Biomechanics and Injury

Biomechanics

  • Applies principles of physics (mechanics) to biological tissues and systems.
    • Mechanical properties of arteries regulate blood flow.
    • Mechanics of insect flight.
    • Mechanics of tissue injury (e.g., bone fracture).
    • Mechanics of tissue remodeling (e.g., muscle hypertrophy).
    • Mechanical properties of scaffolds to seed stem cells.
    • Mechanics and dynamics of prosthetics (design).
    • Mechanics of human movement (e.g., jumping, walking).

Principles of Physics

  • Newton's Laws of Motion
    • 1st Law: Inertia
    • 2nd Law: F = ma (Force = mass x acceleration)
    • 3rd Law: F1 = -F2 (For every action, there is an equal and opposite reaction)
  • Projectile Motion
    • df = di + v_i t - \frac{1}{2} g t^2
      • d_f: final displacement
      • d_i: initial displacement
      • v_i: initial velocity
      • t: time
      • g: acceleration due to gravity
    • vf^2 = vi^2 - 2g(df - di)
      • v_f: final velocity

Injury

  • Definition: Damage caused by physical trauma sustained by tissues of the body.
  • Is injury always bad?
    • No, micro-tears lead to muscle growth (muscle hypertrophy) and bone strengthening (Wolff's Law).
  • Better definition: Damage sustained by tissues that ultimately results in pain and/or loss of function.
  • How does injury occur?
    • Applied force exceeds tissue tolerance.

How Injury Occurs

  • Acute Injury Scenario
    • Applied force exceeds tissue tolerance.
    • Margin of safety failure.
  • Cumulative Injury Scenario
    • Applied force exceeds tissue tolerance over time.
    • Repetitive or constant loads reduce tissue tolerance.
    • Failure margin of safety.

Why Doesn't Injury Always Occur?

  • Benefits of rest and regrowth.
  • Tissue tolerance increases with rest.

Risk of Injury

  • Optimal level of loading exists between high and low ends (Callaghan, 2005).
    • Too little load limits tissue adaptation.
    • Too much load results in tissue breakdown and potential failure.
  • Anisotropy
    • Tissue properties differ depending upon direction of loading.
    • Unique tolerance level for every direction of loading.

Load-Deformation Curves

  • Apply a force (load) to a tissue and monitor how it deforms.
  • Regions of the curve include:
    • Toe region: Very little force to cause deformation.
    • Elastic region: Tissue returns to its original state when force is removed; deformation is reversible.
    • Plastic region: Permanent deformation; not immediately repaired.
    • Yield point: Transition between elastic and plastic regions.
    • Failure point: Tissue failure occurs.
  • Stiffness: \frac{\Delta load}{\Delta deformation}

Stress-Strain Curves

  • Stress: Force applied over an area. Units: N/m^2 or Pa (Pascal).
  • Strain: \frac{lengthf - length0}{length_0}; unitless.
  • Elastic Modulus: \frac{\Delta stress}{\Delta strain} in the elastic region.
    • In tension, this is Young's Modulus.
    • Allows for a normalized comparison between materials and/or tissues.

Pressure

  • Pressure is a specific type of stress.
  • Force acting normal (perpendicular) to a surface.
  • Example: body pressure = 101 mmHg ≈ 133 Pa

Anisotropy (Stress & Strain)

  • Maximum stress and strain depend on the angle of force application.
  • Angle-based tolerance.

Bone Structure

  • Cortical (compact) bone: Most dense.
  • Cancellous (trabecular) bone: Least dense.
  • Marrow cavity.

Bone Mechanics

  • Long bones primarily undergo bending stresses and strains.
  • Ratio of cortical to cancellous bone can define bending stiffness and strength.
  • Lightweight (less metabolic demand).
  • Greater area moment of inertia about its neutral axis (greater bending resistance).
  • Undergo less strain given bending.

Wolff's Law

  • Load governs bone remodeling and growth.
  • Magnitude, type, and direction of loading on bone affect how it will respond biologically.
  • Bone gets stronger in the direction of applied loads and adapts to these loads.
  • Strain in response to stresses stimulates growth.
  • Bone breaks down and resorbs when loading is too low (e.g., astronauts).
  • Similar concepts apply to other tissues (tendon, ligament, muscle, etc.).

Hooke's Law

  • Relates the force applied to a tissue and the amount it deforms.
  • Only valid in the elastic region.
  • F = k \cdot d
    • F: Applied force
    • d: Deformation
    • k: Stiffness (elastic spring constant); resistance of a tissue to deformation.
  • Technically written as F = -k \cdot d as the law describes the restoring force generated.

Viscosity and Viscoelasticity

  • Viscosity: A fluid's resistance to deformation (think of moving your hand through water); damping.
    • F = C \cdot v
      • v: velocity
      • C: damping constant
  • Viscoelasticity: Combining concepts of elasticity and viscosity.
    • Rate-dependent stress-strain characteristics.
    • Time-dependent behavior (stress relaxation, creep, hysteresis).

Viscoelasticity (Deformation & Force)

  • F = k \cdot d + C \cdot v
  • Force/stress within a tissue depends on both stiffness and damping.
  • Stiffness relates to the storage of energy.
  • Damping relates to the dissipation of energy.
  • Ultimate failure: Area under the force-deformation curve = energy stored in the tissue to failure; can be modified.

Failure Tolerance

  • Applied load over time.
  • Loading and rest stimulate tissue adaptation and remodeling, changing k and c (long-term adaptation).
  • Short-term muscle contraction can modify tissue stiffness, damping, and thereby force/energy tolerance.

Stability

  • Related to stiffness, stored energy, and damping.
  • Instability: Excessive or abnormal motion at a joint.
  • Mechanical definition: If a body part or joint is perturbed away from its current state of motion (static or dynamic), will it return to that state?

Mechanical Stability (McGill & Cholewicki, 2001)

  • Energy potential to do work.
  • Stable, less stable, robust to changes (metastable), unstable.
  • Potential energy: m \cdot g \cdot h

Quantified Potential Energy

  • Spring Potential Energy: \frac{1}{2} k \cdot x^2
  • Total system PE = Espring PE + Emuscle.

Quantified Stability

  • If \Delta E < 0, system is stable.
  • If \Delta E > 0, system is unstable.

Risk of Injury (Load)

  • Low loads/low muscle activity: Risk of instability.
  • High loads/high muscle activity: Risk of tissue failure.

How to Use This Information

  • Mechanical testing of tissues to predict tolerance levels.
  • Measure kinetics and kinematics of human movement.
  • Muscle models to predict forces.

Conceptual Hypothesis

  • To best assess injury risk, movement tasks should be screened under demanding conditions; can fatigue be used for this purpose?
  • Hypothesis: When fatigued, people are more likely to adopt movement patterns that will cause injury.