Joint lubrication

Joint Friction & Lubrication

Friction

  • Definition: The resistance to sliding between two bodies in contact due to:
    • Adherence of surfaces to one another
    • Viscosity of the fluid between them

Three Laws of Friction:

  1. Frictional force = coefficient of friction x applied load
  2. Frictional force is independent of contact area and sliding speed
  3. Kinetic friction is independent of sliding speed

Frictional Wear

  • Frictional wear is proportional to sliding distance
    • F = xW
    • Frictional force is proportional to the applied load
    • x is the coefficient of friction of the two bearing surfaces
  • In a rotational system like a hip, frictional torque is more appropriate:
    • Frictional Torque = Frictional force x Radius

Asperities

  • Asperities: Projections that occur from any surface
    • More asperities = more roughness

Roughness

  • Expressed as mean surface roughness, i.e., mean asperity height

Joint Contact Area

  • The contact point between the asperities comprises less than 1% of the apparent contact area
  • Asperities are compressed by contact
    • Asperity deformation is inversely proportional to load and hardness of the material
    • After prolonged contact, bonds form between the asperities
    • Greater energy is required to overcome static friction than to maintain motion (dynamic friction)

Mean Surface Roughness of Orthopaedic Materials

Material Mean Surface Roughness
Polished Exeter Stem 0.01
Ceramic Head 0.02
Metal Head 0.025
Polyethylene Cup 2.0
Articular Cartilage 3.0

Co-efficients of Friction of Articulations

Joint/Material Coefficient of Friction
Native Knee 0.005
Native Hip 0.01
Metal on Polyethylene 0.02
Metal on Metal 0.8

Joint Lubrication

Synovial Fluid

  • Dialysate of blood, devoid of red cells, clotting factors, or hemoglobin
  • Contents:
    1. Plasma Proteins
    2. Lubricin
    3. Hyaluronic Acid
    4. Cells

Cells

  • Type A: Important in phagocytosis
  • Type B: Fibroblast-like, produce synovial fluid
  • Type C: Intermediate, unclear role

Hyaluronic Acid

  • Acts as an elastic solid during high impact due to tangled chains
  • Responsible for non-newtonian fluid properties, behaving like a viscoelastic solid

Lubricin

  • The key lubricating element in the fluid

Plasma Proteins

  • Contain proteinases, collagenase, and prostaglandins (PGs)

Nutrition & Excretion

  • Nutrients enter synovium via diffusion through synovial micro-vessels

  • Plasma proteins diffuse out via lymphatics

  • The process is passive diffusion through the micro-vascular endothelium

  • Altered endothelial permeability (e.g., in rheumatoid arthritis) changes the balance of synovial fluid

Mechanics

  • Viscosity: The internal friction of a fluid
    • Layers of fluid move against each other by shear forces

Newton’s Law of Viscosity:

  • Viscosity = Shear stress / Shear rate

Non-Newtonian Properties

  • Synovial fluid behaves in a non-newtonian fashion:
    1. Thixotropy: Time-dependent decrease in viscosity under constant shearing
    2. Pseudo-plasticity: Disproportionate change in viscosity with shear rate
  • Caused by hyaluronic acid molecules aligning, a phenomenon called Shear Thinning

Types of Lubrication

  • Boundary Lubrication: Surfaces separated by a molecular thickness lubricant
  • Fluid Film Lubrication: The separating fluid film is thicker than the asperities of the surfaces

Boundary Lubrication

  • Occurs when fluid film lubrication is overcome (e.g., prolonged stance)
  • Lubricin forms a gel-like hydrophobic layer

Fluid Film Lubrication

  • Desirable as it prevents asperity contact and wear
  • Types of fluid film lubrication:
    1. Hydrodynamic
    2. Elastohydrodynamic
    3. Micro-elastohydrodynamic
    4. Weeping
    5. Squeeze film lubrication
    6. Boosted lubrication

Types of Fluid Film Lubrication

Hydrodynamic

  • Relies on surfaces not being perfectly parallel
  • Generates a fluid wedge during sliding, holding surfaces apart

Elastohydrodynamic

  • Predominant type in native articular cartilage
  • Deformation under load increases surface area, reducing shear rate and increasing viscosity

Micro-Elastohydrodynamic

  • Occurs under heavy loads, deforming cartilage asperities and improving lubrication

Squeeze Film Lubrication

  • Occurs when surfaces come into contact without sliding (e.g., heel strike)
  • Viscous fluid builds pressure, maintaining a gap between surfaces

Boosted Lubrication

  • Water from synovial fluid is pressurized into the cartilage, leaving a hyaluronic-rich fluid

Weeping Lubrication

  • Compression of surfaces results in tears of lubricant fluid

Gait Cycle Phase and Lubrication

Gait Cycle Phase Predominant Lubrication Type
Initial Contact Squeeze Film
Stance Elastohydrodynamic
Lift Off Boundary & Elastohydrodynamic
Swing Hydrodynamic
Prolonged Stance Boundary, Boosted

Lubrication in Prosthetic Joints

  • In native joints, all types of lubrication occur, but fluid film dominates

  • In prosthetic joints, boundary lubrication and some fluid film types occur (hydrodynamic, squeeze film)

  • MoP: Boundary lubrication dominates

  • MoM & CoC: Fluid film lubrication occurs due to increased radius

Wettability

  • Increased wettability = better lubrication
  • Ceramics are highly wettable, improving lubrication and reducing friction

Large Diameter Articulations

  • True fluid film lubrication may occur with large diameter bearings (e.g., MoM or ceramic bearings)

Sommerfeld Number

  • A unitless number expressing the relationship between fluid film thickness, lubricant, and forces

Lambda Ratio

  • Defines whether fluid film or boundary lubrication predominates
    • 3 = Pure fluid film
    • <1 = Pure boundary lubrication
    • 1-3 = Mixed lubrication

Factors Affecting Lubrication:

  1. Type of load (low/high, sliding/static)
  2. Bearing surfaces (roughness, coefficient of friction, size, shape)
  3. Wettability (affinity for lubricating fluid)
  4. Velocity of motion (shear rate)
  5. Properties of the lubricant (viscosity, non-newtonian behavior)
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