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The Gable bend revisited
ORIGINAL ARTICLE
The Gable bend revisited Stanley Braun, DDS, MME,a and Jose´ L. Garcia, DDSb Indianapolis, Ind, and St Louis, Mo Gable bends are frequently incorporated into a variety of loop configurations to provide appropriate moment-to-force (M/F) ratios in the controlled closure of space between individual teeth or groups of teeth. Appropriate magnitudes and occlusogingival locations of the Gable bends are shown to be vital to maintain the neutral position of the closing loop. Otherwise, the clinician has no meaningful reference point from which to judge the spring’s activation to obtain the force aspect in the M/F ratio. A simple means of preserving the neutral position is shown, with the vertical loop as an example that can be applied to many common loop configurations. (Am J Orthod Dentofacial Orthop 2002;122:523-7)
A
variety of vertical loop configurations are used by clinicians to close spaces between individual teeth or groups of teeth. Gable bends are frequently incorporated into the loop configuration to provide a moment to prevent the root apices of the teeth from moving in a direction opposite to that of their crowns (uncontrolled tipping). In more precise terms, the Gable bend is intended to control the dental centers of rotation through an appropriate moment-to-force (M/F) ratio applied at the springs’ attachments to the teeth. It has been shown that the M/F ratios resulting from activating various loop configurations are insufficient to prevent uncontrolled tipping unless Gable bends are included.1-4 When Gable bends, as shown in Figure 1, are placed in the occlusal portion of a vertical loop configuration, an unintended mesiodistal force is introduced. This force will alter the desired mesiodistal force originally intended because of the crossover of the vertical legs. This crossover foreshortens the horizontal wire length between the brackets. Thus, the Gable bend moment and the mesiodistal force are not independent of each other when the clinician is attempting to achieve predictable M/F ratios. Burstone et al5 have shown that the neutral position of the loop configuration has been altered by the introduction of Gable bends. The neutral position can be defined as the horizontal separation of the vertical legs of the spring before the introduction of a horizontal or mesiodistal force. Thus, if the clinician wishes to generate a known mesiodistal force by separating the vertical legs by a a
Clinical Professor of Orthodontics, Vanderbilt University Medical Center. Private practice, St Louis, Mo. Reprint requests to: Dr Stanley Braun, 7940 Dean Rd, Indianapolis, IN 46240; e-mail, [email protected]. Submitted, October 2001; revised and accepted, February 2002. Copyright © 2002 by the American Association of Orthodontists. 0889-5406/2002/$35.00 ⫹ 0 8/1/126727 doi:10.1067/mod.2002.126727
b
given number of millimeters from the neutral position, he or she cannot make the separation because the neutral position has been altered by the Gable bends. If the Gable bends are positioned in the gingival portion of the vertical loop, a mesiodistal force is produced in a direction opposite that produced by the Gable bends in the occlusal portion of the loop. This is the result of the wire lengthening between brackets because of the separation of the vertical legs (Fig 2). This suggests that appropriate sharing of the Gable bends occlusogingivally can produce a moment that does not materially alter the horizontal force; thus, the initial M/F ratio can be more easily controlled and defined by the clinician. By sharing the Gable bends occlusogingivally, it is possible to maintain the neutral position, and the active force can be judged clinically. It is the purpose of this investigation to illustrate a means of providing more reliable, clinically achievable initial M/F ratios with Gable bends shared occlusogingivally. The vertical loop is used as the basic configuration for illustration purposes from which more general clinical guidelines can be developed that apply to all commonly used loop configurations for closing space between individual teeth or groups of teeth. MATERIAL AND METHODS
Portable strain gauge devices (Orthomeasurements, Division of Young Research & Development, Avon, Conn) capable of measuring forces and couples (moments) in a given plane were used (Fig 3). Each device comprised 2 basic components: an enclosed power supply with a digital readout of moments and forces, and an orthodontic bracket-supporting unit that contained appropriate strain gauge configurations that transmitted electronic signals to the digital readout units. The bracket-support units were affixed to a 523
524 Braun and Garcia
American Journal of Orthodontics and Dentofacial Orthopedics November 2002
Fig 1. Vertical loop containing Gable bends in positions ➀ with subsequent vertical leg crossover.
machine tool table that permitted micrometer adjustments of 1 bracket relative to the other linearly with an accuracy of .001 in. A loop configuration could thus be attached to each bracket, at a specific interbracket distance, and moments and forces could be measured at each bracket location (Fig 4). For illustration purposes, four 6-mm vertical loop springs, fabricated from .017 ⫻ .025-in TMA wire (Ormco Corp, Glendora, Calif), were configured as shown in Figure 5. Mean dimensional values of the 4 springs are shown. There are small dimensional variations because the vertical loops were configured as if in a clinical setting. The interbracket dimension shown in Figure 5 represents the average centerline-to-centerline distance of .018-in slot brackets positioned on the second premolar and on the canine. (It was assumed that the first premolar had been removed.)
RESULTS
In the first series of tests, 0°, 5°, 10°, 15°, and 20° Gable bends were placed into the occlusal positions (➀) of the vertical loops (Fig 5). The resultant moments and mesiodistal forces were recorded at each bracket. The mean values obtained for the 4 experimental loops are shown in Table I. In an identical group of 4 vertical loop configurations, Gable bends were placed in position ➁ (Fig 5). The resulting moments and mesiodistal forces obtained, after bracket engagement, are shown in Table II. Both sets of experimental data are shown graphically in Figure 6. DISCUSSION
One can readily see that undesirable mesiodistal forces are generated whenever occlusal (➀) or gingival
Fig 2. Vertical loop containing Gable bends in positions ➁ with subsequent vertical leg separation.
Braun and Garcia 525
American Journal of Orthodontics and Dentofacial Orthopedics Volume 122, Number 5
Fig 3. Instrumentation used to measure mesiodistal forces of 6-mm vertical loop containing Gable bends.
Fig 5. Mean dimensions of vertical loop configuration tested.
Gable bends of 4° are needed in positions ➁ to provide a ⫹54-g force to restore the vertical legs to their neutral position. Maintenance of the neutral position, irrespective of the variations in the vertical loop configuration (eg, T loop, L loop, and the presence of helices), is vital so that the clinician can judge the correct horizontal separation of the vertical legs to achieve a desired initial M/F ratio.6-8 Constructing a graph for every kind of loop configuration is impractical in a clinical setting. As a practical alternative, the clinician can place desired Gable bends in positions ➀, and with pliers Fig 4. Close-up view of vertical loop being tested.
(➁) Gable bends are placed. These are undesirable in the sense that the clinician loses a reference configuration (vertical legs separated and parallel in this experiment) to properly introduce forecastable mesiodistal forces. The neutral position has been lost. For example, if a clinician were to place 10° Gable bends in positions ➀ (Fig 5; graph of Fig 6), a mesiodistal force of ⫺54 g would result. To eliminate this, an equal mesiodistal force in the opposite direction is required to restore the neutral position. The graph in Figure 6 illustrates that
Mean values of moments and forces generated with Gable bends in occlusal positions
Table I.
Occlusal Gable bend (°) 0 5 10 15 20
Moment at each bracket (g mm)
Mesiodistal force* (g)
20 248 563 808 1081
⫺1 ⫺16 ⫺54 ⫺76 ⫺99
*Negative values indicate force direction related to shortened archwire between brackets. All values are to the nearest whole number.
526 Braun and Garcia
American Journal of Orthodontics and Dentofacial Orthopedics November 2002
Fig 6. Graphic presentation of test data obtained for 6-mm vertical loop.
Mean values of moments and forces generated with Gable bends in gingival positions
Table II.
Occlusal Gable bend (°) 0 5 10 15 20
Moment at each bracket (g mm)
Mesiodistal force* (g)
29 117 189 233 271
0 ⫹71 ⫹116 ⫹185 ⫹242
*Positive values indicate force direction related to lengthened archwire between brackets. All values are to the nearest whole number.
hold the wire in similar positions to those of the brackets, and then bring the plier beaks into horizontal positions, simulating the bracket locations. Note the crossover of the vertical legs of the loop. By experimentally placing Gable bends in positions ➁, one can achieve 0 vertical leg overlap. When crossover is 0, the neutral position has been achieved, and the clinician can now introduce the desired mesiodistal force, a portion of the desired M/F ratio. The mesiodistal forces thus obtained and the moments induced by the Gable bends are not completely independent of each other. As the teeth respond to the initial M/F ratio applied, both the moment and the force decrease, each at its own rate. To maintain relative constancy of the M/F ratio, it is desirable that the decay of each be minimized or
consistent. This is primarily achieved through a lowrate spring. Generally, spring rates can be reduced by using low modulus wire and increased wire length (ie, by introducing helices, bypassing intervening brackets as in the segmented arch technique,8 and using T loops) and by altering the wire cross section. A low spring rate is important because it provides improved constancy in the M/F ratio as the teeth move. Constancy of this ratio is important to provide controlled space closure with predictable, relatively constant centers of rotation. Controlled centers of rotation will reduce undesirable tooth “wiggle” and potential tissue damage.9-12 CONCLUSION
It is apparent that Gable bends should be distributed occlusogingivally in all loop configurations to achieve forecastable M/F ratios at the active and reactive teeth. The vertical loop configuration has been used to illustrate a simple method to achieve this. REFERENCES 1. Proffit WR, Fields HW Jr. Contemporary orthodontics. 2nd ed. St Louis: Mosby; 1993. 2. Smith RJ, Burstone CJ. Mechanics of tooth movement. Am J Orthod 1984;85:294-307. 3. Burstone CJ, Koenig HA. Optimizing anterior and canine retraction. Am J Orthod 1976;70:1-19. 4. Miyakawa O, Shiakawa WN, Matsunra T, Hanada K. A new method for finite element simulation of orthodontic appliance–
American Journal of Orthodontics and Dentofacial Orthopedics Volume 122, Number 5
teeth–periiodontium–alveolus system. J Biomech 1985;18:27784. 5. Burstone CJ, van Steenbergen Z, Henley KJ. Modern edgewise mechanics and the segmented arch technique. Glendora (Calif): Ormco Corp; 1995. 6. Burstone CJ. Application of bioengineering to clinical orthodontics. In: Graber TM, editor. Current orthodontic concepts and techniques. 2nd ed. Philadelphia: WB Saunders Co; 1975. p. 230-58. 7. Tanne K, Keonig HA, Burstone CJ. Moment to force ratios and the center of rotation. Am J Orthod Dentofacial Orthop 1988;94:426-31.
Braun and Garcia 527
8. Burstone CJ. The mechanism of the segmented arch technique. Angle Orthod 1966;36:99-120. 9. Reitan K. Continuous bodily movement and its histologic significance. Acta Odontol Scand 1947;7:115-44. 10. Gianelly AA, Goldman HM. Biologic basis of orthodontics. Philadelphia: Lee & Febiger; 1971. p. 124-59. 11. Sleichter CG. A clinical assessment of light and heavy forces in the closure of extraction cases. Angle Orthod 1971;41:66-75. 12. Hixon EH, Atikian H, Callow GLE, McDonald HW, Tacy RJ. Optimal force, differential force and anchorage. Am J Orthod 1969;55:437-57.
The Gable bend revisited Stanley Braun, DDS, MME,a and Jose´ L. Garcia, DDSb Indianapolis, Ind, and St Louis, Mo Gable bends are frequently incorporated into a variety of loop configurations to provide appropriate moment-to-force (M/F) ratios in the controlled closure of space between individual teeth or groups of teeth. Appropriate magnitudes and occlusogingival locations of the Gable bends are shown to be vital to maintain the neutral position of the closing loop. Otherwise, the clinician has no meaningful reference point from which to judge the spring’s activation to obtain the force aspect in the M/F ratio. A simple means of preserving the neutral position is shown, with the vertical loop as an example that can be applied to many common loop configurations. (Am J Orthod Dentofacial Orthop 2002;122:523-7)
A
variety of vertical loop configurations are used by clinicians to close spaces between individual teeth or groups of teeth. Gable bends are frequently incorporated into the loop configuration to provide a moment to prevent the root apices of the teeth from moving in a direction opposite to that of their crowns (uncontrolled tipping). In more precise terms, the Gable bend is intended to control the dental centers of rotation through an appropriate moment-to-force (M/F) ratio applied at the springs’ attachments to the teeth. It has been shown that the M/F ratios resulting from activating various loop configurations are insufficient to prevent uncontrolled tipping unless Gable bends are included.1-4 When Gable bends, as shown in Figure 1, are placed in the occlusal portion of a vertical loop configuration, an unintended mesiodistal force is introduced. This force will alter the desired mesiodistal force originally intended because of the crossover of the vertical legs. This crossover foreshortens the horizontal wire length between the brackets. Thus, the Gable bend moment and the mesiodistal force are not independent of each other when the clinician is attempting to achieve predictable M/F ratios. Burstone et al5 have shown that the neutral position of the loop configuration has been altered by the introduction of Gable bends. The neutral position can be defined as the horizontal separation of the vertical legs of the spring before the introduction of a horizontal or mesiodistal force. Thus, if the clinician wishes to generate a known mesiodistal force by separating the vertical legs by a a
Clinical Professor of Orthodontics, Vanderbilt University Medical Center. Private practice, St Louis, Mo. Reprint requests to: Dr Stanley Braun, 7940 Dean Rd, Indianapolis, IN 46240; e-mail, [email protected]. Submitted, October 2001; revised and accepted, February 2002. Copyright © 2002 by the American Association of Orthodontists. 0889-5406/2002/$35.00 ⫹ 0 8/1/126727 doi:10.1067/mod.2002.126727
b
given number of millimeters from the neutral position, he or she cannot make the separation because the neutral position has been altered by the Gable bends. If the Gable bends are positioned in the gingival portion of the vertical loop, a mesiodistal force is produced in a direction opposite that produced by the Gable bends in the occlusal portion of the loop. This is the result of the wire lengthening between brackets because of the separation of the vertical legs (Fig 2). This suggests that appropriate sharing of the Gable bends occlusogingivally can produce a moment that does not materially alter the horizontal force; thus, the initial M/F ratio can be more easily controlled and defined by the clinician. By sharing the Gable bends occlusogingivally, it is possible to maintain the neutral position, and the active force can be judged clinically. It is the purpose of this investigation to illustrate a means of providing more reliable, clinically achievable initial M/F ratios with Gable bends shared occlusogingivally. The vertical loop is used as the basic configuration for illustration purposes from which more general clinical guidelines can be developed that apply to all commonly used loop configurations for closing space between individual teeth or groups of teeth. MATERIAL AND METHODS
Portable strain gauge devices (Orthomeasurements, Division of Young Research & Development, Avon, Conn) capable of measuring forces and couples (moments) in a given plane were used (Fig 3). Each device comprised 2 basic components: an enclosed power supply with a digital readout of moments and forces, and an orthodontic bracket-supporting unit that contained appropriate strain gauge configurations that transmitted electronic signals to the digital readout units. The bracket-support units were affixed to a 523
524 Braun and Garcia
American Journal of Orthodontics and Dentofacial Orthopedics November 2002
Fig 1. Vertical loop containing Gable bends in positions ➀ with subsequent vertical leg crossover.
machine tool table that permitted micrometer adjustments of 1 bracket relative to the other linearly with an accuracy of .001 in. A loop configuration could thus be attached to each bracket, at a specific interbracket distance, and moments and forces could be measured at each bracket location (Fig 4). For illustration purposes, four 6-mm vertical loop springs, fabricated from .017 ⫻ .025-in TMA wire (Ormco Corp, Glendora, Calif), were configured as shown in Figure 5. Mean dimensional values of the 4 springs are shown. There are small dimensional variations because the vertical loops were configured as if in a clinical setting. The interbracket dimension shown in Figure 5 represents the average centerline-to-centerline distance of .018-in slot brackets positioned on the second premolar and on the canine. (It was assumed that the first premolar had been removed.)
RESULTS
In the first series of tests, 0°, 5°, 10°, 15°, and 20° Gable bends were placed into the occlusal positions (➀) of the vertical loops (Fig 5). The resultant moments and mesiodistal forces were recorded at each bracket. The mean values obtained for the 4 experimental loops are shown in Table I. In an identical group of 4 vertical loop configurations, Gable bends were placed in position ➁ (Fig 5). The resulting moments and mesiodistal forces obtained, after bracket engagement, are shown in Table II. Both sets of experimental data are shown graphically in Figure 6. DISCUSSION
One can readily see that undesirable mesiodistal forces are generated whenever occlusal (➀) or gingival
Fig 2. Vertical loop containing Gable bends in positions ➁ with subsequent vertical leg separation.
Braun and Garcia 525
American Journal of Orthodontics and Dentofacial Orthopedics Volume 122, Number 5
Fig 3. Instrumentation used to measure mesiodistal forces of 6-mm vertical loop containing Gable bends.
Fig 5. Mean dimensions of vertical loop configuration tested.
Gable bends of 4° are needed in positions ➁ to provide a ⫹54-g force to restore the vertical legs to their neutral position. Maintenance of the neutral position, irrespective of the variations in the vertical loop configuration (eg, T loop, L loop, and the presence of helices), is vital so that the clinician can judge the correct horizontal separation of the vertical legs to achieve a desired initial M/F ratio.6-8 Constructing a graph for every kind of loop configuration is impractical in a clinical setting. As a practical alternative, the clinician can place desired Gable bends in positions ➀, and with pliers Fig 4. Close-up view of vertical loop being tested.
(➁) Gable bends are placed. These are undesirable in the sense that the clinician loses a reference configuration (vertical legs separated and parallel in this experiment) to properly introduce forecastable mesiodistal forces. The neutral position has been lost. For example, if a clinician were to place 10° Gable bends in positions ➀ (Fig 5; graph of Fig 6), a mesiodistal force of ⫺54 g would result. To eliminate this, an equal mesiodistal force in the opposite direction is required to restore the neutral position. The graph in Figure 6 illustrates that
Mean values of moments and forces generated with Gable bends in occlusal positions
Table I.
Occlusal Gable bend (°) 0 5 10 15 20
Moment at each bracket (g mm)
Mesiodistal force* (g)
20 248 563 808 1081
⫺1 ⫺16 ⫺54 ⫺76 ⫺99
*Negative values indicate force direction related to shortened archwire between brackets. All values are to the nearest whole number.
526 Braun and Garcia
American Journal of Orthodontics and Dentofacial Orthopedics November 2002
Fig 6. Graphic presentation of test data obtained for 6-mm vertical loop.
Mean values of moments and forces generated with Gable bends in gingival positions
Table II.
Occlusal Gable bend (°) 0 5 10 15 20
Moment at each bracket (g mm)
Mesiodistal force* (g)
29 117 189 233 271
0 ⫹71 ⫹116 ⫹185 ⫹242
*Positive values indicate force direction related to lengthened archwire between brackets. All values are to the nearest whole number.
hold the wire in similar positions to those of the brackets, and then bring the plier beaks into horizontal positions, simulating the bracket locations. Note the crossover of the vertical legs of the loop. By experimentally placing Gable bends in positions ➁, one can achieve 0 vertical leg overlap. When crossover is 0, the neutral position has been achieved, and the clinician can now introduce the desired mesiodistal force, a portion of the desired M/F ratio. The mesiodistal forces thus obtained and the moments induced by the Gable bends are not completely independent of each other. As the teeth respond to the initial M/F ratio applied, both the moment and the force decrease, each at its own rate. To maintain relative constancy of the M/F ratio, it is desirable that the decay of each be minimized or
consistent. This is primarily achieved through a lowrate spring. Generally, spring rates can be reduced by using low modulus wire and increased wire length (ie, by introducing helices, bypassing intervening brackets as in the segmented arch technique,8 and using T loops) and by altering the wire cross section. A low spring rate is important because it provides improved constancy in the M/F ratio as the teeth move. Constancy of this ratio is important to provide controlled space closure with predictable, relatively constant centers of rotation. Controlled centers of rotation will reduce undesirable tooth “wiggle” and potential tissue damage.9-12 CONCLUSION
It is apparent that Gable bends should be distributed occlusogingivally in all loop configurations to achieve forecastable M/F ratios at the active and reactive teeth. The vertical loop configuration has been used to illustrate a simple method to achieve this. REFERENCES 1. Proffit WR, Fields HW Jr. Contemporary orthodontics. 2nd ed. St Louis: Mosby; 1993. 2. Smith RJ, Burstone CJ. Mechanics of tooth movement. Am J Orthod 1984;85:294-307. 3. Burstone CJ, Koenig HA. Optimizing anterior and canine retraction. Am J Orthod 1976;70:1-19. 4. Miyakawa O, Shiakawa WN, Matsunra T, Hanada K. A new method for finite element simulation of orthodontic appliance–
American Journal of Orthodontics and Dentofacial Orthopedics Volume 122, Number 5
teeth–periiodontium–alveolus system. J Biomech 1985;18:27784. 5. Burstone CJ, van Steenbergen Z, Henley KJ. Modern edgewise mechanics and the segmented arch technique. Glendora (Calif): Ormco Corp; 1995. 6. Burstone CJ. Application of bioengineering to clinical orthodontics. In: Graber TM, editor. Current orthodontic concepts and techniques. 2nd ed. Philadelphia: WB Saunders Co; 1975. p. 230-58. 7. Tanne K, Keonig HA, Burstone CJ. Moment to force ratios and the center of rotation. Am J Orthod Dentofacial Orthop 1988;94:426-31.
Braun and Garcia 527
8. Burstone CJ. The mechanism of the segmented arch technique. Angle Orthod 1966;36:99-120. 9. Reitan K. Continuous bodily movement and its histologic significance. Acta Odontol Scand 1947;7:115-44. 10. Gianelly AA, Goldman HM. Biologic basis of orthodontics. Philadelphia: Lee & Febiger; 1971. p. 124-59. 11. Sleichter CG. A clinical assessment of light and heavy forces in the closure of extraction cases. Angle Orthod 1971;41:66-75. 12. Hixon EH, Atikian H, Callow GLE, McDonald HW, Tacy RJ. Optimal force, differential force and anchorage. Am J Orthod 1969;55:437-57.