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Table 2 Details of the element types and material parameters (with references) included in the FE models

From: An FE investigation simulating intra-operative corrective forces applied to correct scoliosis deformity

Anatomical structure Element type Material parameters References
Vertebral body
- Cortical shell 4-node shell Linear elastic E = 11,300 MPa, ν = 0.2 [25]
- Cancellous bone 8-node brick Linear elastic E = 140 MPa, ν = 0.2 [25]
Vertebral posterior elements 2-node beam Quasi-rigid  
Facet joints 4-node shell As for cortical bone, with exponential softened contact between adjacent facet surfaces  
Intervertebral discs
- Anulus fibrosus 8-node brick Hyperelastic, Mooney-Rivlin C10 = 0.7, C01 = 0.2 [24, 26]
- Collagen fibres Tension-only, ABAQUS ‘rebar’ elements Linear elastic E = 500 MPa, ν = 0.3 [22]
- Nucleus pulposus 4-node, hydrostatic fluid Incompressible [26]
Ribs 4-node shell Linear elastic E = 9,860 MPa, ν = 0.3 [21]
Costal cartilage 4-node shell Linear elastic E = 49 MPa, ν = 0.4 [21]
Sternum/Manubrium 4-node shell Linear elastic E = 9,860 MPa, ν = 0.3 [21]
Costo-vertebral joints 2-node beam Linear elastic Ecompr = 245 N/mm; Torsional stiffness, kt = 4167Nmm/rad; Bending stiffness, kb = 6706Nmm/rad (average antero-posterior and cranio-caudal flexion stiffness) [19, 23]
Ligaments
- Ligamentum flava, supra-/inter-spinous, capsular, inter-transverse 2-node, tension-only connector Piecewise, non-linear elastic [20, 27, 30]
- Anterior/posterior longitudinal ligament 2-node spring Piecewise, non-linear elastic [27]
- Inter-costal connections 2-node, tension-only connector Linear elastic, E = 25 MPa [28]
Implant
- Screws 8-node brick Linear elastic, E = 108,000 MPa, ν = 0.3 Titanium alloy
- Rod 8-node brick and 2-node rigid beam Linear elastic, perfectly plastic E = 108,000 MPa, ν = 0.3 Yield Stress = 390 MPa Titanium alloy