ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

surfaces with two crisscross layers of rebar elements were embedded into the annulus
matrix to simulate the collagen fiber network (Figure 1). The two layers consisted of
rebar elements in +/-30° direction to the horizontal plane [6]. The fibers were assumed
to be linear elastic. The volume content of the fibers with regard to the adjacent element
layer of the annulus matrix was decreased from 23% of the outer layer to 5% of the
innermost fiber layer [7]. This results in a decrease of the cross-sectional area of the
rebars from 0.0295mm² to 0.0016mm² and from 0.026mm² to 0.0026mm² for the L3-L4
and the L4-L5 nucleus, respectively. The spacing between the rebars was set constant to
0.1mm. Secondly, the ‘rigid body’ constraint was used instead of explicitly simulating
the mounting of the specimens with bone cement. As the Young’s modulus of the
potting material is low in comparison to the cortical bone, the deformation of the potting
material can be neglected. The mechanical properties for the healthy model are shown
in Table 1.
Table 1. Material properties for the healthy spinal model
Element type
Young's
Modulus [MPa]
Poisson's
Ratio
References
Cortical shell C3D20 Hex a 12 000.0 0.300 [8]
Cancellous bone C3D20 Hex 150.0 0.300 [9]
Posterior elements C3D10 Tetra b 3 500.0 0.300 [10]
Bony endplate C3D20 Hex 10 000.0 0.300 [11]
Annulus matrix C3D20 Hex 4.2 0.450 [12]
Annulus fibres
Nucleus pulposus
Rebar elements,
C3D20 Hex
C3D15 Penta
500.0 0.300 [13]
c
1.0 0.499 [10]
Capsular ligaments T3D2 24.4 0.300 [14]
a) Hex: hexahedron; b) Tetra: tetrahedron; c) Penta: Pentahedron
In addition to the healthy model, two scales of degenerated FE spinal models were
created by modifying both the material parameters (Table 2) and the geometry of the
intervertebral discs (Figure 1). The latter was realized by reducing the disc height by
15% for the mildly degenerated model and 40% for the fully degenerated model [16].
Furthermore, the cross-sectional area of the nucleus in the transverse plane was reduced
by 51% and 93% for the mildly and fully degenerated models, respectively. With agerelated
degeneration, the nucleus and annulus lose their ability to bind water and hence
become stiffer. The nucleus also loses its incompressibility, because of which the
Poisson’s ratio was decreased from 0.499 to 0.4 and 0.3 for the mildly and fully
degenerated nucleus, respectively. The bony materials, in contrast, show a decreasing
Young’s modulus with the progress of age-related osteoporotic degeneration, which was
also included (Table 2) [16-17]. The three FE models are presented in Figure 1.
Table 2. Young’s modulus changes for different grades of degenerations
Cortical Cancellou Posterior Bony Annulus Nucleus
Shell s bone elements endplate matrix pulposus
Healthy model 12 000.0 150.0 3 500.0 10 000.0 4.2 1.0
Mild degeneration 9 000.0 75.0 2 625.0 7 500.0 5.0 7.0
Full degeneration 8 000.0 35.0 2 345.0 6 700.0 6.0 81.0