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Table 5 Displacement of posterior teeth in the X-, Y- and Z-directions (mm)

From: Biomechanical analysis of effective mandibular en-masse retraction using Class II elastics with a clear aligner: a finite element study

  Axis Control MB DB ML DL AMB
BC5 X-axis 0.047 0.060 0.063 0.053 0.055 0.058
  Y-axis 0.021 0.057 0.050 − 0.035 − 0.031 0.057
  Z-axis − 0.019 − 0.019 − 0.024 − 0.023 − 0.026 − 0.017
R5 X-axis 0.002 − 0.010 − 0.011 − 0.001 − 0.004 − 0.006
  Y-axis − 0.020 − 0.031 − 0.029 − 0.000 − 0.001 − 0.036
  Z-axis − 0.016 − 0.017 − 0.020 − 0.010 − 0.013 − 0.016
MBC6 X-axis 0.045 0.060 0.063 0.048 0.051 0.055
  Y-axis 0.013 0.038 0.036 − 0.031 − 0.029 0.039
  Z-axis − 0.005 0.011 0.006 − 0.021 − 0.023 0.012
DBC6 X-axis 0.047 0.062 0.066 0.052 0.056 0.058
  Y-axis 0.008 0.027 0.021 − 0.033 − 0.033 0.032
  Z-axis 0.005 0.022 0.019 − 0.006 − 0.006 0.022
MLC6 X-axis 0.040 0.042 0.046 0.057 0.058 0.043
  Y-axis 0.016 0.046 0.040 − 0.037 − 0.035 0.046
  Z-axis − 0.011 − 0.010 − 0.012 − 0.002 − 0.004 − 0.010
MR6 X-axis 0.001 0.002 − 0.004 − 0.002 − 0.006 0.002
  Y-axis − 0.002 − 0.020 − 0.017 0.026 0.027 − 0.019
  Z-axis − 0.001 0.007 0.005 0.001 0.000 0.007
MBC7 X-axis 0.044 0.053 0.055 0.049 0.050 0.056
  Y-axis 0.004 0.015 0.011 − 0.018 − 0.017 0.009
  Z-axis 0.009 0.018 0.016 0.009 0.010 0.014
DBC7 X-axis 0.043 0.049 0.052 0.052 0.053 0.051
  Y-axis − 0.003 0.002 − 0.001 − 0.014 − 0.012 − 0.010
  Z-axis 0.024 0.031 0.031 0.031 0.033 0.029
MLC7 X-axis 0.040 0.044 0.047 0.055 0.056 0.043
  Y-axis 0.004 0.017 0.013 − 0.020 − 0.018 0.011
  Z-axis 0.008 0.012 0.012 0.013 0.014 0.012
MR7 X-axis 0.005 0.007 0.007 0.008 0.007 0.006
  Y-axis 0.002 − 0.003 − 0.001 0.003 0.002 0.000
  Z-axis 0.016 0.020 0.021 0.024 0.025 0.020
  1. X: + mesial, -distal; Y: + lingual, -buccal; Z: + occlusal, -apical; BC5: the buccal cusp of the second premolar; R5: the apex of the second premolar; MBC6: the mesiobuccal cusp of the mandibular first molar; DBC6: the distobuccal cusp of the first molar; MLC6: the mesiolingual cusp of the first molar; MR6: the mesial apex of the first molar; MBC7: the mesiobuccal cusp of the second molar; DBC7: the distobuccal cusp of the second molar; MLC7: the mesiolingual cusp of the second molar; MR7: the mesial apex of the second molar