Numerical simulation and biomechanical analysis of an orthodontically treated periodontally damaged dentition

Periodontal considerations during orthodontic intrusion and extrusion in healthy and reduced periodontium

In patients with advanced periodontal disease, pathological tooth migration may occur, which may require subsequent orthodontic treatment for both aesthetic and functional purposes. When planning orthodontic treatment mechanics, intrusive or extrusive forces are frequently indicated. Understanding tissue reactions during these movements is essential for clinicians when devising a comprehensive orthodontic-periodontal treatment plan. This knowledge enables clinicians to be fully aware of and account for the potential effects on the surrounding tissues. The majority of our understanding regarding the behavior of periodontal tissues in both healthy and compromised periodontal conditions is derived from animal studies. These studies offer the advantage of conducting histological and other assessments that would not be feasible in human research. Human studies are nevertheless invaluable in being able to understand the clinically relevant response elicited by the periodontal tissues following orthodontic tooth movement. Animal and human data show that in dentitions with reduced periodontal support, orthodontic intrusion of the teeth does not induce periodontal damage, provided the periodontal tissues do not have inflammation and plaque control with excellent oral hygiene is maintained. On the contrary, when inflammation is not fully controlled, orthodontic intrusion may accelerate the progression of periodontal destruction, with bacterial plaque remnants being displaced subgingivally, leading to further loss of attachment. Orthodontic extrusion, on the other hand, does not seem to cause further periodontal breakdown in dentitions with reduced periodontal support, even in cases with deficient plaque control. This is attributed to the nature of the tooth movement, which directs any plaque remnants coronally (supragingivally), reducing the risk of adverse effects on the periodontal tissues. This specific type of tooth movement can be leveraged to benefit periodontal conditions by facilitating the regeneration of lost hard and soft periodontal tissues in a coronal direction. As a result, orthodontic extrusion can be employed in implant site development, offering an advantageous alternative to more invasive surgical procedures like bone grafting. Regardless of the tooth movement prescribed, when periodontal involvement is present, it is essential to prioritize periodontal therapy before commencing orthodontic treatment. Adequate plaque control is also imperative for successful outcomes. Additionally, utilizing light orthodontic forces is advisable to achieve efficient tooth movement while minimizing the risk of adverse effects, notably root resorption. By adhering to these principles, a more favorable and effective combined orthodontic-periodontal approach can be ensured. The present article describes indications, mechanisms, side effects, and histological and clinical evidence supporting orthodontic extrusion and intrusion in intact and reduced periodontal conditions.

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.

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.

Effects of Periodontal Splints on Biomechanical Behaviors in Compromised Periodontal Tissues and Cement Layer: 3D Finite Element Analysis

Background: In this study, we evaluated the effect of periodontal splints made from different materials on the stress distributions in compromised periodontal tissues and cement layers, using a computer simulation of mastication. Methods: Twenty-five 3D models were created for a segment of mandibular teeth with different periodontal splints bilaterally extended to the canines. The models were divided into five groups according to the different materials and thicknesses (mm) of the splints: the non-splinted group, PEEK 0.7 group, PEEK 1.0 group, FRC group, and titanium group. Each group was subdivided based on five bone loss levels. Tooth 41 of each model was subjected to vertical and oblique (θ = 45°) static loads of 100 N, respectively, onto the incisal edge. The von Mises stresses and maximum principal stress were analyzed using Abaqus software. Results: Oblique loading resulted in higher stresses on periodontal tissues, cement layers, and splints than those caused by vertical loading. The lower the supporting bone level, the greater the stress difference between the splinted groups and the non-splinted group. In model 133,331, with severe bone loss, the maximum von Mises stress values on the alveolar bone in tooth 41 under oblique loading dramatically decreased from 406.4 MPa in the non-splinted group to 28.62 MPa in the PEEK group and to 9.59 MPa in the titanium group. The four splinted groups presented similar stress distributions in periodontal tissues. The lowest stress level on the splint was observed in the PEEK 0.7 group, and the highest stress level was transferred to the cement layer in this group. Stress concentrations were primarily exhibited at the connectors near the load-carrying area. Conclusions: The tested splinted groups were all effective in distributing the loads on periodontal tissues around splinted teeth with similar patterns. Using splinting materials with low elastic moduli reduced the stress concentration at the splint connectors, whereas the tensile stress concentration was increased in the cement layer. Thus, the use of adhesive cement with a higher elastic modulus is recommended when applying less rigid PEEK splints.

Numerical and biomechanical analysis of orthodontic treatment of recovered periodontally compromised patients

OBJECTIVE

Generate a finite element (FE) model to simulate space closure and retraction mechanics for anterior maxillary teeth in periodontally compromised dentition, and compare the biomechanical effect of initial force systems with varying magnitude.

MATERIALS AND METHODS

The geometry of an idealized finite element model (FEM) of a maxilla was adapted such that the teeth showed reduced periodontal support together with extruded and flared incisors. In a first step, leveling and alignment of the front teeth were simulated. In a second step, force systems for orthodontic space closure of residual spaces on both sides distal to the lateral incisors were simulated. A combined intrusion and retraction cantilever was modeled, to simulate en masse retraction mechanics with segmented arches and elastic chains. A commercial FE system was used for all model generations and simulations.

RESULTS

Results of the simulations indicated that a force of 1.0 N is too high for space closure of flared front teeth in periodontally damaged dentition, as extreme strains may occur. En masse retraction using cantilever mechanics with lower forces showed a uniform intrusion and retraction movement and thus proved to be a better option for treating patients with a periodontally compromised dentition.

CONCLUSION

The outcome of this study indicates that increased periodontal stresses resulting from severe attachment loss should be seriously considered by careful planning of the orthodontic mechanics and reduction of the applied forces is suggested. The presented cantilever mechanics seems to be an appropriate means for en masse retraction of periodontally compromised extruded front teeth.

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.

Biomechanical analysis of initial incisor crowding alignment in the periodontally reduced mandible using the finite element method

AIMS

To reduce remaining plaque niches due to dental malocclusion after periodontal treatment and to avoid reinflammation of periodontitis, severe anterior crowding can be treated orthodontically. The treatment indication is motivated by aesthetic and functional needs. In this study the biomechanical behaviour of crowded lower front teeth in reduced periodontium is analysed.

METHODS

Using the finite element (FE) method, a model of the mandible was constructed with an anterior crowding of 4 mm and a vertical bone loss of 4 mm in the front tooth area. A 0.3 mm (0.012″) round superelastic nickel titanium (NiTi) arch wire was fitted to an ideal positioned teeth set-up and was inserted into the brackets of teeth 34 to 44 in the crowded model. The premolars were used as the anchorage unit. Material parameters were adopted from previous investigations, including bone (homogenous, isotropic, E = 2 GPa), teeth (E = 20 GPa) and healthy periodontal ligament (PDL, bilinear elastic; E₁ = 0.05 MPa; E₂ = 0.2 MPa; ε₁₂ = 7%). All simulations were compared to simulations with a physiological periodontal model to assess the effect of bone loss at teeth 42 to 32. Additionally, the influence of three arch wire materials (nonsuperelastic NiTi, superelastic NiTi and stainless steel) were analysed in a reduced model, including only brackets in position of the crowded front teeth, wire and ligatures. Wire force levels and stresses were determined to assess the influence of material variation.

RESULTS

Initial tooth mobility is increased by a factor of 2.5 in case of a moderate periodontal defect. Front teeth with reduced attachment display increased strains in the periodontal ligament up to a factor of 2. Forces in the model with reduced periodontium were decreased by a factor of 2. Comparing different aligning arch wires, stainless steel appears to have the highest force and stress levels. Force levels of this alloy were 7.5 times higher than with the superelastic NiTi wire. Force levels of nonsuperelastic NiTi appeared to be 1.8 times higher than superelastic NiTi. Calculated stresses with stainless steel were 5 times higher than with the nonsuperelastic NiTi and 10 times higher than with superelastic NiTi.

CONCLUSION

Periodontally reduced incisors 42 to 32 are associated with an increased load on periodontal tissue and increased level of tooth mobility during fixed orthodontic treatment. This has to be considered by reducing orthodontic force levels and by selecting mechanics that reduce the load to the tissue.

Simulation of orthodontic force of archwire applied to full dentition using virtual bracket displacement method

OBJECTIVE

Orthodontic force simulation of tooth provides important guidance for clinical orthodontic treatment. However, previous studies did not involve the simulation of orthodontic force of archwire applied to full dentition. This study aimed to develop a method to simulate orthodontic force of tooth produced by loading a continuous archwire to full dentition using finite element method.

METHOD

A three-dimensional tooth-periodontal ligament-bone complex model of mandible was reconstructed from computed tomography images, and models of brackets and archwire were built. The simulation was completed through two steps. First, node displacements of archwire before and after loading were estimated through moving virtual brackets to drive archwire deformation. Second, the obtained node displacements were loaded to implement the loading of archwire, and orthodontic force was calculated. An orthodontic force tester (OFT) was used to measure orthodontic force in vitro for the validation.

RESULTS

After the simulation convergence, archwire was successfully loaded to brackets, and orthodontic force of teeth was obtained. Compared with the measured orthodontic force using the OFT, the absolute difference of the simulation results ranged from 0.5 to 22.7 cN for force component and ranged from 2.2 to 80.0 cN•mm for moment component, respectively. The relative difference of the simulation results ranged from 2.5% to 11.0% for force component, and ranged from 0.6% to 14.7% for moment component, respectively.

CONCLUSIONS

The developed orthodontic force simulation method based on virtual bracket displacement can be used to simulate orthodontic force provided by the archwire applied to full dentition.

Torque differences according to tooth morphology and bracket placement: a finite element study

Introduction

Torque of the maxillary incisors is essential in esthetics and proper occlusion, while torque expression is influenced by many factors. The aim of this finite element study was to assess the relative effect of tooth morphology, bracket prescription, and bracket positioning on tooth displacement and developed stresses/strains after torque application.

Methods

A three-dimensional upper right central incisor with its periodontal ligament (PDL) and alveolus was modelled. The tooth varied in the crown-root angle (CRA) between 156°, 170°, and 184°. An 0.018-inch slot discovery® (Dentaurum, Ispringen, Germany) bracket with a rectangular 0.018 × 0.025-inch β-titanium wire was modelled. Bracket torque prescription varied between 0°, 12°, and 22°, with bracket placement at the centre of the middle, gingival or incisal third of the crown. A total of 27 models were generated and a buccal root torque of 30° was applied. Afterwards, crown and apex displacement, strains in the PDL, and stresses in the bracket were calculated and analysed statistically.

Results

The palatal crown displacement was significantly affected by bracket positioning (up to 94 per cent), while the buccal apex displacement was significantly affected by bracket prescription (up to 42 per cent) and bracket positioning (up to 23 per cent). Strains in the PDL were affected mainly by CRA (up to 54 per cent), followed by bracket positioning (up to 45 per cent). Finally, bracket prescription considerably affected the stresses in the bracket (up to 144 per cent).

Limitations

These in silico results need to be validated in vivo before they can be clinically extrapolated.

Conclusion

Tooth anatomy and the characteristics of the orthodontic appliance should be considered during torque application.

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

Background

Torque of the maxillary incisors is crucial to occlusal relationship and esthetics and can be influenced by many factors. The aim of this study was to assess the relative influence of the material of the orthodontic appliance (adhesive, bracket, ligature, and wire) on tooth displacements and developed stresses/strains after torque application.

Methods

A three-dimensional upper right central incisor with its periodontal ligament (PDL) and alveolus was modeled. A 0.018-in. slot discovery® (Dentaurum, Ispringen, Germany) bracket with a rectangular 0.018 x 0.025-in. wire was generated. The orthodontic appliance varied in the material of its components: adhesive (composite resin or resin-modified glass ionomer cement), bracket (titanium, steel, or ceramic), wire (beta-titanium or steel), and ligature (elastomeric or steel). A total of 24 models were generated, and a palatal root torque of 5° was applied. Afterwards, crown and apex displacement, strains in the PDL, and stresses in the bracket were calculated and analyzed.

Results

The labial crown displacement and the palatal root displacement of the tooth were mainly influenced by the material of the wire (up to 150% variation), followed by the material of the bracket (up to 19% variation). The magnitude of strains developed in the PDL was primarily influenced by the material of the wire (up to 127% variation), followed by the material of the bracket (up to 30% variation) and the ligature (up to 13% variation). Finally, stresses developed at the bracket were mainly influenced by the material of the wire (up to 118% variation) and the bracket (up to 59% variation).

Conclusions

The material properties of the orthodontic appliance and all its components should be considered during torque application. However, these in silico results need to be validated in vivo before they can be clinically extrapolated.

Electronic supplementary material

The online version of this article (doi:10.1186/s40510-017-0161-5) contains supplementary material, which is available to authorized users.

Influence of tooth dimension on the initial mobility based on plaster casts and X-ray images : A numerical study

AIMS

The goal was to determine the influence of different geometric parameters of the tooth on the initial tooth mobility and the position of the center of resistance employing numerical models based on scaled X-ray images and plaster casts.

METHODS

The dimensions of tooth 21 were measured in 21 patients, using radiographs and dental casts. Length and mesiodistal width of the tooth were obtained from the X-ray image and the orovestibular diameter from the plaster cast. Finite element models were generated. Cortical and cancellous bone and the periodontal ligament were simulated to create realistic models. Root length (11-17 mm), mesiodistal width (6-10 mm) and orovestibular thickness (7-9 mm) were varied in 1-mm steps to generate 105 models. In the simulation, each model was loaded with a force of 10 N in vestibulopalatinal direction and with a torque of 10 Nmm to determine tooth displacements and center of resistance.

RESULTS

Initial tooth displacement and thus mobility increased with decreasing total root surface. The shortest, slimmest and thinnest tooth showed a total deflection of 0.14 mm at the incisal edge, while the longest, widest and thickest tooth showed a total deflection of 0.10 mm. Changes in mesiodistal width had the greatest influence on initial tooth mobility and changes in orovestibular thickness the least. The teeth's center of resistance was positioned between 37 and 43% of the root length measured from the cervical margin of the alveolar bone. The center of resistance of the longest dental root investigated was located around 6% more cervically compared to the one of the shortest dental root. The influence of root width and thickness on the position of the center of resistance was significantly lower than root length.

CONCLUSION

Geometric parameters significantly impact initial tooth mobility and position of the center of resistance. Thus, tooth dimensions should be considered in orthodontic treatment planning. Dental radiographs represent a sufficient validation tool to estimate the quality of a pure dental tipping during orthodontic treatment, as the orovestibular thickness has little influence. However, for three-dimensional tooth displacements all geometric parameters should be determined accurately using plaster casts or DVT.

Effect of material variation on the biomechanical behaviour of orthodontic fixed appliances: a finite element analysis

INTRODUCTION

Biomechanical analysis of orthodontic tooth movement is complex, as many different tissues and appliance components are involved. The aim of this finite element study was to assess the relative effect of material alteration of the various components of the orthodontic appliance on the biomechanical behaviour of tooth movement.

METHODS

A three-dimensional finite element solid model was constructed. The model consisted of a canine, a first, and a second premolar, including the surrounding tooth-supporting structures and fixed appliances. The materials of the orthodontic appliances were alternated between: (1) composite resin or resin-modified glass ionomer cement for the adhesive, (2) steel, titanium, ceramic, or plastic for the bracket, and (3) β-titanium or steel for the wire. After vertical activation of the first premolar by 0.5mm in occlusal direction, stress and strain calculations were performed at the periodontal ligament and the orthodontic appliance.

RESULTS

The finite element analysis indicated that strains developed at the periodontal ligament were mainly influenced by the orthodontic wire (up to +63 per cent), followed by the bracket (up to +44 per cent) and the adhesive (up to +4 per cent). As far as developed stresses at the orthodontic appliance are concerned, wire material had the greatest influence (up to +155 per cent), followed by bracket material (up to +148 per cent) and adhesive material (up to +8 per cent).

LIMITATIONS

The results of this in silico study need to be validated by in vivo studies before they can be extrapolated to clinical practice.

CONCLUSION

According to the results of this finite element study, all components of the orthodontic fixed appliance, including wire, bracket, and adhesive, seem to influence, to some extent, the biomechanics of tooth movement.