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Table 2 Initial displacement of selected nodes on X , Y , and Z axes after application of retraction force (×10 −4mm)

From: 3D FEM comparison of lingual and labial orthodontics in en masse retraction

  Xaxis Yaxis Zaxis
Labial Lingual Labial Lingual Labial Lingual
Central incisor Occlusal 25.36 48.24 1.28 2.29 −2.86 −2.34
Apex −11.28 −22.67 −0.98 −3.66 −2.24 −3.98
Lateral incisor Occlusal 30.45 51.28 2.5 3.58 −2.53 −1.35
Apex −12.34 −23.35 −1.87 −3.45 −1.22 −1.48
Canine Occlusal 25.59 22.67 −22.05 −25.73 5.53 11.23
Apex −11.02 −10.85 8.25 9.97 6.29 9.74
Second premolar Buccal cusp 18.97 −15.76 19.87 15.66 9.58 7.53
Lingual cusp 16.24 −12.56 13.43 21.62 11.26 8.25
Apex −4.52 −15.73 −10.52 −9.87 6.08 4.42
First molar Mesio-buccal cusp 12.89 −12.28 9.51 7.98 5.46 4.53
Disto-buccal cusp 6.78 7.34 10.23 8.25 1.89- 2.38
Mesio-lingual cusp 10.67 −11.46 5.03 9.34 6.67 4.86
Disto-lingual cusp 4.54 3.27 5.85 9.67 2.55- 3.06
Mesial apex −2.76 −7.54 −4.32 −3.87 −1.02 2.54
Distal apex −4.66 4.75 −1.23 −3.63 −4.23 −1.18
Second molar Mesio-buccal cusp 2.43 2.23 7.03 5.87 −2.07 0.57
Disto-buccal cusp 1.56 4.98 8.25 6.54 −4.65 −3.39
Mesio-lingual cusp 3.84 3.66 3.84 8.58 −2.46 1.14
Disto-lingual cusp 2.71 4.85 4.15 8.55 −4.58 −2.02
Mesial apex −1.98 3.45 1.84 −2.67 −4.75 −2.28
Distal apex −3.25 4.22 2.42 −2.93 −5.03 −2.44
  1. X: +lingual, −vestibular; Y: +mesial, −distal; Z: +apical, −occlusal.