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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

       
 

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

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

   
 

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
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