10+11 - Biphasic Theory / Poroelasticity - Applications

Question 1

Analogy of poroelasticity

Answer 1

• soil and cartilage both have depth-specific composition
• partly solid partly fluid
• existing theory

Question 2

Connective tissue

Answer 2

• ECM
• – water, fibers, glycoproteins, proteoglycans
• cells
• 60-70% water in cartilage/ligaments

Question 3

Ligaments/tendons

Answer 3

• ligaments = bone to bone, guidance, stability
• tendons = muscle to bone, load transfer
• composition = fb + fibers
• collagen (transfer tensile loads)
• mechanical ppts = non-linear elasticity

Question 4

Cartilage

Answer 4

• function = transmit jt force + min friction
• composition = collagen fibers + proteoglycans + water
• types
  — fibrocartilage (meniscus)
  — elastic cartilage (ear)
  — hyaline cartilage (articular cartilage): high c/ density, variable collagen content
  arcade-like org°
• swelling ppts

Question 5

Poroelasticity

Answer 5

• force distribution
  — elastic stress in matrix
  — hydrostatic px in interstitial water
• joint lubrication: when water is weeped out during compression, thanks to cartilage roughness
• Darcy’s law: Q = - K.A.delta(h)/L
  Q flow out, K hydraulic conductivity, delta(h) height difference, L length
• cartilage permeation: interstitial fluid flow and drag force, shared by fluid px and solid stresses
• theories
  — linear biphasic theory (Mow)
  — Terzaghi’s principle

Question 6

Biphasic creep, stress relaxation

Answer 6

• aggregate modulus H_A = E(1-nu)/(1+nu)(1-2.nu) (because msrmt often in a confined envt)
• total stress = sigma_T = sigma_S + sigma_F
  total = solid + fluid stress
• biphasic stress relaxation = distribution of px over time

Question 7

Donnan osmotic pressure

Answer 7

• proteoglycans in collagen mesh are charged
• need counter-ion
• gives rise to pressure in interstitial fluid
  sigma_T = sigma_S + sigma_F + Pi

Question 8

Implementing poroelasticity

Answer 8

• additional DOFs at nodes
• swelling origins = osmotic px OR charge-to-charge repulsion
  biphasic theory couples fluid motion and ion transport

Question 9

Solute transport and mechanical forces combination

Answer 9

• sequentially coupled models to account for advection
• – poroelastic mechanical model / transport model for IVD
• – FEBio

Question 10

Mechanobiology of fracture healing

Answer 10

• fracture healing
• – need vascularity + cyclic stress
• – osteogenic index = right combination of hydrostatic and shear stress
• mechanoregulation models (Carter, Claes, Prendergast)
• – comparison in vivo and != simulation methods
• – different load magnitude, axes