05 - Intervertebral Disks

Question 1

Intervertebral disk characteristics

Answer 1

• hyperelasticity = rubber-like
  strain-stress derive from strain energy density fct
  non-linearly elastic, isotropic, incompressible, generally strain rate dpdt
• main joint of the spinal column = 1/3 of its height
• role = mechanical: transmit loads
• flexible, bending, flexion, torsion
• size = 7-10 mm thick, 4 cm diam
• anatomy
  — annulus fibrosus = thicker outer ring, concentric lamellae and // collagen fibers at 30° (torsion resistance)
  — nucleus pulposus = gelatinous core, randomly org^d collagen fibers + radially arranged elastin fibers in hydrated gel (high compressive loads)
• degeneration: gel/px loss => load shift from center to periphery

Question 2

DDD = Degenerative Disc Disease

Answer 2

• nucleus become more fibrotic, less gel-like

- treatment = spinal fusion / total disc replacement / focal repair & TE in the future?

Question 3

IVD simulation using FEA

Answer 3

• non linear FEA
• model
• – annulus = 8-node elastic hybrid element
• – nucleus = incompressible fluid
• – bone = rigid body
• – ligaments = connectors
• geometry = based on X-ray CT scan
• validate: with literature data + qltv compression/tension comparison
• IVD’s response (4 load cases): window of stress-strain response for candidate repair material

Question 4

IVD FEM discussion

Answer 4

• good comparison to literature but annulus is assumed homogeneous
• combined load cases dangerous and not assessed

Question 5

Modeling DDD treatment

Answer 5

• case scenario: large herniation, radial tear, annulus defect > 6 mm
• materials = PCL or polyurethan

Question 6

Newton-Raphson method

Answer 6

• non linear FE solution
• iterative method by applying the load in small time steps
• K.d^(t+dt)_n = integr(B.C^tan_n.B^T.dV)
  K tangent stiffness matrix, Ctan Jacobian of constitutive law

Question 7

3-bar truss system workflow

Answer 7

• guess for d
• calculate epsilon
• calc Ctan and sigma
• forces in element coord system
• forces in global coord syst
• assemble global e/ force vector
• assemble global Ktan vector = Ctan.A/L
• BCs
• d_n+1
• repeat until convergence