These models were validated before analysing the stress of the three-joint complex (Table 2). The stiffness results measured from three models of different PI were similar to the results of previous studies from cadavers [17–19] (Fig. 4). We believe that the difference is due to the differences in the model details.
Table 2
Stiffness comparison with the results of the list literature
|
Moment(Nm)
|
Anteflexion(N·m/°)
|
Postextension(N·m/°)
|
Left rotation(N·m/°)
|
Left bending(N·m/°)
|
Heth et al.[17]
|
10
|
1.1
|
2.35
|
1.33
|
2.61
|
Liu et al.[18]
|
10
|
2.35
|
3.58
|
2.86
|
8.98
|
Yamamoto et al.[19]
|
10
|
1.75
|
3.22
|
2.44
|
5.66
|
Low PI
|
10
|
2.02
|
3.05
|
2.53
|
6.18
|
Normal PI
|
10
|
1.83
|
3.18
|
2.58
|
6.43
|
High PI
|
10
|
1.76
|
3.31
|
2.46
|
5.74
|
The age and body mass index (BMI) of the three volunteers were similar, and all were women (Table 2). We measured the pelvic parameters (Table 3), the height of the vertebral body, and the height of the intervertebral space (Table 4) and graded the degree of degeneration of the facet joints (Table 5). In general, the three models were comparable.
Table 3
Demographics for the three groups of different PI
Group
|
Age
|
Gender
|
SS(°)
|
PT(°)
|
PI(°)
|
BMI(kg/㎡)
|
Low PI
|
36
|
F
|
18.03
|
9.95
|
27.44
|
21.48
|
Normal PI
|
38
|
F
|
32.56
|
16.27
|
47.05
|
20.54
|
High PI
|
33
|
F
|
46.26
|
15.38
|
62.28
|
20.87
|
Table 4
Weishaupt classification of facet joint degeneration at L3-S1 of different groups
Group
|
L3/4
|
L4/5
|
L5/S1
|
|
Left
|
Right
|
Left
|
Right
|
Left
|
Right
|
Low PI
|
0
|
0
|
1
|
1
|
1
|
1
|
Normal PI
|
1
|
1
|
1
|
1
|
1
|
1
|
High PI
|
1
|
1
|
1
|
1
|
1
|
1
|
Table 5
The orientation of facet joint at L3-S1 of different groups
Group
|
L3/4
|
L4/5
|
L5/S1
|
|
Left
|
Right
|
Left
|
Right
|
Left
|
Right
|
Low PI
|
51.88
|
49.32
|
50.37
|
49.54
|
44.88
|
44.76
|
Normal PI
|
48.93
|
52.3
|
49.32
|
46.24
|
46.15
|
47.32
|
High PI
|
46.64
|
52.54
|
47.42
|
44.78
|
44.23
|
42.56
|
Table 6
The vertebral height and intervertebral space height at L3-S1 of different groups
Group
|
Vertebral height (mm)
|
Intervertebral space height (mm)
|
|
L3
|
L4
|
L5
|
L3/4
|
L4/5
|
L5/S1
|
Low PI
|
21.50
|
21.08
|
20.93
|
9.51
|
9.41
|
10.19
|
Normal PI
|
21.12
|
21.70
|
21.33
|
11.12
|
10.31
|
9.76
|
High PI
|
23.09
|
24.94
|
25.24
|
11.06
|
9.25
|
9.87
|
In the flexion position, the average von Mises stress of the facet joint decreased with the increase in torque. In the L3/4 segment, the average stress of the right facet joint of the low PI group was the smallest when the torque was 15 Nm (Fig. 5), which was 0.57 MPa. In the L4/5 segment, the average stress of the facet joints in the low PI group was lower than that in the L3/4 segment, and the average stress of the facet joints in the normal PI group and in the high PI group was smaller than that of the low PI group. In the L5/S1 segment, the differences between the three groups were irregular, and the average stress of the facet joints in each group did not change significantly with the increase in torque. As the torque increased during flexion, the average stress of the facet joint gradually decreased, but this trend was obvious in the upper two segments of the lower lumbar spine (L3/4 and L4/5). In the flexion position, the average stress of the facet joints of the L5/S1 segment was less affected by the torque. The intradiscal pressure and maximum von Mises stress of the annulus fibrosus gradually increased with the increase in torque (Figs. 6 and 7). The intradiscal pressure in the small PI group was the highest among the three groups.
In the extension position, with the increase in torque, the average stress of the facet joints of each subject in the three segments typically showed an increasing trend (Fig. 8). The average stress of the facet joints in the high PI group was greater than that in the low PI group or the normal PI group. This phenomenon was significant in the L3-S1 segments. In the extension position, the intradiscal pressure of the low PI group at the L3/4 and L5/S1 segments was greater than that of the other two groups (Fig. 9), and the maximum von Mises stress of the annulus fibrosus in the low PI group was the largest in the three groups under the same loading conditions (Fig. 10).
In the left bending position, the average von Mises stress of the left facet joint was greater than that of the right side. This phenomenon existed in the three different PI groups (Fig. 11), and as the torque increased, the average stress of the left facet joint also increased. On the contrary, the average stress of the contralateral facet joint decreased with the increase in torque. In the three groups, the left facet joint was still significantly affected by torque change. The increase in torque resulted in an increase in the average stress of the concave facet joint, while the average stress on the convex side decreased. In the L5/S1 segment, this trend was no longer significant, especially when the average stress of the right facet joint was only minimally affected by the torque. This feature is more pronounced in the L3/4 and L4/5 segments but less obvious in the L5/S1 segment. The intradiscal pressure and the maximum von Mises stress of the annulus fibrosus in the left bending position changed with torque, but there was no significant difference between the groups (Figs. 12 and 13).
In the right bending position, the average stress of the right facet joints in the three groups was greater than that of the left side (Fig. 14), and the change in the average stress of the left and right facet joints was exactly opposite to that of the left side bending. There were no regular differences in the internal disc pressure and the maximum von Mises stress of the annulus fibrosus in each segment (Figs. 15 and 16). In the lateral bending position, the difference in the average stress of the facet joints between the different PI groups under the same load conditions and segments was not large, and there was no obvious rule among the three groups.
In the left torsion position, the right facet joint is blocked, causing the average stress of the right facet joint to be significantly greater than the average stress of the left facet joint, and as the torque increases, the average stress of the bilateral facet joints also gradually increases. In the L3/4 segment, compared with the other two groups, the average stress of the facet joints in the high PI group was the largest, reaching a maximum in the right facet joint of the high PI group under a torque of 15 Nm, which was 4.21 MPa (Fig. 17). The increase in torque leads to an increase in the average stress of the facet joints, and PI has less influence on the average stress of the facet joints in the left-torsion position; in addition, the intradiscal pressure of the high PI group was the largest among the three groups (Fig. 18), and the maximum von Mises stress of the annulus fibrosus had no obvious regularity (Fig. 19). In the right-torsion position, the average stress of the left facet joints in the three groups was greater than that on the right side (Fig. 20). The maximum intradiscal pressure of the L3/4 segment (Fig. 21) and the maximum von Mises stress of the L5/S1 segment occurred in the high PI group (Fig. 22). We found that PI had little effect on the average stress of the facet joints, and torque had a different effect on the average stress of the facet joints between the upper (L3/4) and lower segments (L5/S1). Torque had a greater effect on the average stress of the facet joints in the L3/4 segment than in the L5/S1 segment.