Continuous arch wire closing loop design, optimization, and verification. Part I

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.

Tooth Movement Efficacy of Retraction Spring Made of a New Low Elastic Modulus Material, Gum Metal, Evaluated by the Finite Element Method

The aim of this study was to evaluate the tooth movement efficacy of retraction springs made of a new β-titanium alloy, “gum metal”, which has a low Young’s modulus and nonlinear super elasticity. Using double loop springs incorporated into an archwire made of gum metal (GUM) and titanium molybdenum alloy (TMA), the maxillary anterior teeth were moved distally to close an extraction space. The long-term movements were simulated by the finite element method. Its procedure was constructed of two steps, with the first step being the calculation of the initial tooth movement produced by elastic deformation of the periodontal ligament, and in the second step, the alveolar socket was moved by the initial tooth movement. By repeating these steps, the tooth moved by accumulating the initial tooth movement. The number of repeating calculations was equivalent to an elapsed time. In the GUM and TMA springs, the anterior teeth firstly tipped lingually, and then became upright. As a result of these movements, the canine could move bodily. The amount of space closure in GUM spring was 1.5 times that in TMA spring. The initial tipping angle of the canine in the GUM spring was larger than that in the TMA spring. The number of repeating calculations required for the bodily movement in the GUM spring was about two times that in the TMA spring. It was predicted that the speed of space closure in the GUM spring was smaller than that in the TMA spring.

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

INTRODUCTION

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

The effect of orthodontic clinical use on the mechanical characteristics of nickel-titanium closed-coil springs

OBJECTIVE

To examine the effect of clinical use on both force retention and the deactivation of closed-coil nickel-titanium (NiTi) springs in a 16-week trial.

METHODS

The force-activation curves for NiTi springs were determined before and after clinical use. The rate of tooth movement and maximum force (MF), hysteresis between activation and deactivation, and mean force of the deactivation plateau (MDF) were examined and correlated as a function of 4, 8, 12 and 16 weeks of clinical use. To recover the force properties, the springs were heat treated at 100°C and the results were compared with the preceding data.

RESULTS

A total of 36 springs were analysed. The MF loss after use was 60, 74, 55, and 48 g for the 4-, 8-, 12- and 16-week springs, respectively. Heat treating had little effect on the MF. Clinical use lowered hysteresis by a mean of 180 g*mm compared with the pre-clinical use data, and heat treating increased the hysteresis by a mean of 59 g*mm above the post clinic testing data. The MDF was nominally 100 g less than the MF. Teeth moved approximately 1 mm/month, independent of the force loss.

CONCLUSIONS

The loss of MF and the lowering of the MDF was not time dependent. Heat treating can partially recover the mechanical properties of the used springs.

Understanding the basis of space closure in Orthodontics for a more efficient orthodontic treatment

Introduction:

Space closure is one of the most challenging processes in Orthodontics and requires a solid comprehension of biomechanics in order to avoid undesirable side effects. Understanding the biomechanical basis of space closure better enables clinicians to determine anchorage and treatment options. In spite of the variety of appliance designs, space closure can be performed by means of friction or frictionless mechanics, and each technique has its advantages and disadvantages. Friction mechanics or sliding mechanics is attractive because of its simplicity; the space site is closed by means of elastics or coil springs to provide force, and the brackets slide on the orthodontic archwire. On the other hand, frictionless mechanics uses loop bends to generate force to close the space site, allowing differential moments in the active and reactive units, leading to a less or more anchorage control, depending on the situation.

Objective:

This article will discuss various theoretical aspects and methods of space closure based on biomechanical concepts.

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 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.

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

INTRODUCTION

The objective of this research was to investigate the mechanical properties at both sides of Opus closing loops by analyzing the effects of loop shape, loop position, coil position, and tipping of the vertical legs.

METHODS

Opus loops were compared with L-loops (with and without a coil) and a T-loop by using finite element analysis. Both upright and tipped vertical loop legs (70°) were tested. Loop response to loop pulling was simulated at 5 loop positions for a 12-mm interbracket distance and 10-mm loop lengths and heights. Three-dimensional models of the closing loops were created by using beam elements with stainless steel properties. The L-loops and Opus loops were directed toward the anterior side. Loop properties (horizontal load/deflection, vertical force, and moment-to-force ratio) at both loop ends were recorded at activation forces of 100 and 200 g.

RESULTS

Upright Opus loops and L-loops showed the highest moment-to-force ratios (8.5-9.3) on the canine bracket when the loop was centered. The Opus loops and L-loops with tipped vertical legs and the T-loop had slightly lower moment-to-force ratios (7.8-8.5), with the maximum values occurring when the loop was placed close to the canine bracket end.

CONCLUSIONS

Upright L-loops showed the highest moment-to-force ratios on canine brackets, whereas backward tipping of the vertical legs shifted mechanical properties closer to those of a T-loop. Loop properties varied with loop configuration and position. Clinicians should understand the specific characteristics of each loop configuration to most effectively exploit them for the desired tooth movements.

Mechanical behaviour of a prototype orthodontic retraction spring: a numerical-experimental study

The purpose of this study was to examine the mechanical behaviour of orthodontic delta retraction springs. Twelve titanium-molybdenum (0.016 × 0.022 inch) delta loops were studied. The springs were analysed by means of the finite element (FE) method and experimental tests using a platform transducer. Each spring was activated from 0 to 6 mm. Statistical analysis of the data was carried out by one-way analysis of variance and Games-Howell parametric multiple comparison test for heterogeneous variances. FE analysis revealed that the stress level varied from 277 to 1273 MPa. At 6.1 mm (773 MPa), the springs were still in the elastic range. Force levels varied from 0.1 N (10 g) to 2.2 N (224 g) at 1.4-8.1 mm of activation for the numerical study and from 0.44 N (45 g) at 1 mm to 2.02 N (206 g) at 6 mm of activation in the experimental study. The spring rate was within the levels that are appropriate for clinical use (34 g/mm). Vertical forces (Fy) showed constancy and were of low magnitude. The anterior moment/force ratio from the experimental tests was 14 at 3 mm of activation decreasing to 10.7, 8.7, and 7.2, for 4, 5, and 6 mm of activation, respectively. The springs could be activated up to 7 mm without exceeding the elastic limit.

Experimental Investigation and Neural Network Modeling for Force System of Retraction T-Spring for Orthodontic Treatment

In this work three different cross section groups of stainless steel T-Spring, for tooth retraction, have been tested; each spring is activated for 1 mm, 2 mm, and 3 mm, and the resultant force system is evaluated by using a testing apparatus. The results showed that when the cross section and activation distances are increased, the horizontal force and moment increased, while for the moment-to-force ratio, the lowest mean value was at the first activation distance of the first group, and the highest mean values were at the third activation distance of the third group. All three groups at all activation distance are insufficient to produce bodily tooth movement. T-springs of the (0.016×0.022 in.) cross section and with frequent activation provide the best in force system production. An artificial neural network model was trained for simulation of the correlation between input parameters: spring cross section and activation distance, and the outputs spring force system. The network model has prediction ability with low mean error of force prediction (5.707%), and for the moment is (4.048%), and it can successfully reflect the results that were obtained experimentally with less costs and efforts.

Optimizing the design of preactivated titanium T-loop springs with Loop software

A TMA (Ormco Corp, Glendora, Calif) T-loop spring (TTLS), preactivated with a gable bend distal to the loop, holds promise for producing controlled tipping of the canines and translation of the posterior segment. However, there is currently no consensus as to where the preactivated gable bend or the loop should be placed, what the height of the loop should be, or how the interbracket distance changes the moments produced. Using the Loop software program (dHal, Athens, Greece), we systematically modified a .017 x .025-in TTLS (10 x 6 mm) that was preactivated with a 45 degrees gable bend distal to the loop, and simulated the effects. As the gable bend was moved posteriorly, the moment increased at the posterior bracket more than it decreased at the anterior bracket. As the loop was brought closer to the anterior bracket, the posterior moment decreased at the same rate that it increased anteriorly. As the loop was increased in size, the moments increased both posteriorly and anteriorly. As the interbracket distance increased, the posterior moment decreased, and the anterior moment remained constant. We concluded that the size of the loop should be slightly increased, to 10 x 7 mm, and it should be placed 2 mm from the anterior bracket, with a preactivation bend of 45 degrees , 4 to 5 mm from the posterior bracket (after 4 mm of activation).

A numerical simulation of orthodontic tooth movement produced by a canine retraction spring

Tooth movements produced by a canine retraction spring were calculated. Although a gable bend and an anti-rotational bend were incorporated into the spring, the canine tipped and rotated initially. Retraction force decreased and moment-to-force ratio increased after the spring legs closed. Then, the initial tipping and rotation began to be corrected. As a result, the canine moved almost bodily after a prolonged period of time. Such tooth movements cannot be estimated from the initial force system. The gable bend decreased tipping movement, but increased rotational movement. On the other hand, the anti-rotational bend decreased rotational movement but increased tipping movement. In other words, one bend decreased the effect of the other, when both bends were incorporated in the spring.

Complete orthodontic load systems on teeth in a continuous full archwire: The role of triangular loop position

INTRODUCTION

A novel approach to characterizing orthodontic spring-generated force and moment systems has been developed. This method allows simultaneous measurement of all 6 force and moment components acting on a tooth.

METHODS

A continuous full archwire space-closure technique was simulated, and the complete force and moment systems acting on the teeth adjacent to the extraction space were measured.

RESULTS AND CONCLUSIONS

The data showed that, in addition to the intended forces and moments, there are nontrivial activation-dependent interactions with the other load components, and these complex relationships are affected by the position of the triangular loop.