Finite element method analysis of the periodontal ligament in mandibular canine movement with transparent tooth correction treatment

Effects of different intrusion patterns during anterior teeth retraction using clear aligners in extraction cases: an iterative finite element analysis

Background

Overtreatment design of clear aligner treatment (CAT) in extraction cases is currently primarily based on the clinical experience of orthodontists and is not supported by robust evidence on the underlying biomechanics. This study aimed to investigate the biomechanical effects of overtreatment strategies involving different maxillary anterior teeth intrusion patterns during anterior teeth retraction by CAT in extraction cases.

Materials and methods

A finite element model of the maxillary dentition with the first premolar extracted was constructed. A loading method of clear aligners (CAs) based on the initial state field was proposed. The iterative method was used to simulate the long-term orthodontic tooth movement under the mechanical load exerted by the CAs. Three groups of CAs were utilized for anterior teeth retraction (G0: control group; G1: incisors intrusion group; G2: anterior teeth intrusion group). Tooth displacement and occlusal plane rotation tendency were analyzed.

Results

In G0, CAT caused lingual tipping and extrusion of the incisors, distal tipping and extrusion of the canines, mesial tipping, and intrusion of the posterior teeth. In G1, the incisors showed minimal extrusion, whereas the canines showed increased extrusion and distal tipping tendency. G2 showed the smallest degree of posterior occlusal plane angle rotation, while the inclination tendency of the canines and second premolars decreased.

Conclusion

1. In CAT, tooth displacement tendency may change with increased wear time. 2. During anterior teeth retraction, the incisor intrusion pattern can provide effective vertical control for the lateral incisors but has little effect on the central incisors. Anterior teeth intrusion patterns can alleviate the inclination of canines and second premolars, resulting in partial relief of the roller-coaster effect.

Effect of material composition and thickness of orthodontic aligners on the transmission and distribution of forces: an in vitro study

OBJECTIVES

To investigate the effects of material type and thickness on force generation and distribution by aligners.

MATERIALS AND METHODS

Sixty aligners were divided into six groups (n = 10): one group with a thickness of 0.89 mm using Zendura Viva (Multi-layer), four groups with a thickness of 0.75 mm using Zendura FLX (Multi-layer), CA Pro (Multi-layer), Zendura (Single-layer), and Duran (Single-layer) sheets, and one group with a thickness of 0.50 mm using Duran sheets. Force measurements were conducted using Fuji® pressure-sensitive films.

RESULTS

The lowest force values, both active and passive, were recorded for the multi-layered sheets: CA Pro (83.1 N, 50.5 N), Zendura FLX (88.9 N, 60.7 N), and Zendura Viva (92.5 N, 68.5 N). Conversely, the highest values were recorded for the single-layered sheets: Duran (131.9 N, 71.8 N) and Zendura (149.7 N, 89.8 N). The highest force was recorded at the middle third of the aligner, followed by the incisal third, and then the cervical third. The net force between the incisal and cervical thirds (FI-FC) showed insignificant difference across different materials. However, when comparing the incisal and middle thirds, the net force (FI-FM) was higher with single-layered materials. Both overall force and net force (FI-FM) were significantly higher with 0.75 mm compared to those with a thickness of 0.50 mm.

CONCLUSIONS

Multi-layered aligner materials exert lower forces compared to their single-layered counterparts. Additionally, increased thickness in aligners results in enhanced retention and greater force generation. For effective bodily tooth movement, thicker and single-layered rigid materials are preferred.

CLINICAL RELEVANCE

This research provides valuable insights into the biomechanics of orthodontic aligners, which could have significant clinical implications for orthodontists. Orthodontists might use this information to more effectively tailor aligner treatments, considering the specific tooth movement required for each individual patient. In light of these findings, an exchangeable protocol for aligner treatment is suggested, which however needs to be proven clinically. This protocol proposes alternating between multi-layered and single-layered materials within the same treatment phase. This strategy is suggested to optimize treatment outcomes, particularly when planning for a bodily tooth movement.

Numerical biomechanical finite element analysis of different trimming line designs of orthodontic aligners: An in silico study

BACKGROUND

A finite element model was used to investigate the effect of different designs and thicknesses of orthodontic aligner margins on their biomechanical behavior.

METHODS

A three-dimensional data set of an upper jaw was imported into the 3-matic software. The upper right central incisor tooth (Tooth 11) was separated from the remaining model, and its periodontal ligament and surrounding bone were designed. Aligners were designed with four different trimming lines (scalloped, straight, scalloped extended, straight extended), each with four different thicknesses (0.3, 0.4, 0.5, and 0.6 mm). The models were imported into a finite element package (Marc/Mentat). A linear elastic constitutive material model was applied. A facial 0.2 mm bodily malalignment of tooth 11 was simulated.

RESULTS

The maximum resultant force was in the range of 1.0 N to 2.2 N. The straight trimming designs deliver higher resultant forces compared with scalloped trimming designs. Increasing the aligner thickness and/or extending the aligner edge beyond the gingival line leads to an increase in the resultant force. All designs showed an uneven distribution of the normal contact forces over the tooth surface with a predominant concentration toward the cervical third and distal third, particularly with the extended trimming designs. All designs showed uncontrolled tipping of the tooth.

CONCLUSIONS

Based on the current model outcomes, the use of a straight extended trimming line design for aligners is favored because of its positive impact on force distribution and, consequently, the control of tooth movement.

CLINICAL RELEVANCE

These findings provide aligner companies and orthodontists a valuable biomechanical evidence and guidance to enhance control over tooth movement and therefore optimize treatment outcomes. This can be achieved by trimming the edges of aligners with a straight extended design and selecting the appropriate aligner thickness.

Biomechanical analysis of peri-prosthetic bone response to hybrid threaded zirconia dental implants: An in silico model

The biomechanical response of mandibular bone determines primary stability and concomitant osseointegration of dental implants. This study explores the impact of nature of loading and bone conditions on biomechanical response of hybrid threaded single-piece zirconia dental implants. To develop such understanding, three implants (SQ_V, V_BUT, and V_V), with different combinations of threads, square (SQ), buttress (BUT), and triangular (V), have been investigated. Finite Element Analysis (FEA) was carried out to simulate implantation at the molar position of mandible of varying densities under axial (≤500 N) and oblique (118.2 N) loadings. Patient-specific bone conditions (for a wider population) were considered by scaling the density and the elastic modulus of mandible to represent, 'weak', 'healthy', and 'strong' bone conditions. FEA results revealed that SQ_V and V_BUT implants exhibited a better biomechanical response without significant variation (<0.5%) in von Mises stress, regardless of bone density and axial loadings. These implants are predicted to perform with clinically acceptable factor of safety under investigated implantation scenarios, whereas V_BUT implant showed a larger variation (∼±12%). FEA simulation with oblique loading further validated such results. The 'weak' bone conditions resulted in maximum peri-implant microstrain, whereas 'strong and healthy' bone exhibited values close to the permissible range of physiological remodeling. The maximum micromotion (∼12.3 ± 6.2 μm for 'weak' bone) at bone-implant interface suggested that implant loosening and impaired osseointegration will not occur in any of selected virtual implantation cases. Both SQ_V and V_BUT implants will be considered further in implant development, involving manufacturing and product prototype validation. Taken together, the critical analysis of FEA results indicates a significant impact of bone density and distinct combinations of external threads on the biomechanical responses, in both the implant and the surrounding bone.

Effect of attachment type on distal bodily movement of the maxillary canine in aligner orthodontics: a finite element study

OBJECTIVES

To clarify the effect of attachment types on bodily movement of the maxillary canine in aligner orthodontics.

MATERIALS AND METHODS

Using an aligner, the canine was moved bodily by 0.1 mm distally as a target position. Orthodontic tooth movement was simulated using the finite element method (FEM). The alveolar socket was displaced in the same manner as the initial movement caused by elastic deformation of the periodontal ligament. First, the initial movement was calculated, and then the alveolar socket was displaced in the same direction and with the same magnitude as the initial movement. These calculations were repeated to move the teeth after placement of the aligner. The teeth and the alveolar bone were assumed to be rigid bodies. A FEM model of the aligner was made based on the crown surfaces. The thickness of the aligner was 0.45 mm, and its Young's modulus was 2 GPa. Three types of attachments-semicircular couple, vertical rectangular, and horizontal rectangular-were placed on the canine crown.

RESULTS

Regardless of the type of attachment, upon placement of the aligner on the dentition the crown of the canine moved to the target position, while the apex hardly moved. That is, the canine tipped and rotated. After repeating the calculation, the canine became upright and moved bodily regardless of the attachment type. In the aligner without an attachment, the canine did not become upright.

CONCLUSIONS

There was almost no difference among attachment types in terms of achieving bodily movement of the canine.

The effect of maxillary molar distalization with clear aligner: a 4D finite-element study with staging simulation

INTRODUCTION

Long-term simulation of tooth movement is crucial for clear aligner (CA) treatment. This study aimed to investigate the effect of maxillary molar distalization with CA via an automatic staging simulation.

METHOD

A finite-element method (FEM) model of maxillary dentition, periodontal ligaments, attachments, and corresponding CA was established, and a prescribed 2-mm distalization with 0.1 mm each step of the second molar was simulated. The long-term tooth movement under orthodontic force was simulated with an iterative computation method. The morphologic changes of CA during staging were simulated with the thermal expansion method.

RESULTS

Twenty steps of molar distalization were simulated. Significant distal tilting of the second molar was revealed, along with the proclination of anterior teeth, which caused the 'reversed bow effect'. For the second molar, 4.63°distal tilting at the 20th step was revealed. The intrusion of the incisors and the second molar were 0.43 mm, 0.39 mm, and 0.45 mm, respectively, at step 20. All the anterior teeth showed a proclination of approximately 1.41°-2.01° at the 20th step. The expression rate of the designed distalization of the second molar was relatively low (approximately 68%) compared to the high efficacy of interdental space opening between molars with CA (approximately 89%).

CONCLUSION

A novel method of simulating long-term molar distalization with CA with FEM was developed. The FEM results suggested distal tilting of the second molar and the proclination of anterior teeth during the molar distalization.

Using digital image correlation to measure displacement and strain during involving distal movement of anterior teeth with clear aligner

To investigate methods to suppress the bowing effects of lingual inclination and anterior tooth extrusion, digital image correlation (DIC) was used to evaluate aligner displacement in three-dimensions through comparing the distal movement of six and four anterior teeth. Computed tomography scans were used to measure aligner thickness and shape. Based on displacement direction and magnitude, a desirable deformation mode with minimal lingual inclination and extrusion was observed during distal movement of four anterior teeth. The aligner had a rigid "constriction zone" between the lateral incisor and the canine, facilitating control localized to the anterior teeth and minimizing the reaction of the molars. The mechanical behavior of aligners was greatly affected by the method of anterior teeth movement and the shape of aligners. DIC-based displacement measurements are useful in investigating correction directionality.

Accumulated biomechanical effects of mandibular molar mesialization using clear aligners with auxiliary devices: an iterative finite element analysis

BACKGROUND

The biomechanics generated by the clear aligner (CA) material changes continuously during orthodontic tooth movement, but this factor remains unknown during the computer-aid design process and the predictability of molars movement is not as expected. Therefore, the purpose of this study was to propose an iterative finite element method to simulate the long-term biomechanical effects of mandibular molar mesialization (MM) in CA therapy under dual-mechanical systems.

METHODS

Three groups including CA alone, CA with a button, and CA with a modified lever arm (MLA) were created. Material properties of CA were obtained by in vitro mechanical experiments. MM was conducted by the rebound force exerted by CA material and the mesial elastic force (2N, 30° to the occlusal plane) applied to the auxiliary devices. Stress intensity and distribution on periodontal ligament (PDL), attachment, button and MLA, and displacement of the second molar (M2) during the iterations were recorded.

RESULTS

There was a significant difference between the initial and cumulative long-term displacement. Specifically, compared to the beginning, the maximum stress of PDL decreased by 90% on average in the intermediate and final steps. The aligner was the main mechanical system at first, and then, the additional system exerted by the button and MLA dominated gradually. The stress of attachments and auxiliary devices is mainly concentrated on their interfaces with the tooth. Additionally, MLA provided a distal tipping and extrusive moment, which was the only group that manifested a total mesial displacement of the root.

CONCLUSIONS

The innovatively designed MLA was more effective in reducing undesigned mesial tipping and rotation of M2 than the traditional button and CA alone, which provided a therapeutic method for MM. The proposed iterative method simulated tooth movement by considering the mechanical characteristic of CA and its long-term mechanical force changes, which will facilitate better movement prediction and minimize the failure rate.

Effect of trimming line design and edge extension of orthodontic aligners on force transmission: A 3D finite element study

OBJECTIVES

To investigate in a numerical study the effect of the geometry and the extension of orthodontic aligner edges and the aligner thickness on force transmission to upper right central incisor tooth (Tooth 11).

METHODS

A three-dimensional (3D) digital model, obtained from a 3D data set of a complete dentulous maxilla, was imported into 3-matic software. Aligners with four different trimming line designs (scalloped, straight, scalloped extended, straight extended) were designed, each with four different thicknesses (0.3, 0.4, 0.5, and 0.6 mm). The models were exported to a finite element (FE) software (Marc/Mentat). A facial 0.2 mm bodily malposition of tooth 11 was simulated.

RESULTS

The maximum resultant force was in the range of (7.5 - 55.2) N. The straight trimming designs had higher resultant force than the scalloped designs. The resultant force increases with increasing the edge extension of the aligner. The normal contact forces were unevenly distributed over the entire surface and were concentrated in six areas: Incisal, Mesio-Incisal, Disto-Incisal, Middle, Mesio-Cervical, and Disto-Cervical. The resultant force increases super linearly with increasing thickness.

CONCLUSIONS

The design of the trimming line, the edge extension, and the thickness of the aligner affect significantly the magnitude of the resultant force and the distribution of normal contact force. The straight extended trimming design exhibited better force distribution that may favor a bodily tooth movement.

CLINICAL RELEVANCE

A straight extended trimming design of an orthodontic aligner may improve the clinical outcomes. In addition, the manufacturing procedures of the straight design are much simpler compared to the scalloped design.

Computer-aided finite element model for biomechanical analysis of orthodontic aligners

OBJECTIVES

To design a finite element (FE) model that might facilitate understanding of the complex mechanical behavior of orthodontic aligners. The designed model was validated by comparing the generated forces - during 0.2-mm facio-lingual translation of upper left central incisor (Tooth 21) - with the values reported by experimental studies in literature.

MATERIALS AND METHODS

A 3D digital model, obtained from scanning of a typodont of upper jaw, was imported into 3-matic software for designing of aligners with different thicknesses: 0.4, 0.5, 0.6, 0.7 mm. The model was exported to Marc/Mentat FE software. Suitable parameters for FE simulation were selected after a series of sensitivity analyses. Different element classes of the model and different rigidity values of the aligner were also investigated.

RESULTS

The resultant maximum forces generated on facio-lingual translation of Tooth 21 were within the range of 1.3-18.3 N. The force was direction-dependent, where lingual translation transmitted higher forces than facial translation. The force increases with increasing the thickness of the aligner, but not linearly. We found that the generated forces were almost directly proportional to the rigidity of the aligner. The contact normal stress map showed an uneven but almost repeatable distribution of stresses all over the facial surface and concentration of stresses at specific points.

CONCLUSIONS

A validated FE model could reveal a lot about mechanical behavior of orthodontic aligners.

CLINICAL RELEVANCE

Understanding the force systems of clear aligner by means of FE will facilitate better treatment planning and getting optimal outcomes.

Establishment, FEM analysis and experimental validation of tooth movement prediction model of orthodontic archwire T-loop

Background

The T-loop has been used clinically to close gap between teeth. And it is a typical orthodontic archwire bending method. However, the design of the T-loop parameters for different patients is based on the clinical experience of the dentists. The variation in dentists' clinical experience is the main reason for inadequate orthodontic treatment, even high incidence of postoperative complications.

Methods

Firstly, the tooth movement prediction model is established based on the analysis of the T-loop structure and the waxy model dynamic resistance. As well as the reverse reconstruction of the complete maxillary 3D model based on the patient CBCT images, the oral biomechanical FEM analysis is completed. A maxillary waxy dental model is manufactured to realize the water-bath measurement experiment in vitro mimicking the oral bio-environment. Thus, the calculated, simulation and experimental data are obtained, as well as obtaining a cloud of total deformation from the simulation analysis.

Results

The growth trend of the 11 sets of simulation data is the same as that of the experimental data. And all of them show that the tooth displacement is positively correlated with the cross-sectional size of the archwire, and the clearance distance. As well as the higher Young's modulus of the archwire material, the greater the tooth displacement. And the effect of archwire parameters on tooth displacement derived from simulation and experimental data is consistent with the prediction model. The experimental and calculated data are also compared and analyzed, and the two kinds of data are basically consistent in terms of growth trends and fluctuations, with deviation rates ranging from 2.17  to  10.00%.

Conclusions

This study shows that the accuracy and reliability of the tooth movement prediction model can be verified through the comparative analysis and deviation calculation of the obtained calculated, simulation and experimental data, which can assist dentists to safely and efficiently perform orthodontic treatment on patients. And the FEM analysis can achieve predictability of orthodontic treatment results.

Effect of Trimming Line Design and Edge Extension of Orthodontic Aligners on Force Transmission: An in vitro Study

OBJECTIVES

To investigate how the stress distribution and forces transmitted from orthodontic aligners to the tooth surface are affected by the geometry and extension of the trimming line.

MATERIALS AND METHODS

Thirty-six aligners were thermoformed from Zendura FLX sheets (0.75 mm thick) and divided into four groups based on the design of the trimming line: Scalloped, Scalloped extended, Straight and Straight extended. Fuji pressure-sensitive films were used for pressure measurement. The pressurized films were scanned and evaluated. Pressures and forces were measured over the entire facial surface of an upper right central incisor (Tooth 11) and at 7 different locations [cervical, middle, incisal, mesio-incisal, mesio-cervical, disto-cervical, and disto-cervical]. In addition, the thickness of the aligners at these 7 sites was measured with a digital caliper.

RESULTS

The active force ranged from (2.2 - 6.9) N, and the average pressure was (1.6 - 2.7) MPa. The highest values were recorded for the (straight extended) design, while the lowest values were recorded for the scalloped design. The forces and stresses were not uniformly distributed over the surface. When the values in each area were compared separately, significant differences were found between the different designs in the cervical area, with the scalloped design transmitting the lowest cervical forces. Aligner thickness was drastically reduced (60-75% thinning) over the entire tooth surface after thermoforming.

CONCLUSIONS

The straight extended design of aligner's trimming line exhibited more uniform force transfer and stress distribution across the surface than the other designs.

CLINICAL RELEVANCE

The trimming line design could have a significant impact on the clinical outcome of orthodontic aligner treatment.

Effects of varying attachment positions on palatal displacement of maxillary incisors with clear aligner therapy

BACKGROUND

Clear aligner therapy (CAT) has evolved as an esthetic alternative to fixed appliance therapy. However, studies on the effects of attachments on CAT are scarce. This research was done to evaluate the effect of labial and/or palatal attachments on maxillary incisor displacement in CAT through finite element analysis (FEA).

MATERIALS AND METHODS

Finite element modeling was used to create four models with aligners. The following combinations were created: (1) without attachments (WO), (2) with labial attachments (WLA), (3) with palatal attachments (WPA), (4) with labial and palatal attachments (WLPA). Maximum displacement, directional displacement and stresses induced following a palatal displacement of 0.25 mm was evaluated for each of the four models.

RESULTS

Models without attachments and those with palatal attachments showed a greater tooth movement at the incisal part of the crown (0.22 mm and 0.24 mm, respectively) than the models with labial and labiopalatal attachments (0.21 mm and 0.19 mm, respectively). The von Mises stresses were concentrated at the middle third of the roots in the model with the labial attachments (30.257 MPa), while in the other three models, stresses were concentrated at the cervical third of the roots.

CONCLUSIONS

Maximum displacement was seen at the incisal third of the maxillary incisors in the model with palatal attachments. The model without attachment generated the highest stresses. However, labial attachments as compared to other models appear to offer some biomechanical advantage by reducing uncontrolled tipping.

Effects of Variable Composite Attachment Shapes in Controlling Upper Molar Distalization with Aligners: A Nonlinear Finite Element Study

The objective of the present study is to describe the stress and displacement patterns created by clear aligners and composite attachments bonded with the acid-etch technique on the labial surface of the maxillary first upper molar during its distalization. Maxillary molar distalization is a clinical orthodontics procedure used to move the first maxillary molar distally. The procedure is useful in patients with some Class II malocclusion allowing the first molar to move into a Class I relationship and the correction of associated malocclusion features. Three finite element models were designed to simulate the alveolar bone, molar tooth, periodontal ligament, aligner, and composite attachments. The first model had no composite attachment, the second model had a vertical rectangular attachment, and the third model had a newly designed attachment. A loading method was developed that mimicked the aligner's molar distal movement. PDL was set as a viscoelastic material with a nonlinear mechanical response. von Mises and maximum principal stresses and tooth displacement patterns were analyzed using dedicated software. All the configurations showed some form of clockwise rotation in addition to the distal movement. The crown portion of the tooth showed maximum displacement in all three models; however, in the absence of attachment, the root apex moved in the opposite direction which was compatible with uncontrolled tipping movement. Simulations with attachments exhibited the best performance regarding the movement patterns. The third group, with the newly designed attachment, exhibited the best performance concerning stress distribution (principal stress and von Mises stresses) and higher stresses in the periodontal ligament and tooth. Incorporating a vertical rectangular attachment in a clear aligner resulted in the reduction of mesiodistal tipping tendency during molar distalization. The third model was the most efficient considering both displacement pattern and stress distribution. The level of stress generated by the third model needs to be further investigated in future studies.

Where is the center of resistance of a maxillary first molar? A 3-dimensional finite element analysis

INTRODUCTION

The center of resistance (C_Res) is regarded as the fundamental reference point for predictable tooth movement. Accurate estimation can greatly enhance the efficiency of orthodontic tooth movement. Only a handful of studies have evaluated the C_Res of a maxillary first molar; however, most had a low sample size (in single digits), used idealized models, or involved 2-dimensional analysis. The objectives of this study were to: (1) determine the 3-dimensional (3D) location of the C_Res of maxillary first molars, (2) evaluate its variability in a large sample, and (3) investigate the effects of applying orthodontic load from 2 directions on the location of the C_Res.

METHODS

Cone-beam computed tomography scans of 50 maxillary molars from 25 patients (mean age, 20.8 ± 8.7 years) were used. The cone-beam computed tomography volume images were manipulated to extract 3D biological structures via segmentation. The segmented structures were cleaned and converted into virtual mesh models made of tetrahedral triangles having a maximum edge length of 1 mm. The block, which included the molars and periodontal ligament, consisted of a mean of 7753 ± 2748 nodes and 38,355 ± 14,910 tetrahedral elements. Specialized software was used to preprocess the models to create an assembly and assign material properties, interaction conditions, boundary conditions, and load applications. Specific loads were applied, and custom-designed algorithms were used to analyze the stress and strain to locate the C_Res. The C_Res was measured in relation to the geometric center of the buccal surface of the molar and the trifurcation of the molar roots.

RESULTS

The average location of the C_Res for the maxillary first molar was 4.94 ± 1.39 mm lingual, 2.54 ± 2.7 mm distal, and 7.86 ± 1.66 mm gingival relative to the geometric center of the buccal surface of the molar and 0.136 ± 1.51 mm lingual (P <0.01), 1.48 ± 2.26 mm distal (P <0.01), and 0.188 ± 1.75 mm gingival (P >0.01) relative to the trifurcation of the molar roots. In the anteroposterior (y-axis) and the vertical (z-axis) planes, the C_Res showed significant association with root divergence (P <0.01).

CONCLUSIONS

The C_Res of the maxillary first molar was located apical and distal to the trifurcation area. It showed significant variation in its location. The 3D location of and also varied with the force direction. In some samples, this deviation was large. For accurate and predictable movement, tooth-specific C_Res need to be calculated.

Simulation of orthodontic tooth movement during activation of an innovative design of closing loop using the finite element method

INTRODUCTION

Although many attempts have been made to study the mechanical behavior of closing loops, most have been limited to analyses of the magnitude of forces and moments acting on the end of the closing loop. The objectives of this study were to simulate orthodontic tooth movement during the activation of a newly designed closing loop combined with a gable bend and to investigate the optimal loop activation condition to achieve the desired tooth movement.

METHODS

We constructed a 3-dimensional model of maxillary dentition reproducing the state wherein a looped archwire combined with a gable bend was engaged in brackets and tubes. Orthodontic tooth movements were simulated for both anterior and posterior teeth while varying the degree of gable bend using the finite element method.

RESULTS

The incorporation of a 5° gable bend into the newly designed closing loop produced lingual crown tipping for the central incisor and bodily movement for the first molar. The incorporation of 10° and 15° gable bends produced bodily movement and root movement, respectively, for the central incisor and distal tipping for the first molar.

CONCLUSIONS

Torque control of the anterior teeth and anchorage control of the posterior teeth can be carried out effectively and simply by reducing by half the thickness of a teardrop loop with a height of 10 mm and a 0.019 × 0.025-in cross-section, to a distance of 3 mm from its apex, and by incorporating various degrees of gable bend into the loop corresponding to the treatment plan.

The effect of tooth morphology and vertical bracket positioning on resultant stress in periodontal ligament - a three dimensional finite element study

Introduction

The purpose of this study is to evaluate the effect of change in vertical placement of bracket and effect of tooth morphology on stress developed on periodontal ligament with the help of three dimensional finite element modeling.

Methods

A three-dimensional model of the maxillary bone, maxillary right central incisor, lateral incisor and canine was designed based on the average dimensions of the anatomy and morphology given by Wheeler's and standard edgewise bracket with Slot of 0.022″ X 0.028″ inch was designed using the finite element method. Brackets were placed on each tooth, on the mentioned labial surface at variable distances from the cusp tip, and a full size archwire was virtually engaged into the bracket, then optimum orthodontic load of 2N is applied and PDL stress were calculated.

Results

The lowest stress values were measured as bracket position changes from crest of teeth to the apical direction. By displacing the bracket gingivally from 1.5 to 6 mm, a 16.2% decrease in stress level for central incisor, for lateral incisor the stress level decrease by 25.8% and for canine the stress level decrease by 21.6% thus our study confirms that variation in vertical bracket position results in change in resultant stress in PDL.

Conclusion

It can be concluded that the variation in the vertical position of the bracket osn different tooth can have an important effect on the stresses developed in the PDL.

Biomechanical Effects of Different Auxiliary-Aligner Designs for the Extrusion of an Upper Central Incisor: A Finite Element Analysis

Aim

To evaluate the biomechanical effects of four different auxiliary-aligner combinations for the extrusion of a maxillary central incisor and to define the most effective design through finite element analysis (FEA).

Materials and Methods

A full maxillary arch (14 teeth) was modelled by combining two different imaging techniques: cone beam computed tomography and surface-structured light scan. The appliance and auxiliary element geometries were created by exploiting computer-aided design (CAD) procedures. The reconstructed digital models were imported within the finite element solver (Ansys® 17). For the extrusion movement, the authors compared the aligner without an attachment with three auxiliary-aligner designs: a rectangular palatal attachment, a rectangular buccal attachment, and an ellipsoid buccal attachment. The resulting force-moment (MF) system delivered by the aligner to the target tooth and the tooth displacement were calculated for each scenario.

Results

The maximum tooth displacement along the z-axis (0.07 mm) was obtained with the rectangular palatal attachment, while the minimum (0.02 mm) was obtained without any attachments. With the ellipsoid attachment, the highest undesired moments M_x and M_y were found. The rectangular palatal attachment showed the highest F_z (2.0 N) with the lowest undesired forces (F_x = 0.4 N; F_y = −0.2 N).

Conclusions

FEA demonstrated that the rectangular palatal attachment can improve the effectiveness of the appliance for the extrusion of an upper central incisor.

A three-dimensional finite element analysis of the effect of archwire characteristics on the self-ligating orthodontic tooth movement of the canine

BACKGROUND:

In orthodontics, the tooth movement is a biologic reaction to applied force systems, brackets, archwires, and periodontium tissue.

OBJECTIVE:

To investigate the effects of the various archwire characteristics like the friction coebetween bracket and archwire, the cross-section shape, and the cross-section dimension, on the displacement and the periodontal ligament (PDL) stresses of canine’s movement in a self-ligating treatment using the finite element (FE) analysis method.

METHODS:

Models of teeth and their supporting tissues, brackets and archwires were constructed. Ten kinds of archwires were used for the simulation.

RESULTS:

Considering the translation movement, the maximum displacement, highest stress, and Rc⁢r increased with an increase in the cross-section area. The maximum displacement and highest stress increased with an increase in the friction coefficient. The Rc⁢r values increased with an increase in the friction coefficient in the round archwires, while decreased with an increase in the rectangular archwires. However, these change tends were different in rotation and inclination movement.

CONCLUSION:

The archwire characteristics (round archwire, rectangular archwire, cross-section area, and friction coefficient) exhibited different effects on the tooth translation, rotation, and inclination. Our results can assist in the improvement of the self-ligating orthodontic treatment.

A numerical-experimental study on thermal evaluation of orthodontic tooth movement during initial phase of treatment

The most desired target of orthodontic treatment is tooth movement as a result of application of efficient force system. In this study, effect of tooth loading is studied on temperature profile around the tooth at early stages of treatment. The basis of temperature variation is increase of cell number and activities in periodontium as a result of compression and tension of this layer. Highest cellular activities occur in the beginning of loading procedure and aim to reduce mechanical stress in the periodontium which finally ends up with orthodontic tooth movement during couple of years. To find out the correlation between temperature variation and the applied force, in vivo experiments are conducted on ten rats and temperature is measured in specific time periods. It is observed that temperature is higher in direction of the net force about 0.3℃. Next, numerical finite element analysis is carried out on the rat tooth model. Mechanical stress results show that regions with compressive stress have rather high temperature in the experiments. Mechanical stress on periodontium-bone interface is multiplied by a coefficient to simulate cellular activities on this boundary as a heat source and thermal analysis is carried out to obtain temperature profile. The thermo-mechanical coefficient is identified for each rat by imposing the experimental temperatures on numerical outputs. For assessment of a treatment efficiency and deduction of the applied force, temperatures could be measured experimentally and compared with the corresponding numerical analysis temperature result obtained by employing the thermo-mechanical coefficient found earlier for each rat.

Biomechanical investigation of orthodontic treatment planning based on orthodontic force measurement and finite element method before implementation: A case study

BACKGROUND

Orthodontic treatment planning (OTP) is primarily depended on clinical experiences of orthodontists at present, while equivocal OTP would increase the possibility of treatment failure.

OBJECTIVE

The objective was to investigate a methodology for quantitatively evaluating OTP, using theoretical analyses, orthodontic forces measurement (OFM) and finite element method (FEM).

METHODS

An OTP was theoretically designed based on a clinical case and forces on incisors in OTP were measured on a specialized platform. Further, FEM simulations were performed on the designed OTP and control group. At last, an 18-month tracking was carried out to observe treatment effects of the designed OTP.

RESULTS

The moving tendencies of incisors were in keeping with ideal treatment from the designed OTP through FEM; the maximal hydrostatic stress and logarithmic strain in periodontal ligament (PDL) decreased by 26.81% and 32.60% compared to the control group. Clinical feedback indicated that a controllable correction of incisors was realized after 18 months, which was in accord with the FEM result and root/bone resorption by reason of stress/strain reduction on PDL did not occur.

CONCLUSIONS

Biomechanical responses of periodontium can be quantitatively estimated using OTM and FEM. This study provided an alternative technological mean for the predictability and optimization of clinical OTP.

Computational design and engineering of polymeric orthodontic aligners

Transparent and removable aligners represent an effective solution to correct various orthodontic malocclusions through minimally invasive procedures. An aligner-based treatment requires patients to sequentially wear dentition-mating shells obtained by thermoforming polymeric disks on reference dental models. An aligner is shaped introducing a geometrical mismatch with respect to the actual tooth positions to induce a loading system, which moves the target teeth toward the correct positions. The common practice is based on selecting the aligner features (material, thickness, and auxiliary elements) by only considering clinician's subjective assessments. In this article, a computational design and engineering methodology has been developed to reconstruct anatomical tissues, to model parametric aligner shapes, to simulate orthodontic movements, and to enhance the aligner design. The proposed approach integrates computer-aided technologies, from tomographic imaging to optical scanning, from parametric modeling to finite element analyses, within a 3-dimensional digital framework. The anatomical modeling provides anatomies, including teeth (roots and crowns), jaw bones, and periodontal ligaments, which are the references for the down streaming parametric aligner shaping. The biomechanical interactions between anatomical models and aligner geometries are virtually reproduced using a finite element analysis software. The methodology allows numerical simulations of patient-specific conditions and the comparative analyses of different aligner configurations. In this article, the digital framework has been used to study the influence of various auxiliary elements on the loading system delivered to a maxillary and a mandibular central incisor during an orthodontic tipping movement. Numerical simulations have shown a high dependency of the orthodontic tooth movement on the auxiliary element configuration, which should then be accurately selected to maximize the aligner's effectiveness.