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Table 1 Elastic [E and ν for elastic material; C10, C20, D, K1 and K2 for a hyperelastic model (Holzapfel strain energy function); E1, E2 and ε12 for bilinear elastic model] and biphasic material properties (k0: initial permeability, e: void ratio, cF,0: initial fixed charged density, nF,0: initial porosity) assigned to the different tissues to simulate the spine behaviour in healthy and degenerated (degenerated annulus—Grade IV) state

From: Is there any advantage of using stand-alone cages? A numerical approach

  Elastic parameters Biphasic parameters
E (MPa) ν k0 (m4/Ns) e cF,0 (meq/mm3) n F,0    
Cortical bone [41, 42] 17,000 0.3 5.77 × 10−18 0.05 0.05    
Cancellous bone [41, 42] 100 0.2 5.55 × 10−11 0.41 0.29    
Endplate [41, 42] 20 0.4 7.22 × 10−13 4 0.8    
Cartilage [40] 35 0.4        
Granular tissue [43] 0.2 0.167        
  1. The pre-stress (equivalent to 5% of space distraction) applied to L4–L5 segment ligaments, in case of stand-alone surgery, is also reported in the last column. The following notation is used for ligaments: ALL—antero-longitudinal ligament; PLL—postero-longitudinal ligament; LF—ligamentum flavum; ITL—intertransverse ligament; SSL—supraspinous ligament; JC—capsular ligament; ISL—interspinous ligament
  Elastic parameters Biphasic parameters
C10 (MPa) C20 (MPa) D (MPa−1) K1 (MPa) K 2 k0 (m4/Ns) e cF,0 (meq/mm3) n F,0
Annulus [39, 44, 45] 0.1 2.5 0.306 1.8 11 1.85 × 10−15 2.7 1.8 × 10−4 0.72
Degenerated annulus [46, 47] 0.45 2.5 0.306 1.8 11 1.45 × 10−15 2.4 0.9 × 10−4 0.7
Nucleus [39, 44, 45] 0.16 0 0.024 1.92 × 10−16 4.8 2.4 × 10−4 0.8
  1. The pre-stress (equivalent to 5% of space distraction) applied to L4–L5 segment ligaments, in case of stand-alone surgery, is also reported in the last column. The following notation is used for ligaments: ALL—antero-longitudinal ligament; PLL—postero-longitudinal ligament; LF—ligamentum flavum; ITL—intertransverse ligament; SSL—supraspinous ligament; JC—capsular ligament; ISL—interspinous ligament
Ligaments [32, 48, 49] Elastic parameters Biphasic parameters
E1 (MPa) E2 (MPa) ε 12 Number of elements Area (mm2) Pre-stress (MPa)    
ALL 7.8 20.0 0.12 10 32.9 0.804    
PLL 1.0 2.0 0.11 9 5.2 0.019    
LF 1.5 1.9 0.062 6 84.2 0.02    
ITL 10.0 59.0 0.18 16 1.8 0.026    
SSL 3.0 5.0 0.2 4 25.2 0.017    
  1. The pre-stress (equivalent to 5% of space distraction) applied to L4–L5 segment ligaments, in case of stand-alone surgery, is also reported in the last column. The following notation is used for ligaments: ALL—antero-longitudinal ligament; PLL—postero-longitudinal ligament; LF—ligamentum flavum; ITL—intertransverse ligament; SSL—supraspinous ligament; JC—capsular ligament; ISL—interspinous ligament
  Elastic parameters Biphasic parameters
Spine level Stiffness (N/mm) ν Number of elements Area (mm2) Pre-stress (MPa)    
JC L1–L2 42.5 ± 0.8 0.4 14 43.8 0.237    
L2–L3 33.9 ± 19.2        
L3–L4 32.3 ± 3.3        
L4–L5 30.6 ± 1.5        
L5-–S1 29.9 ± 22.0        
ISL L1–L2 10.0 ± 5.2 0.4 11 35.1 0.028    
L2–L3 9.6 ± 4.8        
L3–L4 18.1 ± 15.9        
L4–L5 8.7 ± 6.5        
L5–S1 16.3 ± 15.0        
  1. The pre-stress (equivalent to 5% of space distraction) applied to L4–L5 segment ligaments, in case of stand-alone surgery, is also reported in the last column. The following notation is used for ligaments: ALL—antero-longitudinal ligament; PLL—postero-longitudinal ligament; LF—ligamentum flavum; ITL—intertransverse ligament; SSL—supraspinous ligament; JC—capsular ligament; ISL—interspinous ligament