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Table 1 Mechanical properties of poroelastic materials in the FE models for all L2-L3 segments

From: Effects of resting modes on human lumbar spines with different levels of degenerated intervertebral discs: a finite element investigation

a. Elastic properties of the lumbar except nucleus pulposus
Model Material model Material property
   Elastic modulus (MPa) Poissons ratio (μ)
Cancellous bone Linear-elastic 100 0.2
Cortical bone Linear-elastic 10000 0.3
Cartilage endplates Linear-elastic 5 0.1
Annular fiber Linear-elastic 357-550 0.3
Annulus ground substance Hyper-elastic Neo-Hookean C10 = 0.315, D = 0.688
Ligaments/Facet Hyper-elastic Fitting from test data
The linear-elastic properties of cancellous bone, cortical bone, and cartilage endplates were based on Schmidt et al. [19]. The linear-elastic properties of annular fiber were based on Xu et al. [10]. The hyper-elastic properties of annulus ground substance were based on Schmidt et al. [20], Schmidt et al. [21], and Galbusera et al. [32]. The hyper-elastic properties of ligaments/facet were based on Sharma et al. [33].
b. Porous properties of the lumbar spine except nucleus pulposus
Material Permeability (m4/Ns) e0 M (Eq. (1))
Cancellous bone k = 1e−13 0.4  
Cortical bone k = 1e−20 0.02  
Cartilage endplates k0 = 7e−15 4 10
Annulus ground substance k0 = 3e−16 2.33 12
The porous properties of cancellous bone, cortical bone, cartilage endplates, and annulus ground substance were based on Argoubi and Shirazi-Adl [34].
c. Poroelastic material properties of all the nucleus pulposus
Nucleus pulposus Hyper-elastic Poroelastic   
  Neo-Hookean Permeability (m4/Ns) e0 M (Eq. (1))
Grade 0 C10 = 0.12, D = 2.475 k0 = 3e−16 4 10
Grade 1 C10 = 0.185, D = 1.88 k0 = 5e−16 3.44 10
Grade 2 C10 = 0.25, D = 1.285 k0 = 7e−16 2.88 10
Grade 3 C10 = 0.315, D = 0.688 k0 = 9e−16 2.33 10
The hyper-elastic properties of nucleus pulposus for Grade 0 to 3 were based on Schmidt et al. [13], Schmidt et al. [20], and Schmidt et al. [21]. The porous properties of nucleus pulposus for Grade 0 to 3 were based on Johannessen et al. [6], Massey et al. [11], and Argoubi and Shirazi-Adl [34].