Spine Model for Vibration Analysis - Computational Biomechanics of the Musculoskeletal System - page 179

table 15.1
element types and material Properties of Spinal Components

Components element type young's

modulus (mPa)

Poisson's
ratio

Cross-Sectional
area (mm 2 )

density (kg/mm 3 )

Cortical bone 8-node solid 1,200 0.30 1.7 × 10 −6

Cancellous bone 100 0.2 1.1 × 10 −6

Bony posterior
element

3,500 0.25 1.4 × 10 −6

Annulus 4.2 0.45 1.05 × 10 −6

End plate 500 0.25 1.2 × 10 −6

Nucleus pulpous 1 0.49 1.02 × 10 −6

Imaginary cartilage 10 0.4 1.0 × 10 −6

Annulus fiber 3D-cable 500 1.0 × 10 −6

Capsular ligaments 30 1.0 × 10 −6

Intertransverse
ligaments

1.8 1.0 × 10 −6

Supraspinous
ligaments

30 1.0 × 10 −6

Interspinous
ligaments

40 1.0 × 10 −6

Ligamentum flavum 40 1.0 × 10 −6

Anterior
longitudinal
ligaments

63.7 1.0 × 10 −6

Posterior
longitudinal
ligaments

20 1.0 × 10 −6

Anterior sacroiliac
ligaments

20 160 1.0 × 10 −6

Posterior sacroiliac
ligaments

20 300 1.0 × 10 −6

Interosseous
sacroiliac ligament
(regarded as fiber)

500 1.0 × 10 −6

15.3 valIdatIon oF SPIne FInIte element modelS
To validate the L3-L5 segment model, a static FE analysis was conducted (Berkson, Nachemson,
and Schultz 1979; Shirazi-Adl and Drouin 1987; Kim et al. 1991; Kasra, Shirazi-Adl, and Drouin
1992; Goel, Park, and Kong 1994; Pankoke, Hofmann, and Wolfel 2001). For effective comparison
with other published results, the same loads and boundary restrictions were applied. Figure 15.3a
shows that the compressive displacements of the L3-L4 segment and L4-L5 segment fall in the
range of the experimental deviation (Berkson, Nachemson, and Schultz 1979) under a 400-N
compressive force. Figure 15.3b shows the comparison of force-displacement results of the L3-L5
segment between this study and the results of Kim et al. (1991), and indicates that the two results
are in agreement within the compressive displacement of 1.5 mm. After the nucleus was removed
from the L4-L5 spinal segment, the denucleated FE model was also validated against the published
results of Frei et al. (2001). Figure 15.3c shows that the displacements of the intact model and the
denucleated model of the L4-L5 segment all fall in the range of the experimental results (Frei et al.
2001) under 1000-N compressive forces.