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Table 2 Quantification of the first and second molar movements, at anteroposterior, vertical, and transverse directions, according to the HG pull and magnitude of force

From: Tridimensional finite element analysis of teeth movement induced by different headgear forces

Tooth Points Coordinate Quantification of movement (×10−3 mm)
Low pull High pull Combined pull
450 gf 200 gf 500 gf 200 gf 150 gf/150 gf 100 gf/100 gf
First molar Crown        
CMB x −0.3563 −0.1582 −0.0827 −0.0330 −0.1366 −0.0911
  y 0.3004 0.1335 0.5167 0.2066 0.2570 0.1713
  z 1.5992 0.7103 1.4753 0.5898 0.9629 0.6418
CDB x −0.4943 −0.2195 −0.1578 −0.0631 −0.2033 −0.1355
  y −0.0125 −0.0055 0.2696 0.1079 0.0815 0.0544
  z 0.4791 0.2130 0.6867 0.2748 0.3659 0.2440
CML x 0.4528 0.2007 0.5076 0.2027 0.3009 0.2004
  y −0.1989 −0.0884 −0.0808 −0.0323 −0.0871 −0.0581
  z 1.1112 0.4936 1.0832 0.4331 0.6874 0.4582
CDL x 0.3127 0.1385 0.4004 0.1598 0.2236 0.1489
  y −0.2456 −0.1090 −0.1718 −0.0686 −0.1305 −0.0870
  z 0.2066 0.0921 0.3934 0.1576 0.1886 0.1259
Root        
AMB x −0.3529 −0.1566 −0.2535 −0.1012 −0.1897 −0.1264
  y 0.3132 0.1392 0.5190 0.2076 0.2616 0.1744
  z −0.0618 −0.0275 −0.1689 −0.0676 −0.0727 −0.0485
ADB x −0.3348 −0.1490 −0.3785 −0.1516 −0.2238 −0.1493
  y 0.1648 0.0732 0.2564 0.1025 0.1323 0.0882
  z 0.0102 0.0045 −0.0099 −0.0040 0.0000 −0.0000
AL x −0.1809 −0.0801 −0.1218 −0.0486 −0.0946 −0.0630
  y −0.1643 −0.0730 −0.0611 −0.0244 −0.0702 −0.0468
  z −0.0751 −0.0333 −0.1288 −0.0515 −0.0641 −0.0427
Second molar Crown        
CMB x −0.3817 −0.1696 −0.1041 −0.0416 −0.1514 −0.1009
  y −0.0696 −0.0309 0.1015 0.0407 0.0106 0.0071
  z 0.0843 0.0377 0.2831 0.1134 0.1158 0.0773
SOD x −0.2720 −0.1208 −0.0520 −0.0208 −0.1009 −0.0672
  y 0.0289 0.0129 0.0588 0.0235 0.0276 0.0184
  z −0.1529 −0.0680 0.0610 0.0244 −0.0281 −0.0187
SOL x −0.0768 −0.0338 0.1300 0.0522 0.0173 0.0116
  y −0.0381 −0.0169 −0.0283 −0.0113 −0.0207 −0.0138
  z −0.0214 −0.0094 0.1964 0.0787 0.0555 0.0371
Root        
AMB x −0.0434 −0.0193 −0.0856 −0.0343 −0.0406 −0.0271
  y −0.0119 −0.0052 0.0722 0.0289 0.0192 0.0128
  z 0.0076 0.0034 −0.0001 −0.0000 0.0021 0.0014
ADB x −0.0486 −0.0216 −0.0654 −0.0262 −0.0358 −0.0239
  y 0.0092 0.0041 0.0791 0.0317 0.0279 0.0186
  z −0.0089 −0.0040 −0.0244 −0.0098 −0.0105 −0.0070
AL x −0.0161 −0.0072 −0.0192 −0.0077 −0.0111 −0.0074
  y −0.0044 −0.0020 −0.0106 −0.0043 −0.0047 −0.0031
  z −0.0223 −0.0100 −0.0320 −0.0128 −0.0171 −0.0114
  1. Abbreviations: x coordinate anteroposterior direction, y coordinate vertical direction, z coordinate transverse direction, CMB mesiobuccal cusp, CDB distobuccal cusp, CML mesiolingual cusp, CDL distolingual cusp, SOD occluso-distal surface, SOL occluso-lingual surface, AMB mesiobuccal root apex, ADB distobuccal root apex, AL lingual root apex