Unit 2: Bone and cartilage - Subjective Questions

Bone is a specialized connective tissue composed of cells and a mineralized extracellular matrix.

Composition:

• Inorganic component (~65% by weight): Primarily hydroxyapatite crystals . Provides stiffness, hardness, and compressive strength.
• Organic component (~25%): Mainly Type I collagen, plus proteoglycans and non-collagenous proteins. Provides flexibility, tensile strength, and toughness.
• Water (~10%): Contributes to viscoelastic behavior and nutrient transport.

Structural organization:

• Cortical (compact) bone: Dense outer layer, forms osteons (Haversian systems) with central canals carrying blood vessels.
• Cancellous (trabecular) bone: Spongy interior with a lattice of trabeculae, oriented along stress lines.

Bone cells:

• Osteoblasts: Bone-forming cells.
• Osteocytes: Mature cells embedded in lacunae, act as mechanosensors.
• Osteoclasts: Bone-resorbing cells.

The combination of a stiff mineral phase reinforced by a flexible collagen matrix makes bone a natural composite material with excellent strength-to-weight properties.

Bone is a highly vascular tissue requiring an extensive blood supply for nutrition, remodeling, and repair.

Major sources of blood supply to a long bone:

• Nutrient artery: The principal supply; enters through the nutrient foramen in the diaphysis and divides into ascending and descending branches supplying the medullary cavity and inner cortex.
• Periosteal arteries: Supply the outer layers of the cortex; enter where fascia attaches firmly to bone.
• Epiphyseal arteries: Supply the ends (epiphyses) of the bone.
• Metaphyseal arteries: Supply the metaphysis, anastomosing with epiphyseal and nutrient vessels.

Microcirculation:

• Blood flows through Haversian canals (longitudinal) and Volkmann's canals (transverse), forming an interconnected network.
• Nutrients reach osteocytes via canaliculi connecting lacunae.

Flow direction:

• In cortical bone, flow is generally centrifugal (from medulla outward).
• Venous drainage occurs through central veins and periosteal veins.

Adequate circulation is essential for fracture healing, and disruption can lead to avascular necrosis.

Bone exhibits mechanical properties that vary with load type, direction, and rate.

Key definitions:

• Stress (): Force per unit area, , measured in Pascals (Pa).
• Strain (): Relative deformation, (dimensionless).
• Young's modulus (): Slope of the elastic region of the stress-strain curve, , indicating stiffness.

Typical values for cortical bone:

• Young's modulus: (longitudinal).
• Compressive strength: .
• Tensile strength: .
• Shear strength: .

Important characteristics:

• Stronger in compression than tension, and weakest in shear.
• Anisotropic: Properties differ with loading direction.
• Viscoelastic: Stiffness and strength increase at higher strain rates.
• Cancellous bone is much less stiff and strong than cortical bone but absorbs energy well.

Bone behaves elastically at low loads, then yields and fractures beyond its ultimate strength.

Viscoelasticity is the property of a material that exhibits both viscous (fluid-like) and elastic (solid-like) behavior when deformed, so its response depends on time and rate of loading.

Key viscoelastic phenomena in bone:

• Creep: Under a constant applied stress, strain increases gradually with time. Bone slowly deforms over time under sustained load.

• Stress relaxation: Under a constant applied strain, the stress required to maintain it decreases with time.

• Hysteresis: During a loading-unloading cycle, the loading and unloading curves do not coincide; the enclosed area represents energy dissipated as heat.

• Strain-rate dependence: Bone is stiffer and stronger at higher loading rates and more compliant at low rates. This is why bone can absorb more energy before fracture during rapid loading up to a point.

Significance:

• Allows bone to absorb impact energy.
• Explains why fracture behavior differs between slow and fast loading (e.g., falls vs. gradual loading).

The water and collagen content are primarily responsible for the viscous component, while the mineral phase governs elastic stiffness.

The Maxwell model represents a viscoelastic material using a spring (elastic element) and a dashpot (viscous element) connected in series.

Elements:

• Spring:
• Dashpot:

Derivation of governing equation:
Since the elements are in series, the total strain is the sum:

Differentiating with respect to time:

Thus the constitutive equation is:

Behavior:

• Stress relaxation (constant strain, ):
  
  Stress decays exponentially — the model predicts stress relaxation well.

• Creep (constant stress): Strain increases linearly with time (like a viscous fluid), which is unrealistic for solids.

Limitation: Good for modeling stress relaxation but poor for creep in solid materials like bone.

The Voigt (Kelvin-Voigt) model represents a viscoelastic material using a spring and a dashpot connected in parallel.

Elements (parallel arrangement):

• Both elements experience the same strain .
• Total stress is the sum of stresses in each element.

Derivation of governing equation:

Thus the constitutive equation is:

Behavior:

• Creep (constant stress ):
  
  Strain rises exponentially toward an equilibrium value — realistic delayed elastic (creep) response.

• Stress relaxation (constant strain): Since , constant. The model cannot represent stress relaxation.

Limitation: Models creep and recovery well but fails to describe stress relaxation and instantaneous elastic response.

Note: Combining Maxwell and Voigt elements (e.g., the Standard Linear Solid / Kelvin model) captures both creep and relaxation, making it more suitable for bone.

Both models use a spring and dashpot but differ in arrangement and predicted behavior.

Summary:

• Maxwell = good for stress relaxation, poor for creep.
• Voigt = good for creep, poor for stress relaxation.

Since real bone shows both creep and relaxation, a combined model such as the Standard Linear Solid (three-element model) is used for accurate representation.

Articular cartilage is the smooth, load-bearing tissue covering the ends of bones in synovial joints. It is strongly viscoelastic due to its composition.

Composition (biphasic material):

• Solid phase: Collagen fibers (mainly Type II) and proteoglycans forming a porous, permeable matrix.
• Fluid phase: Interstitial water (~70–80%) that flows through the matrix.

Biphasic mechanism of viscoelasticity:

• Under load, fluid is forced out of the porous matrix; the resistance to fluid flow (low permeability) causes time-dependent deformation.
• When load is removed, fluid is reabsorbed and the tissue recovers.
• This fluid–solid interaction dominates the creep and stress relaxation behavior.

Viscoelastic characteristics:

• Creep: Continued deformation under constant load as fluid slowly exudes.
• Stress relaxation: Stress decays under constant deformation as fluid redistributes.
• Rate dependence: Stiffer under rapid loading (fluid trapped, incompressible) and softer under slow loading.

Functions:

• Distributes contact stresses over the joint.
• Provides lubrication and reduces friction.
• Absorbs shock and protects subchondral bone.

The biphasic viscoelasticity is key to load bearing and joint longevity; its degradation leads to osteoarthritis.

Anisotropy means that a material's mechanical properties vary with the direction of loading, unlike an isotropic material whose properties are the same in all directions.

Why bone is anisotropic:

• The microstructure is directional: osteons and collagen fibers are aligned predominantly along the long axis of the bone.
• Mineralization and trabecular orientation follow the habitual lines of stress (Wolff's law).

Effect on mechanical behavior:

• Bone is stronger and stiffer along the longitudinal (axial) direction than in the transverse direction.
• Example (cortical bone): Longitudinal modulus , transverse modulus .
• Strength values also differ: higher axial compressive/tensile strength.

Types of anisotropy:

• Cortical bone is often modeled as transversely isotropic (same properties in the transverse plane, different along the axis).
• More detailed models treat it as orthotropic (three distinct principal directions).

Practical significance:

• Implant and fracture-fixation designs must consider load direction.
• Bone tends to fail along planes of weakness when loaded off-axis.

Thus, treating bone as isotropic would produce inaccurate stress and failure predictions.

Bone can be modeled as a natural composite material consisting of a stiff reinforcing phase embedded in a flexible matrix.

Composite constituents:

• Reinforcing phase: Hydroxyapatite mineral crystals — stiff, brittle, high compressive strength.
• Matrix phase: Collagen fibers — flexible, tough, high tensile strength.

Analogy: Bone is often compared to reinforced concrete, where mineral acts like the aggregate/rebar (stiffness) and collagen like the flexible binder (toughness).

Composite modeling approaches:

• Voigt (parallel / iso-strain) model gives the upper bound of modulus:
  
• Reuss (series / iso-stress) model gives the lower bound:
  
  where = volume fraction, subscripts = mineral, = collagen.

The actual bone modulus lies between these bounds.

Why the composite model is useful:

• Explains why bone is simultaneously stiff and tough — properties neither pure mineral nor pure collagen could achieve alone.
• Accounts for anisotropy through fiber orientation.
• Predicts how changes in mineral content affect stiffness and brittleness (e.g., aging, osteoporosis).

Thus the composite view links microstructure directly to overall mechanical performance.

Wolff's Law states that bone adapts its structure and mass in response to the mechanical loads placed upon it. Bone tissue is deposited where stress is high and resorbed where stress is low.

Bone response to stress (mechanical adaptation):

• Increased loading (e.g., exercise, weight-bearing):

  • Stimulates osteoblast activity.
  • Increases bone density and thickness.
  • Trabeculae reorient along principal stress lines.

• Decreased loading (e.g., bed rest, immobilization, microgravity):

  • Stimulates osteoclast resorption.
  • Leads to bone loss (disuse osteoporosis).

Mechanism (mechanotransduction):

• Osteocytes act as mechanosensors, detecting strain and fluid flow in canaliculi.
• They signal osteoblasts and osteoclasts to remodel bone accordingly.

Remodeling cycle:

1. Activation — osteoclast recruitment.
2. Resorption — old bone removed.
3. Reversal — transition phase.
4. Formation — osteoblasts lay new bone.

Clinical/Practical significance:

• Explains why athletes have denser bones.
• Explains bone loss in astronauts and immobilized patients.
• Basis for weight-bearing exercise in osteoporosis prevention.

Thus bone is a dynamic, self-optimizing tissue that continuously adapts to its mechanical environment.

Osteoporosis is a skeletal disorder characterized by reduced bone mass and deterioration of bone microarchitecture, leading to increased bone fragility and susceptibility to fractures.

Causes / Risk factors:

• Aging — bone resorption exceeds formation.
• Hormonal: Estrogen deficiency (post-menopausal women), reduced testosterone.
• Nutritional: Deficiency of calcium and vitamin D.
• Lifestyle: Physical inactivity, smoking, excessive alcohol.
• Medical: Long-term corticosteroid use, hyperthyroidism, genetic predisposition.

Diagnosis:

• DEXA / DXA scan (Dual-energy X-ray Absorptiometry): Gold standard, measures Bone Mineral Density (BMD).
• T-score interpretation (WHO):
  • Normal:
  • Osteopenia:
  • Osteoporosis:
• Additional: X-rays, quantitative CT, biochemical bone markers.

Treatment:

• Lifestyle/preventive: Calcium and vitamin D supplementation, weight-bearing exercise, quitting smoking/alcohol.
• Pharmacological:
  • Bisphosphonates (e.g., alendronate) — inhibit osteoclasts.
  • Hormone Replacement Therapy (HRT).
  • Selective Estrogen Receptor Modulators (SERMs).
  • Denosumab (anti-RANKL antibody).
  • Teriparatide (anabolic, promotes bone formation).
• Fall prevention to reduce fracture risk.

Significance: Common in elderly and post-menopausal women; early diagnosis and management prevent debilitating fractures (hip, spine, wrist).

Bone tissue exists in two main forms that differ in structure and function.

Key points:

• Cortical bone bears the majority of load in long-bone shafts.
• Trabecular bone aligns along stress lines (Wolff's law) and absorbs impact.
• Osteoporosis affects trabecular bone earlier due to its high surface area and turnover.

The stress-strain curve of bone describes its mechanical response from initial loading to fracture.

Typical curve description:

Key regions:

• Elastic region (linear):

  • Initial straight-line portion.
  • Stress proportional to strain (Hooke's law): .
  • Deformation is fully recoverable.
  • Slope = Young's modulus .

• Yield point:

  • Transition from elastic to plastic behavior.
  • Beyond this, permanent (plastic) deformation begins.

• Plastic region:

  • Curve flattens; microcracks and permanent damage accumulate.
  • Deformation is not recoverable.

• Ultimate strength point:

  • Maximum stress the bone can withstand.

• Fracture point:

  • Bone fails/breaks.

Important quantities:

• Toughness = area under the entire curve = energy absorbed before fracture.
• Resilience = area under the elastic region.

Notes:

• Cortical bone is brittle with a short plastic region.
• Higher strain rates shift the curve upward (stiffer, stronger) due to viscoelasticity.
• Bone withstands more stress in compression than tension.

Creep is the gradual increase in strain of a material under a constant applied stress, while recovery is the gradual return of strain after the load is removed. Bone exhibits both due to its viscoelastic nature.

Kelvin-Voigt model (spring ∥ dashpot):
Governing equation:

Derivation of creep response (constant stress ):

Rearranging:

This is a first-order linear ODE. Solving with initial condition :

where the retardation time .

Interpretation:

• Strain rises exponentially toward the equilibrium value .
• The dashpot delays deformation (no instantaneous jump).

Recovery (stress removed at ):

Strain decays exponentially back to zero — delayed elastic recovery.

Significance for bone: Explains time-dependent deformation under sustained loads and gradual recovery afterward, important in prolonged postures and load-bearing.

Because bone is viscoelastic, its mechanical response depends strongly on the rate at which load is applied (strain rate).

Effects of increasing strain rate:

• Increased stiffness: Young's modulus rises with loading rate.
• Increased strength: Both ultimate and yield strength increase.
• Increased energy absorption: Up to a limit, bone stores more energy before failure.
• More brittle failure at very high rates: At extremely rapid loading, bone can shatter into many fragments (comminuted fracture).

Reason for rate dependence:

• The viscous component (from water and collagen) resists rapid deformation.
• At high rates, fluid within bone cannot redistribute quickly, so the material behaves more rigidly.
• At low rates, viscous flow allows more gradual, compliant deformation.

Illustrative comparison:

• Low strain rate (slow load): Lower modulus, larger deformation before fracture, fewer fragments.
• High strain rate (impact): Higher modulus and strength, but sudden brittle fracture.

Clinical significance:

• Explains different fracture patterns in slow falls vs. high-speed trauma.
• Important in impact protection, sports injuries, and orthopedic testing standards.

Thus, bone strength values must always be reported with the associated strain rate.

Articular cartilage is the hyaline cartilage covering the articulating surfaces of bones in synovial joints. It is avascular, aneural, and alymphatic.

Main functions:

• Load distribution: Spreads joint contact forces over a larger area, reducing peak stress on subchondral bone.
• Low-friction surface: Provides an extremely smooth, lubricated surface (friction coefficient ~0.001–0.01) for smooth joint motion.
• Shock absorption: Its viscoelastic, biphasic nature absorbs and dampens impact energy.
• Wear resistance: Protects underlying bone from mechanical damage over a lifetime of loading.

Structural support of functions (zonal organization):

• Superficial (tangential) zone: Collagen fibers parallel to surface; resists shear and provides a smooth gliding surface.
• Middle (transitional) zone: Randomly oriented fibers; resists compression.
• Deep zone: Fibers perpendicular to bone; resists compressive loads and anchors cartilage.
• Calcified zone: Anchors cartilage to subchondral bone.

Biphasic composition:

• Proteoglycans attract water, creating osmotic swelling pressure that resists compression.
• Collagen network provides tensile strength and constrains swelling.
• Interstitial fluid flow provides load support and lubrication.

Degeneration of this structure leads to osteoarthritis, causing pain and loss of joint function.

Both bone and cartilage are load-bearing connective tissues but differ significantly in structure and mechanics.

Key insights:

• Bone provides rigidity; cartilage provides compliance and cushioning.
• Cartilage viscoelasticity is dominated by interstitial fluid movement, whereas bone's is governed by its solid organic matrix.
• Together they form an efficient load-transfer system at joints.

The Standard Linear Solid (SLS) model, also called the Kelvin model, combines the Maxwell and Voigt elements to more realistically represent viscoelastic solids like bone.

Configuration (common form):

• A spring in parallel with a Maxwell element (spring + dashpot in series), or equivalently a spring in series with a Voigt element.
• Uses three elements: two springs (, ) and one dashpot ().

Governing equation (general form):

where is the relaxed modulus and , are relaxation and retardation times.

Why it is superior:

• Instantaneous elastic response: Unlike Voigt, it shows an immediate strain jump upon loading (due to a spring).
• Realistic creep: Strain increases exponentially to a finite equilibrium (unlike Maxwell's unlimited flow).
• Realistic stress relaxation: Stress decays to a finite non-zero value (unlike Maxwell decaying to zero, and Voigt showing none).
• Finite equilibrium modulus: Captures the fact that bone retains stiffness at long times.

Comparison summary:

• Maxwell: relaxation only.
• Voigt: creep only.
• SLS: captures instantaneous elasticity, creep, and relaxation — matching the observed behavior of bone.

Hence the SLS model provides a more accurate and complete description of bone's viscoelasticity.

Given:

• Length
• Area
• Force
• Young's modulus

Step 1 — Stress:

Step 2 — Strain:

Step 3 — Elongation:

Results:

• Stress
• Strain (0.176%)
• Elongation

Comment on elastic region:

• Cortical bone's tensile strength is and yield strain is around .
• The applied stress () and strain () are well below these limits.
• Therefore, the bone remains within the elastic region and the deformation is fully recoverable.