Table 2 Correlation between mean changes of bone thickness and potential influencing factors; r value (P value)

B1 at T0

− 0.288 (0.099)

− 0.341* (0.048)

− 0.183 (0.301)

− 0.286 (0.102)

0.093 (0.601)

− 0.075 (0.674)

B2 at T0

− 0.214 (0.225)

− 0.333 (0.055)

− 0.327 (0.059)

− 0.435* (0.010)

− 0.085 (0.631)

− 0.281 (0.107)

B3 at T0

− 0.051 (0.775)

− 0.144 (0.417)

− 0.152 (0.391)

− 0.238 (0.176)

− 0.196 (0.268)

− 0.403* (0.018)

θ at T0

− 0.078 (0.662)

− 0.163 (0.357)

− 0.139 (0.433)

− 0.194 (0.270)

− 0.324 (0.062)

− 0372* (0.030)

U1 to FH

− 0.386* (0.024)

− 0.303 (0.081)

− 0.279 (0.111)

− 0.191 (0.280)

− 0.359* (0.037)

− 0.265 (0.130)

U1 to Palatal plane

− 0.428* (0.011)

− 0.339* (0.050)

− 0.428* (0.012)

− 0.248 (0.157)

− 0.448* (0.008)

− 0.354* (0.040)

U1 labial surface to palatal plane

− 0.522** (0.002)

− 0.395* (0.021)

− 0.372* (0.030)

− 0.239 (0.174)

− 0.432* (0.011)

− 0.389* (0.023)

Bone labial surface to palatal plane

− 0.479** (0.004)

− 0.408* (0.017)

− 0.366* (0.033)

− 0.314 (0.070)

− 0.405* (0.018)

− 0.404* (0.018)

ΔB1

1

0.917*** (< 0.001)

0.838*** (< 0.001)

0.742*** (< 0.001)

0.667*** (< 0.001)

0.617*** (< 0.001)

ΔB1/B1 at T0

0.917*** (< 0.001)

1

0.861*** (< 0.001)

0.873*** (< 0.001)

0.689*** (< 0.001)

0.741*** (< 0.001)

ΔB2

0.838*** (< 0.001)

0.861*** (< 0.001)

1

0.938*** (< 0.001)

0.818*** (< 0.001)

0.771*** (< 0.001)

ΔB2/B2 at T0

0.742*** (< 0.001)

0.873*** (< 0.001)

0.938*** (< 0.001)

1

0.762*** (< 0.001)

0.832*** (< 0.001)

ΔB3

0.667*** (< 0.001)

0.689*** (< 0.001)

0.818*** (< 0.001)

0.762*** (< 0.001)

1

0.875*** (< 0.001)

ΔB3/B3 at T0

0.617*** (< 0.001)

0.741*** (< 0.001)

0.771*** (< 0.001)

0.832*** (< 0.001)

0.875*** (< 0.001)

1

Intrusion amount

0.243 (0.166)

0.223 (0.205)

0.186 (0.292)

0.213 (0.226)

0.392* (0.022)

0.386* (0.024)

Retraction amount

0.155 (0.380)

0.128 (0.472)

− 0.004 (0.983)

0.005 (0.978)

− 0.185 (0.294)

− 0.125 (0.483)