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

Progress in Orthodontics

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

	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

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