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Table 2 (a) Stress distribution and displacement in the sutures with miniplate, (b) stress distribution and displacement in the sutures with mini-implant

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

FM

TD–FM

X axis—FM

Y axis—FM

Z axis—FM

ZM

TD–ZM

X axis—ZM

Y axis—ZM

Z axis—ZM

1

0.11096

2.22E−04

4.42E−05

− 9.13E−05

1.87E−04

5.69E−02

1.55E−03

3.81E−05

1.24E−03

8.99E−04

1

0.012632

2.38E−04

5.46E−05

− 8.35E−05

2.13E−04

6.42E−02

1.68E−03

2.37E−04

1.39E−03

1.04E−03

1

0.014168

2.55E−04

6.49E−05

− 7.57E−05

2.39E−04

7.15E−02

1.80E−03

4.36E−04

1.54E−03

1.18E−03

1

6.99E−03

1.79E−04

1.63E−05

− 6.04E−05

1.40E−04

7.65E−02

7.70E−04

6.03E−04

5.61E−04

2.85E−04

1

7.95E−03

1.95E−04

2.59E−05

− 5.18E−05

1.57E−04

8.70E−02

8.38E−04

7.04E−04

6.43E−04

3.48E−04

1

8.91E−03

2.12E−04

3.55E−05

− 4.32E−05

1.75E−04

9.74E−02

9.06E−04

8.05E−04

7.24E−04

4.11E−04

2

1.59E−02

2.76E−04

8.92E−05

− 3.96E−05

2.56E−04

8.13E−02

2.32E−03

4.38E−05

1.90E−03

1.30E−03

2

1.81E−02

3.02E−04

1.02E−04

− 2.35E−05

2.91E−04

9.17E−02

2.50E−03

3.41E−04

2.12E−03

1.51E−03

2

2.03E−02

3.29E−04

1.14E−04

− 1.15E−05

3.25E−04

1.02E−01

2.69E−03

6.38E−04

2.35E−03

1.71E−03

2

1.19E−02

2.68E−04

2.45E−05

− 9.05E−05

2.09E−04

1.17E−01

1.42E−03

1.04E−03

1.14E−03

4.24E−04

2

1.35E−02

2.93E−04

3.89E−05

− 7.77E−05

2.36E−04

1.33E−01

1.56E−03

1.20E−03

1.30E−03

5.07E−04

2

1.52E−01

3.18E−04

5.33E−05

− 6.48E−05

2.63E−04

1.49E−01

1.71E−03

1.35E−03

1.46E−03

5.91E−04

3

2.66E−01

6.70E−04

8.89E−05

− 3.87E−04

4.80E−04

1.41E−01

3.62E−03

1.52E−04

2.85E−03

2.20E−03

3

3.03E−02

7.13E−04

1.14E−04

− 3.68E−04

5.48E−04

1.51E+05

3.93E−03

6.38E−04

3.20E−03

2.54E−03

3

3.40E−02

7.56E−04

1.40E−04

− 3.50E−04

6.17E−04

1.78E−01

4.24E−03

1.12E−03

3.56E−03

2.88E−03

3

1.88E−02

6.73E−04

− 3.53E−05

− 3.84E−04

3.40E−04

1.86E−01

1.75E−03

1.46E−03

1.09E−03

7.43E−04

3

2.14E−02

7.22E−04

− 1.38E−05

− 3.44E−04

3.85E−04

2.11E−01

1.90E−03

1.71E−03

1.26E−03

9.09E−04

3

2.41E−02

7.71E−04

7.72E−06

− 3.05E−04

4.31E−04

2.37E−01

2.05E−03

1.96E−03

1.42E−03

1.07E−03

4

4.59E−03

9.23E−05

6.16E−05

− 3.46E−05

− 5.51E−06

9.27E−03

2.66E−04

9.90E−05

3.43E−05

2.51E−04

4

5.24E−03

1.02E−04

7.24E−05

− 3.07E−05

3.45E−06

1.05E−02

3.03E−04

1.17E−04

6.46E−05

2.86E−04

4

5.89E−03

1.11E−04

8.32E−05

− 2.67E−05

1.24E−05

1.18E−02

3.40E−04

1.36E−04

9.48E−05

3.22E−04

4

5.64E−03

9.13E−05

2.04E−05

5.22E−06

− 2.05E−05

1.54E−01

2.25E−04

− 3.20E−06

9.15E−05

2.02E−04

4

6.44E−03

1.04E−04

2.92E−05

1.23E−05

− 7.21E−06

1.73E−01

2.57E−04

2.19E−05

1.12E−04

2.31E−04

4

7.23E−03

1.16E−04

3.80E−05

1.94E−05

6.05E−06

1.93E−01

2.88E−04

4.70E−05

1.33E−04

2.61E−04

5

6.89E−03

1.38E−04

9.24E−05

− 5.19E−05

− 8.27E−06

1.39E−01

3.98E−04

1.48E−04

5.14E−05

3.76E−04

5

7.86E−03

1.52E−04

1.09E−04

− 4.60E−05

5.18E−06

1.58E−02

4.54E−04

1.76E−04

9.68E−05

4.30E−04

5

8.84E−03

1.67E−04

1.25E−04

− 4.01E−05

1.86E−05

1.77E−01

5.10E−04

2.04E−04

1.42E−04

4.84E−04

5

8.46E−03

1.37E−04

3.05E−05

7.83E−06

− 3.07E−05

2.30E−02

3.38E−04

− 4.80E−06

1.37E−04

3.03E−04

5

9.65E−03

1.56E−04

4.38E−05

1.85E−05

− 1.08E−05

2.60E−02

3.85E−04

3.28E−05

1.68E−04

3.47E−04

5

1.08E−02

1.74E−04

5.70E−05

2.91E−05

9.07E−06

2.89E−02

4.32E−04

7.04E−05

1.99E−04

3.91E−04

6

1.15E−02

2.31E−04

1.54E−04

− 8.65E−05

− 1.38E−05

2.32E−02

6.64E−04

2.47E−04

8.57E−05

6.26E−04

6

1.31E−02

2.54E−04

1.81E−04

− 7.66E−05

8.63E−06

2.63E−02

7.57E−04

2.93E−04

1.61E−04

7.16E−04

6

1.47E−02

2.78E−04

2.00E−04

− 6.68E−05

3.10E−05

2.95E−02

8.50E−04

3.39E−04

2.37E−04

8.06E−04

6

1.41E−02

2.28E−04

5.09E−05

1.30E−05

− 5.11E−05

3.84E−02

5.64E−04

− 8.00E−06

2.29E−04

5.05E−04

6

1.61E−02

2.59E−04

7.30E−05

3.08E−05

− 1.80E−05

4.33E−02

6.41E−04

5.47E−05

2.80E−04

5.79E−04

6

1.81E−02

2.90E−04

9.50E−05

4.85E−05

1.51E−05

4.82E−02

7.19E−04

1.17E−04

3.32E−04

6.65E−04

Appliance system

ZT

TD–ZT

X axis—ZT

Y axis—ZT

Z axis—ZT

ZF

TD–ZF

X axis—ZF

Y axis—ZF

Z axis—ZF

1

9.45E−02

6.62E−04

− 3.46E−05

3.23E−04

4.87E−04

5.86E−03

1.12E−04

2.25E+03

5.58E−05

9.01E−05

1

1.08E−01

7.10E−04

1.15E−05

3.93E−04

5.17E−04

6.62E−03

1.23E−04

3.74E−05

6.03E−05

1.05E−04

1

1.21E−01

7.57E−04

5.77E−05

4.63E−04

5.47E−04

7.38E−03

1.34E−04

5.23E−05

6.48E−05

1.21E−04

1

1.85E−02

5.14E−04

3.13E−04

2.46E−04

3.35E−04

5.05E−03

1.78E−04

7.07E−05

8.68E−05

1.51E−04

1

1.99E−02

5.68E−04

3.67E−04

2.97E−04

3.69E−04

5.64E−03

2.00E−04

8.90E−05

9.74E−05

1.72E−04

1

2.13E−02

6.22E−04

4.21E−04

3.47E−04

4.04E−04

6.23E−03

2.22E−04

1.07E−04

1.08E−04

1.94E−04

2

1.49E−01

1.03E−03

− 3.27E−05

5.14E−04

7.62E−04

8.95E−03

1.74E−04

2.00E−05

9.19E−05

1.42E−04

2

1.69E−01

1.11E−03

3.95E−05

6.25E−04

8.09E−04

1.01E−02

1.90E−04

4.23E−05

9.84E−05

1.65E−04

2

1.90E−01

1.18E−03

1.12E−04

7.36E−04

8.56E−04

1.13E−02

2.06E−04

6.47E−05

1.05E−04

1.88E−04

2

3.72E−02

1.00E−03

5.05E−04

5.56E−04

6.66E−04

8.26E−03

3.13E−04

1.69E−04

1.73E−04

2.53E−04

2

4.02E−02

1.10E−03

6.12E−04

6.66E−04

7.33E−04

9.93E−03

3.52E−04

2.04E−04

1.94E−04

2.88E−04

2

4.32E−02

1.21E−03

7.19E−04

7.77E−04

7.99E−04

1.03E−01

3.91E−04

2.38E−04

2.15E−04

3.22E−04

3

2.05E−01

1.47E−03

− 1.40E−04

6.94E−04

1.07E−03

1.41E−02

2.66E−04

7.82E−05

1.25E−04

2.12E−04

3

2.34E−01

1.58E−03

− 3.83E−05

8.45E−04

1.14E−03

1.60E−02

2.94E−04

1.44E−04

1.36E−04

2.48E−04

3

2.63E−01

1.69E−03

6.36E−05

9.97E−04

1.21E−03

1.78E−02

3.22E−04

1.50E−04

1.47E−04

2.84E−04

3

3.89E−02

1.13E−03

7.87E−04

4.42E−04

7.15E−04

1.28E−01

4.31E−04

1.20E−04

1.85E−04

3.76E−04

3

4.18E−02

1.25E−03

9.05E−04

5.40E−04

7.89E−04

1.42E−01

4.84E−04

1.62E−04

2.08E−04

4.31E−04

3

4.47E−02

1.37E−03

1.02E−03

6.39E−04

8.63E−04

1.56E−02

5.37E−04

2.03E−04

2.31E−04

4.86E−04

4

2.20E−03

1.36E−05

1.09E−05

4.96E−06

7.22E−06

4.90E−05

7.05E−06

6.98E−06

1.49E−06

− 2.18E−07

4

2.51E−03

1.45E−05

1.16E−05

6.63E−06

7.64E−06

5.51E−05

7.45E−06

7.38E−06

1.72E−06

− 7.93E−08

4

2.82E−03

1.53E−05

1.24E−05

8.29E−06

8.06E−06

6.12E−05

7.85E−06

7.77E−06

1.96E−06

5.91E−08

4

1.15E−03

3.98E−05

7.90E−06

1.96E−05

3.10E−05

2.80E−04

1.59E−05

− 8.50E−06

6.77E−06

8.06E−06

4

1.65E−03

4.32E−05

1.22E−05

2.42E−05

3.37E−05

3.09E−04

1.70E−05

− 7.62E−06

7.26E−06

9.25E−06

4

1.78E−03

4.67E−05

1.66E−05

2.88E−05

3.64E−05

3.37E−04

1.80E−05

− 6.74E−06

7.76E−06

1.04E−05

5

3.30E−03

2.05E−05

1.64E−05

7.44E−06

1.08E−05

7.35E−05

1.06E−05

1.05E−05

2.24E−06

− 3.27E−07

5

3.76E−03

2.17E−05

1.75E−05

9.94E−06

1.15E−05

8.26E−05

1.12E−05

1.11E−05

2.59E−06

− 1.19E−07

5

4.22E−03

2.29E−05

1.86E−05

1.24E−05

1.21E−05

9.17E−05

1.18E−05

1.17E−05

2.94E−06

8.86E−08

5

2.28E−03

5.96E−05

1.19E−05

2.95E−05

4.66E−05

4.20E−04

2.39E−05

− 1.28E−05

1.02E−05

1.21E−05

5

2.48E−03

6.48E−05

1.84E−05

3.63E−05

5.06E−05

4.63E−04

2.54E−05

− 1.14E−05

1.09E−05

1.39E−05

5

2.68E−03

7.00E−05

2.49E−05

4.31E−05

5.46E−05

5.06E−04

2.69E−05

− 1.01E−05

1.16E−05

1.57E−05

6

5.50E−03

3.41E−05

2.73E−05

1.24E−05

1.80E−05

1.22E−04

1.76E−05

1.74E−05

3.73E−06

− 5.44E−07

6

6.27E−03

3.61E−05

2.91E−05

1.66E−05

1.91E−05

1.38E−04

1.86E−05

1.84E−05

4.31E−06

− 1.98E−07

6

7.04E−03

3.82E−05

3.09E−05

2.07E−05

2.02E−05

1.53E−04

1.96E−05

1.94E−05

4.89E−06

− 1.48E−07

6

3.80E−03

9.94E−05

1.98E−05

4.91E−05

7.76E−05

7.01E−04

3.99E−05

− 2.13E−05

1.69E−05

2.01E−05

6

4.13E−03

1.08E−04

3.06E−05

6.05E−05

8.43E−05

7.72E−04

4.24E−05

− 1.91E−05

1.82E−05

2.31E−05

6

4.46E−03

1.17E−04

4.14E−05

7.19E−05

9.10E−05

8.43E−04

4.49E−05

− 1.68E−05

1.94E−05

2.61E−05

Appliance system

PM

TD–PM

X axis—PM

Yaxis—PM

Z axis—PM

1

3.06E−02

6.20E−04

4.20E−04

− 9.39E−06

− 1.56E−0

1

3.49E−02

6.91E−04

4.81E−04

5.24E−05

− 1.06E−04

1

3.92E−02

7.63E−04

5.42E−04

1.14E−04

− 5.49E−05

1

2.70E−02

7.30E−04

− 4.81E−05

− 1.65E−04

− 2.22E−04

1

3.08E−02

8.11E−04

− 1.36E−05

− 9.97E−05

− 1.68E−04

1

3.46E−02

8.92E−04

2.09E−05

− 3.46E−05

− 1.13E−04

2

2.04E+00

5.27E−04

3.95E−04

6.61E−05

− 2.14E−04

2

2.32E+00

5.77E−04

4.55E−04

1.15E−04

− 1.85E−04

2

2.60E+00

6.27E−04

5.15E−04

1.64E−04

− 1.56E−04

2

1.73E+00

5.11E−04

− 1.28E−04

− 1.33E−04

− 1.71E−04

2

1.97E+00

5.59E−04

− 8.79E−05

− 9.51E−05

− 1.47E−04

2

2.21E+00

6.06E−04

− 4.81E−05

− 5.68E−05

− 1.24E−04

3

5.60E−02

2.25E−03

1.32E−03

− 3.14E−04

− 8.26E−04

3

6.34E−02

2.48E−03

1.50E−03

− 1.03E−04

− 6.98E−04

3

7.09E−02

2.72E−03

1.69E−03

− 1.08E−04

− 5.70E−04

3

6.21E−02

2.45E−03

7.59E−05

− 6.24E−04

− 9.28E−04

3

7.06E−01

2.67E−03

1.94E−04

− 3.90E−04

− 7.97E−04

3

7.90E−02

2.89E−03

3.13E−04

− 1.56E−04

− 6.66E−04

4

3.96E−01

4.96E−05

4.55E−05

1.78E−05

4.28E−06

4

4.48E−01

5.38E−05

4.92E−05

2.26E−05

6.06E−06

4

5.01E−01

5.80E−05

5.30E−05

2.74E−05

7.83E−06

4

4.15E−01

2.98E−05

− 1.44E−05

1.34E−05

3.12E−06

4

4.70E−01

3.20E−05

− 1.22E−05

1.60E−05

5.59E−06

4

5.25E−01

3.41E−05

− 1.00E−05

1.86E−05

8.07E−06

5

5.94E−01

7.44E−05

6.82E−05

2.68E−05

6.42E−06

5

6.73E−01

8.07E−05

7.38E−05

3.39E−05

9.09E−06

5

7.51E−01

8.70E−05

7.95E−05

4.11E−05

1.18E−05

5

6.23E−01

4.47E−05

− 2.16E−05

2.00E−05

4.68E−06

5

7.05E−01

4.79E−05

− 1.83E−05

2.40E−05

8.39E−06

5

7.88E−01

5.12E−05

− 1.51E−05

2.80E−05

1.21E−05

6

9.90E−01

1.24E−04

1.14E−04

4.46E−05

1.07E−05

6

1.12E+00

1.34E−04

1.24E−04

5.65E−05

1.51E−05

6

1.25E+00

1.45E−04

1.32E−04

6.84E−05

1.96E−05

6

1.04E+00

7.44E−05

− 3.59E−05

3.34E−05

7.80E−06

6

1.18E+00

7.99E−05

− 3.05E−05

4.00E−05

1.40E−05

6

1.31E+00

8.54E−05

− 2.51E−05

4.66E−05

2.02E−05

  1. *Average values of the right side and left side of each suture and the surface landmarks are taken
  2. 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