Mechanical properties of Opus closing loops, L-loops, and T-loops investigated with finite element analysis

Friction and Forces in Orthodontics: Understanding Space Closure

Orthodontic space closure is a critical aspect of treatment aimed at the correct positioning of teeth and is linked to tooth movement and optimal biomechanics. Therefore, the goal of this case study is to elucidate the process, describing the challenges encountered and the solutions adopted, with a focus on the frictionless technique and the use of devices like the Opus Loop to close spaces. Sliding mechanics, known for high friction, and segmental mechanics, characterized by low friction and continuous adjustment, are two significant technologies used. In this specific case, the frictionless methods applied to a 23-year-old female patient with protruding superior labial incisors included: extraction of the first premolars in all four quadrants, followed by consecutive wiring. Retraction was performed using an Opus Loop, significantly improving the patient's facial profile and dental arch over the next year and a half. As a result, the study demonstrates that the Opus Loop greatly reduces friction forces and offers an effective mechanism to influence tooth movement in orthodontic treatment regimens.

Geometrical Effects of Two Different Space Closing Loops and Its Forces and Moments—A FEM Study

Objective

To evaluate the geometrical effects of double keyhole loop (DKHL) and T-loop and its forces and moments during en mass space closure using finite element method.

Materials and Methods

A 3-dimensional finite element model of maxillary arch was created and stimulated for first premolar extraction case with 0.022 slot Roth prescription bracket. DKHL and T-loop arch wire were created using 19×25 stainless steel and was opened 1 mm for activation using 2 different methods. The study was divided into 2 groups based on the loop design, method of activation, and degree of Gable bend. The stress distribution, tooth displacement, and moment-force ratio were calculated.

Result

The overall stress distribution was more or less uniform in all the groups. However, maximum von Mises stress was observed in the second premolar region for both the groups. There was greater torque and vertical control in the anterior segment and better anchorage control in posterior segment with increase in degree of Gable bend for both the loops activated using ligature tie. Moment-force ratio of 8-10 was achieved for both the loops.

Conclusion

Therefore, DKHL was as efficient as T-loop in producing the desirable biomechanical properties during en mass space closure.

Mechanical force system of double key loop with finite element analysis

Background

The mechanics of double key loop (DKL) are not well defined, and this finite element study was designed to explore its force system.

Methods

A simplified 3-dimensional finite element model of single and double key loops with an archwire between the lateral incisor and second premolar was established in Ansys Workbench 17.0. Activation in Type-1 (retraction at the distal end), Type-2 (retraction at the distal key) and Type-3 (Type-2 plus ligation between keys) was simulated. The vertical force, load/deflection ratio and moment/force ratio of stainless-steel and titanium-molybdenum alloy (TMA) loops were calculated and compared.

Results

The double key loop generated approximately 40% of the force of a single key loop. Type-2 loading of DKL showed a higher L/D ratio than Type-1 loading with a similar M/F ratio. Type-3 loading of DKL showed the highest M/F ratio with a similar L/D ratio as single key loop. The M/F ratio in Type-3 loading increased with the decreasing of retraction force. The DKL of TMA produced approximately 40% of the force and moment compared with those of SS in all loading types. When activated at equal distances below 1 mm, the M/F ratios of SS and TMA DKL with equal preactivation angles were almost the same.

Conclusion

The M/F ratio on anterior teeth increases with the preactivation angle and deactivation of DKL. The M/F ratio at a certain distance of activation mainly depends on the preactivation angle instead of the wire material. TMA is recommended as a substitute for SS in DKL for a lower magnitude of force.

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

INTRODUCTION

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Finite element analysis of archwire parameters and activation forces on the M/F ratio of vertical, L- and T-loops

Background

The ability of a loop to generate a certain moment/force ratio (M/F ratio) can achieve the desired tooth movement in orthodontics. The present study aimed to investigate the effects of elastic modulus, cross-sectional dimensions, loop configuration geometry dimensions, and activation force on the generated M/F ratio of vertical, L- and T-loops.

Methods

A total of 120 three-dimensional loop models were constructed with the Solidworks 2017 software and used for simulating loop activation with the Abaqus 6.14 software. Six vertical loop variations, 9 L-loop variations, and 9 T-loop variations were evaluated. In each group, only one parameter was variable [loop height, ring radius, leg length, leg step distance, legs distance, upper length, different archwire materials (elastic modulus), cross-sectional dimension, and activation force].

Results

The simulation results of the displacement and von Mises stress of each loop were investigated. The maximum displacement in the height direction was recorded to calculate the M/F ratio. The quantitative change trends in the generated M/F ratio of the loops with respect to various variables were established.

Conclusions

Increasing the loop height can increase the M/F ratio of the loop. This increasing trend is, especially, much more significant in T-loops compared with vertical loops and L-loops. In vertical loops, increasing the ring radius is much more effective than increasing the loop height to increase the M/F ratio of the loop. Compared with SS, TMA archwire loops can generate a higher M/F ratio due to its lower elastic modulus. Loops with a small cross-sectional area and high activation force can generate a high M/F ratio. The introduction of a leg step to loops does not increase the M/F ratio of loops.

Analysis of reversed L-loops as closing loops with anterior intrusive force

OBJECTIVE

Intrusive forces on anterior brackets are preferable for avoiding overbite deepening. Reversing plain L-loops may create such advantageous force system during space closure.

DESIGN

Force systems of reversed L-loops were compared with T-loops at three interbracket distances (IBD).

SETTING

Computational study.

METHODS

Using finite element analysis, loop response during simulated loop-pulling was determined for plain reversed L- and T-loop configurations at three IBDs and two sizes. Force systems were calculated on both loop ends for two activation forces.

RESULTS

The 12 mm IBD reversed L-loops had almost equal M/F ratios in opposite directions at both ends. A small intrusive force was found at the canine bracket (CB). The 6 mm IBD reversed L-loops showed larger M/F ratios and extrusive forces at the premolar bracket (PB) and smaller M/F with intrusive forces at CB. The force system of 12 mm IBD T-loops showed the similar force systems as off-centered V-bends with extrusive force at CB, whilst plain 6 mm IBD T-loops showed properties similar to centered V-bends with less extrusive force at CB.

CONCLUSIONS

Reversed L closing loops placed no extrusive force on the CB end at various IBDs, indicating that reversed loops will generate an intrusive force at anterior teeth during space closure.

Comparative assessment of the efficacy of closed helical loop and T-loop for space closure in lingual orthodontics-a finite element study

BACKGROUND

Retraction in lingual orthodontics has biomechanical differences when compared to labial orthodontics, which is not yet established. Thus, we have intended to compare the biomechanical characteristics of closed helical loop and T-loop on 1 mm activation with 30° of compensatory curvatures during retraction in lingual orthodontics.

METHODS

STb lingual brackets were indirectly bonded to maxillary typhodont model that was scanned to obtain FEM model. Closed helical loop (2 × 7 mm) and T-loop (6 × 2 × 7 mm) of 0.016″ × 0.016″ TMA wire were modeled without preactivation bends. Preactivation bends at 30° were given in the software. Boundary conditions were set. The force (F) and moment (M) of both the loops were determined on 1 mm activation, using ANSYS software. M/F ratio was also calculated for both the loops.

RESULTS

T-loop exerted less force, thus increased M/F ratio as compared to closed helical loop on 1 mm activation.

CONCLUSIONS

When torque has to be preserved in the anterior segment during retraction in lingual orthodontics, T-loop can be preferred over closed helical loop.

Innovative design of closing loops producing an optimal force system applicable in the 0.022-in bracket slot system

INTRODUCTION

Most closing loops designed for producing higher moment-to-force (M/F) ratios require complex wire bending and are likely to cause hygiene problems and discomfort because of their complicated configurations. We aimed to develop a simple loop design that can produce optimal force and M/F ratio.

METHODS

A loop design that can generate a high M/F ratio and the ideal force level was investigated by varying the portion and length of the cross-sectional reduction of a teardrop loop and the loop position. The forces and moments acting on closing loops were calculated using structural analysis based on the tangent stiffness method.

RESULTS

An M/F ratio of 9.3 (high enough to achieve controlled movement of the anterior teeth) and an optimal force level of approximately 250 g of force can be generated by activation of a 10-mm-high teardrop loop whose cross-section of 0.019 × 0.025 or 0.021 × 0.025 in was reduced in thickness by 50% for a distance of 3 mm from the apex, located between a quarter and a third of the interbracket distance from the canine bracket.

CONCLUSIONS

The simple loop design that we developed delivers an optimal force and an M/F ratio for the retraction of anterior teeth, and is applicable in a 0.022-in slot system.

Effect of apical portion of T-, sloped L-, and reversed L-closing loops on their force systems

OBJECTIVE

To investigate the effect of the position of the apical portion of closing loops on the force system at both loop ends.

MATERIALS AND METHODS

T-loops were compared with backward-sloped L-loops (SL) and reversed L-loops (RL). SL-loops were directed toward the anterior side; RL-loops were directed toward the posterior side. Loop response to loop pulling was determined with finite element analysis at six positions of the apical loop portion for 12-mm interbracket distance and 8-mm loop length and height. Three-dimensional models of the closing loops were created using beam elements with the properties of stainless steel. Loop responses (horizontal load/deflection, vertical force, and moment-to-force ratio) at both loop ends were calculated as well as at 100 g and 200 g activation forces.

RESULTS

T-, SL-, and RL-loops with the same position of the apical portion showed approximately the same force system at both loop ends. This behavior was found across the investigated range through which the loops were moved (interbracket center to posterior bracket).

CONCLUSIONS

The center of the apical portion determined the force system of the closing loops regardless of the position of the loop legs. The centers of the apical portion of the T-, SL-, and RL-loops acted like V-bend positions.

T-loop force system with and without vertical step using finite element analysis

OBJECTIVE

To investigate the effect of vertical steps on a T-loop force system at three interbracket distances (IBDs) and their association with V-bends.

MATERIALS AND METHODS

Loop response during simulated loop pulling was determined for 18 T-loop configurations (6-, 9-, and 12-mm IBD with a 2.5-mm canine bracket (CB) end and 0- (plain), 0.5-, or 1-mm vertical step). Loop length-by-height was 8 × 8 or 10 × 10 mm. Horizontal load/deflection, vertical force (Fy), and moment-to-force (M/F) ratios at loop ends were determined for 100-g and 200-g activation by finite element analysis.

RESULTS

Plain, 12-mm IBD T-loops showed similar force and moment responses as off-centered V-bends (greater moment close to V-bend) without change in moment direction at the premolar bracket (PB) end; plain, 6-mm IBD T-loop responses were similar to those of centered V-bends (equal, opposing moments at each end). Adding vertical steps to the T-loops raised the M/F ratio at the PB ends enough to produce root movement, while lowering the M/F ratios at the CB ends. Increasing the step bends for shorter IBDs increased Fys and caused rapid changes in M/F ratios. Unlike plain T-loops, increasing activation in stepped T-loops caused substantial variations in M/F ratios and in amount and direction of Fys.

CONCLUSIONS

Step bends can dramatically change the force system. Stepped T-loops display combined effects of V-bends and step bends.

Effect of activation and preactivation on the mechanical behavior and neutral position of stainless steel and beta-titanium T-loops

Objective

To quantify, for each activation, the effect of preactivations of differing distribution and intensity on the neutral position of T-loops (7-mm height), specifically the horizontal force, moment to force (M/F) ratio, and load to deflection ratio.

Methods

A total 100 loops measuring 0.017 × 0.025 inches in cross-section were divided into two groups (n = 50 each) according to composition, either stainless steel or beta-titanium. The two groups were further divided into five subgroups, 10 loops each, corresponding to the five preactivations tested: preactivations with occlusal distribution (0°, 20°, and 40°), gingival distribution (20°), and occlusal-gingival distribution (40°). The loops were subjected to a total activation of 6-mm with 0.5-mm iterations. Statistical analysis was performed using comprised ANOVA and Bonferoni multiple comparison tests, with a significance level of 5%.

Results

The location and intensity of preactivation influenced the force intensity. For the M/F ratio, the highest value achieved without preactivation was lower than the height of the loop. Without preactivation, the M/F ratio increased with activation, while the opposite effect was observed with preactivation. The increase in the M/F ratio was greater when the preactivation distribution was partially or fully gingival.

Conclusions

Depending on the preactivation distribution, displacement of uprights is higher or lower than the activation, which is a factor to consider in clinical practice.