our results showed no major differences with regard to the biomechanical behavior of the simulated post-traumatic splints, On the contrary, the three models behaved almost similarly, showing a subtle difference in the maps of stress concentration, and in the maximum (rmax) and minimum (rmin) principal stress values. In addition, contrary to what has been postulated in the proposed hypothesis, with regard to the alveolar bone, stresses increased as the flexibility of the wires decreased (FA > FTM > FN). In the other observed structures (cortical bone and periodontal ligament of adjacent teeth), the wire with intermediate flexibility (FTM) transferred higher stresses, followed by the wire with greater flexibility (FN), and the rigid wire (FA). Thus, the proposed hypothesis was partly rejected, because stress did not vary according to the order of stiffness of the orthodontic wires. Longitudinal clinical follow-up studies on tooth replantation show that achieving absolute immobility of the replanted tooth and total reduction of tension between the surfaces of injured tissues is not necessarily required for their healing (28). This implies that ‘controlled’ mobility and induction of stresses or functional tension of a low magnitude favors the healing of injured tissue (29). The results of present study show that even the most rigid splint (FA), whose wire was larger than the ones typically used for this function, displayed some amount of flexibility, that is, transferred some tension to not only the adjacent teeth and their supporting structures (cortical and alveolar bones and periodontal ligament) but also to the traumatized tissues. This stress distribution pattern was similar to that of the more flexible wires used in this simulation. Thus, the results suggest that biomechanical similarity of wires elicits a similar clinical response is expected. However, to validate the results obtained in this simulation, further clinical and longitudinal followup studies are required regarding the management of tooth avulsion and their post-traumatic contentions when splinted with composite resin and orthodontic wires of different flexibilities. However, the present study has some limitations. It analyses static behavior, involves simplified calculations of mathematical functions, is linear in nature, and did not consider modifications in the distribution of stresses and strains on the geometric structures. Conclusion
The finite element analysis of simulation of post-traumatic splints for tooth replantation showed that the biomechanical behavior of the analyzed bone structures and periodontal ligament was similar for all the three patterns of flexibility/three models tested.
Acknowledgements
This study was supported by the S~ ao Paulo State Research Foundation in Brazil (FAPESP # 2008/ 00209-9). Conflict of interest
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