Effect of force direction and tooth angulation during traction of palatally impacted canines: A finite element analysis


Treatment of a palatally impacted canine (PIC) is associated with demanding anchorage control, increased treatment duration, and undesirable side effects. Accurate PIC localization and force application impact treatment success. The objective of this research was to determine the stresses on the PIC when subjected to initial force activation in various directions (buccal, vertical, and distal) and relative to impaction severity.


Thirty PICs from 21 scans underwent finite element modeling. A prototype 3D model was reconstructed and segmented into its anatomic components. Each PIC was precisely positioned in the prototype model according to impaction position. Stresses in response to a (1.0 N) force in the distal, vertical, and buccal directions were evaluated at different levels of the root (apical, middle, and cervical).


Distal and buccal forces yielded higher stress (6.64 and 6.41 kPa, respectively) than the vertical force (5.97 kPa) on the total PIC root and the apical and cervical root levels, but not at midroot. Statistically significant differences between severity groups were found mostly at the apical level among all force directions, except between distal and buccal forces in the higher severity group. In this group, stress was greatest at the cervical level with the buccal force significantly different from the stresses generated by either the distal or the vertical force.


Vertical forces generated the lowest stresses. Differentially distributed stresses over the root reflected an initial tipping movement. Greater cervical stresses from the buccal force indicate resistance to movement, suggesting treatment initiation with vertical and distal forces over buccal forces, particularly with severely inclined canines.


  • Including individual variations helped to determine response trends to force application.

  • Distal and vertical forces generated the highest and lowest stresses, respectively.

  • Stresses were distributed differentially over the root.

  • Stresses were lowest at the middle level, reflecting an initial tipping movement.

  • Vertical and distal forces are suggested for initial use, buccal force for final alignment.

Guidelines for the traction of a palatally impacted canine (PIC) depend on the accurate localization of the PIC and the severity of its initial position. Accordingly, orthodontic forces would be applied in the proper direction to avoid unwanted consequences of tooth movement, such as longer treatment and root resorption of the adjacent teeth, particularly the lateral incisor.

Approaches to PIC traction varied from direct pull into the arch to the use of auxiliary springs supported by supplementary anchorage (transpalatal bars or mini-implants). The recommended directions of initial pull have included vertical, buccal, and distal forces. , Such forces would also vary with the inclination of the impacted canine. Although the location of impaction has been widely investigated in clinical settings, studies of the relationship between the stresses generated by the orthodontic forces with the severity of impaction are not possible clinically.

For this reason, an engineering tool, the finite element (FE) modeling and analysis, provides the capability of simulating the effect of PIC traction under variable mechanical setups when the exact anatomy of jaws and teeth is reconstructed. The use of FE analysis in orthodontics has become a common research tool, , yet scarce in the investigation of PIC traction. Only 1 study exists in which stresses on the canine were examined in response to varied force angulations using a single simplified model. Accordingly, we hypothesized that understanding and optimizing the mechanics delivered for PIC traction could be achieved through a comprehensive FE analysis applied to PIC locations and angulations accurately, located through 3D imaging from a number of patients. Accounting for individual variation in canine impaction, the FE modeling should help determine the optimal loading directions that yield the least stress on the PIC and therefore minimize potential side effects during treatment.

The aims of this study were to determine stress levels on the impacted canine when subjected to force activation in the buccal, vertical, and distal directions, and compare the generated stresses in relation to the severity of inclination of the impacted canine.

Material and methods

This study was approved by the Institutional Review Board at the American University of Beirut under IRB ID: OTO.JG.05. The material consisted of cone beam computed tomography (CBCT) scans of 21 patients (mean age 16.23 years) who had 30 PICs (12 with unilateral and 9 with bilateral PICs) and sought orthodontic treatment at our institution. The scans had been prescribed specifically for accurate localization of the impacted teeth after clinical examination and initial diagnostic panoramic or periapical radiograph. CBCT scans were selected according to the following criteria: PIC presence unilaterally or bilaterally, and good quality with sufficient field of view covering at least half of the maxilla in unilateral impaction and the entire maxillary arch in bilateral impaction.

Canines were considered to be at a higher potential for impaction when, at the recorded clinical examination, they were not palpable in the vestibule, prompting further radiographic confirmation, and when they had not erupted in the oral cavity beyond the age of 13 years (1 year after the normal maxillary permanent canine eruption age range of 11-12 years ). Exclusion criteria were the presence of a craniofacial anomaly or syndrome and any radiograph of limited field of view or of low resolution that did not allow accurate measurements.

The sample was subdivided into 2 severity subgroups on the basis of the inclination of the PIC to the virtually aligned canine (VAC), the simulated aligned tooth in its final posttreatment position in the arch measured on the reconstructed panoramic section of the CBCT scan ( Fig 1 ). Accordingly, the lower severity subgroup included canines with PIC/VAC ≤ 30° (17.9° ± 6.35°; n = 13) and the higher severity subgroup comprised teeth with PIC/VAC > 30°; (45.7° ± 9.9°; n = 17). The 30° cutoff was chosen because it was close to the mean of the total sample (33.7° ± 16.3°), which coincidentally was an inclination about one third between a normally positioned canine and a horizontally impacted canine.

Finite element modeling

A model was reconstructed from the CBCT scan (PaX-Zenith3D 2009.10; Vatech, Gyeonggi-do, Korea) of a female patient, aged 16 years 3 months, who presented with a maxillary left PIC. The scan, used to model anatomic components, consisted of 296 transversal sections with a 0.2 mm voxel resolution, and of the dimensions 400 × 400 × 296 mm. The CBCT images were saved in Digital Imaging and Communications in Medicine format and loaded into a 3D image–based modeling software Simpleware ScanIP (version 7.0; Synopsis, Exeter, UK). The model was segmented into bone and teeth using adaptive thresholding based on the gray scale value of those components in the scan. The periodontal ligament (PDL), not readily captured on the CBCT scan, was modeled by the duplication and expansion of the roots of all teeth by 1.5 voxel (0.3 mm) ( Fig 2 ).

Fig 1
Illustration of angulation between PIC and the corresponding virtually aligned (VAC) position ( dotted line ), defining the angle PIC/VAC on a CBCT panoramic section. The VAC axis in this patient coincided with the axis of the retained primary canine.

Fig 2
Anatomical reconstruction of the model meshed in ScanIP showing the teeth ( white ), PDL ( orange ), and alveolar bone ( transparent pink ). Global axis repositioned in all CBCT scans to point prosthion.

Individual variation was introduced by reproducing the impacted canine position from the CBCT scans in the prototype model. The global axes of the scans were redefined in all 21 scans to a unified fixed reference point prosthion (most anterior midsagittal point at the alveolar crest) ( Fig 2 ). The 30 PIC 3D coordinates of the crown tip and apex were then measured in ScanIP. These measurements were used to determine the required repositioning of the PIC in the prototype model. The canine meshed stereolithography file was exported along with the prototype FE model to the +CAD module of ScanIP. A customized script was used in +CAD designed to automatically reposition the canine from the original position in the prototype model to the final position measured on the different CBCT scans ( Fig 3 ). Within this script, a right PIC was reproduced as a mirror image of the left prototype canine.

Fig 3
Canine repositioning. Copy of canine mesh inserted in arch ( A ) and repositioned to match position of apex and cusp tip of individual patient ( B ). Canine mesh repositioned and fixed ( C ).

After canine repositioning, bone was remodeled and a PDL layer was created for each of the 30 canines following the above-described steps of PDL modeling. Bone was adjusted to cover the entire root of the canine, thus eliminating any source of variation that was not related to position. The PIC crown was also cleared from any bony contact to allow for accurate detection of stresses on the PDL of the canine. A complete model was created, meshed, and then exported for each canine.

Finite element analysis

The reconstructed model consisted of 639,455 tetrahedral elements and 126,476 nodes. Material properties were defined for the anatomic components and appliances, , which were assumed to be homogeneous and isotropic materials ( Table I ). A full constraint was applied on the maxilla (in translation and rotation) superiorly and posteriorly, representing the attachment to the zygomatic, palatal, and sphenoid bones. A traction force of 1.0 N was applied in 3 different force directions ( Fig 4 , A ): a vertical extrusive force simulating the use of a ballista spring or a palatal spring anchored over a transpalatal bar or a mini-implant ; a distal force reproducing the pull toward a palatal bar or a palatal mini-implant; a buccal force reflecting the direct pull against the archwire. The force was applied from the canine at a point on the archwire in the middle of the space defined for the alignment of the canine. The point of application of the force was at a button attachment placed in the center of the palatal surface of the PIC crown, simulating the clinical situation.

Table I
Material properties used in the FE model
Material Young’s modulus (N/mm 2 = MPa) Poisson’s ratio
Tooth 20,000 0.20
PDL 0.68 0.45
Bone 15,750 0.33
Stainless steel 180,000 0.30

Fig 4
A, Forces ( yellow arrows ) applied on canines shown in vertical ( 1 ), buccal ( 2 ), and distal ( 3 ) directions. Forces were applied to a button attachment on the palatal surface of the canine (nodes highlighted in red ). Model is shown from an oblique occlusal view. B, Element sets in which stresses were evaluated at different levels of the PIC root. Average stress was calculated for each third, the apical level ( a ), midroot level ( b ), cervical level ( c ), and the entire root by averaging all parts of the root.

Von Mises stresses were recorded at the apical, middle, and cervical thirds of the PIC root, and for the whole root with each of the forces. Stresses in the PDL were averaged for each of the 3 levels of the canine root by randomly selecting and averaging the stress values at 300-400 elements around each region on the external surface of the PDL ( Fig 4 , B ).

Statistical analysis

A test of normality revealed that the data were normally distributed in both groups. A mixed between-within subjects 2-way ANOVA was used to test the effect of the between-subjects factor (severity) and the within-subjects factor (force direction) on the canine root stress. When a significant difference was detected, the Bonferroni post-hoc multiple comparison test was applied. P values <0.05 were considered statistically significant. The SPSS statistical software (version 20.0; IBM corporation, Armonk, NY) was employed to perform all statistical analyses.


Distal and buccal forces resulted in higher stress (S = 6.64 and 6.41 kPa, respectively) compared with the vertical force (S = 5.97 kPa) ( Table II ). At the apical third of the PIC root, the stresses generated by different force directions were statistically significantly different (0.023 < P < 0.001). The distal and vertical forces resulted in the highest (S = 7.73 kPa) and least (S = 6.05 kPa) stress, respectively. At the midroot area, stress amounts did not differ significantly between force directions. At the cervical level, the buccal force resulted in the highest stress (S = 7.21 kPa) and the vertical force resulted in the least (S = 6.47 kPa) stress. At the cervical level and over the whole root, stress values were not statistically significantly different between buccal and distal forces but differed significantly between the vertical and distal forces ( P = 0.027 and P <0.001, respectively), and between the vertical and buccal forces ( P = 0.01 and P = 0.02, respectively).

Mar 9, 2020 | Posted by in Orthodontics | Comments Off on Effect of force direction and tooth angulation during traction of palatally impacted canines: A finite element analysis
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