A biomechanical case study on the optimal orthodontic force on the maxillary canine tooth based on finite element analysis

In vitro biomechanics of divot use, and their placement, in orthodontic aligner therapy

INTRODUCTION

To evaluate biomechanics of an aligner utilizing divots and the effect of their vertical placement on the right maxillary central incisor.

METHODS

An in vitro Orthodontic SIMulator (OSIM) was used to test forces and moments generated by aligners incorporating divots. The OSIM arch was scanned to generate a. STL version that was modified to create four models by placing divots on different positions of the right central maxillary incisor: GI - divots on gingival-third of lingual surface and incisal-third of labial surface; GM - divots on gingival-third of lingual surface and middle-third of labial surface; MI - divots on middle-third of lingual surface and incisal-third of labial surface; MM - divots on middle-third of lingual surface and middle-third of labial surface. Aligners (n = 30/model) were fabricated using a 0.75 mm thick polyethylene terephthalate material and Biostar® machine following the manufacturer's recommendations. A one-way MANOVA followed by one-way ANOVA (α = 0.05) was utilized to test effect of models on buccolingual force (Fy) and mesiodistal moment (Mx) at 0.20 mm of lingual displacement of the right maxillary central incisor.

RESULTS

Mean Mx for GI (-5.68 ± 7.38 Nmm), GM (3.75 ± 5.54 Nmm), MI (-4.27 ± 1.48 Nmm) and MM (1.96 ± 0.99 Nmm) models showed statistical differences between GI and GM, GI and MM, GM and MI and MI and MM. GI exerted the largest Fy (1.87 ± 0.75 N) followed by GM (1.10 ± 0.47 N), MI (0.70 ± 0.23 N) and MM (0.28 ± 0.08 N) with significant differences between GI and GM, GI and MI, GI and MM and GM and MM models.

CONCLUSIONS

Vertical divot placement on a right central incisor had a significant effect on aligner biomechanics. Buccolingual forces exerted by models GI, GM and MI were within the range suggested by literature for bodily tooth movement without major root tipping for GM and MI models.

Trabecular Bone Component Assessment under Orthodontic Loads and Movements during Periodontal Breakdown-A Finite Elements Analysis

This numerical analysis, by employing Tresca and Von Mises failure criteria, assessed the biomechanical behavior of a trabecular bone component subjected to 0.6, 1.2, and 2.4 N orthodontic forces under five movements (intrusion, extrusion, tipping, rotation, and translation) and during a gradual horizontal periodontal breakdown (0-8 mm). Additionally, they assessed the changes produced by bone loss, and the ischemic and resorptive risks. The analysis employed eighty-one models of nine patients in 405 simulations. Both failure criteria showed similar qualitative results, with Tresca being quantitatively higher by 1.09-1.21. No qualitative differences were seen between the three orthodontic loads. Quantitatively, a doubling (1.2 N) and quadrupling (2.4 N) were visible when compared to 0.6 N. Rotation and translation followed by tipping are the most stressful, especially for a reduced periodontium, prone to higher ischemic and resorptive risks. In an intact periodontium, 1.2 N can be safely applied but only in a reduced periodontium for extrusion and intrusion. More than 0.6 N is prone to increasing ischemic and resorptive risks for the other three movements. In an intact periodontium, stress spreads in the entire trabecular structure. In a reduced periodontium, stress concentrates (after a 4 mm loss-marker for the stress change distribution) and increases around the cervical third of the remaining alveolar socket.

Evaluation of stress and displacement of maxillary canine during the single canine retraction in the maxillary first premolar extraction cases- A finite element study

OBJECTIVES

This finite element study aimed to simulate maxillary canine movement during anterior teeth retraction.

MATERIALS AND METHODS

Three methods of maxillary canine movement including miniscrew sliding with high hooks (MSH), miniscrew sliding with low hooks (MSL), and the traditional sliding method (TS) without using miniscrews were simulated using three-dimensional finite element analysis. The initial displacement of the maxillary canine, the maximum principal stress of the periodontal ligament and the Von Mises stress were calculated.

RESULTS

The distolingual tipping movements of the canine were shown in three movement modes. MSH showed a small tendency to lingual tipping movement and a extrusion movement while MSL had the largest lingual inclination. TS demonstrated a tendency toward distolingual torsion displacement. Compressive stress values were mainly concentrated in the range - 0.003 to -0.006 MPa. For tensile stress, the distribution of MSH and MSL was concentrated in the range 0.005 to 0.009 MPa, TS was mainly distributed about 0.003 MPa. Von Mises equivalent stress distribution showed no significant difference.

CONCLUSIONS

The loss of tooth torque was inevitable, irrespective of which method was used to close the extraction space. However, miniscrew application and higher hooks reduced the loss of torque and avoided lingual rotation.

CLINICAL RELEVANCE

This study shows that miniscrew implants with different hooks can better control the movement of the maxillary canines. The non-invasive nature of the finite element analysis and its good simulation of dental stress and instantaneous motion trend have a clinical advantage in the analysis of tooth movement.

The osteoclastic activity in apical distal region of molar mesial roots affects orthodontic tooth movement and root resorption in rats

The utilization of optimal orthodontic force is crucial to prevent undesirable side effects and ensure efficient tooth movement during orthodontic treatment. However, the sensitivity of existing detection techniques is not sufficient, and the criteria for evaluating optimal force have not been yet established. Here, by employing 3D finite element analysis methodology, we found that the apical distal region (A-D region) of mesial roots is particularly sensitive to orthodontic force in rats. Tartrate-resistant acidic phosphatase (TRAP)-positive osteoclasts began accumulating in the A-D region under the force of 40 grams (g), leading to alveolar bone resorption and tooth movement. When the force reached 80 g, TRAP-positive osteoclasts started appearing on the root surface in the A-D region. Additionally, micro-computed tomography revealed a significant root resorption at 80 g. Notably, the A-D region was identified as a major contributor to whole root resorption. It was determined that 40 g is the minimum effective force for tooth movement with minimal side effects according to the analysis of tooth movement, inclination, and hyalinization. These findings suggest that the A-D region with its changes on the root surface is an important consideration and sensitive indicator when evaluating orthodontic forces for a rat model. Collectively, our investigations into this region would aid in offering valuable implications for preventing and minimizing root resorption during patients' orthodontic treatment.

GDF15 Contributes to the Regulation of the Mechanosensitive Responses of PdL Fibroblasts through the Modulation of IL-37

During orthodontic tooth movement (OTM), areas of compressive and tensile forces are generated in the periodontal ligament (PdL), a mechanoreactive connective tissue between the teeth and alveolar bone. Mechanically stimulated PdL fibroblasts (PdLFs), the main cell type of PdL, express significantly increased levels of growth differentiation factor 15 (GDF15). In compressed PdL areas, GDF15 plays a fundamental role in modulating relevant OTM processes, including inflammation and osteoclast activation. However, the specific function of this factor in tensile areas has not yet been investigated. Thus, the aim of this study was to investigate the role of GDF15 in the mechanoresponse of human PdLFs (hPdLFs) that were exposed to biaxial tensile forces in vitro. Using siRNA-mediated knockdown experiments, we demonstrated that GDF15 had no impact on the anti-inflammatory force response of elongated hPdLFs. Although the anti-inflammatory markers IL1RN and IL10, as well as the activation of immune cells remained unaffected, we demonstrated an inhibitory role of GDF15 for the IL-37 expression. By analyzing osteogenic markers, including ALPL and RUNX2, along with an assessment of alkaline phosphatase activation, we further showed that the regulation of IL-37 by GDF15 modulates the osteogenic differentiation potential of hPdLFs. Despite bone resorption in tensile areas being rather limited, GDF15 was also found to positively modulate osteoclast activation in those areas, potentially by adjusting the IL-37 levels. In light of our new findings, we hypothesize that GDF15 modulates force-induced processes in tissue and bone remodeling through its various intra- and extracellular signaling pathways as well as interaction partners. Potentially acting as a master regulator, the modulation of GDF15 levels may hold relevance for clinical implications.

Studying the mechanical properties of the mandible and injury prediction under the effect of ossification factors

BACKGROUND AND OBJECTIVE

It is essential to know the quantitative interactions between biological tissues and external mechanical and chemical stimuli. This assists the physicians to better know the quantitative behavior of the tissue and plan more effective therapy. In the literature, the effect of the chemical and mechanical loading was investigated on the bone biological cell activities and some mechanical features, but a lack of prediction of bone injury under the chemical and mechanical factors was sensed. Therefore, the present study aims to investigate the effects of the application of major chemical factors involved in ossification, including RANKL1 (Receptor Activator of Nuclear Factor Kappa Beta Ligand), PTH2 (Parathyroid Hormone), and OPG3 (Osteoprotegerin) on the mandibular bone biological osteoblast and osteoclast activities and mechanical properties. Moreover, the study assesses the bone injury possibility under uniform mastication pressure applied on the premolar tooth in terms of the mechanostat theory undergoing the effects of the chemical factors.

METHODS

A 3D geometry of the mandible-tooth assembly was generated from the CT image dataset. The geometry was next purified, solidified, and exported to FEM4 (Finite Element Method) software to be meshed, where boundary conditions and loading were applied. Moreover, the mathematical system of differential equations to model the chemical factor effects on osteoblast and osteoclast activities as well as bone matrix volume fraction and elastic stiffness relations were applied. Next, the values of the equivalent strain were calculated to predict the injury states of the bone.

RESULTS

The results complied with the literature data. The results showed that RANKL and PTH increased the values of the equivalent strain from 450 με to 11500 με, while OPG reduced that from 450 με to 300 με.

CONCLUSIONS

Therefore, RANKL and PTH doses of this study put the bone at risk of injury compared to the baseline of no dose applied, while OPG secured the bone from injury.

Effects of upper arch expansion using clear aligners on different stride and torque: a three-dimensional finite element analysis

BACKGROUND

During maxillary arch expansion with a clear aligner (CA), buccal tipping of the posterior teeth often occurs, resulting in an unsatisfactory arch expansion effect. The aim of this study was to analyze the appropriate maxillary arch expansion stride length and torque compensation angle for maxillary dentition to achieve an ideal moving state when a CA was used for upper arch expansion.

METHODS

This study established a three-dimensional (3D) finite element model including a CA, maxilla, periodontal ligament (PDL), and maxillary dentition. The stress distribution, stress situation, expansion efficiency, and movement trends of the maxillary dentition during upper arch expansion of different stride (0.1 mm, 0.2 mm, and 0.3 mm) and torque compensation (0°, 0.5°, 1°, and 1.5°) were measured.

RESULTS

Maxillary arch expansion lead to buccal tilt of the posterior teeth, lingual tilt of the anterior teeth, and extrusion of the incisors. As the angle of compensation increased, the degree of buccal tilt on the posterior teeth decreased, with this reducing the efficiency of upper arch expansion. When the stride length was 0.1 mm, the torque compensation was 1.2°, and when stride length was 0.2 mm and the torque compensation was approximately 2°, there was a tendency for the posterior teeth to move bodily. However, when the stride length was 0.3 mm, the increase in torque compensation could not significantly improve the buccal tilt phenomenon. In addition, the equivalent von-Mises stress values of the maxillary root, PDL, and alveolar bone were in the same order of magnitude.

CONCLUSIONS

This study indicated that the posterior teeth cause a degree of buccal tilt when maxillary arch expansion is ensured. The specific torque compensation angle should be determined based on the patient's situation and the desired effect.

Effects of Increasing the Orthodontic Forces over Cortical and Trabecular Bone during Periodontal Breakdown-A Finite Elements Analysis

Background and Objectives: Herein we used numerical analysis to study different biomechanical behaviors of mandibular bone subjected to 0.6 N, 1.2 N, and 2.4 N orthodontic loads during 0-8 mm periodontal breakdown using the Tresca failure criterion. Additionally, correlations with earlier FEA reports found potential ischemic and resorptive risks. Materials and Methods: Eighty-one models (nine patients) and 243 simulations (intrusion, extrusion, rotation, tipping, and translation) were analyzed. Results: Intrusion and extrusion displayed after 4 mm bone loss showed extended stress display in the apical and middle third alveolar sockets, showing higher ischemic and resorptive risks for 0.6 N. Rotation, translation, and tipping displayed the highest stress amounts, and cervical-third stress with higher ischemic and resorptive risks after 4 mm loss for 0.6 N. Conclusions: Quantitatively, rotation, translation, and tipping are the most stressful movements. All three applied forces produced similar stress-display areas for all movements and bone levels. The stress doubled for 1.2 N and quadrupled for 2.4 N when compared with 0.6 N. The differences between the three loads consisted of the stress amounts displayed in color-coded areas, while their location and extension remained constant. Since the MHP was exceeded, a reduction in the applied force to under 0.6 N (after 4 mm of bone loss) is recommended for reducing ischemic and resorptive risks. The stress-display pattern correlated with horizontal periodontal-breakdown simulations.

The effect of space arrangement between anterior teeth on their retraction with clear aligners in first premolar extraction treatment: a finite element study

INTRODUCTION

Clear aligner therapy has become increasingly popular in recent years, although it has encountered several difficulties in premolar extraction treatment. These difficulties include anterior dentition, lingual tipping and extrusion. The design of the present clinical scheme usually set a tiny space between the anterior teeth before retraction in order to obtain an ideal outcome. The objective of our research was to analyze the effect of the existing spaces during retraction.

METHODS

Models including maxillary dentition without first premolars, maxilla, periodontal ligaments, gingiva, or aligners were constructed and imported to an ANSYS workbench. Five groups of models were created: without spaces and with 0.25, 0.50, 0.75 and 1.00 mm spaces between the anterior dentition. A 0.20 mm retraction step was applied to all the groups.

RESULTS

As the spaces between the anterior dentition increased, the bowing effect of the aligner caused by the passive forces decreased gradually. Accordingly, the degree of extrusion of the anterior dentition was alleviated significantly, while sagittal movement was reduced. However, the overall movement tended to be a bodily displacement rather than tipping. Meanwhile, maximum Von Mises stress of the periodontal ligaments (PDLs) was markedly decreased.

CONCLUSION

These analyses indicate that spaces between the anterior dentition during anterior retraction are beneficial for decreasing the tendency for extrusion of the anterior dentition and require provision of anchorage. Appropriate spaces can be designed to lest the lingual tipping and extrusion effect of the anterior teeth while simultaneously reducing the maximum stresses on PDLs.

Orthodontic Internal Resorption Assessment in Periodontal Breakdown-A Finite Elements Analysis (Part II)

This finite elements analysis (FEA) assessed the accuracy of maximum shear stress criteria (Tresca) in the study of orthodontic internal surface resorption and the absorption-dissipation ability of dental tissues. The present study was conducted over eighty-one models totaling 324 simulations with various bone loss levels (0-8 mm), where 0.6 N and 1.2 N were applied in the intrusion, extrusion, rotation, tipping, and translation movements. Tresca criteria displayed localized high-stress areas prone to resorption for all situations, better visible in the dentine component. The internal resorptive risks are less than external ones, seeming to increase with the progression of the periodontal breakdown, especially after 4 mm. The internal and external surface high-stress areas are strictly correlated. The qualitative stress display for both forces was almost similar. The rotation and tipping displayed the highest resorptive risks for the pulp chamber, decreasing with bone loss. The resorptive risks seem to increase along with the progression of periodontal breakdown if the same applied force is kept. The dentine resemblance to ductile based on its high absorption-dissipation ability seems correct. Tresca seems to supply a better predictability of the prone-to-resorption areas than the other failure criteria.

Tribology of Coated 316L SS by Various Nanoparticles

Background

Nanocoating of biomedical materials may be considered the most essential developing field recently, primarily directed at improving their tribological behaviors that enhance their performance and durability. In orthodontics, as in many medical fields, friction reduction (by nanocoatings) among different orthodontic components is considered a substantial milestone in the development of biomedical technology that reduces orthodontic treatment time. The objective of the current research was to explore the tribological behavior, namely, friction of nanocoated thin layer by tantalum (Ta), niobium (Nb), and vanadium (V) manufactured using plasma sputtering at 1, 2, and 3 hours on substrates made of 316L stainless steel (SS), which is thought to be one of the most popular alloys for stainless steel orthodontic archwires. The friction of coated 316L SS archwires coated with Ta, Nb, and V plasma sputtering is hardly mentioned in the literature as of yet.

Results

An oscillating pin-on-plate tribological test using a computerized tribometer was performed by applying a load of 1 N for 20 minutes under the dry condition at room temperature (25°C) to understand their role in the tribological behavior of the bulk material. Ta and Nb were found to reduce the friction of their SS substrate significantly (45 and 55%, respectively), while V was found to deteriorate the friction of its substrate. Moreover, sputtering time had no substantial role in the friction reduction of coatings.

Conclusions

Nanocoating of 316L SS bulk material by Nb and Ta with a 1-hour plasma sputtering time can enhance dramatically its tribological behavior. Higher coating hardness, smaller nanoparticle size, intermediate surface coating roughness, and lower surface binding energy of the coatings may play a vital role in friction reduction of the coated 316L SS corresponding to SS orthodontic archwires, predicting to enhance orthodontic treatment.

Cortical and Trabecular Bone Stress Assessment during Periodontal Breakdown-A Comparative Finite Element Analysis of Multiple Failure Criteria

Background and Objectives: This numerical analysis investigated the biomechanical behavior of the mandibular bone as a structure subjected to 0.5 N of orthodontic force during periodontal breakdown. Additionally, the suitability of the five most used failure criteria (Von Mises (VM), Tresca (T), maximum principal (S1), minimum principal (S3), and hydrostatic pressure (HP)) for the study of bone was assessed, and a single criterion was identified for the study of teeth and the surrounding periodontium (by performing correlations with other FEA studies). Materials and Methods: The finite element analysis (FEA) employed 405 simulations over eighty-one mandibular models with variable levels of bone loss (0-8 mm) and five orthodontic movements (intrusion, extrusion, tipping, rotation, and translation). For the numerical analysis of bone, the ductile failure criteria are suitable (T and VM are adequate for the study of bone), with Tresca being more suited. S1, S3, and HP criteria, due to their distinctive design dedicated to brittle materials and liquids/gas, only occasionally correctly described the bone stress distribution. Results: Only T and VM displayed a coherent and correlated gradual stress increase pattern for all five movements and levels of the periodontal breakdown. The quantitative values provided by T and VM were the highest (for each movement and level of bone loss) among all five criteria. The MHP (maximum physiological hydrostatic pressure) was exceeded in all simulations since the mandibular bone is anatomically less vascularized, and the ischemic risks are reduced. Only T and VM displayed a correlated (both qualitative and quantitative) stress increase for all five movements. Both T and VM displayed rotation and translation, closely followed by tipping, as stressful movements, while intrusion and extrusion were less stressful for the mandibular bone. Conclusions: Based on correlations with earlier numerical studies on the same models and boundary conditions, T seems better suited as a single unitary failure criterion for the study of teeth and the surrounding periodontium.

Assessment of the Orthodontic External Resorption in Periodontal Breakdown-A Finite Elements Analysis (Part I)

This Finite Elements Analysis (FEA) assessed the accuracy of Tresca failure criteria (maximum shear stress) for the study of external root resorption. Additionally, the tooth absorption-dissipation ability was assessed. Overall, 81 models of the second mandibular premolar, out of a total of 324 simulations, were involved. Five orthodontic movements (intrusion, extrusion, rotation, translation, and tipping) were simulated under 0.6 N and 1.2 N in a horizontal progressive periodontal breakdown simulation of 0-8 mm. In all simulations, Tresca criteria accurately displayed the localized areas of maximum stress prone to external resorption risks, seeming to be adequate for the study of the resorptive process. The localized areas were better displayed in the radicular dentine-cementum component than in the entire tooth structure. The rotation and translation seem prone to a higher risk of external root resorption after 4 mm of loss. The resorptive risks seem to increase along with the progression of periodontal breakdown if the same amount of applied force is guarded. The localized resorption-prone areas follow the progression of bone loss. The two light forces displayed similar extensions of maximum stress areas. The stress displayed in the coronal dentine decreases along with the progression of bone loss. The absorption-dissipation ability of the tooth is about 87.99-97.99% of the stress.

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.

An in vivo evaluation of clear aligners for optimal orthodontic force and movement to determine high-efficacy and periodontal-friendly aligner staging

Objectives

To investigate the effect of aligner displacement on tooth movement and periodontal health to improve the efficiency of aligner treatment and explore the mechanism in vivo.

Methods

A two-tooth site was established by a finite element (FE) model to virtually evaluate aligner staging. A randomized controlled experiment was conducted when the tooth sites in beagles were treated with fixed or aligner appliances with different movement and force, and tooth movement and internal structure were recorded during the alignment. After sacrificing five dogs, bone-periodontal ligament (PDL)-tooth specimens were removed and processed to conduct uniaxial compression and tensile tests as well as micro-CT imaging and histological analysis.

Results

Three displacements of 0.25, 0.35 and 0.45 mm were obtained from FE analysis and applied in beagles. In general, aligners had poorer performance on movement compared to fixed systems in vivo, but the aligner with a staging of 0.35 mm had the highest accuracy (67.46%) (P < 0.01). Loaded with severe force, fixed sites exhibited tissue damage due to excess force and rapid movement, while aligners showed better safety. The PDL under a 0.35-mm aligner treatment had the highest elastic modulus in the biomechanical test (551.4275 and 1298.305 kPa) (P < 0.05).

Conclusions

Compared to fixed appliances, aligners achieve slightly slower movement but better periodontal condition. Aligners with an interval of 0.35 mm have the highest accuracy and best PDL biomechanical and biological capacities, achieving the most effective and safest movement. Even with complexity of oral cavity and lack of evaluation of other factors, these results provide insight into faster displacement as a method to improve the efficacy of aligners.

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.

Finite Elements Analysis of Tooth-A Comparative Analysis of Multiple Failure Criteria

Herein Finite elements analysis (FEA) study assesses the adequacy and accuracy of five failure criteria (Von Mises (VM), Tresca, maximum principal (S1), minimum principal (S3), and Hydrostatic pressure) for the study of tooth as a structure (made of enamel, dentin, and cement), along with its stress absorption-dissipation ability. Eighty-one 3D models of the second lower premolar (with intact and 1-8 mm reduced periodontium) were subjected to five orthodontic forces (intrusion, extrusion, tipping, rotation, and translation) of 0.5 N (approx. 50 gf) (in a total of 405 FEA simulations). Only the Tresca and VM criteria showed biomechanically correct stress display during the 0-8 mm periodontal breakdown simulation, while the other three showed various unusual biomechanical stress display. All five failure criteria displayed comparable quantitative stress results (with Tresca and VM producing the highest of all), showing the rotational and translational movements to produce the highest amount of stress, while intrusion and extrusion, the lowest. The tooth structure absorbed and dissipated most of the stress produced by the orthodontic loads (from a total of 0.5 N/50 gf only 0.125 N/12.5 gf reached PDL and 0.01 N/1 gf the pulp and NVB). The Tresca criterion seems to be more accurate than Von Mises for the study of tooth as structure.

Assessment of the Maximum Amount of Orthodontic Force for PDL in Intact and Reduced Periodontium (Part I)

This study examines 0.6 N and 1.2 N as the maximum orthodontic force for periodontal ligament (PDL) at multiple levels of periodontal breakdown, and the relationships with the ischemic, necrotic, and resorptive risks. Additionally, this study evaluates if Tresca failure criteria is more adequate for the PDL study. Eighty-one 3D models (from nine patients; nine models/patients) with the 2nd lower premolar and different degrees of bone loss (0-8 mm) where subjected to intrusion, extrusion, rotation, translation, and tipping movements. Tresca shear stress was assessed individually for each movement and bone loss level. Rotation and translation produced the highest PDL stresses, while intrusion and extrusion determined the lowest. Apical and middle third PDL stresses were lower than the cervical stress. In intact periodontium, the amount of shear stress produced by the two investigated forces was lower than the 16 KPa of the maximum physiological hydrostatic pressure (MHP). In reduced periodontium (1-8 mm tissue loss), the apical amount of PDL shear stress was lower than MHP for both applied forces, while cervically for rotation, translation and tipping movements exceeded 16 KPa. Additionally, 1.2 N could be used in intact periodontium (i.e., without risks) and for the reduced periodontium only in the apical and middle third of PDL up to 8 mm of bone loss. However, for avoiding any resorptive risks, in the cervical third of PDL, the rotation, translation, and tipping movements require less than 0.2-0.4 N of force after 4 mm of loss. Tresca seems to be more adequate for the study of PDL than other criteria.

Assessment of the Maximum Amount of Orthodontic Force for Dental Pulp and Apical Neuro-Vascular Bundle in Intact and Reduced Periodontium on Bicuspids (Part II)

This study examines 0.6 N-4.8 N as the maximum orthodontic force to be applied to dental pulp and apical NVB on intact and 1-8 mm reduced periodontal-ligament (PDL), in connection with movement and ischemic, necrotic and resorptive risk. In addition, it examines whether the Tresca finite-element-analysis (FEA) criterion is more adequate for the examination of dental pulp and its apical NVB. Eighty-one (nine patients, with nine models for each patient) anatomically correct models of the periodontium, with the second lower-premolar reconstructed with its apical NVB and dental pulp were assembled, based on X-ray CBCT (cone-beam-computed-tomography) examinations and subjected to 0.6 N, 1.2 N, 2.4 N and 4.8 N of intrusion, extrusion, translation, rotation, and tipping. The Tresca failure criterion was applied, and the shear stress was assessed. Forces of 0.6 N, 1.2 N, and 2.4 N had negligible effects on apical NVB and dental pulp up to 8 mm of periodontal breakdown. A force of 4.8 N was safely applied to apical NVB on the intact periodontium only. Rotation and tipping seemed to be the most invasive movements for the apical NVB. For the dental pulp, only the translation and rotation movements seemed to display a particular risk of ischemia, necrosis, and internal orthodontic-resorption for both coronal (0-8 mm of loss) and radicular pulp (4-8 mm of loss), despite the amount of stress being lower than the MHP. The Tresca failure criterion seems more suitable than other criteria for apical NVB and dental pulp.

Quantification of orthodontic loads on teeth in the correction of canine overeruption using different archwire designs

INTRODUCTION

This study quantifies the effects of material, size of the continuous archwires, and level of overeruption on the loads on teeth in the correction of overerupted canines.

METHODS

An orthodontic force test (OFT) was used to measure the 3-dimensional loads delivered by the archwires to the brackets attached to the maxillary right incisors, canine, and premolars. Dentoforms simulating canine overeruptions at the 0.5 mm and 1 mm levels were made from computerized tomography scans. Archwires with 2 types of material (stainless steel [SS] and nickel-titanium [NiTi]) and 2 sizes (0.014-in and 0.016-in) were tested, respectively, on the 0.022 × 0.028-in brackets through elastomeric ligatures.

RESULTS

The forces were dominantly intrusive on the canines and extrusive on the first premolars and lateral incisors. The magnitudes of the extrusive forces were about 74% and 52% that of intrusive force on the canines, which range from -0.48 ± 0.01 N to -5.70 ± 0.14 N depending on the wire material, size, and severity of overeruption (P <0.01). The canine intrusive forces created by SS wires were about 3 times higher than that of NiTi wires with the same sizes, 0.016-in archwires were about twice higher than that of 0.014-in with the same materials, and 1 mm overeruption level doubled with respect to 0.5 mm. Significant second-order moment as coupled with the intrusive or extrusive forces.

CONCLUSIONS

The intrusive and extrusive forces on teeth in the correction of canine overeruption can be quantified by the in vitro orthodontic force test, and the effects of the 3 factors significantly affect the loads on the teeth.

The effects of different types of periodontal ligament material models on stresses computed using finite element models

INTRODUCTION

Finite element (FE) method has been used to calculate stress in the periodontal ligament (PDL), which is crucial in orthodontic tooth movement. The stress depends on the PDL material property, which varies significantly in previous studies. This study aimed to determine the effects of different PDL properties on stress in PDL using FE analysis.

METHODS

A 3-dimensional FE model was created consisting of a maxillary canine, its surrounding PDL, and alveolar bone obtained from cone-beam computed tomography scans. One Newton of intrusion force was applied vertically to the crown. Then, the hydrostatic stress and the von Mises stress in the PDL were computed using different PDL material properties, including linear elastic, viscoelastic, hyperelastic, and fiber matrix. Young's modulus (E), used previously from 0.01 to 1000 MPa, and 3 Poisson's ratios, 0.28, 0.45, and 0.49, were simulated for the linear elastic model.

RESULTS

The FE analyses showed consistent patterns of stress distribution. The high stresses are mostly concentrated at the apical area, except for the linear elastic models with high E (E >15 MPa). However, the magnitude varied significantly from -14.77 to -127.58 kPa among the analyzed patients. The E-stress relationship was not linear. The Poisson's ratio did not affect the stress distribution but significantly influenced the stress value. The hydrostatic stress varied from -14.61 to -95.48 kPa.

CONCLUSIONS

Different PDL material properties in the FE modeling of dentition do not alter the stress distributions. However, the magnitudes of the stress significantly differ among the patients with the tested material properties.

Force profile assessment of direct-printed aligners versus thermoformed aligners and the effects of non-engaged surface patterns

Background

The purpose of the study was to measure the forces delivered by direct-printed aligners (DPA) in the vertical dimension and compare the force profile with traditional thermoformed aligners (TFA) and to investigate the impact of non-engaged surface patterns to the properties of DPA and TFA.

Methods

A force-measuring appliance was fabricated capable of displacing the aligner in 0.10 mm increments and measuring the resultant force. Polyethylene terephthalate glycol (ATMOS 0.030″ American Orthodontics) and TC-85DAC resin (Graphy Inc) were used to create TFA and DPA, respectively. Aligners were temperature-controlled prior to and during testing to simulate the oral environment. The resultant forces from displacements ranging from 0.10 to 0.30 mm were measured.

Results

At intraoral temperatures, DPA demonstrated significantly less force than TFA. TFA demonstrated a substantial statistically significant increase in force with each 0.10 mm increase in vertical displacement. DPA demonstrated a much more consistent force profile across the range of displacements. The effects of surface patterns in both DPA and TFA were generally a decrease in force. Statistical significance of surface patterns was detected for TFA at displacements of 0.30 mm and greater and significant for DPA only at a displacement of 0.10 mm. Surface patterns in both DPA and the TFA did not show any statistical difference when assessing force proprieties.

Conclusions

Forces delivered by aligners in the vertical dimension by DPA are more consistent and of lower magnitude than those of TFA aligners. Surface patterns were not capable of altering the force properties of both DPA and TFA.

Assessment of the Best FEA Failure Criteria (Part II): Investigation of the Biomechanical Behavior of Dental Pulp and Apical-Neuro-Vascular Bundle in Intact and Reduced Periodontium

The aim of this study was to biomechanically assess the behavior of apical neuro-vascular bundles (NVB) and dental pulp employing Tresca, Von Mises, Pressure, S1 and S3 failure criterions in a gradual periodontal breakdown under orthodontic movements. Additionally, it was to assess the accuracy of failure criteria, correlation with the maximum hydrostatic pressure (MHP), and the amount of force safe for reduced periodontium. Based on cone-beam computed tomography, 81 3D models of the second lower premolar were subjected to 0.5 N of intrusion, extrusion, rotation, tipping, and translation. A Finite Elements Analysis (FEA) was performed. In intact and reduced periodontium apical NVB, stress (predominant in all criteria) was significantly higher than dental pulp stress, but lower than MHP. VM and Tresca displayed identical results, with added pulpal stress in translation and rotation. S1, S3 and Pressure showed stress in the apical NVB area. 0.5 N seems safe up to 8 mm periodontal breakdown. A clear difference between failure criteria for dental pulp and apical NVB cannot be proved based only on the correlation quantitative results-MHP. Tresca and VM (adequate for ductile materials) showed equivalent results with the lowest amounts of stress. The employed failure criteria must be selected based on the type of material to be analyzed.

The three-dimensional displacement tendency of teeth depending on incisor torque compensation with clear aligners of different thicknesses in cases of extraction: a finite element study

Background

Despite the popularity of clear aligner treatment, the effect of the thickness of these aligners has not been fully investigated. The objective of this study was to assess the effects of incisor torque compensation with different thicknesses of clear aligner on the three-dimensional displacement tendency of teeth in cases of extraction.

Methods

Three-dimensional finite element models of the maxillary dentition with extracted first premolars, maxilla, periodontal ligaments, attachments, and aligners were constructed and subject to Finite Element Analysis (FEA). Two groups of models were created: (1) with 0.75 mm-thick aligners and (2) with 0.5 mm-thick aligners. A loading method was developed to simulate the action of clear aligners for the en masse retraction of the incisors. Power ridges of different heights were applied to both groups to mimic torque control, and the power ridges favoring the translation of the central incisors were selected. Then, we used ANSYS software to analyze the initial displacement of teeth and the principle stress on the PDL.

Results

Distal tipping, lingual tipping and extrusion of the incisors, distal tipping and extrusion of the canines, and mesial tipping and intrusion of the posterior teeth were all generated by clear aligner therapy. With the 0.5 mm-thick aligner, a power ridge of 0.7 mm could cause bodily retraction of the central incisors. With the 0.75 mm-thick aligner, a power ridge of 0.25 mm could cause translation of the central incisors. Aligner torque compensation created by the power ridges generated palatal root torque and intrusion of the incisors, intrusion of the canines, mesial tipping and the intrusion of the second premolar; these effects were more significant with a 0.75 mm-thick aligner. After torque compensation, the stress placed on the periodontal ligament of the incisors was distributed more evenly with the 0.75 mm-thick aligner.

Conclusions

The torque compensation caused by power ridges can achieve incisor intrusion and palatal root torque. Appropriate torque compensation with thicker aligners should be designed to ensure bodily retraction of anterior teeth and minimize root resorption, although more attention should be paid to the anchorage control of posterior teeth in cases of extraction.

Effectiveness of the attachment position in molar intrusion with clear aligners: a finite element study

Objective

To evaluate the biomechanical effects of different attachments’ position for maxillary molar intrusion with clear aligner treatment by finite element analysis.

Methods

Cone-beam computed tomography images of a patient with supra-eruption of the maxillary second molars were selected to construct three-dimensional models of the maxilla, periodontal ligaments, dentition, and clear aligner. The models were divided into four groups depending on the attachment location on the first molar: (1) no attachment (NA), (2) buccal attachment (BA), (3) palatal attachment (PA), and (4) bucco-palatal attachment (BPA). After applying an intrusion of 0.2 mm on the second molar, displacements and stress distributions of the teeth, aligner, and periodontal ligament were analyzed with the finite element software.

Results

All groups displayed equivalent movement patterns of aligners. The NA and BA groups showed buccal tipping of the second molar, while the PA group showed palatal tipping. The BPA group had the highest intruding value and the lowest buccal/palatal tipping value. All groups showed mesial tipping of the second molar. Stress distribution in the periodontal ligament strongly correlated with the attachment position. The BPA group showed the best stress distribution.

Conclusion

Combined BA and PA could effectively prevent buccal and palatal tipping and showed the best efficiency in intruding the second molar. The second molar showed an unavoidable tendency to tip mesially, regardless of the attachment position.

Assessment of the Best FEA Failure Criteria (Part I): Investigation of the Biomechanical Behavior of PDL in Intact and Reduced Periodontium

The accuracy of five failure criterions employed in the study of periodontal ligaments (PDL) during periodontal breakdown under orthodontic movements was assessed. Based on cone-beam computed tomography (CBCT) examinations, nine 3D models of the second lower premolar with intact periodontium were created and individually subjected to various levels of horizontal bone loss. 0.5 N of intrusion, extrusion, rotation, tipping, and translation was applied. A finite Elements Analysis (FEA) was performed, and stresses were quantitatively and qualitatively analyzed. In intact periodontium, Tresca and Von Mises (VM) stresses were lower than maximum physiological hydrostatic pressure (MHP), while maximum principal stress S1, minimum principal stress S3, and pressure were higher. In reduced periodontium, Tresca and VM stresses were lower than MHP for intrusion, extrusion, and the apical third of the periodontal ligament for the other movements. 0.5 N of rotation, translation and tipping induced cervical third stress exceeding MHP. Only Tresca (quantitatively more accurate) and VM are adequate for the study of PDL (resemblance to ductile), being qualitatively similar. A 0.5 N force seems safe in the intact periodontium, and for intrusion and extrusion up to 8 mm bone loss. The amount of force should be reduced to 0.1-0.2 N for rotation, 0.15-0.3 N for translation and 0.2-0.4 N for tipping in 4-8 mm periodontal breakdown. S1, S3, and pressure criteria provided only qualitative results.

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.

Intrusion of overerupted periodontally compromised posterior teeth using orthodontic mini‐implants: a mechanobiological finite element study

INTRODUCTION

The intrusion of posterior teeth had been considered challenging up to the development of orthodontic mini implants. In periodontally compromised teeth, the challenge is even greater, because of the root resorption risk due to periodontal ligament over-compression. Still, the precise strategy to determine the force reduction level remains uncertain.

OBJECTIVE

The objective of the study was to determine, by a finite element analysis (FEA), the force reduction needed to avoid root resorption and maintain the efficiency of orthodontic mechanics of periodontally compromised teeth similar to the sound one.

METHODS

An anatomical model was constructed representing a premolar inserted into a maxillary bone. Based on the initial model (R0), three bone height loss conditions were simulated (R2 = 2 mm, R4 = 4 mm, and R6 = 6 mm). Two intrusive movements were simulated: pure intrusion (bilateral mini implant) and uncontrolled-tipping intrusion (buccal mini implant). The hydrostatic stress at the periodontal ligament was used to evaluate the risk of root resorption due to over-compression.

RESULTS

For bilateral mini implant intrusion, the force had to be decreased by 16%, 32% and 48% for R2, R4 and R6, respectively. For buccal mini implant intrusion, the required reductions were higher (20%, 36% and 56%). A linear relationship between the intrusive force reduction and the alveolar bone height loss was observed in both intrusion mechanics.

CONCLUSIONS

According to the FE results, 8% or 9.3% of force reduction for each millimetre of bone height loss is suggested for intrusion with bilateral or buccal mini implant, respectively. The buccal mini implant anchorage must be associated with a supplemental strategy to avoid buccal crown tipping.

Application Research of Tooth Arrangement Based on Rotation Matrix Calculation and Resistance Detection in Oral

The goal of this research was to provide a new approach for analyzing orthodontic teeth arrangement inside oral depending on the rotation matrix computation and resistance detection. The present method includes the following operations within a certain therapy period: first three-dimensional positions of the tooth were evaluated with a pierced laser beam and a three-dimensional system of surface-scanning. Second, the three-dimensional shape data was automatically registered at maxillary 1^st molars, and methods of coordinate had been normalized. Third, a translation vector and rotation matrix had been evaluated from automatic registration of two position data of a particular tooth. Fourth, the limited spiral axes of teeth had been measured as the zero rotational dislocation locus; and impressions for a model of the dental cast had been taken at five different points: shortly before and after device was fitted, and ten days, one month, and two months after the treatment started. The results showed that existing analysis approach could more quickly classify a specific tooth's movement by spinning all over and translating along a finite helical axis. It can provide statistical visual three-dimensional data on complex tooth arrangement throughout orthodontic therapy.

Super-elasticity in vitro assessment of CuNiTi wires according to their Austenite finish temperature and the imposed displacement

OBJECTIVES

To assess the super-elasticity of CuNiTi wires (Ormco, Glendora, Calif) according to their Austenite finish temperature (Af) and to the imposed displacement. The secondary objective was to compare the wire dimensions with the stated measurements and to study interbatch variability.

MATERIALS AND METHODS

10 types of CuNiTi wires (Ormco, Glendora, Calif) (n = 350) were investigated at 36 ± 1°C, with conventional brackets (Victory Series, 3M Unitek, Monrovia, Calif). Tensile test with coronoapical displacement ranging from 1 to 5 mm of the canine bracket was imposed. The wire dimensions were initially measured from two batches (n = 10).

RESULTS

Dimensional heterogeneity varied by ± 2.00% compared to the manufacturer's data, and even up to 5.54% for 0.014-inch CuNiTi (P = .00069). However, all unloading forces were reproducible. In decreasing order, the forces delivered by a CuNiTi 27 were greater than those with CuNiTi 35 and 40. The super-elasticity was expressed only for displacements of 1 to 2 mm, at best up to 3 mm for 0.014-inch CuNiTi 27.

CONCLUSIONS

The value of Af as well as the amount of imposed displacement seem to influence the expression of the super-elasticity of CuNiTi wires and the amount of corrected malocclusion. Among the tested wires, under these experimental conditions, 0.014-inch wire could be suitable as a first archwire. CuNiTi 35, therefore, seems to offer the best compromise among the force level, the expression of super-elasticity and the amount of malocclusion correction.

An analysis of the optimal intrusion force of the maxillary central incisor with root horizontal resorption using the finite element method and curve fitting

There are no studies on the optimal intrusion force in orthodontic patients with the existing root resorption (RR). The study aimed to analyze the optimal intrusion force for central incisors with existing horizontal root resorption using the finite element method (FEM). We calculated the optimal intrusion force using the finite element method and curve fitting. We found that with the increase of the maxillary central incisor's root horizontal resorption length, the optimal intrusion force interval's median gradually increases. If the resorption length is more significant than 1/2 of the root length, it is not recommended to use intrusion force theoretically.

Mechanical evaluation for three-dimensional printed orthodontic springs with different heights-in vitro study

BACKGROUND

The orthodontic spring materials in use have a significant influence on the applied forces. The prerequisite to identify the in vitro< force deflection of the CAD/CAM fabricated springs is considered mandatory to identify the material characteristics. The purpose of the present investigation was to evaluate the mechanical load on 3D printed springs using different coil heights.

MATERIAL AND METHODS

The springs were digitally designed with different coil heights using Autodesk Netfabb CAD software (San Rafael, CA, USA). Test specimens were manufactured using 3D printable experimental flexible material (Code: BM2008, GC, Tokyo, Japan). The specimens were divided according to the coil height into five groups, group A (n=4mm), group B (n=6mm), group C (n=8mm), group D (n=10mm) and group E (n=12mm). All group specimens were mechanically tested using a universal testing machine. Statistical analysis was performed using K-S-Test to compare the values of each to the control group (p< 0.001).

RESULTS

The highest value in all groups was achieved by 5.43 N/mm in group A, while the lowest value was achieved by 0.11 N/mm in group E.

CONCLUSIONS

3D printed springs are mechanically affected by the coil heights and there is a direct correlation to the resulting force. Furthermore, the variations within the investigated groups must be thoroughly investigated prior to clinical application. Key words:CAD/CAM, 3D printing, Orthodontics, mechanical testing, material evaluation.

Overall stress in periodontal ligament under orthodontic movement during a periodontal breakdown

INTRODUCTION

This research aimed to assess qualitatively and quantitatively the overall stress in the periodontal ligament during gradual periodontal breakdown (0-8 mm) under orthodontic movements. Correlations between the applied forces, the level of bone loss, the decrease of force magnitude, and the increase of stress were also assessed.

METHODS

On the basis of cone-beam computed tomography examinations (voxel size, 0.075 mm), nine 3-dimensional models of a mandibular second premolar with intact periodontium were created and then individually subjected to various levels of horizontal bone loss. Orthodontic forces (intrusion at 0.2 N; extrusion, rotation, and tipping at 0.6 N; translation at 1.2 N) were applied on the brackets. Finite elements analysis was performed, and von Mises (VM) stresses were quantitatively and qualitatively determined.

RESULTS

Rotation and translation induced the highest stress apically and cervically, whereas intrusion determined the lowest. Apical stress was lower than cervical stress. In intact periodontium, VM stress was under maximum hydrostatic pressure (MHP) and maximum tolerable stress (MTS). In reduced periodontium, VM stress was lower apically than MHP, whereas cervically, the rotation, translation, and tipping exceeded MHP.

CONCLUSIONS

A force of 1.2 N seemed safe to be used in the intact periodontium. Forces higher than 0.6 N could produce stresses exceeding MHP and MTS endangering the reduced periodontium. VM stress failure criterion (despite its limited use) seemed to be more adequate for accurate quantitative results. An overall correlation between the applied force, VM stress increase, and periodontal breakdown applicable to all 5 movements could not be established. This was possible only for individual movements.

An in vitro evaluation of orthodontic aligner biomechanics around the maxillary arch

INTRODUCTION

The objective of this study was to evaluate the forces and moments exerted by orthodontic aligners on 3 different displaced maxillary teeth and their adjacent supporting teeth.

METHODS

An in vitro orthodontic simulator was used to measure the forces and moments of a 0.75-mm thick glycol-modified polyethylene terephthalate material for 3 maxillary teeth: central incisor, canine, and second premolar. Forces and moments were recorded for tested teeth displaced lingually one by one for 0.20 mm. Repeated measures of multivariate analysis of variance was used to assess the outcome.

RESULTS

The mean buccolingual force applied on a displaced canine (2.25 ± 0.38 N) was significantly (P <0.001) more than the central incisor (1.49 ± 0.18 N) and second premolar (1.50 ± 0.16 N). The mean moment (that tends to tip the teeth buccally) exerted on a canine (-20.11 ± 5.27 Nmm) was significantly more (P <0.001) than the central incisor (-8.42 ± 1.67 Nmm) and second premolar (-11.45 ± 1.29 Nmm). The forces and moments acting on teeth adjacent to the displaced tooth were clinically significant and acted in opposing directions to those on the displaced tooth.

CONCLUSIONS

The results of this study highlighted that for the same amount of displacement on a given tooth, the forces and moments imposed by the orthodontic aligner depend on location around the arch. These findings highlight the need to further study aligner mechanics around the dental arch and optimize aligner design to impose desired mechanical loads to avoid detrimental effects during orthodontic tooth movement.

Stress evaluation of different implant lengths on atrophic edentulous mandibles with fixed full-arch implant-supported prosthesis: a finite element analysis

Finite element analysis was used to compare the effect of different implant lengths on atrophic mandible with full-arch fixed prostheses. Four models were constructed with different implant lengths: 4, 6, 8 and 10 mm. A 100-N occlusal load was applied. The stress at the bone level, implant, and prosthetic components were obtained. Similar behavior was observed for all groups, except for 4 mm, which showed more discrepant values ​​for all prosthetic components. Although longer implants presented better biomechanical behavior, the 4 mm implant seems to be a viable alternative for severely atrophic mandibles, however, further studies need to be carried out.

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.

Compressive stress in periodontal ligament under orthodontic movements during periodontal breakdown

INTRODUCTION

This analysis aimed to assess quantitatively and qualitatively the compressive stress (S3) in periodontal ligament in a gradual periodontal breakdown (0-8 mm) under orthodontic movements. Correlations between the applied forces, the level of bone resorption, the decrease of force magnitude, and S3 increase were also conducted.

METHODS

On the basis of cone-beam computed tomography examinations (voxel size, 0.075 mm), nine 3-dimensional models of the second mandibular premolar with intact periodontium were created and then individually subjected to various levels of horizontal bone loss. Orthodontic forces (intrusion: 0.2 N; extrusion, rotation, tipping: 0.6 N; translation: 1.2 N) were applied on the brackets. Finite elements analysis was performed, and S3 stresses were quantitatively and qualitatively determined.

RESULTS

Translation and rotation induced the highest stress apically and cervically, whereas intrusion determined the lowest. Apical stress was lower than cervical stress. In intact periodontium, only intrusion and extrusion exhibited S3 stresses lower (apically and cervically) than maximum hydrostatic pressure (MHP) and maximum tolerable stress (MTS). In reduced periodontium, S3 stress (except for intrusion) exceeded MHP and MTS.

CONCLUSIONS

In reduced periodontium, forces of 0.2 N seems safe to be used. Forces of 0.6-1.2 N may produce stresses exceeding both MTS and MHP, endangering the periodontium. S3 failure criterion (despite its widely use) seems not to be adequate for accurate quantitative results when evaluating the stress in the periodontal ligament while remaining adequate for qualitative results. An overall correlation between the applied force, S3 increase, and periodontal breakdown applicable to all 5 movements could not be established-this was possible only for sole movements.

Numerical simulation of optimal range of rotational moment for the mandibular lateral incisor, canine and first premolar based on biomechanical responses of periodontal ligaments: a case study

OBJECTIVES

The objective of this study was to investigate the optimal range of rotational moment for the mandibular lateral incisor, canine and first premolar to determine tooth movements during orthodontic treatment using hydrostatic stress and logarithmic strain on the periodontal ligament (PDL) as indicators by numerical simulations.

MATERIAL AND METHODS

Teeth, PDL and alveolar bone numerical models were constructed as analytical objects based on computed tomography (CT) images. Teeth were assumed to be rigid bodies, and rotational moments ranging from 1.0 to 4.0 Nmm were exerted on the crowns. PDL was defined as a hyperelastic-viscoelastic material with a uniform thickness of 0.25 mm. The alveolar bone model was constructed using a non-uniform material with varied mechanical properties determined based on Hounsfield unit (HU) values calculated using CT images, and its bottom was fixed completely. The optimal range values of PDL compressive and tensile stress were set as 0.47-12.8 and 18.8-51.2 kPa, respectively, whereas that of PDL logarithmic strain was set as 0.15-0.3%.

RESULTS

The rotational tendency of PDL was around the long axis of teeth when loaded. The optimal range values of rotational moment for the mandibular lateral incisor, canine and first premolar were 2.2-2.3, 3.0-3.1 and 2.8-2.9 Nmm, respectively, referring to the biomechanical responses of loaded PDL. Primarily, the optimal range of rotational moment was quadratically dependent on the area of PDL internal surface (i.e. area of PDL internal surface was used to indicate PDL size), as described by the fitting formula.

CONCLUSIONS

Biomechanical responses of PDL can be used to estimate the optimal range of rotational moment for teeth. These rotational moments were not consistent for all teeth, as demonstrated by numerical simulations.

CLINICAL RELEVANCE

The quantitative relationship between the area of PDL internal surface and the optimal orthodontic moment can help orthodontists to determine a more reasonable moment and further optimise clinical treatment.

Dynamic measurement of orthodontic force using a tooth movement simulation system based on a wax model

BACKGROUND

Orthodontic force is often statically measured in general, and only the initial force derived from appliances can be assessed.

OBJECTIVE

We aimed to investigate a technological method for measuring dynamic force using tooth movement simulation.

METHODS

Tooth movement was simulated in a softened wax model. A canine tooth was selected for evaluation and divided into the crown and root. A force transducer was plugged in and fixed between the two parts for measuring force. Forces on this tooth were derived by ordinary nickel-titanium (Ni-Ti) wire, hyperelastic Ni-Ti wire, low-hysteresis (LH) Ti-Ni wire and self-made glass fibre-reinforced shape memory polyurethane (GFRSMPU) wire. These forces were measured after the tooth movement.

RESULTS

The canine tooth moved to the desired location, and only a 0.2 mm deviation remained. The changing trends and magnitudes of forces produced by the wires were consistent with the data reported by other studies. The tooth had a higher moving velocity with ordinary Ni-Ti wires in comparison to the other wires. Force attenuation for the GFRSMPU wire was the lowest (40.17%) at the end of the test, indicating that it provided light but continuous force.

CONCLUSIONS

Mimicked tooth movements and dynamic force measurements were successfully determined in tooth movement simulation. These findings could help with estimating treatment effects and optimising the treatment plan.

Orthodontic force prediction model of T-loop closing spring based on dynamic resistance model

Malocclusion has been seriously endangering human oral function. The most effective and mature therapy is orthodontic treatment. But the relationship between the shape of the T-loop and the orthodontic force is unclear, and the precise mathematical model has not been established. In this article, the dynamic orthodontic force prediction model of the T-loop was established by analyzing the treatment process of the T-loop. The model was based on the dynamic resistance model of waxy dental jaw, the theory of beam deformation, and the deformation characteristics of the T-loop. In the experimental process, 11 kinds of orthodontic archwires were used as experimental samples, including 2 kinds of common archwire materials, 7 kinds of cross-sectional sizes, and 10 kinds of clearance distances. The T-loop was put into the extraction space and immersed in 75°C constant temperature water for 2 min. And the experimental data were measured and collected by the dynamic force measuring device. The experimental results show that the cross-sectional size and the clearance distance are positively correlated with the orthodontic force. The influence of the clearance distance on the orthodontic force is greater than that of the cross-section size. The deviation rates between the experimental values of orthodontic force and the theoretical values are between 1.10% and 9.09%, which verifies the accuracy of the dynamic orthodontic force prediction model. The model can predict the orthodontic force, improve the treatment effect, shorten the treatment cycle, and provide reference and guidance for orthodontists to carry out orthodontic treatment safely and effectively.