1. Bone Structure 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

2. 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

3. Compartments of Long Bone Cortical (compact) bone Dense outer layer Woven - found in young subjects (<14-16 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

4. Compact Bone Structure

5. Osteon Cortical bone composite: hollow osteon an artery or vein (Haversian canal system) transversely connecting Volkmann’s canals Major blood vessels enter through ligament attachments near the ends

6. Osteon Structure

7. 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  500kPa) in synovial fluid

8. 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 (3Ca 3 (PO 4 ) 2.Ca(OH) 2 ), ~1/3 water cells - osteoblasts and osteoclasts

9. 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 E tangent = 1.24 GPa Bone composite in tension: E=18 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

10. 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, ρ –measured after fat and oil are removed by boiling –estimated by radiographic densitometry –trabecular and cortical bone material are about equal: ρ = 1.85 - 2.00 g/cm 3 –but apparent ρ of trabecular bone is 0.15 - 1.0 g/cm 3  Mineral content = ash weight (700 °C )/dry weight (60°C for 7 days)

11. 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)

12. Bone Stress-Strain Relation

13. Strain Rate

14. Effects of Strain-Rate Using d=0.057, E (Young’s modulus) would vary ~15% during the range of strain rates that occur during normal activity Ramberg-Osgood Equation: *Units of c, GPa

15. 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

16. Bone Strength Measures Strength Properties Ultimate Tensile Strength UTS124 MPa Ultimate Tensile Strain1.41% Ultimate Compressive Strength170 MPa Ultimate percentage contraction1.85% Ultimate bending strength160 MPa Ultimate torsional shear strength54 MPa for dense cortical region of the diaphysis much lower for spongy cancellous bone

17. Stiffness and strength of some other materials

18. 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% < lamellar type of loading:

19. 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/cm 3 - lower mineral content, 59% - lower E, 7.4 GPa - higher fracture work 6186 Jm -2 Cow Femur- higher density 2.06 g/cm 3 - higher mineral 67% - higher E 13.5 Gpa - lower fracture work 1710 Jm -2

20. 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.diaphysis cortical bone The epiphyses at the ends of long bone contain spongy trabecular bone, and are capped with articular cartilage.epiphyses trabecular bonearticular cartilage The basic unit of compact bone is the osteon, which forms the Haversion canal system.osteon, Bone is a composite of water, hydroxyapatite and collagen.composite 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.standard uniaxial testingelastic modulus ultimate tensile stress Bone strength and stiffness vary with density, mineral content, and structure