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

Maruo, Ivan Toshio; Maruo, Hiroshi; Saga, Armando Yukio; de Oliveira, Dauro Douglas; Argenta, Marco André; Tanaka, Orlando Motohiro

doi:10.1186/s40510-016-0130-4

Progress in Orthodontics

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

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

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