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Table 3 Comparison of displacement of the surface landmarks in the maxillofacial structures with maxillary protraction without maxillary expansion (Simulation A) when 250-g force was applied

From: Biomechanical effects of Skeletally anchored Class III elastics on the maxillofacial complex: a 3D finite element analysis

   Angle of force 10° to occlusion Angle of force 20° to occlusion Angle of force 30° to occlusion
X (mm) Y (mm) Z (mm) X (mm) Y (mm) Z (mm) X (mm) Y (mm) Z (mm)
Simulation A          
  Maxilla ANS 0.011 − 0.396 0.180 0.006 − 0.347 0.055 0.006 − 0.296 0.010
Point A 0.011 − 0.429 0.180 0.006 − 0.371 0.012 0.006 − 0.313 0.020
U1 point 0.018 − 0.560 0.196 0.013 − 0.483 0.115 0.012 − 0.405 0.065
  Mandible Point B 0.000 0.008 − 0.032 0.00 0.005 − 0.018 0.00 0.005 − 0.016
Pogonion 0.000 0.017 − 0.032 − 0.001 0.010 − 0.018 0.00 0.009 − 0.016
Condylion − 0.002 − 0.007 0.004 0.002 − 0.003 0.002 0.002 − 0.003 0.001
Simulation B
  Maxilla ANS 0.214 − 0.065 − 1.324 0.150 − 0.057 − 1.191 0.133 − 0.052 − 1.059
Point A − 0.134 − 0.262 − 1.324 − 0.116 − 0.227 − 1.191 − 0.089 − 0.175 − 1.059
U1 point − 1.674 − 0.556 − 1.743 − 1.506 − 0.482 − 1.569 − 1.399 -0.371 − 1.394
  Mandible Point B 0.000 0.004 − 0.008 0.000 0.002 − 0.008 0.000 0.002 − 0.007
Pogonion 0.000 0.007 − 0.008 0.000 0.004 − 0.008 0.000 0.004 − 0.007
Condylion 0.001 − 0.002 0.001 0.001 − 0.001 0.001 0.001 − 0.001 0.001
  1. X, lateral displacement (+, lateral; −, median). Y, antero-posterior displacement (+, posteriorly; −, anteriorly). Z, Vertical displacement (+, superiorly; −, inferiorly).
  2. U1 point—on the incisal edge of maxillary central incisor
  3. L1 point—on the incisal edge of mandibular central incisor