FAB - Week 2 (Part 1) - Bone and Cartilage biomechanics

Bone Structure and Function

• Vital Roles:
  • Mechanical support.
  • System of levers to transmit forces.
  • Protection for vital organs.
• Architecture: Architecture reflects loading.
• Bone Strength: Dependent on amount, density, and arrangement of bone material.

Bone Composition

Cortical (Compact) Bone

• High density: 2 \frac{g}{cm^3}
• Low porosity: 5-30%
• Contains Haversian systems.

Cancellous (Spongy/Trabecular) Bone

• Less dense, filled with spaces.
• Low density: ~0.1-1.4 \frac{g}{cm^3}
• High porosity: 30-90%
• No Haversian systems.

Mechanical Properties of Bone

• Vary depending on:
  • Type of bone (cancellous vs. cortical).
  • Location and shape of the bone (e.g., rib vs. femur).
• No standard value for strength or Young’s modulus (slope of stress-strain curve).
• Stress: Stress = \frac{Force}{CSA}
• Strain: Strain = \frac{\Delta length}{original \ length} * 100
• Modulus: Modulus = \frac{\Delta stress}{\Delta strain}
• High modulus indicates stiffer material; low modulus indicates more compliant material.

Bone Loading Modes

• Unloaded
• Tension
• Compression
• Bending
• Shear
• Torsion
• Combined loading

Compression

• Can lead to oblique fracture or cracking of osteons.
• Common in vertebrae, especially in osteoporosis (OP).
• Can be caused by strong muscle contraction.

Shear

• Can result in a transverse fracture.

Bending

• Neutral axis experiences no net stress.
• Bending stresses are largest on the cortex.
• Can cause a combined fracture.
• Transverse fracture on the side experiencing tension.
• Oblique fracture on the side experiencing compression.
• Butterfly fragment indicates bending.

Torsion

• Results in a spiral fracture.
• Tension along spiral stress lines.
• Stresses are maximal at outer surfaces.

Bone Strength and Material Properties

• Bone is strongest in compression.
• Bone is anisotropic/orthotropic:
  • Anisotropic: Material properties (e.g., modulus - E) are direction dependent.
  • Transversely Orthotropic: One axis of symmetry (e.g., femur).
    • Young’s modulus in the axial direction is different from the transverse directions: Ex = Ey \neq E_z

Bone Loading: Viscoelasticity

• Bone is viscoelastic (VE): Exhibits viscous (fluid) and elastic (solid) properties.
• Hysteresis:
  • Load-elongation curve follows different path in loading versus unloading.
  • Hysteresis effect is measured by the difference in the area under the loading versus unloading curves.
  • Hysteresis area represents energy lost due to internal friction.

Bone Loading: Time Dependence

• Load Relaxation: Constant length results in a decrease in load over time.
• Creep: Constant load results in an increase in length over time.
• Stretching example: Static or cyclic stretching leads to a reduction in the sense of stretch (load) with time or repetitions and an increase in the range of motion (length) with time or repetitions.

Bone Loading: Rate Dependence

• The stress-strain relationship for a VE material depends on strain rate.
• VE materials become stiffer and store more energy to failure when loaded at higher strain rates.
• Cortical bone is more brittle at high strain rates; fail strain is lower.
• Bone is ~30% stronger in brisk vs. slow walking; fail stress is lower.

Bone Loading: Fatigue Failure

• Fractures can be produced by a few reps of a high load or vice versa.
• If fail stress is applied, the material fails on the first cycle.
• If applied stress is below fail stress, it takes more cycles to produce failure.
• Bone fatigues when the frequency of loading precludes the remodeling necessary to prevent failure (e.g., stress fractures).
• Results in growth of defect (crack propagation).

Bone Loading: Maturation

• Ligament substance matures quicker than the bone-ligament junction.
• Bone-ligament junction is stronger in maturity vs. mid-substance.

Bone and Age

• Geometry and material properties change with age.
• Age (>35 years):
  • Young’s modulus decreases by 2.3% every 10 years.
  • Fracture toughness decreases by 4%.
  • Bending strength decreases by 3.7%.
• Unclear whether changes are due to altering mineral content or bone structure.

Bone Loading: Remodeling

• Balance between the number and magnitude of cyclic strains.
• Wolf’s Law: Bone is laid down in areas of high stress and reabsorbed in areas of low stress.

Bone Loading: Activity

• Alterations due to exercise are less than those due to inactivity.
• Mechanical properties are influenced by stress and strain duration related to physiological activities such as exercise and immobilization.
  • Decrease stress increases bone resorption.
  • Increase stress increases bone deposition.

Exercise for Bone Health

• Influences bone mass and strength at all ages of skeletal development.
  • Promotes bone mass accrual and optimization of geometry during childhood.
  • Most effective during the peri-pubertal period.
  • Consolidates or aids maintenance of bone during adulthood.
  • Maintains or attenuates the loss of bone mass and strength during old age.
• More evidence for changes in bone density and composition vs. geometry.
• Loading intensity (i.e., impulse) is more important than duration.
  • High impact (>3xBW) = high strain rate = greater bone adaptation.
  • Examples: Running, jumping, landing, resistance training (>80% 1RM).
• LIFTMOR trial at Griffith University (see YouTube video).

Articular Cartilage (AC)

• Location: Articulating bone ends of diarthrodial joints.
  • Thickness: 1-6 mm.
• Function:
  • Transfers forces.
  • Distributes loads.
  • Facilitates smooth joint rotations.
  • Reduces friction: μ = 0.002 (artificial joint ~ 0.06).
• Composition: Chondrocytes (cells) + Extracellular Matrix (ECM).

AC Composition

Chondrocytes

• <10% of AC volume.
• Produce, organize, and maintain the ECM.
• Minimal contribution to biomechanical properties.

ECM

• Predominantly collagen (type II), proteoglycans, and water.
• Determines the mechanical properties of AC.
• Differentiation of ECM regions: Pericellular, territorial & inter-territorial regions.

AC Structure - Chondrocyte Arrangement

• Chondrocytes randomly distributed in the superficial zone.
• Chondrocytes arranged in columns in the middle and deep zones.

AC Structure - Collagen Arrangement

• Zones:
  • Superficial tangential (10-20%)
  • Middle (40-60%)
  • Deep (30%)
  • Calcified cartilage
  • Subchondral bone
  • Cancellous bone

AC Composition: ECM Detail

• ECM consists predominantly of collagen, proteoglycan & water.
• Collagen
  • Most abundant protein in the body
  • AC primarily Type II collagen.
  • High tensile stiffness & strength (Similar to nylon & aluminium!).
  • Insignificant compressive stiffness.

AC Composition: Proteoglycans (PGs)

• Many PG types in AC.
• Aggrecans (predominant GAG):
  • Hyaluronan protein core.
  • Keratan sulphate (KS) chains.
  • Chondroitin sulphate (CS) chains.
• Aggrecans bind to hyaluronan to form “PG macromolecule,” which contributes to the stability of the ECM.

PGs Resist Compression

• Glycosaminoglycans (GAGs) are negatively charged.
• Compression forces GAGs together, creating high charge-charge repulsive forces.

AC Viscoelasticity - Creep

• Initial rapid displacement of tissue due to fluid exudation (viscous).
• Many hours to reach equilibrium.
• Up to 50% of interstitial fluid may be exuded.
• Fluid re-uptake occurs once load is removed/reduced.
• AC is viscoelastic – showing creep.

AC Viscoelasticity - Load Relaxation

• Gradual reduction in tissue stress with constant loading (load relaxation).
• A-B: Fluid exuded out of the tissue, leading to rapid cartilage deformation and increased stress.
• C-D: Fluid moves within tissue, with no deformation and a reduction in stress.
• E: Internal equilibrium is progressively achieved after fluid exudation has terminated.

Cartilage Response to Loading - Summary

• Compression loads:
  • GAGs resist compression through repulsive forces.
  • Initial loading: Internal fluid pressure transfers load across joint through hydrostatic pressure.
  • Continued loading: Fluid is extruded, and matrix (Collagen & PGs) takes up more of the stress.
• Shear loads:
  • Carried from the joint surface to the superficial zone as a tensile stress in collagen fibers.
  • Transferred from superficial zone down through middle and deep zones to bone as a shear stress.

Acute Response of AC: Exercise Loading

• 2.4-8.6% loss of patellar cartilage volume immediately after 100 knee bends (squats).
• Recovery time for 100 knee bends > 90 minutes.
• Dose and ROM dependent cartilage strain

Cartilage Wear Mechanisms

• Interfacial wear High impact loading
• Micro-structural changes with OA
• Macro-structural changes with OA:
  1. Cartilage softening
  2. Cartilage fibrillation/fissuring
  3. Partial thickness loss
  4. Full thickness loss with bone exposed

Loading and OA Risk: Animal Studies

• Low intensity/volume: catabolic response (↓ PG synthesis & ↓ AC thickness).
• Moderate intensity/volume: anabolic response (↑ PG synthesis & ↑ AC thickness).
• High intensity/volume: catabolic response (↓ PG synthesis & ↓ AC thickness).
• Age of onset and rate of activity intensity/volume change appears to play a role.
• Previously sedentary/immobilized older animals that undergo a rapid increase in intensity/volume (to a moderate level) experience ↑ OA risk.
• ACL deficient and meniscectomized animals experience ↑ OA risk.

Loading and OA Risk: Human Studies

• Low to moderate intensity/volume of running does not appear to increase OA risk in healthy joints.
• In previously injured joints (e.g., ACL reconstruction, meniscectomy), intensity and volume of running are positively associated with OA risk.

Exercise and OA Risk

• Table 2 summarizes crude and adjusted risk of severe knee osteoarthritis requiring knee arthroplasty (logistic regression model).
• Factors include age, body mass index, smoking, physical work stress, knee injury and physical exercise.