Biomechanics of Fracture Fixation, Arthroplasty, and Gait

Biomechanics of Fracture Fixation: Introduction and Fracture Stability

• Two Main Areas of Study: The study of fracture fixation biomechanics is divided into: (1) criteria for achieving fracture stability and promoting bone healing, and (2) the characterization of techniques and devices used to mechanically stabilize a fracture.
• Clinical Goal of Treatment: The primary goal is rapid healing without significant deformity or limb shortening to restore the patient to a prefracture level of function.
• Immobile Patients: In the elderly, rapid mobilization is essential to prevent the deleterious consequences of prolonged bed stay.
• Factors Influencing Stability: Fracture stabilization is determined by the location and type of fracture, muscle and body forces acting on it, and passive soft tissue constraints (ligaments and fascia).
• Inherent Stability:     - Simple fractures may be inherently stable under low loading (e.g., requiring only a sling for a clavicle or a cast).     - Midshaft comminuted femur fractures require major surgical intervention and internal fixation.     - Osteotomy: A surgically created fracture used for the correction of deformity; it allows close approximation of fracture ends.     - Stability can be facilitated by interdigitation of bone ends, such as inserting a tapered bone end into the medullary cavity (though this creates a displacement deformity).
• Traditional Non-Surgical Methods: Includes traction, casts, and braces. These externally applied forces stabilize the fracture by limiting muscle or soft tissue forces that lead to deformity.

Fracture Healing and Micromotion

• Healing Paradigms:     - Controversy exists regarding whether completely rigid fixation is optimal.     - Micromotion: Low levels of displacement appear advantageous by providing mechanical signals that stimulate biologic repair.     - Gross Motion: Excessive motion (as seen in rib fractures) can still lead to healing, but usually results in nonunion and fibrocartilage formation.     - Rigid Fixation: May lead to delayed healing, bone atrophy, and a lack of the external stimuli necessary for the healing process.
• Tissue Differentiation: The amount of local strain ($Strain = \frac{\Delta L}{L_0}$) in the healing region is thought to determine whether the tissue formed is fibrocartilage or bone.
• External Promotion of Healing: Clinical methods include ultrasound or electromagnetic fields (e.g., pulse ultrasound therapy).
• Biologic Agents: Growth factors (e.g., Simpson et al., 2006) can be injected into the fracture or used in biodegradable coatings on devices.
• Load Bearing vs. Load Sharing:     - Load Bearing: The fixation device carries all or most of the load.     - Load Sharing: The load is distributed between the device and the bone.     - Stress Shielding: Occurs when a device carries the entire load, promoting localized osseous resorption (Wolff’s Law) due to bone unloading.     - Osteopenia: Initial bone loss beneath plates is often caused by vascular disruption during application rather than purely stress shielding (Perren, 2002).
• Stages of Bone Repair:     1. Hematoma and Inflammation     2. Callus Formation (Mineralization increases mechanical strength; callus forms periosteally and endosteally).     3. Replacement by Woven Bone.     4. Remodeling into Lamellar or Trabecular Bone.
• Mechanical Geometry of Callus: Callus enlarges the bone diameter at the fracture site. Since stiffness in bending and torsion is related to the moment of inertia, this increased diameter increases stiffness even before the tissue reaches full maturity.
• Vascularity: Adequate blood supply is vital. Surgeons must preserve the periosteum and soft tissue to ensure early revascularization.

Fracturing Fixation Devices and Materials

• Fixation Selection Factors: Mechanical loading types (tension, bending, torsion), magnitude of forces, and cyclic nature (risk of fatigue failure). Bone quality (strength) is also critical.
• Common Materials:     - Stainless Steel (316L).     - Titanium Alloy ($Ti-6Al-4V$).     - Cobalt-Chromium Alloy.
• Biodegradable Polymers: Interest in polylactic acid (PLA).     - Advantages: More flexible, promotes load bearing, no secondary surgery for removal, avoids stress shielding.     - Disadvantages: Much lower mechanical strength than metals; degradation products can cause untoward biologic responses.
• Case Study 15-2: Fixation Plate Failure: A 25-year-old man with a radius fracture had a plate fail after 20 years due to fatigue. Fatigue occurs even when loads are below ultimate stress because microdamage accumulates over millions of cycles.

Specific Fixation Techniques

• Wires: Solid or cable; used as cerclage (wrapping around bone) or bone sutures. Requires equal tension at multiple sites to prevent motion/nonunion. Issues include fatigue breakage and periosteal blood supply compromise.
• Staples: Often used to tack fragments before rigid fixation. Nitinol (shape-memory alloy) staples can effect compression when heated to body temperature.
• Kirschner Wires (K-wires): Used for percutaneous pinning or holding fragments; lack stability for primary fixation in weight-bearing bones. Non-parallel insertion is required to prevent "pistoning."
• Tension Band Technique: K-wires combined with looped/tightened sutures to increase mechanical stability significantly.
• Screws:     - Types: Cortical (tighter pitch) and Cancellous (vaster pitch/deeper threads).     - Holding Power Factors: Outer thread diameter, thread configuration, thread length, and bone quality.     - Lag Modality: The screw is free in the proximal fragment (no proximal threads or enlarged hole) so that tightening pulls the distal fragment toward the head, creating interfragmentary compression.     - Tapping: Many screws are self-tapping; pretapping has minimal effect on holding ability.
• Plates:     - Placement: Optimally placed on the tension side of the bone. Placing a plate on the compression side causes the fracture to gap when loaded.     - Rigidity: Rigidity ($EI$) is a product of the modulus ($E$) and the moment of inertia ($I$). For a rectangular plate, $I = \frac{bh^3}{12}$, where $b$ is the base and $h$ is height.     - Compression Plates: Achieve compression via offset countersunk screw holes or by pre-bending the plate (straightening action pulls bone together).
• Intramedullary (IM) Nails: Used in the medullary cavity; closer to the neutral bending axis than external plates. Bending and torsional stiffness are proportional to $(diameter)^4$. One large nail is more rigid than multiple smaller rods.
• External Fixators: Multiple transcutaneous pins stabilized by external bars/rings. Most rigid when pins are large, short, and located close to the fracture.

Biomechanics of Hip Arthroplasty

• Aseptic Loosening: The most common cause of failure in Total Hip Arthroplasty (THA), related to polyethylene wear and periprosthetic bone loss.
• Direct Measurement of Hip Forces: Measured via instrumented implants with strain gauges (first by Rydell in 1966).     - Walking Peaks: 1.8 to 4.6 times body weight ($BW$). The pattern shows two peaks similar in magnitude (early stance and late stance).     - Stumbling: Bergmann et al. (2004) recorded forces up to 7.2 times $BW$.     - Stair Climbing: Peak forces of 2.6 to 5.5 times $BW$.
• Analytic Hip Force Modeling:     - Mechanical Equilibrium: Internal forces/moments must equal and opposite external forces.     - Statically Indeterminate Problem: More muscles cross the hip than there are available equations.     - Reduction Methods: Combining individual muscles into functional groups (effective for hinge joints like the knee).     - Optimization Methods: Using mathematical criteria (e.g., minimizing muscle stress or maximizing endurance) to select the most likely solution from infinite possibilities.     - Parametric Approach: Predicts a "solution space" of all physiologically possible muscle activity combinations (Hurwitz et al., 2003).
• Case Study 16-1: Cemented Total Hip Replacement: A 65-year-old woman with osteoarthrosis. Post-surgery, her head-neck angle was in valgus. Valgus reduces bending moments in the stem but increases joint reaction force because the abductor lever arm shortens, requiring more muscle force to balance body weight.

Factors Influencing Hip and Knee Loading

• Gait Patterns: Patients after THR often move slower and have reduced ground reaction forces. Preoperative gait adaptations often persist 1 year after surgery.
• Hip Offset: The perpendicular distance between the femoral head and the femoral shaft. Changing offset alters leg alignment and muscle moment arms.
• Joint Geometry: Moving the hip center medially, inferiorly, and anteriorly minimizes predicted joint forces by maximizing abductor muscle capacity.
• Activity Level: Steps per day is a surrogate for loading cycles. While simulation studies assume 1 million steps/year, actual data shows ranges from 5,078 to 12,288 steps/day. Some highly active patients take up to 16,392 steps/day.
• Stress Shielding in Hip Stems: Stiffer implants (Cobalt-chromium) cause a greater reduction in bone strain energy density compared to flexible materials (Titanium or Composites).
• Polyethylene Wear: Cross-linking polyethylene using radiation (highly cross-linked polyethylene) increases wear resistance but may increase brittleness.

Motion and Forces at the Knee Joint

• Degrees of Freedom: The knee has six degrees of freedom: three translations and three rotations.
• Kinematics during Level Walking:     - Heel-strike: Almost fully extended.     - Midstance: Max of 15° to 20° flexion.     - Toe-off: Occurs at approximately 63% of the gait cycle.
• Femoral Rollback: Flexion is a combination of rolling, sliding, and spinning. Rolling predominates at 0°-20°; sliding predominates beyond 30°.
• Screw-home Mechanism: The femur rotates externally during knee flexion and internally during knee extension (or vice versa for the tibia) as it moves a greater distance on the lateral plateau compared to the medial plateau.
• Forces at the Knee:     - Axial Contact Forces: 2.2 to 2.8 times $BW$ during walking.     - Shear Forces: Approximately 0.3 times $BW$.     - Stair Maneuvers: Increase load readings by about 30%.
• Wear Mechanisms:     - Surface Fatigue: Pitting and delamination due to fluctuating stresses.     - Adhesive/Abrasive Wear: Generates submicron-sized particles that lead to osteolysis.     - Cross-shear: Movement perpendicular to the main motion direction; increases wear rate significantly.

Biomechanics of Gait

• Anatomic Considerations:     - Hip: Triaxial (flexion-extension, adduction-abduction, internal-external rotation).     - Knee: Three degrees of freedom, primary motion is flexion-extension.     - Ankle/Foot: The talocrural joint permits only plantarflexion and dorsiflexion.     - Upper Body: Pelvis plus thorax is often called the HAT segment (Head, Arms, Trunk).
• Gait Cycle (Stride):     - Stance Phase (60% of stride): Consists of initial contact (0%), loading response (0-12%), midstance (12-30%), terminal stance (30-50%), and pre-swing (50-60%).     - Swing Phase (40% of stride): Consists of initial swing (60-73%), midswing (73-87%), and terminal swing (87-100%).
• Time-Distance Variables (Adult Free Walking Velocity):     - Cadence: 90-140 steps/minute.     - Velocity: 0.9-1.8 m/sec.     - Step Length: 0.56-1.1 m.     - Stride Length: 1.2-1.9 m.     - Step Width: 7.7-9.6 cm.
• Kinematics:     - Hip: Flexed 30° at initial contact; extends to 10° at terminal stance.     - Knee: Flexes to 20° in midstance, extends, then flexes to 60-70° in midswing.     - Ankle: Plantarflexes 7° after initial contact, then dorsiflexes to 15° during midstance.
• Kinetics (Joint Moments):     - Hip Moment: Adductor at contact, switches to abductor peak of 0.7 Nm/kg in loading response.     - Knee Moment: Extensor peak of 0.6 Nm/kg in midstance.     - Ankle Moment: Plantarflexor (extensor) peak of 1.6 Nm/kg at 45% of the stride.
• Muscular Control:     - Gluteus Maximus: Active from initial contact to middle of loading response.     - Quadriceps (Vasti): Control knee flexion collapse via eccentric contraction during weight acceptance.     - Plantarflexors: Soleus and Gastrocnemius restrain forward rotation of the tibia during midstance.
• Pathologic Gait Patterns:     - Trendelenburg Gait: Lateral drop of the pelvis due to weak hip abductors.     - Lateral Lurch: Trunk displacement toward the affected limb to reduce the required abductor moment.     - Quadriceps Avoidance Gait: Seen in ACL deficiency (Case Study 17-1); reduction of the knee extensor moment (sometimes by 140%) to prevent unrestrained anterior translation of the tibia.

Practice Questions and Summary Points

• Question 1 (Fixation Plate): Titanium modulus is lower; to match stiffness, the plate must be thicker. Since stiffness relates to thickness cubed ($h^3$), a 25% increase in thickness may be sufficient.
• Question 2 (IM Nails): Rigidity relates to $(diameter)^4$, thus one large diameter provides much greater stability than several smaller rods with smaller diameters.
• Question 3 (Joint Modeling): Approaches include Reduction (simplifying), Optimization (mathematical constraints), and Dynamic solution (muscle recruitment based on external moments).
• Summary of Joint Power: Joint power is the product of angular velocity and internal moment ($W/kg$). Positive value indicates energy generation (concentric); negative value indicates energy absorption (eccentric).