Torque differences due to the material variation of the orthodontic appliance: a finite element study

Influence of elastomeric and steel ligatures on periodontal health during fixed appliance orthodontic treatment: a systematic review and meta-analysis

INTRODUCTION

Metallic and elastomeric ligatures are widely used in orthodontics to secure the archwire within the bracket slots, but elastomeric ligatures have traditionally been associated with increased microbial colonization, which could adversely affect periodontal health.

AIM

This systematic review compares the periodontal effects of elastomeric and steel ligatures used for orthodontic fixed appliances.

METHODS

Unrestricted literature search of 7 databases (MEDLINE, Scopus, Web of Science, Embase, Cochrane Database of Systematic Reviews, Cochrane Central Register of Controlled Trials, and Virtual Health Library) up to July 2023 were performed for randomized / non-randomized clinical studies on humans comparing the two ligation methods during fixed-appliance therapy. After duplicate study selection, data extraction, and risk-of-bias assessment with the Risk of Bias (RoB) 2 or the Risk Of Bias In Non-randomized Studies - of Interventions (ROBINS-I) tool, random-effects meta-analyses of Mean Differences (MD) or Standardized Mean Differences (SMD) and their 95% confidence intervals (CIs) were carried out, followed by assessment of certainty of existing evidence with the Grades of Recommendation, Assessment, Development, and Evaluation (GRADE) approach.

RESULTS

A total of 11 studies (3 randomized / 8 non-randomized) with 354 patients (mean age 14.7 years and 42% male) were included. No statistically significant differences were seen for plaque index (5 studies; SMD = 0.48; 95% CI = -0.03 to 1.00; P = 0.07), gingival index (2 studies; MD = 0.01; 95% CI = -0.14 to 0.16; P = 0.89), probing pocket depth (2 studies; MD = 0; 95% CI = -0.17 to 0.16; P = 0.97), or Streptococcus mutans counts (4 studies; SMD = 0.40; 95% CI=-0.41 to 1.20; P = 0.21). Elastomeric ligatures were associated with moderately increased total bacterial load (3 studies; SMD = 0.43; 95% CI = 0.10 to 0.76; P = 0.03). Confidence in these estimates was low in all instances due to the inclusion of non-randomized studies with high risk of bias.

CONCLUSIONS

Existing low quality evidence indicates that ligature method does not seem to influence the periodontal health during fixed treatment, even if elastomeric ligatures are associated with a moderate increase of bacterial load.

REGISTRATION

PROSPERO (CRD42023444383).

A Hypothesis Testing of Archwire Rounding for the Efficacy of Torque Springs in Orthodontics: A Finite Element Study

BACKGROUND

Achieving the proper buccolingual inclination of teeth is a cornerstone in orthodontic treatment, directly impacting the attainment of ideal occlusal relationships and long-term stability. A practical torque expression that moves the tooth in its proper position across all three planes is imperative to finish orthodontic cases optimally. The primary focus of this research is to investigate Burstone's hypothesis about Warren torque springs when applied to the rectangular wire. Additionally, it examines the hypothesis of rounding these wires in between the bracket wings of the target tooth to be moved. This study aims to determine whether the rounding of wires, in conjunction with the use of torque springs, influences orthodontic outcomes, addressing a notable gap in current literature and resolving controversies in orthodontic practice.

METHODS

A three-dimensional set of maxillary teeth was modeled. A 0.022" MiniSprint™ brackets and Stainless steel archwires of 0.019" × 0.025" and 0.017" × 0.025" (Forestadent, Pforzheim, Germany) were generated. Warren torque spring was modeled and used in the simulation on the upper right central incisor. Four case scenarios were simulated. In two scenarios, the archwires were untouched for both archwire sizes. In comparison, in the other two scenarios, each archwire size was rounded for the upper right maxillary incisor bracket area. Stresses in the Warren torque springs were calculated, the root tip displacement in the four scenarios was measured in millimeters, and both were analyzed.

RESULTS

The root tip displacement was highly affected by rounding the archwire. The increase in root tip displacement was 1538% for the Warren torque spring on 0.019" × 0.025" and 783% for 0.017" × 0.025". The amount of root tip displacement was about 18.8 mm for 0.017" × 0.025" with rounding and 12.2 mm for 0.019" × 0.025". The concentration of the stresses in the Warren torque spring was in the neck of the spring next to the coils.

CONCLUSION

Rounding the archwires while using the Warren torque spring on a rectangular archwire will increase the efficiency of the spring and, in turn, will exhibit more torque on the tooth. Smaller dimensions of rectangular archwires will give more torque in conjunction with Warren torque springs compared to larger sizes of archwires.

Incisor torque expression characteristics in two passive self-ligating brackets placed at different heights. A finite element investigation

Objective

This study investigated torque expression in maxillary incisors using two passive self-ligating bracket types (Damon Q and Pitts 21) placed at different heights using the Finite element method.

Materials and methods

Two passive self-ligating brackets, Damon Q (Ormco, USA) and Pitts 21 (OC Orthodontics, USA) were 3D modeled using micro-computed tomography. Damon Q (0.022ˮ x 0.028″ slot size) and Pitts 21 (0.021ˮ x 0.021″ slot size) brackets were placed on a maxillary central incisor at predetermined vertical heights. Arch wires of size 0.019ˮ x 0.025″ stainless steel (Damon Q) and 0.020ˮ x 0.020" Titanium Molybdenum (Pitts 21) were placed in the bracket slots.

Results

Pitts 21 brackets showed higher torquing moments at all bonding heights as compared to Damon Q brackets. The minimum torquing moment was 9.03Nmm at 5 mm for Damon Q and the maximum torquing moment was 14.92Nmm for Pitts 21 at a bracket bonding height of 8 mm. Total deformation for Pitts 21 at a height of 5 mm from the incisal edge was 0.61 × 10-6mm as compared to that of Damon Q which was 0.41 × 10-6mm. Lowest Von Mises stress values were at 27.07 MPa in Damon Q brackets at a bracket height of 5 mm from the incisal edge. Highest Von Mises stress values were 36.80 MPa for Pitts 21 brackets at a bracket height of 8 mm from the incisal edge.

Conclusion

Pitts 21 brackets exhibited superior torquing characteristics compared to Damon Q. Total deformation in Pitts 21 was higher than Damon Q at all tested bracket bonding heights.

The crucial role of periodontal ligament's Poisson's ratio and tension-compression asymmetric moduli on the evaluation of tooth displacement and stress state of periodontal ligament

The hydrostatic stress in the periodontal ligament (PDL) evaluated by finite element analysis is considered an important indicator for determining an appropriate orthodontic force. The computed result of the hydrostatic stress strongly depends on the PDL material model used in the orthodontic simulation. This study aims to investigate the effects of PDL Poisson's ratio and tension-compression asymmetric moduli on both the simulated tooth displacement and the PDL hydrostatic stress. Three tension-compression symmetric and two asymmetric PDL constitutive models were selected to simulate the tensile and compressive behavior of a PDL specimen under uniaxial loading, and the resulting numerical results were compared with the in-vitro PDL experimental results reported in the literature. Subsequently, a tooth model was established, and the selected constitutive models and parameters were employed to assess the hydrostatic stress state in the PDL under two distinct loading conditions. The simulated results indicate that PDL Poisson's ratio and tension-compression asymmetry exert substantial influences on the simulated PDL hydrostatic stress. Conversely, the elastic modulus exhibits minimal impact on the PDL stress state under the identical loading conditions. Furthermore, the PDL models with tension-compression asymmetric moduli and appropriate Poisson's ratio yield more realistic hydrostatic stress. Hence, it is imperative to employ suitable Poisson's ratio and tension-compression asymmetric moduli for the purpose of characterizing the biomechanical response of the PDL in orthodontic simulations.

Comparative study of biomechanical effects between two types of 2 × 4 techniques employing a rocking-chair archwire: a three-dimensional finite element analysis

OBJECTIVES

After bonding brackets to the first deciduous molar in a 2 × 4 technique, a three-dimensional finite element analysis (3D FEA) is used to demonstrate the biomechanical changes in an orthodontic system. This study aims to opt for the appropriate type of orthodontic technology by analyzing and comparing the mechanical systems produced by two types of 2 × 4 techniques employing rocking-chair archwires.

MATERIALS AND METHODS

Herein, the maxilla and maxillary dentition are modeled by cone beam computed tomography (CBCT) and 3D FEA. Common clinically used 0.016-inch round archwires (material: titanium-molybdenum alloy and stainless-steel) and 0.018-inch round archwires (material: titanium-molybdenum alloy and stainless-steel) are bent into the shape of a rocking chair with a depth of 3 mm. The forces and moments applied to the brackets are transferred to the dentition to evaluate the biomechanical effects of the 2 × 4 technique after the bracket is bonded to the first deciduous molar.

RESULTS

For the central incisor, the teeth-moving distance in all three directions increases with bracket bonding to the first deciduous molar applying the 0.016-inch rocking-chair archwire. For the lateral incisor, the tooth root moves toward the gingival side when using 0.016-inch and 0.018-inch archwires. Moreover, for the same archwire size, the lateral incisors move toward the gingival side by bonding the bracket to the first deciduous molar. After bonding a bracket to the first deciduous molar, using rocking-chair archwires of 0.016 inch or 0.018 inch, the buccal movement distance of the first molar crown increases in the X-axis direction. In the Y-axis and Z-axis directions, the modified 2 × 4 technique significantly increases the effect of backward-tipping compared with the traditional 2 × 4 technique.

CONCLUSIONS

In clinical practice, the modified 2 × 4 technique can be used to increase the movement distance of anterior teeth to a certain extent and accelerate the orthodontic teeth movement. Moreover, the modified 2 × 4 technique is better in anchorage conservation of the first molar than the traditional technique.

CLINICAL RELEVANCE

Although the traditional 2 × 4 technique is widely used in early orthodontic treatment, we found mucosal damage and abnormal archwire deformation might affect orthodontic treatment time and effect. The modified 2 × 4 technique is a novel approach that avoids these drawbacks and improves orthodontic treatment efficiency.

Efficacy of a four-curvature auxiliary arch at preventing maxillary central incisor linguoclination during orthodontic treatment: a finite element analysis

BACKGROUND

Correct torque of the incisors is beneficial in the assessment of the effects of orthodontic treatment. However, evaluating this process effectively remains a challenge. Improper anterior teeth torque angle can cause bone fenestrations and exposure of the root surface.

METHODS

A three-dimensional finite element model of the maxillary incisor torque controlled by a homemade four-curvature auxiliary arch was established. The four-curvature auxiliary arch placed on the maxillary incisors was divided into four different state groups, among which 2 groups had tooth extraction space retracted traction force set to 1.15 N. Initial displacements and pressure stresses of the periodontal tissue in the maxillary incisors and molars were calculated after torque forces (0.5, 1, 1.5, and 2 N) were applied to the teeth at different stable states.

RESULTS

The effect of using the four-curvature auxiliary arch on the incisors was significant but did not affect the position of the molars. Given the absence of tooth extraction space, when the four-curvature auxiliary arch was used in conjunction with absolute anchorage, the recommended force value was < 1.5 N. In the other 3 groups (i.e., molar ligation, molar retraction, and microimplant retraction groups), the recommended force value was < 1 N. The application of a four-curvature auxiliary arch did not influence the molar periodontal and displacement.

CONCLUSION

A four-curvature auxiliary arch may treat severely upright anterior teeth and correct cortical fenestrations of the bone and root surface exposure.

Torque Comparison Between Two Passive Self-Ligating Brackets with Respect to Interbracket Wire Dimensions and Types: A Finite Element Analysis

Objective:

This study aimed to analyze the expression of torque between 2 passive self-ligating brackets by simulating different clinical situations using finite element analysis.

Material and Methods:

Two passive self-ligating brackets, that is, Damon Q (Ormco, Glendora, California) and Smart Clip (3M Unitek, Monrovia, California), were 3D modeled using micro-computed tomography. ANSYS V14.5 software was used for analysis. Archwire and bracket interactions were simulated to measure torque expression by changing wire alloys (stainless steel [SS] and titanium molybdenum [TMA]) and interbracket dimensions.

Results:

Damon Q brackets generated higher torque values compared to Smart Clip brackets with both SS and TMA wires. Damon Q brackets generated the highest torquing moment of 25.72 Nmm and 7.45 Nmm, while Smart Clip brackets generated 22.25 Nmm and 7.31 Nmm with 0.019 × 0.025″ SS and TMA wires, respectively, at an interbracket distance of 12 mm. Torquing moments decreased for Damon Q and Smart Clip brackets when wire length increased from 12 mm to 16 mm.

Conclusion:

Damon Q with 0.019 × 0.025″wires exhibited superior torquing characteristics as compared to Smart Clip brackets with similar archwires.

Influence of Mouthwash Rinsing on the Mechanical Properties of Polymeric Ligature Ties Used for Dental Applications

Mouthwashes are used during dental treatments to mitigate the complications caused by poor oral hygiene. However, these solutions also affect the properties of dental appliances, including those used in orthodontics. This point has been investigated in this study focusing on the changes in mechanical properties of polymeric orthodontic ligature ties. Commercial ties from four brands were characterized in terms of their maximum forces and displacement, delivery forces, molecular structures, and microscopic morphology. These properties were compared against the ties, which were rinsed with commercial mouthwashes from three manufacturers. The results showed that mouthwash rinsing significantly reduced the maximum bearable forces of ligature ties by up to 73.1%, whereas the reduction in their maximum displacement was up to 74.5% across all tested brands. Significant changes in microscopic morphology of ligature ties were observed after mouthwash rinsing, but not their molecular structure. Furthermore, mouthwash rinsing also reduced the delivery forces from ligature ties by between 20.9 and 32.9% at their first deformation cycle. It can be concluded from this study that mouthwashes have significant impact on the mechanical properties of polymeric orthodontic ligature ties and could also potentially affect the overall efficacy of orthodontic and other dental treatments.

Incisor and profile alterations in extraction cases treated with standard Edgewise and pre-adjusted appliances: A controlled before-and-after study

BACKGROUND

Even though treatment of Class II malocclusion with premolar extractions and incisor retraction might affect incisor inclination and soft tissue profile, the effects of bracket prescription on this have not been thoroughly assessed.

METHODS

Fifty patients (mean age: 13.6 years; 34% male) receiving extraction-based treatment with either standard Edgewise or pre-adjusted appliances were included. Between-group differences in the incisor inclination assessed with lateral cephalograms were analyzed statistically with linear/logistic regression at 5%.

RESULTS

Treatment-induced changes included retroclination of the upper/lower incisors (-3.0° and -2.0°, respectively), retraction of the upper/lower incisors (-3.4 mm and -1.5 mm, respectively), retraction of the upper/lower lip (-2.1 mm and -2.0 mm, respectively), and enlargement of the nasolabial angle (+1.6°). Analysis of the data adjusting for confounders indicated that the pre-adjusted group, after treatment, had larger inclination of the upper or lower incisors (+3.2° and +4.5°, respectively), more prominent upper incisors relative to the facial plane (+1.3 mm), and smaller interincisal angle (-7.3 or -7.7°). Post-treatment upper incisor inclination fell within the cephalometric norm significantly more in the pre-adjusted than in the standard Edgewise group (odds ratio 4.3; 95% confidence interval 1.1-16.6). No differences were found in lower incisor prominence, upper/lower lip prominence, or nasolabial angle.

CONCLUSIONS

Pre-adjusted appliances were associated with increased inclination of the upper and lower incisors, with more prominent upper incisors, and with more acute interincisal angle after retraction compared with standard Edgewise appliances. However, such differences did not translate in greater retraction of the upper/lower lips and greater nasolabial angle.

Expression of Torque and Its Effect on Various Biological Structures Caused by Varying Archwire Material: A 3D FEM Study

Objective:

Studying torque expression and biomechanical effects of various wires on giving palatal root torque, using finite element (FE) method (FEM).

Conclusion:

TMA wires are most favourable for torquing, in terms of torque expression and susceptibility to root resorption.

Materials and Method:

Geometric model of maxillary right central incisor was developed, using computed tomography (CT) scan. 0.022" × 0.028" Standard edgewise brackets and 10-mm-long stainless steel (SS), titanium molybdenum (TMA) and titanium niobium (TiNb) archwires of dimension 0.019" × 0.025" were modeled and a palatal root torque of 25 degrees was applied on all wires. The angular displacement of the crown and root and nodal displacement at the incisal edge and root apex in y and z axis were analyzed along with stresses on periodontal ligament (PDL), bone, cementum, enamel, and bracket.

Results:

Buccal crown and palatal root movement was seen, which was maximum for SS and least for TMA. Angular displacement was also highest for SS. Compressive stresses were concentrated at the bucco-cervical and linguo-apical regions in the PDL, cementum, and bone and tensile stresses were concentrated in the linguo-cervical regions. In the enamel, the bracket attachment site showed maximum stresses, and slot base showed higher values of stresses than wings. All stress values were highest for SS and least for TMA.

Orthodontically induced root resorption: A critical analysis of finite element studies' input and output

INTRODUCTION

Orthodontically induced inflammatory root resorption (OIIRR) constitutes an undesirable risk connected to orthodontic treatment. Finite element analysis (FEA) is a powerful tool to study the risk of OIIRR. However, its efficiency in predicting OIIRR depends on the insertion of the correct inputs and the selection of an output coherent with the clinical failure mechanism.

METHODS

By combining a systematic review with a 3-dimensional FEA, this article discusses which are the implications of using certain periodontal ligament (PDL) properties (linear and nonlinear models) and failure criteria. Six orthodontic loading regimes were simulated in a maxillary premolar: pure intrusion, buccal tipping, and their combination applied with either a light (25 cN) or a heavy (225 cN) force. Three stress parameters in the PDL were compared: von Mises stress, minimum principal stress_, and hydrostatic stress (σ_H).

RESULTS

The comparison between linear and nonlinear models showed notable differences in stress distribution patterns and magnitudes. For the nonlinear PDL, none of the light-force models reached the critical compressive hydrostatic stress of 4.7 kPa, whereas all the heavy-force models reached it. In addition, the regions of critical compressive σ_H matched with the regions with resorption craters in clinical studies. In linear models, the σ_H critical value of 4.7 kPa was reached even in the light-force scenario.

CONCLUSIONS

Only compressive hydrostatic stress in PDL satisfied the requirements to be used as an FEA indicator of OIIRR. However, the requirements were satisfied only when a nonlinear PDL model was considered.

Biomechanical analysis of occlusal modes on the periodontal ligament while orthodontic force applied

OBJECTIVE

The study objective was to investigate four common occlusal modes by using the finite element (FE) method and to conduct a biomechanical analysis of the periodontal ligament (PDL) and surrounding bone when orthodontic force is applied.

MATERIALS AND METHODS

A complete mandibular FE model including teeth and the PDL was established on the basis of cone-beam computed tomography images of an artificial mandible. In the FE model, the left and right mandibular first premolars were not modeled because both canines required distal movement. In addition, four occlusal modes were simulated: incisal clench (INC), intercuspal position (ICP), right unilateral molar clench (RMOL), and right group function (RGF). The effects of these four occlusal modes on the von Mises stress and strain of the canine PDLs and bone were analyzed.

RESULTS

Occlusal mode strongly influenced the distribution and value of von Mises strain in the canine PDLs. The maximum von Mises strain values on the canine PDLs were 0.396, 1.811, 0.398, and 1.121 for INC, ICP, RMOL, and RGF, respectively. The four occlusal modes had smaller effects on strain distribution in the cortical bone, cancellous bone, and miniscrews.

CONCLUSION

Occlusal mode strongly influenced von Mises strain on the canine PDLs when orthodontic force was applied.

CLINICAL RELEVANCE

When an FE model is used to analyze the biomechanical behavior of orthodontic treatments, the effect of muscle forces caused by occlusion must be considered.

Comparation of three methods for measuring the Edge Bevel Radius of rectangular orthodontic wires: An in-vitro study

OBJECTIVE

To establish a simplified method for measuring the edge bevel radius of 0.019×0.025-in steel rectangular orthodontic wires, achievable in the clinical environment, and to compare it with the photographic method.

MATERIALS AND METHODS

Aided by the AutoCAD™ 2016 software, the theoretical mathematical relationship was determined between the edge rounding radius and cross-sectional dimensions (height, width, diagonals), through rectangle drawings that represent cross-sections. Two hundred segments (n=20) were obtained from the posterior portions of 100 archwires from 10 brands (Dentaurum™; American-Orthodontics™; GAC™; 3M-Unitek™; Abzil™; Morelli™; Orthometric™; Aditek™; A-Company™; Orthomundi™). The cross-sectional measures of each segment were obtained with a micrometer and a caliper, and the edge bevel radii of these segments were calculated with the use of a mathematical formula. For the "gold standard", the segments were included longitudinally in a phenolic resin cylinder, cross-sectioned, polished, and photographed in scanning electron microscope (SEM). The images were amplified 770× and the radii were measured with an acetate template. The micrometer and caliper measuring methods were subjected to Bland-Altman analysis and compared with the gold standard (SEM), considering ±10μm as the maximum acceptable difference between methods.

RESULTS

In the micrometre measurement, 95% of the differences from the standard were within the limits of agreement (-7.21 and 5.56μm). For the caliper method, 95% of the differences were between -5.46 and 19.83μm, which exceeded the fixed limit ±10μm.

CONCLUSION

The calculation method with micrometre measurements is equivalent to the photographic method, but there is no such equivalence for the caliper measurements.

Mandible Integrity and Material Properties of the Periodontal Ligament during Orthodontic Tooth Movement: A Finite-Element Study

We used the finite-element method (FEM) to investigate the effects of jawbone model integrity and the material properties of the periodontal ligament (PDL) on orthodontic tooth movement. Medical imaging software and computer-aided design software were used to create finite-element models of a partial and complete mandibles based on dental cone beam computed tomography images of the human skull. Additionally, we exerted an orthodontic force on the canine crown in the direction of an orthodontic miniscrew under a lower molar root to compare the von Mises strain on the canine PDL in three models: a partial mandible model under orthodontic force (Model 1), a complete mandible model under orthodontic force (Model 2), and a complete mandible model under orthodontic force with clench occlusion in the intercuspal position (ICP; Model 3). Additionally, in the complete mandible model under orthodontic force with ICP occlusion, we analyzed the effects of a PDL with a low (Model 4), moderate (Model 5), and high (Model 6) linear elastic modulus and a PDL a bilinear elastic modulus (Model 7). The simulation results for mandible integrity indicated that the maximum von Mises strains on the canine PDL for Models 1, 2, and 3 were 0.461, 0.394, and 1.811, respectively. Moreover, for the models with different PDL material properties, the maximum von Mises strains on the canine PDLs for Models 4, 5, 6, and 7 were 6.047, 2.594, 0.887, and 1.811, respectively. When the FEM was used to evaluate tooth movement caused by orthodontic force, the transformation of a complete mandible model into a partial mandible model or alteration of the elastic modulus of the PDL influenced the biomechanical responses of the PDL. Additionally, the incorporation of daily ICP occlusion resulted in a larger effect.

Different sliding mechanics in space closure of lingual orthodontics: a translational study by three-dimensional finite element method

Lingual orthodontics have become popular in modern society as they do not cause aesthetic impairment. From the translational medicine point of view, the use of biomechanical analysis to solve a clinical problem has rarely been reported. Here, we combined the clinical trial and 3-D finite element (FE) method to translate the clinical problem to the FE analysis and back to clinic. Twenty upper premolar extraction cases treated with customized lingual appliances were recruited in this study. Cephalometric films and cast records analysis showed that the "bowing effect", which is a major side effect in lingual orthodontics, occurred during the first treatment stage with single lingual cable retraction. In order to translate the problem to biomechanical research, we introduced the 3-D finite element (FE) model of a customized lingual orthodontic system. The 3-D FE model including the maxilla, periodontal ligament (PDL), and dentition was constructed from human computed tomography data. The tendency of tooth movements in three dimensions and stress distribution in the PDL were analyzed by different mechanical loading methods. 3-D FE analysis confirmed the "bowing effects" and unexpected tooth movements with application of single lingual retraction force. Interestingly, we found that applying forces on both buccal and lingual sides, called "double cable" mechanics, could prevent the "bowing effect". For the clinical trial, we applied the "double cable" force during space closure stage for 4 months, and confirmed "double cable" mechanics could correct and prevent the "bowing effect" clinically. Based on our results, both buccal and lingual forces should be used during space closure in lingual orthodontics to prevent and correct the "bowing effect". Moreover, the magnitude of buccal force should not be lower than the force on the lingual side.

ORTHODONTIC PROCESS SAFETY EVALUATION BASED ON PERIODONTAL LIGAMENT CAPILLARY PRESSURE AND OGDEN MODEL

Taking the lower maxillary incisors as an example and the orthodontic forces along the near–far middle direction, the orthodontic forces along the crown–root direction and the orthodontic moment around the tongue–cheek direction as loading condition, the biomechanical simulation of the tooth is carried out by the method of finite element simulation in this paper. The CT images of the skull are segmented and denoised by Mimics. The solid models of teeth, periodontal ligament (PDL), alveolar bone and brackets are established by Gomagic and Solidworks. The material characteristics of the PDL are defined by the two-order Ogden hyperelastic model. Taking the PDL capillary pressure as a criterion for orthodontic safety, combined with the stress response of PDL, the safe orthodontic force range of mandibular central incisors is obtained by ANSYS finite element software.

Coordinating bracket torque and incisor inclination : Part 3: Validity of bracket torque values in achieving norm inclinations

PURPOSE

To analyze common values of bracket torque (Andrews, Roth, MBT, Ricketts) for their validity in achieving incisor inclinations that are considered normal by different cephalometric standards.

METHODS

Using the equations developed in part 1 (eU1_(BOP) = 90° - BT_(U1) - TCA_(U1) + α₁ - α₂ and eL1_(BOP) = 90° - BT_(L1) - TCA_(L1) + β₁ - β₂) (abbreviations see part 1) and the mean values (± SD) obtained as statistical measures in parts 1 and 2 of the study (α₁ and β₁ [1.7° ± 0.7°], α₂ [3.6° ± 0.3°], β₂ [3.2° ± 0.4°], TCA_(U1) [24.6° ± 3.6°] and TCA_(L1) [22.9° ± 4.3°]) expected (= theoretically anticipated) values were calculated for upper and lower incisors (U1 and L1) and compared to targeted (= cephalometric norm) values.

RESULTS

For U1, there was no overlapping between the ranges of expected and targeted values, as the lowest targeted value of (58.3°; Ricketts) was higher than the highest expected value (56.5°; Andrews) relative to the bisected occlusal plane (BOP). Thus all of these torque systems will aim for flatter inclinations than prescribed by any of the norm values. Depending on target values, the various bracket systems fell short by 1.8-5.5° (Andrews), 6.8-10.5° (Roth), 11.8-15.5° (MBT), or 16.8-20.5° (Ricketts). For L1, there was good agreement of the MBT system with the Ricketts and Björk target values (Δ0.1° and Δ-0.8°, respectively), and both the Roth and Ricketts systems came close to the Bergen target value (both Δ2.3°). Depending on target values, the ranges of deviation for L1 were 6.3-13.2° for Andrews (Class II prescription), 2.3°-9.2° for Roth, -3.7 to -3.2° for MBT, and 2.3-9.2° for Ricketts.

CONCLUSIONS

Common values of upper incisor bracket torque do not have acceptable validity in achieving normal incisor inclinations. A careful selection of lower bracket torque may provide satisfactory matching with some of the targeted norm values.

Coordinating bracket torque and incisor inclination : Part 2: Reproducibility and statistical measures of the torque coordination angle (TCA)

PURPOSE

To determine the reproducibility and statistical measures of the torque coordination angle (TCA).

METHODS

A total of 107 final cephalograms and corresponding casts were included, all reflecting treatment outcomes that met high qualitative standards, one of them being a Peer Assessment Rating (PAR) score of ≤3. Based on these records, the TCA was measured as a parameter to identify differences related to tooth morphology and bracket position between the torque-relevant reference plane at the bracket base and the long axis of a tooth. All measurements were performed on upper and lower central incisors (U1 and L1).

RESULTS

Several reproducibility assessments for the TCA measurements yielded good results, including objectivity at 1.26 ± 0.81° (U1) or 1.41 ± 1.18° (L1), examiner reliability at 1.30 ± 0.97° (U1) or 1.25 ± 0.82° (L1), and method reliability at 1.80 ± 1.13° (U1) or 1.53 ± 1.07° (L1). The statistical measures revealed a high degree of interindividual variability. With bracket placement 4.5 mm (U1) or 4.0 mm (L1) above the incisal edge, the differences between the maximum and minimum TCA values were similarly large in both jaws (21.0° for U1 or 20.0° for L1), given mean TCA values of 24.6 ± 3.6° (U1) or 22.9 ± 4.3° (L1). Moving the bracket placement from 3.5 to 5.5 mm (U1) or from 3.0 to 5.0 mm (L1) changed the mean TCA values by 4.5° (U1) or 3.2° (L1).

CONCLUSIONS

The TCA is a suitable cephalometric parameter to identify differences related to tooth morphology and bracket placement. Given its high interindividual variability, the fixed torque value of a specific bracket system should not be expected to produce the same incisor inclinations across patients.