Topic 4: Bone Structure and Testing

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Topic 4 BoneStructure and Testing

• Bone is a hard connective tissue
• Infinitesimal strain and linear elasticity are
  appropriate
• Bone mechanics is a well established branch of
  biomechanics
• Particular aspects often studied
• failure and healing
• remodeling and growth
• optimal design and functional adaptation
• prostheses for repair or replacement
• microstructural basis of bone mechanical
  properties

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Long Bone

• Diaphysis (shaft)
• hollow tube of dense cortical compactum
• central cavity (medulla) contains the bone marrow
• Metaphyses (expansions at ends)
• surmounted by epiphyses
• calcification of cartilage takes place at
  epiphyseal plate (growth plate) until eventually
  fusing with metaphysis
• Articular cartilage

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Compartments of Long Bone

• Cortical (compact) bone
• Dense outer layer
• Woven - found in young subjects (lt14-16 yr.) or
  after injury
• Laminar - replaces woven
• Haversian - formed by vascularization of woven
  bone proportion increases with age
• Trabecular (cancellous) bone
• Epiphysis, metaphysis and endostium
• Spongy structure
• High surface area e.g. in human pelvis,
  trabecular surface area 20x periostial surface
  area
• Periostium
• Surrounds entire bone except the articulating
  surfaces
• Osteogenic inner layer
• Fibrous outer layer

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Compact Bone Structure
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Osteon

• Cortical bone composite
• hollow osteon
• an artery or vein (Haversian canal system)
• transversely connecting Volkmanns canals
• Major blood vessels enter through ligament
  attachments near the ends

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Osteon Structure
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Cartilage

• connective tissue matrix
• cartilage cells chondrocytes
• fetal skeleton is cartilaginous (dense cellular)
• specialized cartilage types remain in adults
• Hyaline (glassy) cartilage - articular, costal,
  nasal, tracheo-bronchial
• White fibrocartilage - intervertebral discs,
  articular discs - much collagen
• Yellow elastic fibrocartilage - ears, larynx,
  epiglottus - rich in elastin fibers
• coefficient of friction
• 0.0026 (s 500kPa) in synovial fluid

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Bone Composition

• Composite material
• 1/3 organic - extracellular collagen fiber
  matrix running in lamellae, impregnated with
• 1/3 mineral - dense inorganic calcium phosphate
  50x50x200 Å crystals of hydroxyapatite
  (3Ca3(PO4)2.Ca(OH)2),
• 1/3 water
• cells - osteoblasts and osteoclasts

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Bone as a Composite Material

• Bone is a composite of collagen fibers
  hydroxyapatite
• 2/3 dry wt (50 volume) is hydroxyapatite
  crystals
• Hydroxyapatite E 165 GPa similar to steel (200
  GPa)
• Collagen is nonlinear at high load Etangent
  1.24 GPa
• Bone composite in tension E18 GPa
• Bone strength is greater than either of its main
  constituents
• Soft collagen prevents hydroxyapatite from
  brittle fracture
• Stiff hydroxyapatite prevents collagen from
  yielding
• Composite properties depend on structure and
  bonding between the components
• Bone density increases with mineral content and
  has been correlated (partially) with strength

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Bone Material Testing

• Properties change during storage
• Drying affects composition and mechanical
  properties
• Typical storage methods
• Saline (briefly)
• Saline and alcohol (50/50)
• Freezing (in plastic bag) after wrapping in moist
  gauze or leave muscle on
• Embalming (changes properties)
• Density, ?
• measured after fat and oil are removed by boiling
• estimated by radiographic densitometry
• trabecular and cortical bone material are about
  equal ? 1.85 - 2.00 g/cm3
• but apparent ? of trabecular bone is 0.15 - 1.0
  g/cm3
• Mineral content ash weight (700 C )/dry weight
  (60C for 7d)

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Bone Mechanical Testing

• Uniaxial tensile testing usually done on
  standardized specimens
• l is the gauge length
• Results depend on strain-rate
• Other testing methods
• three-point bending
• uniaxial compression
• torsion (shear)
• ultrasonic (transverse wave speed depends on
  shear modulus)

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Bone Stress-Strain Relation
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Strain Rate
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Effects of Strain-Rate
Using d0.057, E (Youngs modulus) would vary
15 during the range of strain rates that occur
during normal activity
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Bone Mechanical Properties

• Adult human (20-40 years) femoral compact bone
  (wet)
• stress-strain behavior of dry bone is linear to
  failure at uniaxial strain of 0.4
• failure occurs at around 1.2 strain and the
  curve is nonlinear about 0.4
• properties vary with age, mode of loading, strain
  rate, testing environment
• Elastic Properties
• Modulus of elasticity E (tension) 17.6 GPa
• Modulus of elasticity E (compression) 4.9 GPa
• Shear Modulus G (Torsion) 3.2 GPa

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Bone Strength Measures

• Strength Properties
• Ultimate Tensile Strength UTS 124 MPa
• Ultimate Tensile Strain 1.41
• Ultimate Compressive Strength 170 MPa
• Ultimate percentage contraction 1.85
• Ultimate bending strength 160 MPa
• Ultimate torsional shear strength 54 MPa
• for dense cortical region of the diaphysis
• much lower for spongy cancellous bone

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Stiffness and strengthof some other materials
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Bone Strength Determinants

• The most studied aspect of bone mechanics
• Bone strength and fracture depend on
• specimen preparation - wet, dry, embalmed
• orientation - axial, transverse
• region
• axial strength is highest at mid-diaphysis
• transverse strength is highest at ends
• age - decreases with age
• type - strength of Haversian bone is 30 lt
  lamellar
• type of loading

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Bone Strength and Fracture

• Axial tension failure
• failure surface is perpendicular to load at high
  strain rate
• at low strain rate surface is rougher because
  osteons are pulled out
• Compression - fracture plane is at 60 to the
  load axis
• Fracture studied by energy needed to propagate
  crack
• Bone mineralization affects strength
• Deer Antler - lower density, 1.86 g/cm3
• - lower mineral content, 59
• - lower E, 7.4 GPa
• - higher fracture work 6186 Jm-2
• Cow Femur - higher density 2.06 g/cm3
• - higher mineral 67
• - higher E 13.5 Gpa
• - lower fracture work 1710 Jm-2

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Topic 4 Summary of Key Points

• Bone is a hard and can be approximated as
  linearly elastic
• The shaft (diaphysis) of long bone consists of
  compact cortical bone.
• The epiphyses at the ends of long bone contain
  spongy trabecular bone, and are capped with
  articular cartilage.
• The basic unit of compact bone is the osteon,
  which forms the Haversion canal system.
• Bone is a composite of water, hydroxyapatite and
  collagen.
• Typical compact bone under standard uniaxial
  testing, has an elastic modulus of 18 GPa, an
  ultimate tensile stress of 140 MPa, an ultimate
  tensile strain of 1.5, and a yield strain of
  0.08. Trabecular bone is less stiff, less dense
  and less strong.
• Bone strength and stiffness vary with density,
  mineral content, and structure