INTRODUCTION

The orthodontic response to a load is divided into three elements of tooth displacement: initial strain, lag phase, and progressive tooth movement. An initial strain of 0.4 to 0.9 mm occurs within about 1 week because of periodontal ligament displacement, bone strain, and extrusion. Initial tooth displacement occurs within seconds, and this leads to a buildup of stresses within the periodontal ligament, which is supposed to be a critical rate-limiting step for the osteogenic response responsible for bone remodeling.1

Previously, initial tooth displacements and resulting stresses within the periodontal ligament were studied with the use of both analytical and physical models.

Synge2 determined analytically the stress distributions for two root shapes: a flat two-dimensional wedge and a three-dimensional cone of revolution. Dyment and Synge3 determined values for elastic coefficients of the periodontal ligament. Three-dimensional stress distributions were identified by Haack and Heft.4 More recently, initial tooth displacements with stress in the periodontal ligament under orthodontic loading were studied by Yoshida et al,5 Jeon et al,6 and Geramy,7 who used the finite element method. However, attempts at mathematical modeling through an analytical approach, as well as with photoelastic techniques, and many studies in which finite element methods were used have been characterized by assumptions such as the following:

• —The anatomy of the root, periodontal ligament, and alveolar bone was represented by idealized geometric forms.

• —The physical characteristics of the supporting structures were assumed to be homogeneous, isotropic, and linear, whereas the structures of interest were nonhomogeneous, anisotropic, and nonlinear.

These shortcomings in the studies on initial tooth displacement under the influence of external force could be overcome by the noninvasive techniques of laser holography. Tooth movements were studied with the use of laser holography by Burstone et al,8 Burstone and Pryputniewciz,9 Dermaut et al,10–12 and Vanden Bulcke et al.13 Billiet et al14 studied initial displacements on a macerated human skull with the use of double-exposure holography.

Retraction of canines into the space created by extraction of first premolars is one of the most exacting procedures in successful orthodontic treatment. Current methods used for canine retraction consist of frictional or sliding and frictionless mechanics. In an attempt to discern the effects of various force systems for canine retraction, a series of studies were conducted.

The stresses produced in the periodontal ligament when the crown of a tooth is subjected to a force have important ramifications in the study of orthodontic tooth movement and periodontal research. Generally, it is agreed that uncontrolled tipping produces a concentration of stresses within the periodontal ligament, and this can be detrimental to periodontal health, particularly in the adult orthodontic patient.15 The constant search for an orthodontic force system that would produce near bodily tooth movement has been ongoing.

The objective of this study was to estimate and compare the magnitude and direction of initial displacement of the canine as produced by four canine retraction springs.

MATERIALS AND METHODS

A freshly macerated mandible that met the criteria of well-aligned teeth and intact dental arches was obtained 6 hours post mortem and was stored in Ringer's lactate solution at pH 7.4 at room temperature, to minimize postmortem changes in the mechanical properties of tissues.16 The mandibular first premolars were extracted, and strap-up was done with a 0.018 inch preadjusted edgewise appliance (Roth prescription, 3M Unitek, Monrovia, Calif), such that a 016 × 022 inch SS wire entered passively (Figure 1). The experiment was conducted on the right side of the mandible.

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This experiment was conducted at the Physics Department of Anna University in Chennai. The holographic unit consisted of a helium-neon (He-Ne) laser with a wavelength of 0.06238 micron, as well as a beam splitter, mirrors, beam expanders, an object, a photographic plate and plate holder, and a special table. The mandible was used as the object. Rigid fixation of the mandible was ensured as follows: The mandible was fixed firmly to an optical plate with a cyanoacrylate quick-setting adhesive. It was ligated to the optical plate, and self-curing acrylic was added at the inferior border of the mandible. The optical plate was held firmly with a special clamp that was mounted on a special table; this prevented ground vibrations from reaching the top of the table. The output from the laser was split into two parts by a beam splitter. One part was expanded by a beam expander and was used to illuminate the object. The scattered wave from the object was called the object wave (Figures 2 and 3). The second part was expanded by a beam expander, was reflected by a mirror, and was allowed to superimpose on the object wave on the recording plane, namely, the photographic plate. This wave was called the reference wave, and this procedure gave rise to an interference pattern that formed the hologram once it had been developed and processed. The hologram contained information not only about the amplitude but also about the phase of the object wave. So that the image could be viewed, the hologram was illuminated with another wave, called the reconstruction wave, which was identical to the reference wave used during formation of the hologram.

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The method used to record initial displacement of the canine was double-exposure holographic interferometry. The normal state of the object was recorded on the holographic plate. On the same recording plate before processing, another exposure was given that corresponded to the deformed position of the object (after load application). This doubly exposed plate was processed. On reconstruction, this gave rise to two images: one corresponding to the original position, and another corresponding to the deformed position. These two reconstructed image waves interfered, giving rise to an image with a number of bright and dark fringes on the image (Figure 4). From this fringe pattern, the magnitude and direction of displacement of the object could be calculated. The canine was loaded by the following systems: nickel-titanium (Ni-Ti) closed coil springs, open coil springs each with a 0.030 inch lumen and a 0.010 inch diameter for sliding mechanics, and a PG retraction spring (016 × 022 inch SS) and T-loop retraction spring (TMA, 0.016 × 0.022 inch) for sectional mechanics (Figures 5 through 8). Double-exposure holographs were taken at 30 seconds post loading. Loading was done with a force of 4 oz, 5 oz, and 6 oz for each spring. Force was measured with a Dontrix gauge (ETM Corporation, Glendora, Calif), and a time gap of 15 minutes was provided between recordings. The holographic plates were processed, and the images were photographed.

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Quantitative interpretation was done through adaptation of the equation for fringe interpretation by Charles M. Vest.17 This yielded the displacement Z(X) = Nλ/2, where N refers to the order of the fringes. Through simple counting of the fringes to a given location, the magnitude of displacement could be calculated, and by measurement of the angulation of the fringes in relation to the long axis of the tooth, the direction of displacement could be estimated.

RESULTS

The PG spring produced the greatest displacement for a given force among the force systems used, followed by open coil, closed coil, and T-loop (Table 1).

Table 1.  Magnitude of Displacement

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In relation to the x-axis (ie, mesiodistal displacement), maximum tipping was observed with the open coil spring at 6 oz, followed by the PG spring at 6 oz and the closed coil spring at 6 oz. The T-spring showed minimum tipping at all force levels (Table 2).

Table 2.  Direction of Displacement

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DISCUSSION

The initial displacements produced by four different canine retraction springs were studied through the technique of laser holography. Measurements were taken as prescribed by standard textbooks on laser holography such as Holographic Interferometry by Charles M. Vest.17 The magnitudes of displacement produced by canine retraction springs—two with sliding mechanics (closed coil spring, open coil spring) and two with sectional mechanics (PG spring, T-loop)—were measured and compared. The PG spring produced maximum displacement for a given force, followed by open coil spring, closed coil spring, and T-loop. Total displacement increased proportionately with increases in force, which varied at 4 oz, 5 oz, and 6 oz for each canine retraction spring. The direction of displacement (ie, indicative of the amount of tipping) was highest for the open coil spring, followed by the PG spring, closed coil spring, and T-loop.

Ni-Ti closed coil springs produced a displacement of 6.328 × 10⁻⁴ mm at 4 oz. With a 1 oz increase in force, an increase of 3.164 × 10⁻⁴ mm in magnitude and an increase of 2 degrees in direction were observed. Storey1819 recommended a force of 150 to 200 g for canine retraction. However, the tipping produced would warrant careful calibration of force levels.

Open coil springs produced greater displacement compared with closed coil springs—9.492 × 10⁻⁴ mm at 4 oz, increased by 6.328 × 10⁻⁴ mm for each 1 oz increase in force. However, the tipping was greater by 2 degrees than with the closed coil spring for a given force. Further, it produced significant displacement of the lateral incisor in the opposite direction.

Open coil springs are used for initial retraction of canines in cases of blocked out lateral incisors. Our findings indicate the necessity for careful calibration of force levels and constant monitoring of tipping and periodontal health whenever these are used for initial retraction of canines, particularly in adult orthodontic patients.

Increased tipping coupled with a high magnitude of displacement would produce an increased concentration of stress within the periodontium. From our observations, it is evident that the concentration of stress in the periodontal ligament would be greatest with the PG spring at 6 oz of force, followed by the open coil spring at 6 oz of force.

However, when the force was decreased to 5 oz with the PG spring, both tipping and the magnitude of displacement were drastically reduced. At 4 oz of force, these springs produced tipping that was much less than with the closed coil and open coil springs, as well as a magnitude of displacement of 15.620 × 10⁻⁴ mm, which was equal to that of the open coil spring at 5 oz or the closed coil spring at 4 oz. These findings are in accordance with the recommendations of Paul Gjessing,20 who advocated a distal driving force of 100 to 120 g for the PG spring.

The T-loop produced the lowest magnitude of displacement for a given force. It produced a displacement of 6.328 × 10⁻⁴ mm at 4 oz of force, which was increased by an order of 3.164 × 10⁻⁴ mm for each increase in force of 1 oz. The direction of fringes indicated that this spring produced very much less tipping. The lower magnitude of displacement could have occurred because bodily tooth movement requires higher force levels than does tipping. Burstone21 recommended a force of 200 g for the T-loop retraction spring. Further, the reduced tipping produced by the T-loop coupled with low strain levels would produce a lower concentration of stresses within the periodontal ligament compared with other canine retraction springs.

CONCLUSION

• A force of up to 6 oz can be applied with T-loop retraction spring without producing undue tipping. The T-loop may be preferred whenever retraction with minimal tipping is desired.

• A PG spring may be preferred over other springs whenever a higher magnitude of displacement is desirable for a given force.

• Closed coil springs may be preferred whenever a reasonable magnitude of displacement is required and reasonable tipping is allowed.

• A force of 4 oz appears to be ideal for PG and coil springs.