Development and Kinematic Verification of a Finite Element Model for the Lumbar Spine: Application to Disc Degeneration
Table 1
Mechanical properties of materials.
Material
Young modulus (MPa)
Poisson coefficient
Element type
Number of elements
Outer vertebral endplates
12000
0.3
Tetrahedron
3578
Intermediate vertebral endplates
6000
0.3
Tetrahedron
2244
Centre of the vertebral endplates
2000
0.3
Tetrahedron
831
Walls of the vertebral body
12000
0.3
Tetrahedron
37205
Cancellous bone (inside vertebrae)
100
0.2
Tetrahedron
44954
Posterior vertebra
3000
0.3
Tetrahedron
47134
Cartilage
50
0.4
Wedge
3086
Annulus fibrosus
4.2
0.45
Hexahedron
8288
Nucleus pulposus*
Incompressible material
Tetrahedron
14410
Annulus fiber layers 1
360
0.3
Truss**
592
Annulus fiber layers 2
408
0.3
Truss**
592
Annulus fiber layers 3
455
0.3
Truss**
592
Annulus fiber layers 4
503
0.3
Truss**
592
Annulus fiber layers 5
550
0.3
Truss**
296
Ligament
Young modulus (MPa)
Transition strain (%)
Element type
Number of elements
Anterior longitudinal ligament
7.8
12.0
Wedge**
9046
20.0
Posterior longitudinal ligament
10.0
11.0
Wedge**
3844
50.0
Ligamentum flavum
15.0
6.2
Tetrahedron**
3042
19.0
Intertransverse ligament
10.0
18.0
Tetrahedron**
6678
59.0
Capsular ligament
7.5
25.0
Membrane**
3220
33.0
Interspinous ligament
8.0
20.0
Tetrahedron**
2856
15.0
Supraspinous ligament
10.0
14.0
Tetrahedron**
2657
12.0
Iliolumbar ligament
7.8
12.0
Wedge**
816
20.0
*
= 0.0343 MPa; = 0.1369 MPa. An elastic analysis with Young modulus of 1.0 MPa and Poisson ratio of 0.49 was carried out with similar results and a volume change less than 0.6%.
**Only tension.
