Summery of “FEA of Spinal Cord Injury in the Rat”, Maikos (2008)
Finite Element Model Generation
1. Components: (1) Gray matter (2) White matter (3) CSF (4) Dura metter (5) Spinal column (6) Impactor. Cord length was 1.4 cm.
2. Dura, CSF and spinal cord: Deformable solid elements, partitioned into sub-units, mashed with eight-node, reduced integration, hexahedron, “hourglass control” element for use with Abaqus Explicit. Components were merged while maintaining distinct boundaries. Independent element sets in each component, but with common nodes at the boundary. 94893 nodes and 54926 elements in the model.
3. Spinal column: Triangular surface mesh. 14,004 nodes and 27,929 elements.
4. Impactor: Rigid cylinder of mass (10g) and diameter (2.5mm). Peak compression of ~2mm in under 4msec.
Material Properties – Standard Model (Homogeneous)
1. Isotropic and homogeneous with identical material properties assigned to GM and WM in a non-linear, viscoelastic, hyperelastic model.
2. Ogden model: (GM, WM, Dura)
|[pic] |(30) |
λi: deviatoric principal stretches, J: volume ratio between current and reference configurations. N: complexity of the law. Gi, αi and Di: material-dependent parameters. Setting N=1 to make G=shear modulus. An Ogden fitting of Fiford (2005)* produced an quasi-static shear modulus ~200kPa.
|[pic] |(31) |
V: Poisson’s Ratio. Then adjusting the model to achieve the temporal profile of impactor displacement matched from experiments.
3. Viscoelastic portion with a Prony series exponential decay:
|[pic] |(32) |
gk: relative relaxations. τk: characteristic time constants. Shear...