Stress distribution and displacement in the maxillofacial complex during intrusion and distalization of the maxillary arch using miniplates versus mini-implants: a 3-dimensional finite element study

Somaskandhan, Abinaya; Kumar, N M. Vijay; Vijayalakshmi, R. Devaki

doi:10.1186/s40510-023-00455-6

Progress in Orthodontics

Table 3 Stress distribution and displacement in anatomical landmarks

From: Stress distribution and displacement in the maxillofacial complex during intrusion and distalization of the maxillary arch using miniplates versus mini-implants: a 3-dimensional finite element study

Appliance system	Frontal process	TD	X-axis	Y-axis	Z-axis	ANS	TD	X-axis	Y-axis	Z-axis
1	1.16529	3.51E−04	− 1.97E−05	− 1.07E−04	2.33E−04	5.69E−01	8.52E−04	− 3.01E−04	− 4.40E−04	4.88E−04
1	1.31896	3.80E−04	1.77E−05	− 1.02E−04	2.55E−04	6.44E−01	8.91E−04	− 2.84E−04	− 4.05E−04	5.23E−04
1	1.47264	4.08E−04	5.51E−05	− 9.63E−05	2.78E−04	7.20E−01	9.31E−04	− 2.68E−04	− 3.69E−04	5.58E−04
1	5.12E−01	3.19E−04	3.19E−04	− 1.79E−04	1.90E−04	1.23E+00	8.69E−04	− 2.47E−04	− 4.54E−04	4.82E−04
1	5.85E−01	3.42E−04	3.42E−04	− 1.64E−04	2.09E−04	1.40E+00	9.11E−04	− 2.22E−04	− 4.15E−04	5.20E−04
1	6.57E−01	3.64E−04	3.64E−04	− 1.49E−04	2.29E−04	1.57E+00	9.52E−04	− 1.96E−04	− 3.77E−04	5.58E−04
2	1.58E+00	3.36E−04	1.81E−05	− 2.69E−05	2.40E−04	8.22E−01	8.95E−04	− 3.27E−04	− 2.81E−04	6.48E−04
2	1.79E+00	3.69E−04	6.31E−05	− 1.60E−05	2.64E−04	9.31E−01	9.40E−04	− 3.06E−04	− 2.39E−04	6.90E−04
2	2.00E+00	4.03E−04	1.08E−04	− 5.12E−06	2.89E−04	1.04E+00	9.84E−04	− 2.85E−04	− 1.96E−01	7.32E−04
2	7.15E−01	2.94E−04	9.45E−05	− 1.17E−04	2.21E−04	1.80E+00	9.06E−04	− 2.36E−04	− 2.89E−04	6.40E−04
2	8.16E−01	3.17E−04	1.19E−04	− 1.04E−04	2.42E−04	2.05E+00	9.57E−04	− 2.05E−04	− 2.45E−04	6.86E−04
2	9.17E−01	3.40E−04	1.43E−04	− 9.06E−05	2.63E−04	2.30E+00	1.01E−03	− 1.74E−04	− 2.00E−04	7.32E−04
3	3.01E+00	1.11E−03	− 7.92E−05	− 4.91E−04	6.92E−04	1.50E+00	2.58E−03	− 7.53E−04	− 1.63E−03	1.29E−03
3	3.41E+00	1.19E−03	1.62E−05	− 4.68E−04	7.63E−04	1.70E+00	2.69E−03	− 7.11E−04	− 1.53E−03	1.39E−03
3	3.81E+00	1.27E−03	1.12E−04	− 4.45E−04	8.35E−04	1.90E+00	2.80E−03	− 6.68E−04	− 1.43E−03	1.49E−03
3	1.47E+00	1.10E−03	− 1.53E−05	− 6.37E−04	5.90E−04	3.13E+00	2.64E−03	− 6.11E−04	− 1.67E−03	1.28E−03
3	1.67E+00	1.17E−03	2.78E−05	− 5.82E−04	6.54E−04	3.57E+00	2.75E−03	− 5.45E−04	− 1.56E−03	1.38E−03
3	1.88E+00	1.25E−03	7.09E−05	− 5.27E−04	7.18E−04	4.00E+00	2.86E−03	− 4.79E−04	− 1.45E−03	1.49E−03
4	4.20E−01	8.59E−05	4.32E−05	− 4.50E−05	1.01E−05	3.84E−01	2.35E−04	− 1.95E−06	− 8.14E−06	− 8.80E−04
4	4.77E−01	9.21E−05	5.14E−05	− 3.00E−05	1.90E−05	4.36E−01	2.44E−04	4.42E−06	− 8.70E−07	− 1.79E−04
4	5.34E−01	9.83E−05	5.96E−05	− 3.48E−05	2.78E−05	4.88E−01	2.53E−04	1.08E−05	6.40E−06	− 1.70E−04
4	4.65E−01	1.01E−04	1.40E−05	− 3.91E−07	− 1.16E−05	5.40E−01	2.31E−04	− 1.43E−05	− 3.71E−06	− 1.73E−04
4	5.30E−01	1.11E−04	2.60E−05	9.50E−06	2.87E−06	6.15E−01	2.42E−04	− 6.69E−06	4.18E−06	− 1.62E−04
4	5.96E−01	1.20E−04	3.80E−05	1.94E−05	1.74E−05	6.90E−01	2.53E−04	9.24E−07	1.21E−05	− 1.51E−04
5	6.30E−01	1.29E−04	6.48E−05	− 6.75E−05	1.52E−05	5.76E−01	3.53E−04	− 2.93E−06	− 1.22E−05	− 2.82E−04
5	7.16E−01	1.38E−04	7.71E−05	− 5.98E−05	2.85E−05	6.54E−01	3.66E−04	6.62E−06	− 1.30E−06	− 2.68E−04
5	8.02E−01	1.47E−04	8.94E−05	− 5.22E−05	4.17E−05	7.32E−01	3.79E−04	1.62E−05	9.61E−06	− 2.55E−04
5	6.97E−01	1.52E−04	2.10E−05	− 5.87E−07	− 1.75E−05	8.09E−01	3.47E−04	− 2.15E−05	− 5.56E−06	− 2.59E−04
5	7.95E−01	1.66E−04	3.90E−05	1.42E−05	4.31E−06	9.22E−01	3.63E−04	− 1.00E−05	6.27E−06	− 2.43E−04
5	8.93E−01	1.81E−04	5.70E−05	2.91E−05	2.61E−05	1.03E+00	3.79E−04	1.39E−06	1.81E−05	− 2.26E−04
6	1.05E+00	2.15E−04	1.08E−04	− 1.12E−04	2.53E−05	9.60E−01	5.88E−04	− 4.88E−06	− 2.04E−05	− 4.70E−04
6	1.19E+00	2.30E−04	1.29E−04	− 9.97E−05	4.74E−05	1.09E+00	6.10E−04	1.10E−05	− 2.17E−06	− 4.47E−04
6	1.34E+00	2.46E−04	1.49E−04	− 8.69E−05	6.95E−05	1.22E+00	6.32E−04	2.70E−05	1.60E−05	− 4.25E−04
6	1.16E+00	2.53E−04	3.50E−05	− 9.79E−07	− 2.91E−05	1.35E+00	5.78E−04	− 3.58E−05	− 9.27E−06	− 4.32E−04
6	1.33E+00	2.77E−04	6.50E−05	2.37E−05	7.18E−06	1.54E+00	6.05E−04	− 1.67E−05	1.04E−05	− 4.04E−04
6	1.49E+00	3.01E−04	9.50E−05	4.85E−05	4.35E−05	1.72E+00	6.32E−04	2.31E−06	3.02E−05	−3.76E−04

Appliance system	Point A	TD	X-axis	Y-axis	Z-axis	Prosthion	TD	X-axis	Y-axis	Z-axis
1	5.97E−01	1.12E−03	− 4.38E−04	− 7.01E−04	5.55E−04	1.59E+00	1.34E−03	− 4.93E−04	− 8.80E−04	6.18E−04
1	6.62E−01	1.16E−03	− 4.19E−04	− 6.62E−04	6.02E−04	1.80E+00	1.40E−03	− 4.64E−04	− 8.38E−04	6.75E−04
1	7.27E−01	1.20E−03	− 4.00E−04	− 6.22E−04	6.50E−04	2.01E+00	1.45E−03	− 4.34E−04	− 7.96E−04	7.31E−04
1	5.30E−01	1.12E−03	− 4.41E−04	− 7.07E−04	4.97E−04	1.33E+00	1.34E−03	− 5.00E−04	− 8.84E−04	5.79E−04
1	5.88E−01	1.15E−03	− 4.20E−04	− 6.70E−04	5.42E−04	1.51E+00	1.40E−03	− 4.67E−04	− 8.46E−04	6.31E−04
1	6.45E−01	1.18E−03	− 3.99E−04	− 6.32E−04	5.86E−04	1.69E+00	1.45E−03	− 4.34E−04	8.08E−04	6.83E−04
2	8.99E−01	1.22E−03	− 4.90E−04	− 6.10E−04	7.47E−04	2.44175	1.48E−03	− 5.89E−04	− 8.25E−04	8.31E−04
2	9.96E−01	1.27E−03	− 4.60E−04	− 5.57E−04	8.07E−04	2.76E+00	1.55E−03	− 5.55E−04	− 7.68E−04	9.03E−04
2	1.09E+00	1.31E−03	− 4.31E−04	− 5.03E−04	8.66E−04	3.08E+00	1.63E−03	− 5.21E−04	− 7.12E−04	9.74E−04
2	7.99E−01	1.17E−03	− 4.93E−04	− 5.99E−04	6.69E−04	2.03E+00	1.46E−03	− 6.03E−04	− 8.17E−04	7.76E−04
2	8.83E−01	1.21E−03	− 4.62E−04	− 5.55E−04	7.24E−04	2.30E+00	1.53E−03	− 5.62E−04	− 7.67E−04	8.41E−04
2	9.66E−01	1.26E−03	− 4.31E−04	− 5.10E−04	7.78E−04	2.56E+00	1.61E−03	− 5.21E−04	− 7.16E−04	9.07E−04
3	1.49E+00	3.35E−03	− 1.10E−03	− 2.35E−03	1.45E−03	3.97E+00	3.93E−03	− 1.22E−03	− 2.84E−03	1.63E−03
3	1.65E+00	3.45E−03	− 1.05E−03	− 2.24E−03	1.58E−03	4.50E+00	4.08E−03	− 1.14E−03	− 2.73E−03	1.78E−03
3	1.81E+00	3.54E−03	− 1.00E−03	− 2.13E−03	1.71E−03	5.02E+00	0.004226	− 1.07E−03	− 2.61E−03	1.93E−03
3	1.32E+00	3.35E−03	− 1.10E−03	− 2.37E−03	1.31E−03	3.33E+00	3.93E−03	1.24E−03	− 2.85E−03	1.53E−03
3	1.46E+00	3.44E−03	− 1.05E−03	− 2.27E−03	1.43E−03	3.77E+00	4.08E−03	1.15E−03	− 2.75E−03	1.67E−03
3	1.61E+00	3.53E−03	− 9.92E−04	− 2.16E−03	1.55E−03	4.20E+00	4.23E−03	1.07E−03	− 2.65E−03	1.81E−03
4	9.25E−01	2.30E−04	− 2.73E−05	4.74E−05	− 1.77E−04	8.16E−01	2.25E−04	− 6.05E−06	5.57E−05	− 1.85E−04
4	1.05E+00	2.38E−04	− 1.58E−05	5.39E−05	− 1.67E−04	9.21E−01	2.33E−04	− 1.03E−06	6.18E−05	− 1.78E−04
4	1.18E+00	2.46E−04	− 4.34E−06	6.04E−05	− 1.57E−04	1.03E+00	2.40E−04	3.99E−06	6.79E−05	− 1.71E−04
4	8.70E−01	2.36E−04	3.12E−05	4.87E−05	− 1.83E−04	7.32E−01	2.29E−04	9.13E−06	5.91E−05	− 1.86E−04
4	9.85E−01	2.46E−04	4.02E−05	5.57E−05	− 1.74E−04	8.26E−01	2.37E−04	1.37E−05	6.57E−05	− 1.78E−04
4	1.10E+00	2.55E−04	4.92E−05	6.27E−05	− 1.65E−04	9.19E−01	2.46E−04	1.84E−05	7.23E−05	− 1.70E−04
5	1.39E+00	3.45E−04	− 4.10E−05	7.11E−05	− 2.65E−04	1.22E+00	3.38E−04	− 9.08E−06	8.35E−05	− 2.78E−04
5	1.58E+00	3.57E−04	− 2.38E−05	8.09E−05	− 2.50E−04	1.38E+00	3.49E−04	− 1.55E−06	9.27E−05	− 2.67E−04
5	1.77E+00	3.69E−04	− 6.51E−06	9.07E−05	− 2.36E−04	1.54E+00	3.61E−04	5.99E−06	1.02E−04	− 2.56E−04
5	1.31E+00	3.54E−04	4.68E−05	7.31E−05	− 2.75E−04	1.10E+00	3.44E−04	1.37E−05	8.87E−05	− 2.79E−04
5	1.48E+00	3.68E−04	6.03E−05	8.36E−05	− 2.61E−04	1.24E+00	3.56E−04	2.06E−05	9.85E−05	− 2.67E−04
5	1.65E+00	3.82E−04	7.38E−05	9.40E−05	− 2.47E−04	1.38E+00	3.68E−04	2.75E−05	1.08E−04	− 2.56E−04
6	2,31,339	5.74E−04	− 6.83E−05	1.18E−04	− 4.41E−04	2.04E+00	5.63E−04	− 1.51E−05	1.39E−04	− 4.63E−04
6	2.63E+00	5.95E−04	− 3.96E−05	1.35E−04	− 4.17E−04	2.30E+00	5.82E−04	− 2.58E−06	1.54E−04	− 4.45E−04
6	2.94E+00	6.15E−04	− 1.08E−05	1.51E−04	− 3.93E−04	2.57E+00	6.01E−04	9.98E−06	1.70E−04	− 4.27E−04
6	2.18E+00	5.91E−04	7.80E−05	1.22E−04	− 4.58E−04	1.83E+00	5.73E−04	2.28E−05	1.48E−04	− 4.64E−04
6	2.46E+00	6.14E−04	1.00E−04	1.39E−04	− 4.35E−04	2.06E+00	5.93E−04	3.44E−05	1.64E−04	− 4.45E−04
6	2.75E+00	6.37E−04	1.23E−04	1.57E−04	− 4.11E−04	2.30E+00	6.14E−04	4.59E−05	1.81E−04	− 4.26E−04

Appliance system	Maxillary process of zygoma	TD	X-axis	Y-axis	Z-axis
1	3.24E+00	1.09E−03	− 1.37E−04	7.52E−04	6.89E−04
1	3.65E+00	1.19E−03	− 9.33E−05	8.86E−04	7.47E−04
1	4.05E+00	1.30E−03	− 4.93E−05	1.02E−03	8.05E−04
1	3.07E+00	5.40E−04	3.18E−04	2.44E−04	2.57E−04
1	3.38E+00	5.96E−04	3.56E−04	3.68E−04	3.06E−04
1	3.69E+00	6.52E−04	3.94E−04	4.91E−04	3.54E−04
2	4.83E+00	1.67E−03	− 1.95E−04	1.26E−03	9.81E−04
2	5.42E+00	1.83E−03	− 1.32E−04	1.45E−03	1.06E−03
2	6.02E+00	1.98E−03	− 6.85E−05	1.63E−03	1.14E−03
2	4.52E+00	1.08E−03	5.54E−04	7.81E−04	3.91E−04
2	4.97E+00	1.20E−03	6.11E−04	9.53E−04	4.55E−04
2	5.43E+00	1.32E−03	6.68E−04	1.12E−03	5.18E−04
3	8.18E+00	2.49E−03	− 3.05E−04	1.50E−03	1.66E−03
3	9.20E+00	2.71E−03	− 1.94E−04	1.85E−03	1.81E−03
3	1.02E+01	2.93E−03	− 8.32E−05	2.20E−03	1.96E−03
3	7,73,533	1.80E−03	8.16E−04	1.37E−04	6.72E−04
3	8.52E+00	1.98E−03	9.12E−04	4.59E−04	8.00E−04
3	9.31E+00	2.15E−03	1.01E−03	7.81E−04	9.27E−04
4	6.37E−01	2.54E−04	6.87E−05	6.51E−05	2.36E−04
4	6.94E−01	2.72E−04	7.88E−05	7.93E−05	2.55E−04
4	7.52E−01	2.90E−04	8.89E−05	9.36E−01	2.74E−04
4	5.85E−01	2.51E−04	− 4.40E−05	7.79E−05	2.26E−04
4	6.54E−01	2.67E−04	− 3.52E−05	9.36E−05	2.44E−04
4	7.24E−01	2.83E−04	− 2.63E−01	1.09E−04	2.61E−04
5	9.55E−01	3.80E−04	1.03E−04	9.77E−05	3.54E−04
5	1.04E+00	4.07E−04	1.18E−04	1.19E−04	3.83E−04
5	1.13E+00	4.35E−04	1.33E−04	1.40E−04	4.12E−04
5	8.77E−01	3.76E−04	− 6.59E−05	1.17E−04	3.39E−04
5	9.82E−01	4.00E−04	− 5.27E−05	1.40E−04	3.66E−04
5	1.09E+00	4.25E−04	− 3.95E−05	1.64E−04	3.92E−04
6	1.59E+00	6.34E−04	1.72E−04	1.63E−04	5.91E−04
6	1.74E+00	6.79E−04	1.97E−04	1.98E−04	6.38E−04
6	1.88E+00	7.24E−04	2.22E−04	2.34E−04	6.86E−04
6	1.46E+00	6.27E−04	− 1.10E−04	1.95E−04	5.65E−04
6	1,63,588	6.67E−04	− 8.79E−05	2.34E−04	6.09E−04
6	1.81E+00	7.08E−04	− 6.59E−05	2.73E−04	6.53E−04

*Average values of the right side and left side of each suture and the surface landmarks are taken. Appliance system 1—Miniplate—200 g of force, Appliance system 2—Miniplate—300 g of force, Appliance system 3—Miniplate—500 g of force, Appliance system 4—Mini-implant—200 g of force, Appliance system 5—Mini-implant—300 g of force, Appliance system 6—Mini-implant—500 g of force, FM fronto-maxillary suture, ZM zygomatico-maxillary suture, ZT zygomatico-temporal suture, ZF zygomatico-frontal suture, PM pterygo-maxillary suture, TD total displacement, ANS anterior nasal spine

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