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 Table of Contents  
ORIGINAL ARTICLE
Year : 2022  |  Volume : 14  |  Issue : 4  |  Page : 185-192

Third-order effects and maxillary incisor control in lingual orthodontics – A finite element study of a ribbon arch and edgewise straight wire system


1 Department of Orthodontics, Government Dental College, Silchar, Assam, India
2 Department of Oral and Maxillofacial Surgery, GNRC Hospitals, Oral and Maxillofacial Surgery, Guwahati, Assam, India
3 Department of Orthodontics, I.T.S. Dental College Hospital and Research Centre, Greater Noida, Uttar Pradesh, India

Date of Submission09-Jun-2021
Date of Decision30-Jan-2022
Date of Acceptance15-Feb-2022
Date of Web Publication15-Nov-2022

Correspondence Address:
Siddhartha Kaustav Konwar
Ratnakunj, House No. 3, Seuji Path, Hatigaon, Guwahati - 781 038, Assam
India
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Source of Support: None, Conflict of Interest: None


DOI: 10.4103/ijds.ijds_93_21

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  Abstract 


Introduction: The aim of the present study was to analyze the effects of retraction mechanics on torque control when retraction forces were applied on the maxillary anterior dentition in two distinct lingual appliance systems. Materials and Methods: A three-dimensional bilateral maxillary model was created where the first premolar extraction case was included. 150 g (1.47 N) of retraction force was applied on each side from canine (C) hook to molar for both edgewise straight wire system and ribbonarch appliances. Results: In the edgewise appliance, it was observed in the X-axis that there was less amount of tipping of the six anterior teeth of the canine and central incisor (CI) when compared with the lateral incisor (LI) at occlusal point. In the Y-axis, overall extrusion was observed. In the Z-axis, there was less lingual crown movement. In the ribbonarch appliance, it was observed in the X-axis that there was less tipping, prominently in the canine and CI than in the LI. In the Y-axis, overall extrusion was observed. In the Z-axis, there was less lingual crown movement, whereas the CI and canine showed less movement when compared with the LI. Conclusions: It was observed that there was greater torque loss and extrusion in the edgewise appliance along with greater maximum principal stress in the cervical half of the facial side in the periodontal ligament (PDL) and minimum principal stress on the cervical half of the palatal side in the PDL when compared with the ribbonarch appliance.

Keywords: Finite element modeling, lingual orthodontics, periodontal ligament


How to cite this article:
Konwar SK, Goswami M, Kalha AS, Singh V. Third-order effects and maxillary incisor control in lingual orthodontics – A finite element study of a ribbon arch and edgewise straight wire system. Indian J Dent Sci 2022;14:185-92

How to cite this URL:
Konwar SK, Goswami M, Kalha AS, Singh V. Third-order effects and maxillary incisor control in lingual orthodontics – A finite element study of a ribbon arch and edgewise straight wire system. Indian J Dent Sci [serial online] 2022 [cited 2022 Dec 9];14:185-92. Available from: http://www.ijds.in/text.asp?2022/14/4/185/361200




  Introduction Top


Today, people are more aware that dental esthetics, a pleasing smile, and a good occlusion make a impact on the social performance of individuals. A percentage of adult patients inclined toward lingual orthodontics have markedly increased. Lingual appliances have biomechanics that are similar to that of conventional orthodontics and for their application, special care must be taken because of the change in the point of application of force, the center of resistance, and the direction of force. Understanding the biomechanics of tooth movement and biology of the surrounding structures is very important for optimizing the orthodontic tooth movement where the torque loss of the maxillary anterior teeth during retraction is much more pronounced in the lingual appliances because of the differences in the distance between the bracket slot and labial surface of the tooth in ribbonarch appliance and edgewise appliance.

Tooth movement in orthodontics is a periodontal ligament (PDL) phenomenon and for an efficient tooth movement, it is necessary for the orthodontist to understand the nature of the force being applied and the stress distribution in and around the periodontal tissue.[1] There is an alteration in the stress–strain distribution in the PDL and the surrounding alveolar bone, leading to alveolar displacement of the tooth.[2]

Clinically, measuring the stress and movements at various locations within the PDL is difficult. Though a variety of methods were employed for analyzing dental stresses, they failed to clarify the changes around the PDL and in the bone. Strain gauge technique is another method of measuring tooth displacements, but they cannot be placed directly in the PDL without damaging the surrounding tissue.

These constraints can be overcome by the use of finite element modeling (FEM) as shown in various studies.[3] The FEM is a powerful tool for solving stress–strain problems, which makes it the most suitable method for simulating tooth movement and optimizing orthodontic mechanics. The use of different kinds of en-masse retraction techniques in lingual orthodontics to study the three-dimensional control of maxillary anterior teeth has been attempted in many studies previously.[3] Moreover, the crown–root angulation of maxillary incisors is significantly different from other teeth in the arch due to which the efficient control of anterior torque during retraction continues to be a challenge in the lingual technique.[4] The aim of this study is to determine the amount of displacement, the stress–strain patterns in the PDL when en-masse forces of retraction are applied on the maxillary anterior teeth, and a comparison of the same in customized ribbonarch and (edgewise) straight wire system in the lingual appliances.


  Materials and Method Top


A three dimensional (3D) model of maxilla, with supporting structures like PDL, alveolar bone, teeth were created. Maxillary tooth dimensions were standardized according to the established values from S. J. Nelson et al.[5] The 3D models were created using Solid Works Software version 14 from “Dassault Systemes Solid Works Corporation” (Waltham, MA 02451, USA) version 8000. Ansys Software version 17 from ANSYS Inc. (Canonsburg, PA 15317, USA) was used for finite element analysis.

The solid model was divided into discrete parts called “elements.” The total number of elements used in this study was 24,704 and the number of nodes was 47,306. The 3D model was restrained by applying degree of freedom. Symmetry boundary conditions [Figure 1] and fixed support were applied in the 3D FEM, and fixed support was given at the base of the model [Figure 2].
Figure 1: Symmetry boundary conditions

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Figure 2: Fixed support

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A 3D bilateral maxillary model was created where the first premolar extraction case was included. 150 g (1.47 N) of retraction force was applied on each side. In the experimental setup, six anterior teeth were consolidated with .009” stainless steel ligature wire and force was applied from the canine hook to molar for both (edgewise) straight wire lingual appliance and ribbonarch lingual appliance [Figure 3] and [Figure 4]. The brackets for both ribbonarch appliance and edgewise appliance, archwire, and power arm were created using Solid Works Software version 14 from “Dassault Systemes Solid Works Corporation “(Waltham, MA 02451, USA) with the slot dimension of 0.018” × 0.025.”
Figure 3: Edgewise straight wire appliance experimental setup with consolidation

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Figure 4: Ribbonarch appliance experimental setup with consolidation

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Statistical analysis

Data were entered into Microsoft Excel spreadsheet and then checked for any missing entries. Analyses were performed on SPSS Statistics 21.0 (SPSS Software, IBM Corp., Armonk, NY, USA). Statistical comparisons were done to assess intergroup differences between ribbonarch appliances and (edgewise) straight wire appliances. As all the variables, i.e., tension, compression, and displacement, were continuous variables, descriptive statistics were presented in the form of means and standard deviation. Statistical significance of intergroup comparisons was checked by Mann–Whitney U-test. The level of statistical significance was set at 0.05.


  Results Top


A standard retraction assembly for the anterior segment was created by using 0.018”×0.025” stainless steel “working archwire “for both (edgewise) straight wire lingual appliance and ribbon arch lingual appliance. A standard retraction force of 150 g (1.47 N)/side was applied. In all the experiments, global coordinate system was applied, where X-axis represents tip (transverse plane) direction, Y-axis represents intrusion–extrusion (vertical plane) direction, and Z-axis represents torque (sagittal plane) direction. In all the experimental models, maximum principal stress represents a positive strain (tension) and the minimum principal stress represents a negative strain (compression).

In the first experimental setup of (edgewise) straight wire appliance, anterior six teeth were consolidated with ligature wire and force was applied from the canine to molar hook. In the X-axis, it was observed that there was less amount of tipping of the anterior teeth in the central incisor (CI) and the canine at the occlusal point when compared with the lateral incisor (LI) at occlusal point. In the Y-axis, overall extrusion of the six anterior teeth was observed. In the Z-axis there was less lingual crown movement of the anterior six teeth. Therefore, torque loss was minimal [Table 1] and [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10].
Table 1: Displacement in edgewise straight wire appliance setup with anterior consolidation in mm

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Figure 5: Displacement in X-axis at occlusal point in (edgewise) straight wire appliance with anterior segment consolidation

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Figure 6: Displacement in Y-axis at occlusal point in (edgewise) straight wire appliance with anterior segment consolidation

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Figure 7: Displacement in Z-axis at occlusal point in (edgewise) straight wire appliance with anterior segment consolidation

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Figure 8: Displacement in X-axis at apex point in (edgewise) straight wire appliance with anterior segment consolidation

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Figure 9: Displacement in Y-axis at apex point in (edgewise) straight wire appliance with anterior segmen tconsolidation

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Figure 10: Displacement in Z-axis at apex point in (edgewise) straight wire appliance with anterior segment consolidation

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Within the anterior six segment, the highest maximum principal stress (tension/positive strain) was observed in the LI which was assumed to be due to the proximity to the canine. Also, the highest minimum principal stress (compression/negative strain) was observed in the LIs [Table 2] and [Figure 11] and [Figure 12].
Table 2: Tension-Compression in the PDL in edgewise straight wire appliance setup with anterior consolidation in Mpa

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Figure 11: Maximum principal stress (tension/positive strain) in periodontal ligament in (edgewise) straight wire appliance with anterior segment consolidation

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Figure 12: Minimum principal stress (compression/negative strain) in periodontal ligament in (edgewise) straight wire appliance with anterior segment consolidation

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In the second experimental setup of ribbonarch appliance, anterior six teeth were consolidated with ligature wire and force was applied from the canine to molar hook. In the X-axis, there was less tipping of the anterior six teeth, prominently in the CI and canine at occlusal point than in the LI. In the Y-axis, overall extrusion of the six anterior teeth was observed. In the Z-axis, there was less lingual crown movement of the anterior six teeth, whereas the CI and canine in the occlusal point showed less movement when compared with the LI. Therefore, torque loss was minimal [Table 3] and [Figure 13], [Figure 14], [Figure 15], [Figure 16], [Figure 17], [Figure 18].
Table 3: Displacement in ribbonarch appliance setup with anterior consolidation in mm

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Figure 13: Displacement in X-axis at occlusal point in ribbonarch appliance with anterior segment consolidation

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Figure 14: Displacement in Y-axis at occlusal point in ribbonarch appliance with anterior segment consolidation

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Figure 15: Displacement in Z-axis at occlusal point in ribbonarch appliance with anterior segment consolidation

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Figure 16: Displacement in X-axis direction at apex point in ribbonarch appliance with anterior segment consolidation

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Figure 17: Displacement in Y-axis direction at apex point in ribbonarch appliance with anterior segment consolidation

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Figure 18: Displacement in Z-axis direction at apex point in ribbonarch appliance with anterior segment consolidation

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Within the anterior six segment, the highest maximum principal stress (tension/positive strain) was observed in the LI which could be due to proximity to the canine. In addition, the highest minimum principal stress (compression/negative strain) was observed in the LI [Table 4] and [Figure 19] and [Figure 20].
Table 4: Tension-Compression in the PDL in Ribbonarch appliance setup with anterior consolidation in Mpa

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Figure 19: Maximum principal stress (tension/positive strain) in periodontal ligament in ribbonarch appliance with anterior segment consolidation

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Figure 20: Minimum principal stress (compression/negative strain) in periodontal ligament in ribbonarch appliance setup with anterior

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[Table 5] and [Graph 1] show the intergroup comparison of mean displacement in X, Y, and Z axes among the CI, LI, and canine (C) in edgewise appliance (with consolidation) group with that found in ribbonarch appliance (with consolidation) group.
Table 5: Intergroup comparison of mean displacement in X, Y and Z axis (among CI, LI and C) in (edgewise) straight wire appliance and ribbonarch appliance group with anterior consolidation

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Mean displacements in X, Y, and Z axes were not found to be significantly different between both the appliances in the consolidation group (P > 0.05) at the occlusal point.

Mean displacements in X, Y, and Z axes were not found to be significantly different between both the appliances in the consolidation group (P > 0.05) at the apex point.

[Table 6] and [Graph 2] show the intergroup comparison of mean tension and compression among the CI, lateral incisor LI, and canine (C) in edgewise appliance (with the consolidation) group with that found in ribbonarch appliance (with the consolidation) group.
Table 6: Intergroup comparison of mean tension andm ean compression (among CI, LI and C) in (edgewise) straight wire appliance and ribbonarch appliance with anterior consolidation

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There was no statistically significant difference between both the appliances (P = 0.513) in mean tension in edgewise appliance and ribbonarch appliance groups.

There was no statistically significant difference between both the appliances (P = 0.513) in mean compression in edgewise appliance and ribbonarch appliance groups.


  Discussion Top


Esthetic considerations, especially for young adults, had become a crucial factor in selecting orthodontic treatment during the last decade, which has led to the widespread use and development of various lingual orthodontic systems, which has brought about a unique challenge to the orthodontic community. There has been a timely change from metal brackets to the clear ceramic brackets to the lingual appliances. With the improvements in bonding technique of lingual brackets and new archwire material, the lingual technique has become more precise and simpler than before.

The biomechanics of torque control in lingual systems is different from that of labial systems due to morphology of the palatal surface of anterior teeth and reduced distance between the point of force application and the center of resistance of the tooth. Understanding the biomechanics and the factors affecting the type of movement is of utmost importance to achieve a good treatment outcome. Studies have been conducted in the past to understand the forces and the moments involved in the biomechanics.[6],[7],[8],[9],[10],[11],[12]

Space closure should result in translation of teeth with little or no tipping. Smith and Burstone stated that the forces applied to a tooth produced bodily movement, rotation, or a combination of both, depending on the relationship of the line of action of the force to the center of resistance of the tooth.[13] When space is closed with more amount of lingual tipping, additional time is required to upright the roots.

In the present study, a maxillary 3D model and maxillary teeth were constructed by using Solid Works Software version 14. The finite element study showed the amount of displacement and the stress–strain patterns in the PDL when en-masse retraction force is applied on the maxillary anterior teeth. Forces of 150 g (1.47 N) on each side were applied as it is considered within the physiological limits for retraction of teeth as suggested by Ricketts et al.[14] The cross-section of the wire was not changed and the working archwire of 0.018” ×0.025” stainless steel was used for the experiment.

Luca Lombardo et al.(2014) concluded that under retraction forces and with consolidation of the anterior segment, vertical bowing effects were observed in the entire dentition, which confirms that there was greater amount of crown movement in the lingual direction. Scuzzo and Takemoto[15] have also stated that the application of lingual crown torque can generate a distal uprighting effect on the posterior dentition which results in greater anchorage control.

In the present study, when compared among the appliances (i.e., edgewise appliance and ribbonarch appliance) with consolidation, it was found that the amount of torque loss (Z-axis) and extrusion (Y-axis) was more in the edgewise appliance when compared with that of the ribbonarch appliance.

Proffit (2000) has noted that the stress in the PDL is the key biomechanical phenomenon of tooth movement.[16] In the present study, after retraction forces were applied in the models where the anterior six teeth were consolidated in both (edgewise) straight wire and ribbonarch appliance, it was found that the amount of maximum principal stress (tension/positive strain) in the cervical half of the labial side in the PDL and minimum principal stress (compression/negative strain) in the cervical half of the palatal side in the PDL were found to be significantly higher. It was also found that the amount of maximum principal stress (tension/positive strain) and minimum principal stress (compression/negative strain) were more in the edgewise appliance with consolidation when compared with the ribbonarch appliance. The results from the present study were also in agreement with the findings of Mascarenhas et al.(2015)[17] who reported that when tipping forces are applied on a crown of a tooth, the PDL is compressed near the apical half of the labial side and at the cervical half of the palatal side, however tension was observed at the apical half of the lingual side and at the cervical half of the labial side.

Clinically, the present study has a direct influence on the control of the anterior six teeth where the amount of torque loss (Z-axis) and extrusion (Y-axis) was greater in the (edgewise) straight wire appliance than in the ribbonarch appliance. The amount of retraction force and the point of application of force should be customized according to the different types of treatment modalities to achieve a good treatment outcome, which is of utmost importance in lingual orthodontics.


  Conclusions Top


On comparing the two lingual appliance systems, i.e., the (edgewise) straight wire appliance and the ribbonarch appliance, it was found that there was greater torque loss and extrusion in the (edgewise) straight wire appliance when compared with the ribbonarch appliance in both consolidated groups (where force was applied from the canine hook to molar).

On comparing the two lingual appliance systems, i.e., the (edgewise) straight wire appliance and the ribbonarch appliance, it was found that there was greater maximum principal stress (tension/positive strain) in the cervical half of the labial side in the PDL and minimum principal stress (compression/negative strain) in the cervical half of the palatal side in the PDL in the (edgewise) straight wire appliance when compared to the ribbonarch appliance in both consolidated groups (where force was applied from the canine hook to molar).

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.



 
  References Top

1.
Vikram NR, Senthil Kumar KS, Nagachandran KS, Hashir YM. Apical stress distribution on maxillary central incisor during various orthodontic tooth movements by varying cemental and two different periodontal ligament thicknesses: A FEM study. Indian J Dent Res 2012;23:213-20.  Back to cited text no. 1
  [Full text]  
2.
Cattaneo PM, Dalstra M, Melsen B. Moment-to-force ratio, center of rotation, and force level: A finite element study predicting their interdependency for simulated orthodontic loading regimens. Am J Orthod Dentofacial Orthop 2008;133:681-9.  Back to cited text no. 2
    
3.
Liang W, Rong Q, Lin J, Xu B. Torque control of the maxillary incisors in lingual and labial orthodontics: A 3-dimensional finite element analysis. Am J Orthod Dentofacial Orthop 2009;135:316-22.  Back to cited text no. 3
    
4.
Heravi F, Salari S, Tanbakuchi B, Loh S, Amiri M. Effects of crown-root angle on stress distribution in the maxillary central incisors' PDL during application of intrusive and retraction forces: A three-dimensional finite element analysis. Prog Orthod 2013;14:26.  Back to cited text no. 4
    
5.
Wheelers RC. Wheeler's Dental Anatomy, Physiology and Occlusion. 9th ed. Philadelphia: W. B. Saunders; 2009.  Back to cited text no. 5
    
6.
Lombardo L, Scuzzo G, Arreghini A, Gorgun O, Ortan YO, Siciliani G. 3D FEM comparison of lingual and labial orthodontics in en masse retraction. Prog Orthod 2014;15:38.  Back to cited text no. 6
    
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Williams KR, Edmundson JT. Orthodontic tooth movement analysed by the Finite Element Method. Biomaterials 1984;5:347-51.  Back to cited text no. 7
    
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Tanne K, Koenig HA, Burstone CJ. Moment to force ratios and the center of rotation. Am J Orthod Dentofacial Orthop 1988;94:426-31.  Back to cited text no. 8
    
9.
Puente MI, Galbán L, Cobo JM. Initial stress differences between tipping and torque movements. A three-dimensional finite element analysis. Eur J Orthod 1996;18:329-39.  Back to cited text no. 9
    
10.
Güray E, Orhan M. “En masse” retraction of maxillary anterior teeth with anterior headgear. Am J Orthod Dentofacial Orthop 1997;112:473-9.  Back to cited text no. 10
    
11.
Yoshida N, Jost-Brinkmann PG, Koga Y, Mimaki N, Kobayashi K. Experimental evaluation of initial tooth displacement, center of resistance, and center of rotation under the influence of an orthodontic force. Am J Orthod Dentofacial Orthop 2001;120:190-7.  Back to cited text no. 11
    
12.
Tominaga JY, Tanaka M, Koga Y, Gonzales C, Kobayashi M, Yoshida N. Optimal loading conditions for controlled movement of anterior teeth in sliding mechanics. Angle Orthod 2009;79:1102-7.  Back to cited text no. 12
    
13.
Smith RJ, Burstone CJ. Mechanics of tooth movement. Am J Orthod 1984;85:294-307.  Back to cited text no. 13
    
14.
Ricketts RM, Bench RW, Gugino CF, Hilgers JJ. Bioprogressive Therapy. Denver: Rocky Mountain Orthodontics; 1979.  Back to cited text no. 14
    
15.
Scuzzo G, Takemoto K. Biomechanics and comparative biomechanics. In: Scuzzo G, Takemoto K, editors. Invisible Orthodontics. Berlin: Quintessenz Verlags-GmBh; 2003. p. 55-60.  Back to cited text no. 15
    
16.
Proffit WR. Contemporary Orthodontics. 3rd ed. St. Louis: Mosby-Year Book; 2000.  Back to cited text no. 16
    
17.
Mascarenhas R, Chatra L, Shenoy S, Husain A, Mathew JM, Parveen S. A comparative study of forces in labial and lingual orthodontics using finite element method. J Indian Orthod Soc 2015;49:15-8.  Back to cited text no. 17
  [Full text]  


    Figures

  [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10], [Figure 11], [Figure 12], [Figure 13], [Figure 14], [Figure 15], [Figure 16], [Figure 17], [Figure 18], [Figure 19], [Figure 20]
 
 
    Tables

  [Table 1], [Table 2], [Table 3], [Table 4], [Table 5], [Table 6]



 

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