| Abstract|| |
Objective: The aim of the study was to analyze the displacement and stress pattern in periodontal ligament (PDL) of palatally impacted canines (PIC) lateral incisors (LI) and first premolars (FP) adjacent to the impacted teeth when different magnitudes of orthodontic extrusion forces were applied along with variation in the inclination of the impacted teeth. Methodology: A three-dimensional finite element model of a maxilla containing a palatally impacted canine was made with three different inclinations of the palatally impacted canine (model one, model two, and model three). Forces of 50, 70, and 100 g were loaded on the impacted tooth. Results: There was steady increase in the initial rate of displacement in the three teeth when the magnitude of the force that was applied on to the PIC increased. The initial rate of displacement was more in the FP tooth as compared to LI and the impacted teeth. The von Mises stress on the PDL varied along with the variation in the inclination of the impacted canine. Conclusion: The study showed that there was variation in the displacement and the stress distribution in the impacted canine when it was placed in different angulations. The rate of displacement of the impacted teeth reduced when the crown of the palatally impacted canines (PIC) was inclined more mesial. The use of minimal forces is ideal to extrude the impacted canines as observed from the study that the PDL stress increases with increase in the magnitude of force.
Keywords: Finite element analysis on impacted canine, impacted canine, palatal-impacted canine
|How to cite this article:|
Nagendraprasad K, Mathew S, Shivamurthy P, Sabrish S. Displacement and periodontal stress analysis on palatally impacted canine - A finite element analysis. Indian J Dent Res 2019;30:788-93
|How to cite this URL:|
Nagendraprasad K, Mathew S, Shivamurthy P, Sabrish S. Displacement and periodontal stress analysis on palatally impacted canine - A finite element analysis. Indian J Dent Res [serial online] 2019 [cited 2022 Oct 7];30:788-93. Available from: https://www.ijdr.in/text.asp?2019/30/5/788/273412
| Introduction|| |
Management of impacted canines in the field of orthodontics has been an age-old phenomenon. Eruption of a permanent tooth can be delayed even after completion of root development. A tooth that is not expected to erupt within a reasonable time under these circumstances is termed as impacted tooth. The most common teeth to be impacted are the third mandibular molars, maxillary canine stands second in line to it with a prevalence rate of 1.5%. Impacted permanent maxillary canine is seen in 1%–2% of the population. The condition is more than twice as common in girls (1·2%) than in boys (0·5%). Canine impaction is found palatal to the arch in 85% of cases and labial/buccal in 15%. Palatal displacement of the maxillary canines is defined as the developmental dislocation to a palatal site often resulting in tooth impaction requiring combined surgical and orthodontic treatment. The prevalence of palatally displaced canines fluctuates between 0.8 and 5.2%.
The maxillary canine is the last tooth to erupt in the upper arch with a deciduous predecessor and therefore, is most susceptible to environmental influences such as crowding. The etiology of ectopic canine is multifactorial. The exact etiology of palatally impacted maxillary canine is unknown; however, two common theories may explain the phenomenon: the guidance theory and the genetic theory. Guidance theory of palatal canine displacement proposes that the congenitally missing lateral incisors (LIs), supernumerary teeth, odontomas, transposition of teeth, and other mechanical determinants interfere with the path of eruption of the canine. The second theory states that there is genetic influence on palatally displaced canines.
It has been estimated that 0.6%–0.8% of children under the age of 10–13 years have permanent incisors root resorb as a result of ectopic position of canine. Cone beam computed tomography (CBCT) scanning has detected root resorption in 66.7% of permanent LIs adjacent to ectopic maxillary canines. The distance and direction of movement of impacted canines during treatment are determined by the canine's initial vertical and horizontal position. During tooth movement, changes in the periodontium occur, depending on the magnitude, direction, and duration of force applied. Histological techniques only provide limited information regarding the changes undergone by supporting structures during orthodontic treatment.
Force, magnitude and direction are important factors in evaluating orthodontic appliances and tissues reactions to treatment. The force delivered by an orthodontic appliance can be determined by direct measurement through suitable instruments utilizing mathematical calculation. For the same reason, a clinical study in which force variables are controlled is likely to provide more information than the data taken from patients in day-to-day orthodontic practice. The finite element method, which was introduced as one of the numerical analyses, has become an useful technique for stress analysis in biological systems.
Finite element analysis (FEA) is progressively used in the field of orthodontics due to its ability to deliver detailed yet precise information regarding stress on load application. Middleton et al. stated that the data obtained from FEA is more accurate than any of the other experimental methods currently in use. It also allows for complete control over the variables in use while studying a homologous sample. In the field of orthodontic biomechanics, besides the macroforce system, micromechanical data such as stress distribution on tooth, periodontal ligament (PDL), and alveolar bone are important as they can open our minds to the biologic properties of tooth movement, root resorption, and bone remodeling. In such circumstances, a three-dimensional geometric model in a computer helps us to conduct experiments without the involvement of patients and by using an experiment model. Based on the application of FEA in the field of orthodontics, the same was used in this study with an aim to analyze the displacement and stress distribution on the PDL of palatally impacted maxillary canines and the adjacent lateral incisors and first premolars during orthodontic extrusion.
| Methodology|| |
The analytic model was developed from a CBCT image of maxilla of a patient obtained from the archives of the Department of Oral Medicine and Radiology from our institution. The CBCT obtained from an individual was diagnosed as having an unilateral palatally impacted canine (PIC). In this model, the position of PIC was classified under Sector I according to Lindauer et al. classification of the palatally impacted canine (Sector I - position of palatally impacted canine is in the area distal to a line tangent to the distal heights of contour of the LI crown and root). CBCT scan data of the maxilla were processed using MIMICS 13 software. Here, the DICOM images of the CBCT scan were selected and converted into binary stereolithography format. Further, this was converted into geometric model consisting of surfaces and lines. Once the surface model was obtained, it was exported to Finite Element Modeling tool the Hyper Mesh version 11.0 (Altair Engineering, inc, Michigan, USA).
All teeth were aligned and the bone covering the palatal surface of the impacted canine was removed, exposing it to the palatal vault such that a virtual eyelet attachment could be placed for the application of load on it. Using Ansys version 14.5 (ANSYS Inc, Pennsylvania, USA), the arch wire with a cross section of 0.019 × 0.025 inch, orthodontic braces, and a simple eyelet attachment for the impacted canine was modeled by beam 188 elements. Once the finite element model of the maxilla was created as derived from the patient, it was termed as model one (M1); from this two other models were derived, model two (M2) where canine was placed under Sector II (mesial to sector I, but distal to a line bisecting the mesiodistal dimension of the LIs along the long axis of the LI crown and root), and model three (M3) canine placed in Sector III (mesial to sector II, but distal to a line tangent to the mesial heights of contour of the lateral crown and root) based on Lindauer et al. classification. In this study, the apical root position of the impacted canine remained constant as derived from the CBCT of the patient in all the models [Figure 1]. The vertical positioning of the crown tip was approximately at the apical third of the root of the LI and was not in contact with it on the palatal side. The thickness of the PDL was considered to be uniform (0.25 mm). The material properties assigned were the Young's Modulus (or modulus of elasticity) and the Poisson's ratio, they were assumed to be isotropic and homogenous [Table 1].
|Figure 1: Palatal view of the finite element models showing the three different positions of impacted canine in three models|
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|Table 1: Material properties assigned to the various structures in this study|
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The top of the maxillary bone was constrained in all the directions and a load in the local coordinate system was applied. Forces of 50, 70, and 100 g were applied on the models. The force was directed from the main archwire at a point from the center of the wire spanning between the mesial surface of the first premolar (FP) bracket to the distal surface of the LI bracket and to the eyelet attachment on PIC. The vector of the force acting on the impacted teeth was a combination of buccal and extrusive component [Figure 2]. The displacement and the von Mises stress of the teeth under various loads; PIC, LI, and the FP placed adjacent to the impacted teeth were analyzed and recorded.
|Figure 2: The finite element model of the eyelet attachment and the vector of force|
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| Results|| |
The von Mises stress on the PDL and the displacements of LI, PIC, and FP on the impacted side of maxilla were only calculated in all the three models. The results of the same were produced in colorful band, different colors representing various stress levels and displacement. The figures show the distribution of stress and displacement according to a liner color scale, where red indicate areas with the highest stress and blue the lowest. The units of von Mises stress on PDL of the teeth are expressed as Megapascal and the initial rate of displacement in microns or millimeter. The transparent net diagram in the displacement pictures of teeth indicates its original position and the colored teeth being its displaced position postload application [Figure 3]. The resulting picture depicting the displacement as obtained from the models suggested that the FP crown tipped mesial, the LI crown tipped distal and the crown of PIC displaced labio-incisally in the direction of the orthodontic extrusion force. We have not gone into the details on the 3D evaluation of the displacement in various planes (facial/buccal, palatal mesial, or distal) as this was not in our objectives.
|Figure 3: Direction of initial displacement seen in the three teeth under load application|
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When three loads of increasing magnitude (50, 70, and 100 g) were applied on the models (M1, M2, and M3) individually there was a steady increase in the rate of initial displacement in the three teeth, but the displacement of the FP was maximum as compared to the lateral and the impacted canine in all models [Table 2]. The von Mises stress on the PDL of the three teeth gradually increased with increase in magnitudes in individual models, but the pattern of stress distribution in the three teeth varied between the models. In M1 and M2, the maximum von Mises stress was on the PDL of FP [Table 2]. In M3, the maximum stress in the PDL was on the PIC, but its rate of displacement reduced as compared to M1 and M2. We found that there was hardly any difference in the displacement values between M2 and M3 and there was a huge difference in the values of M1 and M3.
|Table 2: Compilation of all the numerical values as derived from the finite element models|
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| Discussion|| |
Treatment of impacted teeth has always been a challenge for orthodontists. The orthodontic force applied to extrude an impacted tooth often produces side effects such as intrusion of the adjacent teeth or even canting of the occlusal plane. Successful extrusion and alignment of such teeth require efficient mechanics with minimal to no side effects. Force system supplied by orthodontic appliances acts in all three dimensions of space. Liu et al. stated that clearly knowing the data of forces and movements can guide us to design an appropriate treatment plan and help in accurate tooth movement.
We decided to use and test 50, 70, and 100 g of force in our study as determined from previous studies where they had mentioned the use of different magnitudes of forces to extrude palatally impacted canine in vivo.,,, To include and test the various magnitudes of orthodontic forces, would be beyond the scope of this study, so a baseline force starting from 50 g was chosen as the minimal force and thereby increasing its magnitude to 70 and 100 g gradually.
When three different forces of increasing magnitudes were applied on the models (M1, M2, and M3) individually, the overall initial rate of displacement of the three teeth gradually increased. The rate of initial displacement varied among the three teeth. The rate of displacement was comparatively high in relation to the FP, followed by the impacted canine and the least being the LI [Table 2]. The reason for this phenomenon was suggested to be due to the variations seen in the tooth root length, morphology, the alveolar bone height, or even the teeth inclination.
Tanne et al., conducted a finite element study on the patterns of initial tooth displacements associated with various root lengths and alveolar bone heights. They concluded in their study that root length and alveolar bone height affect the pattern of initial tooth displacement both in the center of resistance and the centers of rotation. They also state that the anatomic variations in the root length and alveolar bone height should be evaluated so as to produce optimal and desired tooth movement. The reason for the maximum displacement in the premolars as compared to the LIs in our models for the given clinical situation was because root of the FP was comparatively shorter than the laterals and had only a single root instead of two thereby decreasing its anchorage capacity, making it prone to displacement.
Another FEA study by Gerami et al., on displacement and force distribution of mandibular anterior teeth placed in different inclinations under occlusal loads concluded that there was correlation between different inclinations of teeth to the rate of displacement and the von Mises stress generated in the PDL. In our study, it was seen that the FP root that was placed almost at 90 degrees to the occlusal plane was having the least resistance to displacement. The LI was placed at an inclination to the occlusal plane so that the surface area of contact between the roots and the alveolar bone increased, thus influencing it to have the least rate of displacement when compared to the impacted tooth. The impacted teeth was encircled by more bone thereby showing greater resistance to displacement when compared to the FP, but it is arguable that the displacement was more in the impacted teeth when compared to the LIs which suggested that there was least amount of side effect on the laterals as compared to the FP. This discovery has led us into a new topic of interest for which there could be other similar studies conducted in the future.
When the rate of initial displacement among the three teeth was compared between the three models, it showed that there was a steady decline in the displacement of FP as the crown of the impacted canine moved more mesial [Figure 4] and Graph 1]. On the contrary, the rate of displacement in relation to the impacted canine and the LI increased as the inclination of the impacted canine moved more mesial but was comparatively less than the FP.
|Figure 4: Graphs representing the overall rate of displacement and the von Mises stress among the three models|
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Periodontal response to orthodontic forces is a key for treatment goals. The von Mises stress in the PDL of the three teeth increased with increase in the magnitude of force in individual models [Table 2]. When the von Mises stress of the PDL in the three teeth was compared between the three models, we observed a steady decline in the overall stress on the PDL of the teeth as the impacted canine inclined more mesially [Figure 4] and Graph 2]. This steady decline was in coordinance with the steady decline seen in the overall rate of initial displacement. We observed that the periodontal stress on the FP was more in M1 and M2 followed by the LIs and the least being in the PIC, suggesting that more distal the position of the impacted teeth in relation to the lateral root, lesser is the stress on its PDL when an extrusive force was applied. In other words, we can say that when the PIC is impacted more distal to the roots of laterals, there is increased stress on the PDL of anchoring teeth (laterals and the FP) when the extrusion forces are applied on it, irrespective of the magnitude of the force that was applied in this study. Hence, suggesting the use of lighter forces is ideal, as these studies included forces ranging from 50 g and further studies that involve a forces of a lesser magnitude should be tested to check for any variations. In the M3, the PDL stress was maximum in the PIC as compared to the premolar and the lateral, but the displacement of of PIS was less as compared to the first premolar. This pattern of stress variation suggested that more mesially inclined the impacted canine is, greater the von Mises stress on its periodontal ligaments. In such conditions, the extrusive forces to be kept as minimal would be ideal. According to this study, a force even lesser than 50 g would be advisable to extrude the impacted canine that is inclined more mesial (M3). Excessive periodontal stress is a major cause for external apical root resorption. It would be best if the orthodontic force is evenly distributed in the PDL. This theory holds good for the impacted teeth. It is much easier to drag the impacted tooth if the periodontal stress is less and even.
Wang et al. had conducted a FEA study to see the periodontal stress distribution on impacted canines when forces were applied in different vectors to its long axis. The impacted canine in their study model was placed at a fixed angle to the occlusal plane and applied force in three different planes, one being parallel to its long axis, the other at 45° angle and last was vertical to the tooth's long axis. When the models were loaded, they observed that as the direction of force was in line with the long axis of the impacted tooth, the maximum stress was smaller and its distribution average, indicating a good response for extrusion of the impacted tooth. When the direction of the force was placed at an angle to the long axis of the tooth, it becomes larger, so the maximum stress was larger and concentrated to one area, this might be deleterious to extrude the impacted tooth. Hence, they concluded, when the traction angle is smaller between the tooth long axis and the direction of force, there are more advantages to the eruption of the impacted tooth. In a situation, it would be impractical to apply a force along the long axis of an impacted tooth as this would be bound by other anatomical structures in the arch such as other erupted teeth. For example, for the given clinical situation seen in our study, if we had to direct the force parallel to the long axis of the impacted tooth, we might have to pass the extrusive force vector between the laterals and the centrals and end up placing the canine in between them. Such biomechanical principles are impossible and inappropriate to obtain due to both esthetic and functional constraints. Hence, in our study, the stress on the PDL of the impacted tooth was concentrated in one particular region only; that is on the cervical one-third region of the PIC root on the palatal side in all the models [Figure 5] and also when the angle between the traction direction and the long axis of the tooth increased the periodontal stress on the teeth. We can say that for a given particular case in our study, the above results can be accepted. There is no set range of numerical values in FEA that can suggest that the obtained numerical values are appropriate to the biological tissues. The analysis was entirely on the change in the linear values based on an ascending or a descending scale. Since PDL is nonlinear and anisotropic in reality, more accurate response can be determined by assigning nonlinear material properties. Further, the nonlinear finite strain viscoelastic model can simulate both the creeping and nonlinear load displacement behavior which may be the best fitting model for understanding the mechanical properties of PDL. Assuming the PDL as a homogeneous and linear-elastic properties response should still provide useful information as the displacements are relatively small.
|Figure 5: Region of stress concentration on the periodontal ligament of palatal impacted canine|
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Orthodontic extrusion of a palatal impacted canine or any impacted tooth for that reason is time-consuming and very taxing on the anchor tooth; hence, source of anchorage should be enhanced throughout its orthodontic disimpaction mechanics. This study can give us an insight as to how the PDL and teeth respond when a teeth is disimpacted orthodontically. Further FEA studies that can depict many other clinical situations can help us orthodontist to modify our mechanics and benefit the situation of the patient. This method can be used in as a diagnostic aid in providing a proper treatment plane of a given situation. Very few to no studies are present in literature till date having similar design as the present study. This study is the first of its kind to be documented.
| Conclusion|| |
The findings of this study showed how the inclinations of the palatally impacted maxillary canines affect the mechanical response of teeth.
- With the extrusion of palatally impacted canines, there is displacement in the FP and the LI, but the rate of displacement of the FP was more as compared to the LI indicating that there is maximum side effect on the FP as compared to the laterals
- The initial rate of displacement of the FP reduced when the palatal impacted canine inclined more mesial on the contrary the displacement of impacted canine increased but remained comparatively less than the FP
- When the inclination of the PIC is less mesial, i.e., when the angle between the midline and the long axis of the PIC is more there is increased side effects on the FP; hence, a minimal force ranging from 50 g to 70 g can be ideal to extrude the teeth.
- If the crown tip of the impacted canines is inclined more toward the midline, more will be the PDL stress on the teeth, so orthodontic extrusion forces less than 50 g is more ideal.
I would like to thank Mr. Naghabushan who helped me in providing the software and all the technical support that was needed throughout the study.
Financial support and sponsorship
Conflicts of interest
There are no conflicts of interest.
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Dr. Komal Nagendraprasad
#20,5th Cross, RT Nager, Bengaluru - 560 032, Karnataka
Source of Support: None, Conflict of Interest: None
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5]
[Table 1], [Table 2]