Table 2.
Force distribution within clear aligner and comparisons of the forces in group A1–5
| Tooth number | Force direction | A0 | A1 | A2 | A3 | A4 | A5 |
|---|---|---|---|---|---|---|---|
| 37 | Fx¶ | 0.26 ± 0.35 | 1.00 ± 1.58‡‖ | 1.82 ± 0.54‡§‖ | −0.43 ± 0.71*† | −0.13 ± 0.92†‖ | −1.68 ± 0.96*†§ |
| Fy¶ | 1.37 ± 0.27 | 0.58 ± 0.98‡§‖ | 0.70 ± 0.81‡§‖ | −0.74 ± 0.44*† | −0.67 ± 1.10*†‖ | −1.80 ± 0.73*†§ | |
| Fz** | −0.94 ± 0.12 | 0.34 ± 0.17‡ | 0.65 ± 0.25 | 0.71 ± 0.18*§ | 0.44 ± 0.15‡ | 0.49 ± 0.24 | |
| 36 | Fx¶ | −1.11 ± 0.14 | 0.64 ± 0.39§‖ | 1.21 ± 0.56§ | 1.30 ± 0.39§ | 2.85 ± 0.76*†‡§ | 1.58 ± 0.47*§ |
| Fy¶ | −2.43 ± 0.24 | −0.33 ± 1.71‖ | −0.27 ± 0.59 | 0.12 ± 0.59 | 0.70 ± 2.12 | 1.38 ± 0.60* | |
| Fz¶ | 1.77 ± 0.12 | −0.63 ± 0.48 | −0.96 ± 0.33 | −0.78 ± 0.30 | −1.11 ± 0.57 | −1.11 ± 0.25 | |
| 35 | Fx¶ | 2.75 ± 0.37 | 0.03 ± 0.26§‖ | 0.47 ± 0.53§‖ | 0.62 ± 0.34§‖ | 1.78 ± 0.58*†‡ | 1.50 ± 0.58*†‡ |
| Fy¶ | 0.38 ± 0.36 | −0.74 ± 0.80‡§‖ | −0.93 ± 0.63‡§‖ | 0.82 ± 0.47*† | 0.88 ± 1.13*† | 1.61 ± 0.57*† | |
| Fz¶ | −1.74 ± 0.26 | 0.20 ± 0.80‡§‖ | −0.40 ± 0.45§‖ | −0.82 ± 0.31*§ | −1.63 ± 0.48*†‡ | −1.13 ± 0.41*† | |
| 33 | Fx¶ | −0.16 ± 0.12 | −1.19 ± 0.21†‡§‖ | −2.20 ± 0.17*‡§‖ | −0.63 ± 0.09*†§ | −1.79 ± 0.11*†‡‖ | −0.62 ± 0.13*†§ |
| Fy** | −0.30 ± 0.17 | 0.40 ± 0.14†‡§‖ | −0.65 ± 0.22*§‖ | −0.80 ± 0.11*§‖ | −2.39 ± 0.38*†‡ | −2.05 ± 0.34*†‡ | |
| Fz¶ | −0.34 ± 0.23 | −0.24 ± 0.72 ‡§‖ | 0.31 ± 0.46 §‖ | 0.87 ± 0.26 *§‖ | 1.68 ± 0.40*†‡ | 2.11 ± 0.47 *†‡ | |
| 32 | Fx¶ | 0.14 ± 0.05 | −0.51 ± 0.13†‡§‖ | −0.96 ± 0.09*‡§‖ | −0.23 ± 0.08*†§ | −0.72 ± 0.04*†‡‖ | −0.26 ± 0.08*†§ |
| Fy¶ | 0.01 ± 0.07 | 0.15 ± 0.18§‖ | 0.08 ± 0.13 | 0.03 ± 0.17 | −0.08 ± 0.09* | −0.03 ± 0.11* | |
| Fz¶ | −0.84 ± 0.12 | 0.05 ± 0.25†‡§ | −0.33 ± 0.19*§ | −0.27 ± 0.15*§ | −0.67 ± 0.21*†‡‖ | −0.18 ± 0.15§ | |
| 31 | Fx¶ | 0.14 ± 0.09 | −0.14 ± 0.12 | −0.25 ± 0.10 | −0.15 ± 0.05 | −0.17 ± 0.09 | −0.15 ± 0.16 |
| Fy¶ | −0.46 ± 0.15 | 0.18 ± 0.27†§‖ | 0.74 ± 0.20*‡ | 0.31 ± 0.29† | 0.55 ± 0.27* | 0.58 ± 0.22* | |
| Fz¶ | −0.72 ± 0.13 | −0.40 ± 0.30†§‖ | −1.53 ± 0.33*‡§ | −0.75 ± 0.18†§‖ | −2.55 ± 0.28*†‡‖ | −1.23 ± 0.22*‡§ | |
| 41 | Fx¶ | 1.12 ± 0.10 | −0.03 ± 0.11§ | −0.04 ± 0.09§ | 0.07 ± 0.07 | 0.14 ± 0.08*† | 0.08 ± 0.10 |
| Fy¶ | 0.23 ± 0.10 | −0.04 ± 0.27 | 0.03 ± 0.28 | 0.11 ± 0.29 | −0.14 ± 0.27 | 0.18 ± 0.20 | |
| Fz** | −1.26 ± 0.13 | −0.46 ± 0.34†§‖ | −1.30 ± 0.46*§ | −0.86 ± 0.14§‖ | −2.36 ± 0.30*†‡‖ | −1.12 ± 0.14*‡§ | |
| 42 | Fx** | 0.81 ± 0.12 | −0.34 ± 0.09†‖ | −0.59 ± 0.06*‡§‖ | −0.23 ± 0.08†§ | −0.42 ± 0.06†‡‖ | −0.20 ± 0.06*†§ |
| Fy** | 0.04 ± 0.03 | −0.23 ± 0.05†‖ | −0.40 ± 0.14* | −0.24 ± 0.05‖ | −0.38 ± 0.15 | −0.37 ± 0.09*‡ | |
| Fz** | 0.93 ± 0.19 | −0.03 ± 0.19 †‡§‖ | −0.28 ± 0.10*§‖ | −0.34 ± 0.12 *§‖ | −1.08 ± 0.19 *†‡‖ | −0.62 ± 0.09 *†‡§ | |
| 43 | Fx** | 1.58 ± 0.16 | −1.42 ± 0.13†‡§‖ | −2.39 ± 0.16*‡‖ | −0.83 ± 0.29*†§ | −2.20 ± 0.15*‡‖ | −0.88 ± 0.24*†§ |
| Fy¶ | 0.25 ± 0.15 | −0.02 ± 0.37†‡§‖ | −0.94 ± 0.19*§‖ | −1.21 ± 0.23*§‖ | −3.18 ± 0.30*†‡‖ | −2.59 ± 0.40*†‡§ | |
| Fz** | −0.10 ± 0.31 | 0.11 ± 0.34‡§‖ | 0.49 ± 0.36‡§‖ | 1.07 ± 0.37*†§‖ | 1.89 ± 0.46*†‡ | 2.11 ± 0.35 | |
| 45 | Fx** | 0.85 ± 0.41 | −0.18 ± 0.51‡§‖ | 0.20 ± 0.45§‖ | 1.06 ± 0.82*§ | 2.32 ± 0.39*†‡ | 1.84 ± 0.38*† |
| Fy** | 0.36 ± 0.41 | −0.86 ± 0.53‡§‖ | −1.12 ± 0.62‡§‖ | 0.73 ± 0.95*† | 1.13 ± 0.41*†‖ | 1.81 ± 0.46*†§ | |
| Fz** | −0.18 ± 0.13 | 0.08 ± 0.23‡§‖ | −0.04 ± 0.29‡§‖ | −0.77 ± 0.45*†§ | −1.43 ± 0.28*†‡‖ | −0.65 ± 0.28*†‡ | |
| 46 | Fx** | −1.55 ± 0.43 | 0.63 ± 0.53†§ | 1.75 ± 0.52*‡‖ | 0.23 ± 1.18†§ | 1.77 ± 0.56*‡‖ | 0.80 ± 0.57†§ |
| Fy** | −2.02 ± 0.47 | 0.07 ± 0.64 | 0.64 ± 0.43 | −0.17 ± 1.36 | 0.63 ± 0.66 | 0.83 ± 0.61 | |
| Fz¶ | 1.71 ± 0.21 | −0.46 ± 0.28 | −0.44 ± 0.22 | 0.04 ± 0.50 | −0.27 ± 0.23 | −0.02 ± 0.40*†§ | |
| 47 | Fx** | −0.21 ± 0.78 | 0.86 ± 0.93‖ | 1.32 ± 0.36‖ | 0.17 ± 0.93 | 0.76 ± 0.73‖ | −0.81 ± 0.73*†§ |
| Fy** | 1.43 ± 0.44 | 0.48 ± 0.56‖ | 0.64 ± 0.34§‖ | 0.08 ± 0.58‖ | 0.04 ± 0.42†‖ | −0.90 ± 0.40*†‡§ | |
| Fz** | −1.58 ± 0.18 | 0.06 ± 0.13‖ | −0.04 ± 0.12‖ | −0.04 ± 0.40 | 0.00 ± 0.15‖ | −0.34 ± 0.18*†§ |
Values are presented as mean ± standard deviation.
Group A0 was used as the reference data, and the figures from other groups were obtained by subtracting from the A0.
FDI tooth numbering system was used.
Fx, force along the x-axis: positive values represent mesial forces; Fy, force along the y-axis: positive values represent extrusive forces; Fz, force along the z-axis: positive values represent labial or buccal forces.
Significantly different from *group A1, †group A2, ‡group A3, §group A4, and ‖group A5 on the same tooth.
¶Bonferroni’s test, p < 0.05.
**Dunnett’s T3, p < 0.05.
See Table 1 for definitions of each group.