Biomechanics of Bone

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About Skeletal System and Bone
Mechanical Properties of the Bone
Adaptive Response of the Bone Under Different Loading
Degenerative Changes in Bone
Failure of the Bone

1. Frankel V.H. & Nordin M (2001): Biomechanics of Bone. In Nordin M. & Frankel VH (eds): Basic Biomechanics of the Musculoskeletal System. Philadelphia, PS, USA: Lippincott Williams & Wilkins. pp.26-58.
2. Hall SJ, 2003. Basic Biomechanics, 4^th ed. Boston, MA, McGraw-Hill. pp. 87-116.
3. Whiting W.C. & Zernicke R.F. (1998): Biomechanics of Musculoskeletal Injury. Champaign, IL, USA: Human Kinetics. pp.87-100.

About Skeletal System and Bone

Functions of the Skeletal System

• mechanical functions
  • to protect vital organs
  • to provide rigid kinematic links
  • to provide attachments sites for muscle
  • to facilitate muscle action and bone movement

• physiological functions
  • to produce blood cells (hematopioesis)
  • to maintain calcium metabolism (mineral hemeostasis)

Unique Characteristics of the Bone

• the hardest structure in the body
  • high content (60-70% of dry weight) of mineral materials e.g. calcium and phosphate

• metabolically active throughout life
  • excellent capacity for self-repair
  • changes in properties and configuration in response to changes in mechanical loads, systemic hormones, and serum calcium levels

Structure of the Long Bone

• structures based on position
  • diaphysis
  • epiphysis
  • metaphysis

• types of bone tissue： based on porosity
  • cortical bone (compact bone)
    • 5-30% of porosity
  • cancellous bone (trabecular bone or spongy bone)
    • 30-90% of porosity

Composition of the Bone Tissue

• cells
  • osteoblast： located on bone surface
  • osteocyte：  located in lacuna
  • osteoclast： located on bone surface
• extracellular matrix
  • mineralized type I collagen fibers： 90% of the extracellular matrix and 25-30% of dry weight
  • ground substance： glycosaminoglycans (GAGs)
  • water： 25% of total weight and 85% in the organic matrix

Fundamental Unit： Osteon (Haversian System)

• size： ~200m  in diameter

• component：
  • Haversian canal： a canal, in the center of the osteon, containing blood vessels and nerves
  • interstitial lamellae： concentric rings  of mineralized matrix surrounding the Haversian canal
  • lacunae： the interface between lamellae, containing osteocyte and canaliculi
  • cement line： boundary of the osteon

Bone Modeling and Remodeling

• bone modeling： the process by which bone mass increased to alter the size, shape, and structure of the bone (new bone formation)

• bone remodeling： the process through which bone mass adapts, with altering its size, shape, and structure, to the mechanical demands placed upon it (activation-resorption-formation process of bone)
  • step I： activation of osteoclasts
  • step II： resorption the existing bone by osteoclasts
  • step II： new bone deposit by osteoblasts

• differences between modeling and remodeling

  	Modeling	Remodeling
  process	continuous	cyclical
  stimulus for activation	not required	required
  coupling of formation and resorption	system?	local

• Wolff's Law (1892)
  • static stress model
  • Bone is deposited where needed and resorbed where not needed.
  • current concept： Bone modeling and remodeling occurs in response to the mechanical demands placed upon it.

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Mechanical Properties of the Bone

Bone Strength

• As the load increases, load and deformation increase in a relatively linear relationship, obeying Hooke's law and, after the yield point, smaller and smaller increases in load produce greater and greater deformation
• ultimate stress the bone can sustain before failure
  • failure point in the stress-strain curve
• ultimate strain the bone can sustain before failure
• energy the bone can store before failure
• size of the area under the entire curve
• If the applied load is at the plastic region and removed later, the bone does not return to its original configuration (hysteresis)

Bone Stiffness

• elastic modulus： the slope of the stress-strain curve in the elastic region
• metal >> glass > bone

Anisotropic Behavior of the Bone

anisotropy： the property of a material which exhibits different mechanical properties when loaded in different direction Stiffness with respect to tension is maximal for axial loads and minimal for perpendicular loads. for ultimate stress of cortical bone: compression > tension > shear
	Adapted from Nordin M & Frankel VH (2001). Basic Biomechanics of the Musculoskeletal System.(p.54)

Bone Geometry

• In tensile or compressive load, the load to failure and the stiffness are proportional to the cross-sectional area of the bone
• moment of inertia
  • in a rectangular beam： I = BH³/12
  • in a tube-like bone： I = mr²

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Adaptive Response of the Bone Under Different Loading

Factors that affect the structure, composition, and quality of bone

• external factors
  • mechanical loads：  gravity, physical activity, or immobilization
• internal factors
  • systemic calcium level： nutrition
  • hormone level： gender, growth, menopause, or degeneration

Gravity

• positive correlation between body weight and bone mass
• fast loss of bone mass in the weight-bearing joints of astronauts

Muscle Activity

contraction of muscle alters the stress distribution in the bone contraction of the gluteus medius muscle produces great compressive stress on the superior cortex of the neck of the femur, neutralizing the tensile stress and thereby allowing the femoral neck sustain more load

Strain Rate Dependency

• The stiffness of a bone changes with the rate of loading

• when loads are applied at higher rate within the physiological limit, the bone
  • becomes stiffer
  • sustains a higher load to failure
  • stores more energy before failure

• when a bone fractures, the stored energy is released.
  • single bone crack for a low-energy fracture
  • comminuted fracture of bone for a higher-energy fracture
  • severe destruction of bone before failure

Fatigue of Bone Under Repetitive Loading

Stress fracture may occur when a load of lower magnitude is applied repetitively.
march fracture spondylolithesis

Physical Activity

• relationship between physical activity and bone mass
  • growing bone responds to low or moderate exercise through significant increase in new cortical and trabecular bone
  • a threshold of physical activity exists above which some bone respond negatively
  • moderate to intense physical training can generate modest increase in bone density (1-3%) in men and premenopause women
  • the long-term effect of exercise are retained only by continuing to exercise
  • individuals with extremely low initial bone mass may have more to gain from exercise than those with moderately reduced bone mass

• effects
  • increase bone mass
  • increase cortical thickness
  • increase bone mineral content

Immobilization or Implantation

bed rest： ~ 1% of loss of bone mass per week immobilization in body cast： a threefold decrease in load to failure and energy storage capacity in the vertebrae that have been immobilized in body cast for 60 days immobilization with metal implant decrease in bone diameter and bone strength due to resorption of the bone under the metal plate increase in bone deposit at the bone-screw interface

Adapted from Nordin M & Frankel VH (2001). Basic Biomechanics of the Musculoskeletal System.(p.54)

Artificial Defects

stress raiser： defect length < bone diameter the stresses concentrate around the defect the weakening effect is marked under torsion loading (60% of decrease) example： compression hip screw open section defect：  defect length > bone diameter only the shear stresses at the periphery of the bone resist the torsion the shear stresses at the interior of the bone run in the same direction of the torsion. example： bone graft

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Degenerative Changes of the Bone

• progressive loss of bone density (osteoporosis) with normal aging process

• structural changes with aging
  • marked reduction in amount of the cancellous bone
  • decrease in the diameter and thickness of the cortical bone due to resorbed longitudinal trabeculae

changes in mechanical properties decrease in strength, deformation ability, and energy storage capacity the ultimate stress was approximately the same for the young and the old bones the old bone can withstand only 1/2 of the strain that the young bone can aggravating factors gender： Both men and women lose cortical bone at the same rate but women lose trabecular bone more rapidly than men age post-menopause： 1.5-3% of loss per year after menopause endocrine abnormality inactivity disuse calcium deficiency

Adapted from Nordin M & Frankel VH (2001). Basic Biomechanics of the Musculoskeletal System.(p.54)

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Failure of the Bone

• Failure of bone may occur when the applied stresses exceed the ultimate strength limit, which may result from excessive stresses, or weak material, or both.

• possible causes of bone failure
  • excessive acting forces
  • unfavorable acting moments
  • small bone dimension
  • excessive repetition of load application

• osteoporosis
  • a disease or phenomenon marked by reduced bone mineral mass and then changes in bone geometry
  • a function of normal aging process
  • the amount of bone mass at one site is not necessarily correlated to that at the other sites

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