Dental Science - Original Article A study on evaluation of center of resistance of maxillary four incisors during simultaneous intrusion and retraction: A finite element study J. Aruna
Department of Orthodontist, Vinayaga Missions Sankarachariyar Dental College, No.11/11 Tharun Dental Clinic, Salem, India Address for correspondence: Dr. J. Aruna, E‑mail: arunaortho2013@
gmail.com
Received : 30-03-14 Review completed : 30-03-14 Accepted : 09-04-14
ABSTRACT Aim: The aim of this study is to evaluate the center of resistance of maxillary incisors during simultaneous intrusion and retraction. Subjects and Methods: In this study, the following steps were employed namely, (1) Preprocessing ‑ the creation of geometric model, mesh generation and boundary conditions. (2) Postprocessing ‑ the tooth movement and determination of center of resistance. Results: The center of the mid‑sagittal plane approximately 6 mm apical and 4 mm posterior to a line perpendicular to the occlusal plane from the labial alveolar crest of the central incisor resistance for the maxillary four incisors was located within the. Conclusion: Finite element is a sound mechanical method of analysis as it was sufficient enough to provide insight into interactions between orthodontic forces, and dental tissues and reliability of this study. Further by using this study clinically, the center of resistance can be precisely located in single rooted tooth during orthodontic treatment.
KEY WORDS: Centre of resistance, finite element, maxillary central incisors
S
ound orthodontic therapy has its basis in mechanics, a field of engineering, which has increasing greater application in health sciences today. When an object is subjected to a single force, it will display a tipping or a bodily movement and is mainly determined by the location of the center of resistance of the object and the distance from the force vector to this center of resistance. The knowledge of precise location of such a center of resistance, which is the point of the greatest resistance to the movement of a tooth, helps in controlling the type of movement by varying the ratio of the moment to force. Over the years, numerous methods have been used to determine the center of resistance of the teeth as precisely as possible.[1] In our study, the center of resistance was measured using a more efficient and sophisticated method that is a finite element method of analysis. Access this article online Quick Response Code:
Website: www.jpbsonline.org DOI: 10.4103/0975-7406.137387
Subjects and Methods Before discussing the methodology, a detailed understanding of finite element method and its significance is essential. The basic idea in finite element method is to find the solution for a complicated problem by replacing it by a simpler one. In finite element method, the actual continuum or body of the matter is represented as an assemblage of subdivisions called finite elements. These elements are considered to be interconnected at specified points, which are called nodes or nodal points. The nodes usually lie on the element boundaries where adjacent elements are considered connected. A variety of element types and shapes are available to provide users with the required flexibility to meet the compatibility and completeness requirements. It is useful in solving complex structural problems by dividing the complex structures into many simpler and smaller segments. The technical improvement in computers and finite element software, has improved accuracy and speed of this analysis. In the general field of medicine, the finite element method has been applied mainly to orthopedic research.
How to cite this article: Aruna J. A study on evaluation of center of resistance of maxillary four incisors during simultaneous intrusion and retraction: A finite element study. J Pharm Bioall Sci 2014;6:S49-51.
Journal of Pharmacy and Bioallied Sciences July 2014 Vol 6 Supplement 1
S49
Aruna: Evaluation of center of resistance of maxillary four incisors
Software used in the study
distally to the existing tooth [Figure 4].
1. Microsoft windows 98 SE (operating system) 2. Computer aided designing (CAD) or modeling software – PROE‑2001 3. MSC – NASTRAN version ‑ 4.5 (software for finite element analysis).
Finite element model generation (Mesh generation) This forms the backbone of the finite element analysis. In this stage, the geometric model is converted into the finite element model. Finite element software used for the study was MSC–NASTRAN–V–4.5. The CAD model was meshed or divided into several three‑dimensional tetrahedral shaped finite elements [Table 1].
In this study the following steps were employed namely, • Preprocessing • Postprocessing. In preprocessing, the creation of geometric model, mesh generation, and boundary conditions were applied. In the case of postprocessing simulating, the tooth movement and determination of center of resistance were done. Preprocessing Creation of geometric model Before developing a finite element model of any system, a geometric model should be generated using CAD software. The software used is PRO‑E‑2001. The three‑dimensional model to create is a maxillary four incisors and its surrounding structures such as alveolar bone and its periodontal ligament. The morphological dimensions of the teeth used were as given by Wheeler’s[2] dental anatomy – (6th edition). From the standard dimensions, the bounding points of the cross‑section (in space X, Y, and Z coordinates) were determined and plotted in the CAD graphics screen. With the bounding points called the key points, smooth lines were drawn connecting all the key points simulating the profile of the natural tooth. With the sketch model, volume for the section of the body is created (solid modeling) [Figures 1 and 2]. In a similar manner, the periodontal ligament surrounding the tooth and alveolar bone were also modeled [Figure 3]. As it was difficult to obtain the hourglass shape of the periodontal ligament in our study, it was assumed to be 0.25 mm thickness around the radicular portion, although the thickness varies from the alveolar crest to the apex. The alveolar bone was modeled as a rectangular block of structure with labial thickness of 3 mm apically and 5 mm
Tetrahedral elements are used in order to precisely mesh the curved and irregular regions present in the tooth [Figure 5]. The mechanical properties of each material such as bone, periodontal ligament and the tooth are taken from the previously published values[3] [Table 2]. Boundary conditions The boundary conditions with the areas where the model was restrained from any further movements were assigned as follows, At the superior surface of the bone model (area representing the palatal surface), the area was constrained at their bases to avoid overall rigid body motion 3 [Figure 5]. Postprocessing (simulating the movements and its analysis) The three‑dimensional model was oriented in such a way that the mesiodistal plane was represented by X axis, the vertical plane by the Y axis and the labiolingual plane by the Z axis. To evaluate the center of resistance the force was applied at a distance of 5.2 mm from the incisal edge of the modeled tooth in the labiolingual direction (along the Z axis). The magnitude of force given was 15 g of intrusive force and 120 g of retractive force for each tooth. Determination of center of resistance Center of resistance of a tooth is a point through which a pure force if acts will produce linear movement without rotation. Since, it is a geometric property the finite element analysis itself can easily locate it.[4]
Discussion The location of center of resistance has been studied over the
Figure 1: Sectioned natural tooth Figure 2: Sectioned natural tooth
Figure 3: Periodontal ligament surrounding alveolar bone and tooth are modeled
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Figure 4: Alveolar bone modeled in rectangular block Journal of Pharmacy and Bioallied Sciences July 2014 Vol 6 Supplement 1
Aruna: Evaluation of center of resistance of maxillary four incisors
Table 1: Number of elements and nodes in the model Tooth
Elements
Nodes
Maxillary four incisors
117,044
26,277
Table 2: Mechanical properties for tooth, periodontal ligament and alveolar bone[2] Material Tooth Periodontal ligament Alveolar bone
Young’s modulus (kg/mm2)
Poisson’s ratio
2.0×103 6.8×10−2 1.4×103
0.15 0.49 0.15
approximated to parabolid, conical or wedge shape leading to different results. To overcome, these disadvantages and pitfalls the finite element method was chosen for this study. The essence of this method is that a predetermined force is idealized into an assemblage of separated finite regions or elements. These are then considered to be interconnected at specific points called nodes on their common boundaries.[5]. The results obtained in this study is in accordance with the study of Matsui et al.[9]
References 1.
Figure 5: Superior surface of bone model
years with numerous model systems, these studies include, analytical models, direct measurement in vivo, [5] photo elastic technique,[6] strain gauge technique,[7] laser reflection technique, and holographic method, etc. Although these model systems have provided some insight into the displacement characteristics of the tooth to the applied forces, these studies have obvious limitations such as direct measurement in vivo have a distinct disadvantage of being invasive.[8] Furthermore, it is difficult to apply controlled force variables on human subjects because of anatomic constraints.[3] The major limitation in studies that used physical models was that synthetic substances were used to simulate the periodontal ligament. Many of those materials did not have physical properties exactly duplicating that of the periodontal ligament. In the analytical techniques, the root morphology has been
Journal of Pharmacy and Bioallied Sciences July 2014 Vol 6 Supplement 1
2. 3. 4. 5. 6. 7. 8. 9.
Shroff B, Lindauer SJ, Burstone CJ, Leiss JB. Segmented approach to simultaneous intrusion and space closure: Biomechanics of the three‑piece base arch appliance. Am J Orthod Dentofacial Orthop 1995;107:136‑43. Wheeler RC. A Textbook of Dental Anatomy and Physiology. 4th ed. Philadelphia: WB Saunders; 1965. p. 125‑44. Profit WR. Text book of Contemporary Orthodontics. 5th ed. South East Asian Edition. Mosby Elsevier. 2013. p. 331-358. Tanne K, Sakuda M, Burstone CJ. Three‑dimensional finite element analysis for stress in the periodontal tissue by orthodontic forces. Am J Orthod Dentofacial Orthop 1987;92:499‑505. Nägerl H, Burstone CJ, Becker B, Kubein‑Messenburg D. Centers of rotation with transverse forces: An experimental study. Am J Orthod Dentofacial Orthop 1991;99:337‑45. Baeten LR. Canine retraction: A photoelastic study. Am J Orthod 1975;67:11‑23. Andersen KL, Pedersen EH, Melsen B. Material parameters and stress profiles within the periodontal ligament. Am J Orthod Dentofacial Orthop 1991;99:427‑40. Jeon PD, Turley PK, Moon HB, Ting K. Analysis of stress in the periodontium of the maxillary first molar with a three‑dimensional finite element model. Am J Orthod Dentofacial Orthop 1999;115:267‑74. Matsui S, Caputo AA, Chaconas SJ, Kiyomura H. Center of resistance of anterior arch segment. Am J Orthod Dentofacial Orthop 2000;118:171‑8.
Source of Support: Nil, Conflict of Interest: None declared.
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Copyright of Journal of Pharmacy & Bioallied Sciences is the property of Medknow Publications & Media Pvt. Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use.
Department of Orthodontist, Vinayaga Missions Sankarachariyar Dental College, No.11/11 Tharun Dental Clinic, Salem, India Address for correspondence: Dr. J. Aruna, E‑mail: arunaortho2013@
gmail.com
Received : 30-03-14 Review completed : 30-03-14 Accepted : 09-04-14
ABSTRACT Aim: The aim of this study is to evaluate the center of resistance of maxillary incisors during simultaneous intrusion and retraction. Subjects and Methods: In this study, the following steps were employed namely, (1) Preprocessing ‑ the creation of geometric model, mesh generation and boundary conditions. (2) Postprocessing ‑ the tooth movement and determination of center of resistance. Results: The center of the mid‑sagittal plane approximately 6 mm apical and 4 mm posterior to a line perpendicular to the occlusal plane from the labial alveolar crest of the central incisor resistance for the maxillary four incisors was located within the. Conclusion: Finite element is a sound mechanical method of analysis as it was sufficient enough to provide insight into interactions between orthodontic forces, and dental tissues and reliability of this study. Further by using this study clinically, the center of resistance can be precisely located in single rooted tooth during orthodontic treatment.
KEY WORDS: Centre of resistance, finite element, maxillary central incisors
S
ound orthodontic therapy has its basis in mechanics, a field of engineering, which has increasing greater application in health sciences today. When an object is subjected to a single force, it will display a tipping or a bodily movement and is mainly determined by the location of the center of resistance of the object and the distance from the force vector to this center of resistance. The knowledge of precise location of such a center of resistance, which is the point of the greatest resistance to the movement of a tooth, helps in controlling the type of movement by varying the ratio of the moment to force. Over the years, numerous methods have been used to determine the center of resistance of the teeth as precisely as possible.[1] In our study, the center of resistance was measured using a more efficient and sophisticated method that is a finite element method of analysis. Access this article online Quick Response Code:
Website: www.jpbsonline.org DOI: 10.4103/0975-7406.137387
Subjects and Methods Before discussing the methodology, a detailed understanding of finite element method and its significance is essential. The basic idea in finite element method is to find the solution for a complicated problem by replacing it by a simpler one. In finite element method, the actual continuum or body of the matter is represented as an assemblage of subdivisions called finite elements. These elements are considered to be interconnected at specified points, which are called nodes or nodal points. The nodes usually lie on the element boundaries where adjacent elements are considered connected. A variety of element types and shapes are available to provide users with the required flexibility to meet the compatibility and completeness requirements. It is useful in solving complex structural problems by dividing the complex structures into many simpler and smaller segments. The technical improvement in computers and finite element software, has improved accuracy and speed of this analysis. In the general field of medicine, the finite element method has been applied mainly to orthopedic research.
How to cite this article: Aruna J. A study on evaluation of center of resistance of maxillary four incisors during simultaneous intrusion and retraction: A finite element study. J Pharm Bioall Sci 2014;6:S49-51.
Journal of Pharmacy and Bioallied Sciences July 2014 Vol 6 Supplement 1
S49
Aruna: Evaluation of center of resistance of maxillary four incisors
Software used in the study
distally to the existing tooth [Figure 4].
1. Microsoft windows 98 SE (operating system) 2. Computer aided designing (CAD) or modeling software – PROE‑2001 3. MSC – NASTRAN version ‑ 4.5 (software for finite element analysis).
Finite element model generation (Mesh generation) This forms the backbone of the finite element analysis. In this stage, the geometric model is converted into the finite element model. Finite element software used for the study was MSC–NASTRAN–V–4.5. The CAD model was meshed or divided into several three‑dimensional tetrahedral shaped finite elements [Table 1].
In this study the following steps were employed namely, • Preprocessing • Postprocessing. In preprocessing, the creation of geometric model, mesh generation, and boundary conditions were applied. In the case of postprocessing simulating, the tooth movement and determination of center of resistance were done. Preprocessing Creation of geometric model Before developing a finite element model of any system, a geometric model should be generated using CAD software. The software used is PRO‑E‑2001. The three‑dimensional model to create is a maxillary four incisors and its surrounding structures such as alveolar bone and its periodontal ligament. The morphological dimensions of the teeth used were as given by Wheeler’s[2] dental anatomy – (6th edition). From the standard dimensions, the bounding points of the cross‑section (in space X, Y, and Z coordinates) were determined and plotted in the CAD graphics screen. With the bounding points called the key points, smooth lines were drawn connecting all the key points simulating the profile of the natural tooth. With the sketch model, volume for the section of the body is created (solid modeling) [Figures 1 and 2]. In a similar manner, the periodontal ligament surrounding the tooth and alveolar bone were also modeled [Figure 3]. As it was difficult to obtain the hourglass shape of the periodontal ligament in our study, it was assumed to be 0.25 mm thickness around the radicular portion, although the thickness varies from the alveolar crest to the apex. The alveolar bone was modeled as a rectangular block of structure with labial thickness of 3 mm apically and 5 mm
Tetrahedral elements are used in order to precisely mesh the curved and irregular regions present in the tooth [Figure 5]. The mechanical properties of each material such as bone, periodontal ligament and the tooth are taken from the previously published values[3] [Table 2]. Boundary conditions The boundary conditions with the areas where the model was restrained from any further movements were assigned as follows, At the superior surface of the bone model (area representing the palatal surface), the area was constrained at their bases to avoid overall rigid body motion 3 [Figure 5]. Postprocessing (simulating the movements and its analysis) The three‑dimensional model was oriented in such a way that the mesiodistal plane was represented by X axis, the vertical plane by the Y axis and the labiolingual plane by the Z axis. To evaluate the center of resistance the force was applied at a distance of 5.2 mm from the incisal edge of the modeled tooth in the labiolingual direction (along the Z axis). The magnitude of force given was 15 g of intrusive force and 120 g of retractive force for each tooth. Determination of center of resistance Center of resistance of a tooth is a point through which a pure force if acts will produce linear movement without rotation. Since, it is a geometric property the finite element analysis itself can easily locate it.[4]
Discussion The location of center of resistance has been studied over the
Figure 1: Sectioned natural tooth Figure 2: Sectioned natural tooth
Figure 3: Periodontal ligament surrounding alveolar bone and tooth are modeled
S50
Figure 4: Alveolar bone modeled in rectangular block Journal of Pharmacy and Bioallied Sciences July 2014 Vol 6 Supplement 1
Aruna: Evaluation of center of resistance of maxillary four incisors
Table 1: Number of elements and nodes in the model Tooth
Elements
Nodes
Maxillary four incisors
117,044
26,277
Table 2: Mechanical properties for tooth, periodontal ligament and alveolar bone[2] Material Tooth Periodontal ligament Alveolar bone
Young’s modulus (kg/mm2)
Poisson’s ratio
2.0×103 6.8×10−2 1.4×103
0.15 0.49 0.15
approximated to parabolid, conical or wedge shape leading to different results. To overcome, these disadvantages and pitfalls the finite element method was chosen for this study. The essence of this method is that a predetermined force is idealized into an assemblage of separated finite regions or elements. These are then considered to be interconnected at specific points called nodes on their common boundaries.[5]. The results obtained in this study is in accordance with the study of Matsui et al.[9]
References 1.
Figure 5: Superior surface of bone model
years with numerous model systems, these studies include, analytical models, direct measurement in vivo, [5] photo elastic technique,[6] strain gauge technique,[7] laser reflection technique, and holographic method, etc. Although these model systems have provided some insight into the displacement characteristics of the tooth to the applied forces, these studies have obvious limitations such as direct measurement in vivo have a distinct disadvantage of being invasive.[8] Furthermore, it is difficult to apply controlled force variables on human subjects because of anatomic constraints.[3] The major limitation in studies that used physical models was that synthetic substances were used to simulate the periodontal ligament. Many of those materials did not have physical properties exactly duplicating that of the periodontal ligament. In the analytical techniques, the root morphology has been
Journal of Pharmacy and Bioallied Sciences July 2014 Vol 6 Supplement 1
2. 3. 4. 5. 6. 7. 8. 9.
Shroff B, Lindauer SJ, Burstone CJ, Leiss JB. Segmented approach to simultaneous intrusion and space closure: Biomechanics of the three‑piece base arch appliance. Am J Orthod Dentofacial Orthop 1995;107:136‑43. Wheeler RC. A Textbook of Dental Anatomy and Physiology. 4th ed. Philadelphia: WB Saunders; 1965. p. 125‑44. Profit WR. Text book of Contemporary Orthodontics. 5th ed. South East Asian Edition. Mosby Elsevier. 2013. p. 331-358. Tanne K, Sakuda M, Burstone CJ. Three‑dimensional finite element analysis for stress in the periodontal tissue by orthodontic forces. Am J Orthod Dentofacial Orthop 1987;92:499‑505. Nägerl H, Burstone CJ, Becker B, Kubein‑Messenburg D. Centers of rotation with transverse forces: An experimental study. Am J Orthod Dentofacial Orthop 1991;99:337‑45. Baeten LR. Canine retraction: A photoelastic study. Am J Orthod 1975;67:11‑23. Andersen KL, Pedersen EH, Melsen B. Material parameters and stress profiles within the periodontal ligament. Am J Orthod Dentofacial Orthop 1991;99:427‑40. Jeon PD, Turley PK, Moon HB, Ting K. Analysis of stress in the periodontium of the maxillary first molar with a three‑dimensional finite element model. Am J Orthod Dentofacial Orthop 1999;115:267‑74. Matsui S, Caputo AA, Chaconas SJ, Kiyomura H. Center of resistance of anterior arch segment. Am J Orthod Dentofacial Orthop 2000;118:171‑8.
Source of Support: Nil, Conflict of Interest: None declared.
S51
Copyright of Journal of Pharmacy & Bioallied Sciences is the property of Medknow Publications & Media Pvt. Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use.
