Effect of clear aligner type on maxillary full-arch intrusion: 3D analysis using finite element method.

BACKGROUND: Vertical maxillary excess (VME) is one of the most common reasons for seeking orthodontic treatment. Total intrusion with aligners is a promising alternative to surgery in some cases. Considering the elastic deformation of aligners, this study aimed to evaluate the possible desirable and undesirable teeth displacements during full maxillary arch intrusion using clear aligners and temporary anchorage devices (TADs). METHODS: The maxillary arch and clear aligners were modeled in SolidWorks. Four aligner brands including Leon, Duran, Duran Plus, and Essix Plus were selected based on their material properties. Anterior and posterior intrusion forces of 80 and 300 g were applied from attachments between the canines and first premolars and between the first and second molars, respectively. Vertical and anteroposterior tooth displacements were determined. RESULTS: The greatest intrusion was recorded at the buccal of the second molar, followed by the first molar. The lowest value was measured at the palatal of the molars with all aligners except Duran, which indicated minimal intrusion in the central incisor. All teeth were mesially displaced at the incisal/occlusal except incisors that moved distally. All apices showed distal movement. CONCLUSIONS: Total intrusion using clear aligners may be accompanied by other tooth movements, including buccal tipping and mesial-in rotation of the molars, retrusion of incisors, and mesial movement of other teeth.

Perceptions of mandibular asymmetry among orthodontists, oral and maxillofacial surgeons, and laypersons.

Background: Facial asymmetry is one reason orthodontic patients seek treatment. This study assessed the effect of mandibular asymmetry on facial esthetics and treatment needs perceived by laypersons, orthodontists, and maxillofacial surgeons. Materials and Method: In this descriptive cross-sectional study, the frontal image of a model was captured and symmetrized from the facial midline using Adobe Photoshop software. The mandible was rotated 0°-8° with 1° intervals. Images were presented to 41 laypersons, 39 orthodontists, and 29 surgeons using an online questionnaire. The observers rated each image's esthetics with a 0-100 Visual Analog Scale and determined their treatment need by choosing one of the following three choices: No need for treatment, needs treatment, acceptable, but better to be treated. Analysis of variance for repeated measurements model. The regression method, Kruskal-Wallis analysis, was used for statistical analysis and the level of significance was set as P < 0.05. Results: The images with 0° and 1° rotation received the highest esthetic rates among all three groups, while the images with 8° rotation were the least attractive ones. Furthermore, the image esthetic ratings significantly affected their treatment need. Mandibular asymmetry diagnosis threshold was 1° for orthodontists, and 3° for both laypersons and surgeons. The treatment need threshold was 5°, 6°, and 7° for surgeons, orthodontists, and laypersons, respectively. Conclusion: The esthetics of images decreased when mandibular asymmetry increased. Treatment need was also related to increased asymmetry. Orthodontists were the most sensitive group in diagnosis, while surgeons were the most sensitive ones when it came to treatment.

Evaluation of different models of intrusive force application and temporary anchorage device (TAD) placement in total arch intrusion using clear aligners; a finite element analysis.

INTRODUCTION: Present study aims to evaluate different models of total arch intrusion using clear aligners in a finite element setup, which might be helpful in gummy smile patients who seek this treatment modality. METHODS: Four patterns of intrusive forces were applied on each side of the upper arch aligner model: (1) Distal to the lateral incisors (facial - 80 g) and distal to the first molar (palatal - 150 g). (2) Distal to the lateral incisors (facial - 80 g) and distal to the first molars (facial - 80 g and palatal - 80 g). (3) Distal to the canines (facial - 80 g) and distal to the first molars (facial - 150 g). (4) Distal to the lateral incisors (facial - 80 g) and mesial to the first molars (facial - 150 g). Vertical and horizontal movements of the teeth were measured. RESULTS: Extrusion movements were solely detected at buccal cusps of the first and second molars in the first model. Palatal movements of posterior teeth were detected in this model. Model II showed a homogeneous intrusion in anterior and posterior teeth and the amount of palatal movements of posterior teeth was reduced compared to model I. In contrast to Model IV, Model III had more intrusion in the posterior compared to anterior teeth. Facial movements of posterior teeth were detected in the third and fourth models. Incisor teeth showed facial movements among all of the models except for the lateral incisor in the third model. CONCLUSIONS: Each model of force application, causes different outcomes and side effects which is beneficial in certain clinical situations.

An expansion to the Nägerl's theory of proportionality in reduced alveolar bone height models: a 3D finite element analysis.

INTRODUCTION: Orthodontic tooth movement is a basic theme in an orthodontic treatment. According to Nägerl, A nearer force application to the center of resistance will bring a farther center of rotation to the center of resistance. The main goal of this study was to evaluate this theory of proportionality by Finite element method (FEM) and find out its applicability in a bone loss situation. MATERIALS AND METHODS: Three 3D FEM of an upper central incisor were designed in Solidworks 2016, the first one with a healthy bone height (model 1), with 3 mm of bone loss (model 2) and with 4.5 mm of bone loss (model 3). An 0.5 N force was applied in different predefined locations on the labial surface of the crown in model 2. This was 0.2 N for the model 3. The exact location of the center of resistance (Cres), center of rotation (Crot) for each force application point was calculated using a C++ code specially design for this study in all models. RESULTS: An apical shift of the Cres positions were shown in gradual steps of bone loss from 7.9708 mm incisal from the apex to 6.6292 mm in model 2 and 5.6105 mm in model 3. Modification of the location of the Crot in different force magnitudes and points of force applications were shown whit a constant a*b. CONCLUSION: In healthy teeth and teeth with alveolar bone loss, Cres located in the apical third of the root. The product of the distance between the point of force application and Cres ("a") and the Cres and Crot ("b") is constant, thus; Nägerl theory is applicable in both healthy and reduced bone height. In this way, applying a single force nearer to the cervical point will result in a more apical location of the Crot, reducing the angle change in the long axis of the tooth.

Comparison of the debonding force of metal, glass and polyethylene Fiber reinforced composite retainers: Mechanical and finite element analyses.

OBJECTIVE: The studies evaluating the efficiency of fiber reinforce composite (FRC) retainers are few and contradictory. This study aimed to compare the debonding force of metal, glass FRC (GFRC) and polyethylene FRC (PFRC) retainers, assess the interactions between the materials and forces, and pattern of load distribution by finite element analysis (FEA). MATERIALS AND METHODS: Forty-eight sound lower incisors were collected and randomly assigned to 3 groups (n=8; each sample included 2 teeth). Next, 15mm of the three retainers (multi-stranded metal wire, GFRC, and PFRC) were bonded to the lingual surface of the teeth and debonding force was measured by a universal testing machine. For FEA, 3D models were designed. The data related to geometrical models and material properties were transferred to ANSYS software. A 187-Newton load was applied to the incisal edge of the two centrals. Then different parameters were assessed. The three groups were compared by one-way Anova and Tukey's test. Type one error was considered to be 0.05. RESULTS: The debonding force decreased in the order: Metal (143.71N)≥GFRC (108.29N)>PFRC (45.08N). The difference between metal retainer and GFRC was not significant. In contrast, PFRC group showed significantly lower debonding force compared to other groups (P<0.05). FEA showed stress peak value in metal-composite interface. Maximum total deformation was noted in central, followed by lateral and canine. CONCLUSIONS: Glass-FRC can serve as an alternative to metal retainers as the difference in debonding force is not significant. However, the difficulty of repairing or replacing the Glass-FRC should be taken into account given the large number of failure in the interproximal dental area.

Effects of Diode and Nd:YAG Laser Irradiation on Friction Forces Between Two Types of Ceramic Brackets and Rhodium-Coated Archwires.

Introduction: Ceramic brackets have gained increasing popularity among dental clinicians and orthodontic patients but friction is a major concern when using them. This study sought to assess the effects of diode and Nd:YAG (neodymium-doped yttrium aluminum garnet) laser irradiation on friction forces between two types of ceramic brackets and rhodium-coated esthetic archwires. Methods: Thirty polycrystalline and 30 poly-sapphire brackets were divided into 6 groups (n=10) as follows: (I) control polycrystalline brackets (no laser irradiation), (II) polycrystalline brackets subjected to diode laser irradiation, (III) polycrystalline brackets subjected to Nd:YAG laser irradiation, (IV) control poly-sapphire brackets (no laser irradiation), (V) poly-sapphire brackets subjected to diode laser irradiation, and (VI) poly-sapphire brackets subjected to Nd:YAG laser irradiation. The bracket slots were laser-irradiated on a custom-made table. Sixty 5-cm pieces of rhodium-coated archwires were used for the friction test in a universal testing machine at a speed of 10 mm/min. Ten brackets from the six groups underwent scanning electron microscopy (SEM), X-ray diffraction (XRD) and energy-dispersive X-ray spectroscopy (EDX). Results: The frictional resistance value of polycrystalline brackets was significantly higher than that of poly-sapphire brackets, irrespective of laser type (P <0.05). Irradiation of diode and Nd:YAG lasers, compared with the control group, had no significant effect on friction, irrespective of bracket type (P >0.05). Conclusion: It appears that diode and Nd:YAG laser irradiation cannot significantly decrease the friction. Future studies are warranted on different laser types with variable exposure.

Shear bond strength of APC Plus adhesive coated appliance system to enamel in wet and dry conditions: An in vitro study.

OBJECTIVE: It is claimed that a hydrophilic primer, called the moisture insensitive primer (MIP), can be used with both dry and wet enamel surfaces. This study sought to assess the shear bond strength (SBS) of APC Plus adhesive coated appliance system to enamel using MIP in wet and dry conditions. MATERIALS AND METHODS: This in vitro experimental study evaluated 24 extracted maxillary premolars with intact buccal enamel. The teeth were randomly divided into two groups (n=12), and APC Plus premolar brackets were bonded to their buccal surface using moisture insensitive primer (MIP) under wet and dry enamel conditions. The SBS values were measured by a universal testing machine. The adhesive remnant index (ARI) score was also determined under a stereomicroscope. Data were analyzed using t-test and Mann-Whitney test at P<0.05 level of significance. RESULTS: The SBS in wet condition was significantly lower than that in dry condition (mean value of 18.37MPa versus 25.5MPa, P<0.001). The two groups had no significant difference regarding the ARI scores (P>0.05). However, in both groups, less adhesive was left on the tooth surface. This suggests that bond failure occurred at the adhesive-enamel interface. CONCLUSIONS: APC Plus adhesive coated appliance system in combination with hydrophilic MIP can be effective in clinical conditions with high risk of moisture contamination.

The Effect of Remineralizing Agents With/Without CO2 Laser Irradiation on Structural and Mechanical Properties of Enamel and its Shear Bond Strength to Orthodontic Brackets.

Introduction: Remineralizing agents may be used for the treatment of white spot lesions (WSLs) prior to bracket bonding. However, some concerns exist regarding their possible interference with the etching and bonding process, negatively affecting the bond strength. This study aimed to assess the effect of two remineralizing agents with/without CO2 laser irradiation on the mechanical properties and shear bond strength (SBS) of demineralized enamel to the orthodontic bracket. Methods: This study evaluated 60 premolar teeth in 6 groups (n=10) as follows: (I) sound enamel, (II) demineralized enamel, (III) Nupro remineralizing agent (N), (IV) Nupro and CO2 laser (N/L), (V) Teethmate remineralizing agent (T), and (VI) Teethmate and CO2 laser (T/L). The remineralizing agents were applied to the enamel surfaces after their immersion in a demineralizing solution for 5 days. In groups IV and VI, the CO2 laser with a 10.6 µm wavelength, 10 ms pulse duration, a 50 Hz repetition rate, 0.3 mm beam diameter and 0.7 W power was irradiated after applying the remineralizing agents. Brackets were bonded to the enamel surfaces and SBS was measured by a universal testing machine. For the assessment of enamel microhardness, 20 sections of molar teeth were divided into 4 groups (n=5; N, N/L, T, T/L) and their microhardness was measured before demineralization, after demineralization and after remineralization. X-ray diffraction (XRD) analysis, field-emission scanning electron microscopy (FESEM) and energy-dispersive spectrometry (EDS) were carried out to assess the formation of hydroxyapatite. The atomic percentages of the C, O, P, Ca, Na, Si, F and Ca/P ratio were determined by EDS analysis. Results: The SBS significantly decreased in group II (P<0.001). There was no significant difference among the groups I, III, IV, V and VI (P<0.05). This finding was similar to the microhardness results, which showed an increase in microhardness after remineralization (P<0.05), with no difference among the remineralizing agents. The Ca/P ratio was the highest in the Nupro group and the lowest in the demineralized group. Conclusion: Remineralizing agents can significantly improve the microhardness and structural properties of demineralized enamel to a level similar to that of sound enamel with no adverse effect on SBS to orthodontic brackets.

Cephalometric and Anthropometric Changes and Their Relation to Patients' Satisfaction After Orthognathic Surgery.

OBJECTIVE: The aim of this prospective study was to evaluate the correlation between cephalometric and anthropometric facial changes and satisfaction level of class III patients after bimaxillary orthognathic surgery. METHODS AND MATERIALS: Totally, 29 class III patients (mean age = 24.23 ±â€Š4.2) undergoing one-piece Lefort 1 osteotomy and mandibular setback were included. Pre- and postoperative lateral cephalograms were taken. Thirteen cephalometric and 17 anthropometric facial measurements were evaluated. A 6-item questionnaire of Rustemeyer's study was used to assess patient's satisfaction after surgery. The Wilcoxon signed-rank test, paired sample t test and Spearman's correlation analysis were used as statistical analysis. RESULTS: Facial aesthetic and masticatory improvement was highly significant (P < 0.001), while opinion differences between patients and relatives/friends were not significant (P = 0.334). Increased upper lip length (P = 0.037) and decreased nasal tip protrusion-nose height index (P = 0.017) correlated positively with aesthetic improvements after surgery. CONCLUSION: Although the association between parameters and satisfaction questionnaire was found, other influential factors should be considered before surgery as well.

Anthropometric Facial Changes After Orthognathic Surgery and Their Relation With Oral Health Related Quality of Life.

PURPOSE: The aim of the present study was to determine the impacts of orthognathic surgery on soft tissue on frontal and profile views and their relation with patient's quality of life. METHODS: Twenty-nine patients with severe skeletal class III malocclusion who were candidate for bimaxillary orthognathic surgery consisted of 1-piece Lefort I surgery with bilateral sagittal split osteotomy were selected. Oral health was assessed by short from of Oral Health Impact Profile-14 questionnaire. Facial anthropometric measurements were conducted before starting any treatment and 6 months after orthognathic surgery according to Farkas anthropometric study. The correlation between facial changes due to treatment and oral health were tested by Pearson correlation analysis. RESULTS: No significant differences were observed in Oral Health Impact Profile-14 scores with regard to genders. Decreased vermilion total upper lip height index correlates positively with feeling difficult to relax. Increasing in medial-lateral cutaneous upper lip height index correlates negatively with dissatisfaction with diet. Increased upper face-face height index correlates positively with feeling uncomfortable to eat any foods and feeling a bit irritable with other people. CONCLUSION: Oral health-related quality of life can be affected not only by the objective aesthetic criterion but also by different factors like their attitude toward aesthetic, surgery side effects.

Comparing short dental implant and standard dental implant in terms of marginal bone level changes: A systematic review and meta-analysis of randomized controlled trials.

PURPOSE: To compare short implants (SH; 4-8 mm) to standard implants (ST; longer than 8 mm) in edentulous jaws, evaluating pri-implant marginal bone levels (MBLs) changes, implant failures (IFs), complications, and prosthesis failures (PFs). MATERIALS AND METHODS: Electronic searches were conducted through the PubMed, Web of Science, EMBASE, Scopus, the Cochrane Central Register of Controlled Trials, and ClinicalTrials.gov to locate all randomized controlled trials (RCTs) comparing SH to ST. Meta-analysis procedures were performed on the weighted mean difference (WMD) and standardized mean difference (SMD) of MBLs using Stata. RESULTS: Twenty-three articles were included in this review. The WMD of MBLs when comparing SH to ST in both jaws up to 1-year follow-up was statistically significant preferring SH (WMD: -0.09 [CI: -0.12, -0.06], I2 : 67.0%). The efficacy of SH vs ST on SMD of MBLs was moderate (SMD: -0.43 [CI: -0.57, -0.28], I2 : 55.7%). There were no significant differences in IF (RR: 0.75 [0.44,1.27]) and PF (RR: 0.58 (0.22,1.581), and significantly higher biological complications (RR: 0.25 [0.15, 0.40]) for SH was observed compared to the ST in both jaws up to 1-year follow-up. CONCLUSIONS: SH and ST implants showed the comparable outcomes except biological complication preferring SH. Future systematic review and meta-analysis with longer and larger RCTs are required to confirm the present outcomes.

Comparison of Short and Standard Implants in the Posterior Mandible: A 3D Analysis Using Finite Element Method.

OBJECTIVES: This study aimed to analyze functional stresses around short and long implant-supported prostheses with different crown heights. MATERIALS AND METHODS: Four three-dimensional (3D) models were designed with SolidWorks 2015. In models 1 (control) and 2, three dental implants (second premolar 4.1×8 mm, molars: 4.8×8 mm) were placed. In models 3 and 4, three dental implants (second premolar 4.1×4 mm, molars: 4.8×4) were placed. Residual bone height was 10 mm in groups 1 and 2 (grafted bone) models and 6 mm in groups 3 and 4. The crown heights were modeled at 11.5 mm for groups 1 to 3, and 15 mm for group 4. The applied oblique force was 220 N to simulate chewing movements. The maximum von Mises and principal stresses on the implants and the supporting tissues were compared using the 3D finite element method. RESULTS: In all models, the highest stress value was seen within the most coronal part of bone (crestal bone), which was cortical or grafted bone. The highest stress values in the bone supporting the implant neck were seen in the premolar region of each model, especially in model 4 (291.16 MPa). The lowest stress values were demonstrated in the molar region of model 3 (48.066 MPa). The model 2 implants showed the highest von Mises stress concentrated at their neck (424.44 MPa). CONCLUSIONS: In atrophic posterior mandible with increased crown height space, short implants with wider diameter seem to be a more feasible approach compared to grafting methods.

A comparison of mechanical characteristics of four common orthodontic loops in different ranges of activation and angular bends: The concordance between experiment and finite element analysis.

PURPOSE: Several methods have been used to analyse different characteristics of orthodontic loops, which are generally divided into two categories: Experimental methods, Analytical and numerical methods such as finite element methods (FEM). The main goal of this study was to compare the results of FEM and experimental methods in determining mechanical characteristics (moment, force and M/F in various ranges of activation and different angular bends) of four common orthodontic loops to find the level of concordance between them. METHODS AND MATERIALS: Experimental method: 60 closing loops were prepared and divided into four groups. Universal testing machine was used for two reasons: tensile tests were performed to check the horizontal force component; compression tests were designed to check the vertical force component. To measure the moment at the two ends of the loops, they were activated by 0.1mm, 0.3mm, 0.7mm, 1mm, 1.25mm and 1.5mm. The vertical component of the force was calculated at the centre of the loops. Each group was divided to three subgroups, depending on the amount of applied angular bend: 0°, 20°, 40°. Finite element method (FEM): three-dimensional model loops were designed by special software. Then, strong meshing software meshed them. Loops were activated in the same range attempted in the experimental method. Then, force, moment and M/F were assessed. RESULTS: It can be understood from the results of both methods that the values of force and moment increase when the activation range and angular bend increase, and M/F increases when the activation range decreases and angular bend increases. The highest concordance between the two methods was related to M/F, force and moment. CONCLUSION: Experimental results and FEM predictions are in good agreement when determining the mechanical characteristics of the loops.

Stress Distribution in Splinted and Unsplinted Implant-Supported Maxillary Overdentures: A 3D Finite Element Analysis.

INTRODUCTION: This study was accomplished to assess the biomechanical state of splinting in implant-supported maxillary overdentures. MATERIALS AND METHODS: Two models of maxillary overdentures were designed in SolidWorks 2011. The first model included 4 separate implants and ball abutments, whereas the second one included 4 splinted implants connected with a bar. Evaluation was performed in ANSYS Workbench software with 200 N load applied at the molar-premolar region, bilaterally. The maximum equivalent stress and strain (von Mises) was recorded and analyzed along a path between the implants in the crestal bone and the prosthetic attachments. RESULTS: First model presented higher values of strain in prosthetic attachment and higher values of von Mises stress in crestal bone. The second model presented higher stress concentration in the gingival tissue of premolar area (near the bar), whereas the peak stress values were reported within the most distal part of the soft tissue support of the prosthesis in the first model (unsplinted). CONCLUSION: Splinting maxillary overdentures implants is associated with significant lower stress levels in the surrounding bone tissue.

Effect of Quaternary Ammonium Salt on Shear Bond Strength of Orthodontic Brackets to Enamel.

OBJECTIVES: This study sought to assess the effect of quaternary ammonium salt (QAS) on shear bond strength of orthodontic brackets to enamel. MATERIALS AND METHODS: In this in vitro experimental study, 0, 10, 20 and 30% concentrations of QAS were added to Transbond XT primer. Brackets were bonded to 60 premolar teeth using the afore-mentioned adhesive mixtures, and the shear bond strength of the four groups (n=15) was measured using a universal testing machine. After debonding, the adhesive remnant index (ARI) score was determined under a stereomicroscope. Data were analyzed using one-way ANOVA. RESULTS: The mean and standard deviation of shear bond strength of the control and 10%, 20% and 30% groups were 23.54±6.31, 21.81±2.82, 20.83±8.35 and 22.91±5.66 MPa, respectively. No significant difference was noted in shear bond strength of the groups (P=0.83). Study groups were not different in terms of ARI scores (P=0.80). CONCLUSIONS: The results showed that addition of QAS to Transbond XT primer had no adverse effect on shear bond strength of orthodontic brackets.

Effect of Sodium Fluoride Mouthwash on the Frictional Resistance of Orthodontic Wires.

OBJECTIVES: The friction between the brackets and orthodontic wire during sliding mechanics inflicts difficulties such as decreasing the applied force and tooth movement and also the loss of anchorage. Therefore, many studies have focused on the factors that affect the friction. The purpose of this study was to assess the effect of 0.05% sodium fluoride mouthwash on the friction between orthodontic brackets and wire. MATERIALS AND METHODS: Four types of orthodontic wires including rectangular standard stainless steel (SS), titanium molybdenum alloy (TMA), nickel-titanium (NiTi) and copper-nickel-titanium (Cu-NiTi) were selected. In each group, half of the samples were immersed in 0.05% sodium fluoride mouthwash and the others were immersed in artificial saliva for 10 hours. An elastomeric ligature was used for ligating the wires to brackets. The frictional test was performed in a universal testing machine at the speed of 10 mm/minute. Two-way ANOVA was used for statistical analysis of the friction rate. RESULTS: The friction rate was significantly higher after immersion in 0.05% sodium fluoride mouthwash in comparison with artificial saliva (P=0.00). Cu-NiTi wire showed the highest friction value followed by TMA, NiTi and SS wires. CONCLUSIONS: According to the results of the current study, 0.05% sodium fluoride mouthwash increased the frictional characteristics of all the evaluated orthodontic wires.

Asymmetric Head Gear: A Comparison between Unilateral Outer Bow Expansion and Unilateral Outer Bow Shortening - an Energy Approach using the Finite Element Method.

OBJECTIVE: To compare the influence of outer bow length difference and unilateral outer bow expansion on the 'asymmetric effect' of the headgear. METHODS: Twelve 3D finite element models of a headgear with two tubes were designed, which were similar except for the outer bow length or the degree of unilateral expansion in Solid-Works 2011. A 3N force was applied to the outer bow ends in ANSYS Workbench 12.1 and the distalising, lateral forces to molars, moments and the energy of the system were evaluated. RESULTS: As the degree of unilateral expansion increased, the net differences in all findings were increased up to a point, and then changed. There was an increasing pattern in the length difference group. Buccal movement was observed in the intact/shorter side molar. CONCLUSION: Unilateral shortened outer bow asymmetric headgears are more efficient and more predictable in clinical application than the unilateral outer bow expansion.

Finite element analysis of the convergence of the centers of resistance and rotation in extreme moment-to-force ratios.

The aim of this study was to investigate how very high and very low M/F ratios affect the location of the center of rotation (CRo). A 3D model of a mesiodistal slice of the mandible was used for this purpose. The model comprised the lower right central incisor, its PDL, the spongy and cortical bone, and a bracket on the labial surface of the bracket. A couple of 1N was applied to the bracket slot to find the level of the center of resistance (Cre). In a second stage, we attempted to produce bodily movement by applying the appropriate M/F ratio. M/F ratios of ±100, 200, 400, and 800 were applied to the last tenths of a millimeter of a pre-activated loop. Higher M/F ratios with positive or negative values, at constant force, increased both incisal and apical movements. The change in the tooth inclination before and after force application matched the difference produced by the different M/F ratios. It was found that a single center of rotation can be constructed for any tooth position. However, this single point does not act as the center of rotation during the entire movement.