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Chapter 6: Biomechanics

Sources: Miller's Review of Orthopaedics 9th Ed, Rockwood & Green's Fractures in Adults 10th Ed 2025, Bailey & Love's Short Practice of Surgery 28th Ed

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6.1 Introduction to Biomechanics

• Explains how and why fractures occur in specific patterns
• Guides principles of fracture fixation (plates, nails, screws)
• Helps understand joint replacement and implant longevity
• Underpins understanding of gait, posture, and deformity

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6.2 Basic Definitions

Force

Stress (σ)

Strain (ε)

Elasticity (Young's Modulus / Elastic Modulus, E)

• Stainless steel: E = 200 GPa
• Titanium alloy: E = 110 GPa
• Cortical bone: E = 17 GPa (in compression)
• PMMA (bone cement): E = 3 GPa
• Cancellous bone: E = 0.1-5 GPa
• UHMW Polyethylene (arthroplasty): E = 0.9 GPa

Stiffness

Toughness (Strain Energy)

Resilience

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6.3 The Stress-Strain Curve

Stress
  |         Ultimate strength
  |              *
  |          /     \
  |    Yield/       \ ← Failure
  |    point         *
  |   /
  |  / ← Slope = Young's Modulus (E)
  | /
  |/_________________________ Strain
   Elastic    Plastic
   region     region

• Ductile (e.g., stainless steel, titanium): large plastic deformation zone between yield and failure - bends before breaking
• Brittle (e.g., bone cement, cast iron): small or no plastic zone - shatters suddenly

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6.4 Mechanical Properties of Bone

Types of Bone and Their Properties

Bone Strength by Loading Direction

Stress Risers

• A hole measuring 20-30% of bone diameter reduces strength by up to 50% (regardless of whether a screw fills it)
• Cortical defects can reduce strength by 70% or more
• Oval defects produce smaller stress risers than rectangular defects
• Screw hole area returns to normal 9-12 months after screw removal

Stress Shielding

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6.5 Types of Loading

1. Compression

• Force directed along the long axis, pushing surfaces together
• Bone is strongest under compression
• Produces crush or impaction fractures (e.g., vertebral body compression fracture, tibial plateau fracture)
• Fracture line tends to be oblique

2. Tension

• Force pulling the bone apart (distracting)
• Less common as a pure force in bone
• Produces transverse fractures perpendicular to the load axis
• Examples: avulsion fractures (e.g., 5th metatarsal base avulsion by peroneus brevis), patella fracture (pull of quadriceps)

3. Bending

• Eccentric loading or direct blows create a bending moment
• One side is in tension, the opposite side is in compression
• Fracture begins on the tension side (bone is weaker in tension than compression)
• Continues transversely/obliquely and may bifurcate to produce a butterfly fragment
• High-velocity bending: comminuted butterfly fracture
• Four-point bending: produces a segmental fracture

4. Shear

• Load parallel to the bone surface; fracture parallel to the load
• Occurs commonly around joints (e.g., condylar shear fractures)
• Most dangerous to cartilage (articular cartilage is weakest in shear)

5. Torsion

• Twisting force about the longitudinal axis
• Creates shear and tensile stresses
• Maximum tensile stress acts at 45° to the long axis
• Produces characteristic spiral fracture
• Greatest torsional stresses on the outer (periosteal) surface
• Example: spiral tibial fracture (toddler's fracture, ski boot fracture)

6. Combined / Axial Loading with Bending

• Most real-world fractures involve combined loads
• Oblique fractures from combined compression + bending
• Comminuted fractures from high energy with multiple loading vectors

Summary: Fracture Patterns by Loading Mode

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6.6 Wolff's Law

Key Points

• Increased mechanical loading → increased bone density (osteoblast activity)
• Decreased loading / immobilization → bone resorption (osteoclast activity, disuse osteoporosis)
• Trabecular bone in the femoral head and neck follows lines of compressive and tensile stress (visible on X-ray as Ward's triangle)
• Piezoelectric effect: mechanical stress generates small electric potentials in bone, which stimulate osteoblastic activity (electronegativity in areas of compression = bone formation)

Hueter-Volkmann Law (closely related)

• Compressive forces inhibit growth at the growth plate
• Tensile forces stimulate growth at the growth plate
• Clinical relevance: coxa valga in paralytic hips (loss of compressive forces), Blount's disease (excessive compression on medial tibial physis)

Clinical Applications of Wolff's Law

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6.7 Lever Systems in the Human Body

• Fulcrum (F): pivot point (joint)
• Effort (E): force applied (muscle)
• Load/Resistance (R): weight being moved

Classes of Levers

Clinical Importance: Hip Joint (Bergmann's Principle)

• The abductor lever arm (trochanter to hip center) ≈ 5 cm
• The body weight lever arm (hip center to body center of gravity) ≈ 10 cm
• Therefore, abductor muscles must generate ~2-3× body weight
• Total joint reaction force at the hip = 2.5-3.5× body weight during walking

• Using a walking stick on the contralateral side (reduces abductor demand)
• Valgus osteotomy (increases abductor lever arm)
• Weight loss (reduces body weight lever arm)
• Restoring femoral offset in THA

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6.8 Gait Biomechanics

The Gait Cycle

Phases of the Gait Cycle

Subdivisions of Stance Phase (5 sub-phases)

Subdivisions of Swing Phase (3 sub-phases)

Ground Reaction Forces During Gait

• Peak forces = 1.2× body weight during normal walking
• Running: 2-3× body weight
• Hip joint reaction: ~3-4× body weight during walking; ~7× during jogging
• Knee joint reaction: ~3-4× body weight during stair climbing

Energy Conservation in Gait

1. Pelvic rotation (reduces vertical oscillation)
2. Pelvic tilt (reduces vertical oscillation)
3. Knee flexion in stance (reduces vertical oscillation)
4. Foot and ankle mechanism
5. Knee mechanisms
6. Lateral trunk shift

Abnormal Gait Patterns

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6.9 Clinical Applications: Fracture Fixation and Implants

Principles of Fracture Fixation

• Achieved with: interfragmentary lag screws, compression plates
• Required for: articular fractures, simple diaphyseal fractures with direct reduction

• Achieved with: intramedullary nails, bridging plates, external fixators
• Required for: comminuted diaphyseal fractures

Plates

Intramedullary Nails

• Load-sharing device (nail within medullary canal)
• Aligned close to the mechanical axis → favorable bending moment
• Resists torsion better with locking screws
• Reaming increases endosteal contact and nail diameter → increased torsional stiffness

Screws

• Lag screw: compresses fracture surfaces (gliding hole in near cortex, threaded into far cortex)
• Cancellous vs cortical screws: cancellous have larger thread pitch and depth for softer bone

Implant Materials

Tension Band Wiring

• Olecranon fractures (pull of triceps converted to compression)
• Patella fractures (pull of quadriceps)
• Medial malleolus avulsion

External Fixator

• Pins/wires through bone connected to external frame
• Relative stability (secondary bone healing)
• Used: open fractures, polytrauma, temporary stabilization, infected non-union

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6.10 Summary Tables

Table A: Key Biomechanical Definitions

Table B: Fracture Pattern by Loading Mode

Table C: Gait Cycle Summary

Table D: Lever Classes in the Body

Table E: Implant Material Properties

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6.11 Clinical Pearls

1. Bone is strongest in compression, weakest in shear. Design of implants and rehabilitation must respect this.
2. Spiral fractures indicate torsion - always raise concern about non-accidental injury in children (toddler's fracture vs. abuse).
3. A screw hole reduces bone strength by up to 50% even when filled - warn patients about early unrestricted activity after plate removal.
4. Wolff's law explains disuse osteoporosis after casting, bed rest, or spinal cord injury. Early weight-bearing prevents bone loss.
5. Walking stick on the opposite (contralateral) side reduces hip joint reaction force by ~30% - teach patients this biomechanical principle.
6. Trendelenburg gait = weak ipsilateral hip abductors. The pelvis drops on the contralateral (unaffected) side. Compensated Trendelenburg = trunk lurches toward affected side to reduce abductor load.
7. Locking plates do not compress the fracture - they act as fixed-angle internal fixators. Do not use them like compression plates.
8. The tension band principle applies anywhere a tensile load can be redirected to compression: patella, olecranon, medial malleolus.
9. Titanium is preferred over stainless steel near joints (MRI compatibility) and in osteoporotic patients (lower modulus = less stress shielding).
10. During walking, hip forces are higher than at rest - do not restrict all weight-bearing in hip fracture patients without reason; controlled loading promotes healing.
11. Butterfly fragment indicates bending mechanism - look for an associated direct blow or indirect bending force.
12. Bone cement (PMMA) is brittle - weak in tension, stronger in compression. This is why cemented stems must be loaded in compression (optimal stem design).
13. The "neutral axis" in a loaded beam is the zone of zero stress - intramedullary nails placed near the neutral axis are biomechanically superior to plates placed on the cortical surface.
14. Anisotropy of bone: Cortical bone is stronger along its long axis (osteon orientation) than perpendicular to it - this guides implant screw orientation.
15. Viscoelasticity of bone: Bone absorbs more energy at high strain rates (high-velocity trauma) but also becomes stiffer and fails more suddenly.

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6.12 MCQs (20-30 Questions)

• A) Force × Area
• B) Force / Area ✓
• C) Deformation / Original length
• D) Load / Deformation

• A) Toughness
• B) Resilience
• C) Young's modulus (E) ✓
• D) Yield strength

• A) Compression
• B) Bending
• C) Torsion ✓
• D) Tension

• A) Compression
• B) Tension
• C) Shear ✓
• D) Bending

• A) Bone remodels in response to hormonal stimuli
• B) Bone remodels in response to mechanical stresses ✓
• C) Compressive forces stimulate bone growth at physis
• D) Bone is strongest in torsion

• A) 40%
• B) 50%
• C) 60% ✓
• D) 70%

• A) First class
• B) Second class
• C) Third class ✓
• D) Fourth class

• A) Torsion
• B) Shear
• C) Bending ✓
• D) Compression

• A) 0.9 GPa
• B) 3 GPa
• C) 17 GPa ✓
• D) 110 GPa

• A) 10%
• B) 25%
• C) 50% ✓
• D) 75%

• A) Stainless steel (200 GPa)
• B) Titanium alloy (110 GPa)
• C) Cobalt-chrome (200 GPa)
• D) PMMA (3 GPa) ✓ (closest in value among options, though still higher than bone's 17 GPa; titanium is still preferred clinically - note: this question tests relative knowledge - PMMA = 3 GPa, bone = 17 GPa, titanium = 110 GPa; titanium is actually the implant metal closest)

Correction note for students: Among metals used for orthopaedic implants, titanium (110 GPa) has the lowest modulus and is closest to cortical bone (17 GPa). PMMA (3 GPa) is lower but is not a structural implant.

• A) Cobalt-chrome
• B) Stainless steel
• C) Titanium ✓
• D) PMMA

• A) They compress the fracture
• B) They act as fixed-angle internal fixators ✓
• C) They are stronger than conventional plates in axial loading
• D) They have less stress at end screws than conventional plates

• A) Hip flexors
• B) Knee extensors
• C) Hip abductors (gluteus medius) ✓
• D) Ankle dorsiflexors

• A) Compression to shear
• B) Tension to compression ✓
• C) Torsion to bending
• D) Shear to tension

• A) Equal to body weight
• B) 1.5× body weight
• C) 2-3× body weight ✓
• D) 5-6× body weight

• A) Spiral fracture
• B) Transverse fracture
• C) Butterfly fracture
• D) Segmental fracture ✓

• A) Tension inhibits growth; compression stimulates growth
• B) Compression inhibits growth; tension stimulates growth ✓
• C) Shear forces cause growth arrest
• D) Torsional forces determine growth direction

• A) Stance phase
• B) Swing phase
• C) Double-limb support ✓
• D) Terminal stance

• A) Increased bone formation
• B) Disuse osteoporosis under the implant ✓
• C) Faster fracture healing
• D) Wolff's law reversal

• A) Have constant stiffness regardless of loading rate
• B) Have rate-dependent mechanical properties ✓
• C) Do not exhibit hysteresis
• D) Have identical loading and unloading stress-strain curves

• A) Young's modulus
• B) Yield strength
• C) Resilience
• D) Toughness ✓

• A) Compression
• B) Shear
• C) Tension ✓
• D) Torsion

• A) In the right hand (ipsilateral)
• B) In the left hand (contralateral) ✓
• C) In either hand equally
• D) Only on stairs

• A) Distance between contralateral foot contacts
• B) Distance between two successive contacts by the same limb ✓
• C) Time for one complete gait cycle
• D) Distance traveled per cadence unit

• A) Excessive compression
• B) Tensile and fatigue loading ✓
• C) Shear at interfaces
• D) Thermal degradation

• A) Trendelenburg gait
• B) Antalgic gait ✓
• C) Steppage gait
• D) Scissor gait

• A) Harvey Cushing
• B) Julius Wolff ✓
• C) John Hunter
• D) Hermann von Meyer

• A) Maximum stress the material can sustain
• B) Point of fracture
• C) Transition from elastic to plastic behavior ✓
• D) Slope of the elastic region

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6.13 Viva Questions

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6.14 Key Examination Points

These are the facts most commonly tested in MBBS/USMLE/DNB and viva examinations.

1. Stress = Force/Area; Strain = ΔL/L₀; E = Stress/Strain - know the formulae cold
2. Bone is strongest in compression, weakest in shear
3. Torsion → Spiral fracture; Bending → Transverse + butterfly; Tension → Transverse
4. Wolff's law = bone adapts to mechanical stress; piezoelectric effect mediates this
5. Hueter-Volkmann: compression inhibits physeal growth; tension stimulates it
6. Stance 60%, Swing 40% of gait cycle; double-limb support is absent in running
7. Trendelenburg sign: pelvis drops CONTRALATERAL to weak hip abductors
8. Most muscles = 3rd class levers (effort between fulcrum and resistance); sacrifices force for speed
9. Walking stick contralateral side reduces hip joint reaction force
10. Titanium closest modulus to bone among structural implant metals (110 GPa vs. bone 17 GPa)
11. Stress shielding → disuse osteoporosis under plate (Wolff's law)
12. Screw hole reduces strength by 50% (20-30% of bone diameter)
13. Locking plate = fixed-angle internal fixator (does NOT compress fracture)
14. Tension band converts tension to compression (olecranon, patella, medial malleolus)
15. Absolute stability = primary healing (no callus); Relative stability = secondary healing (callus)
16. PMMA is brittle - weak in tension, stronger in compression; fatigue failure is common
17. Butterfly fragment = high-velocity bending mechanism
18. Steppage gait = foot drop (weak tibialis anterior); Antalgic = pain; Scissors = spasticity
19. Young's modulus of cortical bone ≈ 17 GPa (memorize alongside steel 200 GPa, titanium 110 GPa)
20. Comminution = function of energy absorbed; more energy = more fragments

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