Deformation of SS key loops after loading of 5 N was showed in Fig. 4 and showed different patterns. The horizontal part of single loop showed the least distal extension. In DKL, both mesial and distal loops were activated. In Type-1 loading, the distal loop opened greater than the mesial loop did, and the distal loop moved occlusally. In Type-2 loading, mesial loop opened greater than the distal loop did, and the horizontal archwire was almost at the original level. Type-3 loading activated the mesial and distal loop to almost the same distance and the distal loop shift occlusally a little.
The displacement of distal end under retraction force on SS loops was listed in Table 1 and Fig. 5-A. For the single key loop in Type-1 loading, L/D ratio in horizontal direction was around 10.2 N/mm. For the DKL in Type-1 loading, the horizontal L/D ratio was 4.37 N/mm, about 43% of single key loop. For DKL in Type-2 loading, its horizontal L/D ratio of 6.05 N/mm was higher than that in Type-1 loading, but lower than that in Type-3 loading. The distal extension of DKL with preactivation angles of 5°, 10° and 15° in Type-3 loading started at retraction force of about 1 N, 2 N and 4 N respectively. L/D ratio of DKL at preactivation angle of 5° was 9.37 N/mm, and it increased to 10.8 N/mm when preactivation angle was up to 15°. L/D ratio of DKL in Type-3 loading was close to that of single key loop in Type-1 loading.
Table 1
Displacement (mm) of distal end in stainless steel single and double key loops under different loading types
Force (N) | Type-1 Single | Type-1 | Type-2 | Type-3 + 5 | Type-3 + 10 | Type-3 + 15 |
1 | 0.098 | 0.229 | 0.165 | 0.003 | 0.004 | 0.004 |
2 | 0.196 | 0.458 | 0.331 | 0.090 | 0.009 | 0.009 |
3 | 0.294 | 0.687 | 0.496 | 0.198 | 0.054 | 0.015 |
4 | 0.392 | 0.915 | 0.661 | 0.305 | 0.143 | 0.024 |
5 | 0.491 | 1.144 | 0.826 | 0.414 | 0.241 | 0.107 |
6 | 0.589 | 1.373 | 0.992 | 0.523 | 0.350 | 0.196 |
7 | 0.687 | 1.602 | 1.157 | 0.632 | 0.461 | 0.287 |
8 | 0.785 | 1.831 | 1.322 | 0.740 | 0.567 | 0.394 |
Table 2
Displacement (mm) of distal end in TMA single and double key loops under different loading types
Force (N) | Type-1 Single | Type-1 | Type-2 | Type-3 + 5 | Type-3 + 10 | Type-3 + 15 |
1 | 0.250 | 0.582 | 0.421 | 0.120 | 0.012 | 0.024 |
2 | 0.499 | 1.165 | 0.832 | 0.371 | 0.191 | 0.063 |
3 | 0.749 | 1.747 | 1.262 | 0.622 | 0.437 | 0.272 |
4 | 0.999 | 2.330 | 1.683 | 0.873 | 0.688 | 0.512 |
5 | 1.249 | 2.912 | 2.103 | 1.124 | 0.939 | 0.763 |
6 | 1.498 | 3.495 | 2.524 | 1.374 | 1.190 | 1.013 |
7 | 1.748 | 4.077 | 2.945 | 1.625 | 1.440 | 1.264 |
8 | 1.998 | 4.660 | 3.365 | 1.876 | 1.691 | 1.515 |
For TMA loops in Type-1 loading, the L/D ratio of single key loop was 4.00 N/mm and L/D ratio of DKL was 1.72 N/mm. L/D ratio of DKL in Type-2 loading was 2.37 N/mm. The distal extension of TMA DKL with preactivation angles of 5°, 10° and 15° in Type-3 loading started at retraction force of about 0.5 N, 1 N and 2 N respectively. L/D ratio of TMA DKL in Type-3 loading was close to that of single TMA key loop in Type-1 loading, keeping at around 4 N/mm. The results were approximately 40% of the corresponding value of SS key loops (Table 2, Fig. 5-B).
Table 3
Reaction force and moment on mesial end of stainless steel key loops and the moment/force ratio in different loading types
| Retraction Force (N) | X (N) | Z (N) | Moment (N.mm) | M/F (mm) |
Type-1 Single | 2 | 2.00 | -0.742 | 7.06 | 3.53 |
4 | 4.00 | -1.483 | 14.12 | 3.53 |
6 | 6.00 | -2.225 | 21.18 | 3.53 |
Type-1 | 2 | 2.00 | -0.417 | 7.11 | 3.56 |
4 | 4.00 | -0.835 | 14.22 | 3.56 |
6 | 6.00 | -1.252 | 21.33 | 3.56 |
Type-2 | 2 | 1.98 | 0.223 | 6.48 | 3.27 |
4 | 3.96 | 0.445 | 12.97 | 3.27 |
6 | 5.94 | 0.668 | 19.46 | 3.27 |
Type-3 + 5 | 0 | 0.00 | -0.517 | 8.79 | / |
1 | 0.99 | -0.308 | 9.54 | 9.62 |
2 | 1.98 | -0.167 | 11.43 | 5.77 |
4 | 3.96 | -0.058 | 18.20 | 4.59 |
6 | 5.94 | 0.028 | 25.35 | 4.26 |
Type-3 + 10 | 0 | 0.00 | -1.105 | 18.78 | / |
1 | 0.99 | -0.895 | 19.51 | 19.69 |
2 | 1.98 | -0.685 | 20.24 | 10.21 |
4 | 3.96 | -0.379 | 23.64 | 5.96 |
6 | 5.94 | -0.202 | 29.26 | 4.92 |
Type-3 + 15 | 0 | 0.00 | -1.690 | 28.73 | / |
1 | 0.99 | -1.480 | 29.46 | 29.73 |
2 | 1.98 | -1.273 | 30.23 | 15.26 |
4 | 3.96 | -0.862 | 31.83 | 8.03 |
6 | 5.94 | -0.591 | 35.84 | 6.03 |
Table 4
Reaction force and moment on mesial end of TMA key loops and the moment/force ratio in different loading types
| Retraction Force (N) | X (N) | Z (N) | Moment (N.mm) | M/F (mm) |
Type-1 Single | 2 | 2.00 | -0.742 | 7.06 | 3.53 |
4 | 4.00 | -1.483 | 14.12 | 3.53 |
6 | 6.00 | -2.225 | 21.18 | 3.53 |
Type-1 | 2 | 2.00 | -0.417 | 7.11 | 3.56 |
4 | 4.00 | -0.835 | 14.22 | 3.56 |
6 | 6.00 | -1.252 | 21.33 | 3.56 |
Type-2 | 2 | 1.98 | 0.223 | 6.48 | 3.27 |
4 | 3.96 | 0.445 | 12.97 | 3.27 |
6 | 5.94 | 0.668 | 19.46 | 3.27 |
Type-3 + 5 | 0 | 0.00 | -0.023 | 3.68 | / |
1 | 0.99 | -0.064 | 5.39 | 5.44 |
2 | 1.98 | -0.003 | 9.14 | 4.61 |
4 | 3.96 | 0.027 | 16.74 | 4.22 |
6 | 5.94 | 0.086 | 24.34 | 4.10 |
Type-3 + 10 | 0 | 0.00 | -0.479 | 8.15 | / |
1 | 0.99 | -0.291 | 9.24 | 9.32 |
2 | 1.98 | -0.164 | 11.38 | 5.74 |
4 | 3.96 | -0.069 | 18.39 | 4.64 |
6 | 5.94 | -0.010 | 25.99 | 4.37 |
Type-3 + 15 | 0 | 0.00 | -0.745 | 12.67 | / |
1 | 0.99 | -0.557 | 13.76 | 13.88 |
2 | 1.98 | -0.378 | 15.02 | 7.58 |
4 | 3.96 | -0.167 | 20.05 | 5.06 |
6 | 5.94 | -0.108 | 27.66 | 4.65 |
As to the vertical fore at the mesial end of SS single and double key loop, it was negative in Type-1 loading regardless of the force level, indicating an extrusive force acted on the anterior teeth. On the contrary, vertical force at the mesial end was positive for DKL in Type-2 loading, meaning an intrusive force on anterior teeth. Vertical force of DKL at mesial end in Type-3 loading after engagement (Retraction force = 0) was extrusive and the magnitude increased with the preactivation angle. At preactivation angle of 5°, the extrusive force decreased with the increase of retraction force and the vertical force became intrusive when retraction force was above 6 N. However, the vertical force kept extrusive in Type-3 loading at preactivation angles of 10° and 15° (Table 3). For TMA loops, vertical forces at mesial end were similar in direction as those of SS loops, but the magnitudes were less when subjected to the same retraction force. In Type-3 loading of TMA DKL with preactivation angle of 5°, the vertical force become intrusive when the retraction force was up to 4 N (Table 4).
Moment on the mesial end in all loading types increased with the increased distal traction force (Table 3). For SS loops in Type-1 loading, the moment increased proportionally and the M/F ratio kept at 3.53 mm. Adding of a parallel key loop in DKL induced no change of the M/F ratio. Moment in Type-2 loading of DKL also increased proportionally with the distal force and the M/F ratio increased to 3.27 mm, which was close to that in Type-1 loading.
Moment in Type-3 loading of DKL increased with the preactivation angle and retraction force. After simulative engagement of SS DKL in bracket without retraction, the moment on mesial end was 8.79, 18.78 and 28.73 N·mm at preactivation angles of 5°, 10° and 15°. All M/F ratios in Type-3 loading of DKL were higher than in Type1 and Type-2 loading. As the retraction force raised up, the moment at mesial end increased but the M/F ratio decreased inversely. The highest M/F ratio in the conditions with preactivation angles of 5°, 10° and 15° were 9.62, 19.69 and 29.73 mm respectively under 1 N retraction force. The M/F ratios under 6 N retraction force were 4.26, 4.92 and 6.03 mm respectively, showing less difference (Table 3).
For TMA loops (Table 4), the moments at mesial in Type-1 and Type-2 loadings under equal retraction force were almost the same and the corresponding M/F ratios were the same as that of SS loops. In Type-3 loading of DKL, the moment at mesial end after simulative engagement was 3.68, 8.15 and 12.67 N.mm at preactivation angles of 5°, 10° and 15°. M/F ratio of TMA DKL under the same retraction force was lower than that of SS DKL with equal preactivation angle. The highest M/F ratio at preactivation angles of 5°, 10° and 15° was 5.44, 9.32 and 13.88 mm under 1 N retraction force. Its M/F ratio under 6 N retraction force varied between 4.10 and 4.65 mm.
Change of M/F ratio against the distal retraction force was showed in Fig. 6. At the same level of retraction force, the M/F ratio increased with the practivation angle. The M/F ratio of SS DKL was higher than that of TMA DKL under the same level of retraction force. Almost overlapping in the fitting curve of SS + 5 and TMA + 10, and overlapping of SS + 10 and TMA + 20 suggested their equal M/F ratio under the same retraction force.
As showed in Fig. 7, the M/F ratio decreased with the extension of distal end. M/F ratio in all conditions was all above 4.03 mm. M/F of DKL with higher preactivation angle was above those with lower angles. At an equal amount of distal extension, M/F ratio of DKL increased with the practivation angle. The fitting curves of SS and TMA DKL with equal preactivation angle were close to each other, indicating similar M/F ration at the same distance of activation.