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Course topics

Course topics. Muscle biomechanics Tendon biomechanics Bone biomechanics. Bone. Provide mechanical support for each body segment Act as a lever system to transfer muscle forces Must be stiff yet flexible strong yet light. N&F, Fig 1-2. Compact bone (40X). Cancellous bone (30X).

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Course topics

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  1. Course topics • Muscle biomechanics • Tendon biomechanics • Bone biomechanics

  2. Bone • Provide mechanical support for each body segment • Act as a lever system to transfer muscle forces • Must be • stiff yet flexible • strong yet light

  3. N&F, Fig 1-2

  4. Compact bone (40X) Cancellous bone (30X) trabeculae Haversian canal N&F, Fig 1-3

  5. Classifications • Classifications • Biomechanical properties similar, difference is in density (porosity) • Cancellous is less dense (weaker) • Made of trabeculae oriented in direction of forces commonly experienced • Irregular lamellae – layers of mineralized matrix • Cortical • Cylindrical lamellae • Functional unit is the osteon

  6. Bone Synonyms Compact = cortical Cancellous = trabecular

  7. Definitions • Load (N) • Deformation (mm) • Stress (N/m2; Pa) • Strain (mm/mm; mm/mm*100%) • Stiffness (N/m) • Elastic Modulus (Pa)

  8. Tissue Mechanics:Equations and Values Force = F = kDL Stress = F / A Strain = ∆L / L Elastic modulus = E =Stress/Strain Stiffness = k = EA / L Elastic energy = 0.5k(DL)2 Elastic energy = 0.5 F DL 10,000 cm2 = 1 m2 • Tendon: • E (tendon or ligament) = 1.5 109Pa • Tendon safe limits: • Stress (Ultimate strength) = 100 MPa • Strain = 8% strain • Bone: • E (bone) = 17 x 109 Pa • Bone safe limits: • Tension = 150 MPa stress, 0.7% strain • Compression = 190 Mpa stress, 1% strain

  9. B,B’,B* C,C’,C* D,D’ Energy needed to yield? Energy needed to fracture?

  10. Bone is a Composite Material One phase: mineral (strong and brittle) Other phase: collagen (weak and ductile) Strong vs Weak: Ultimate Stress Ductile vsBrittle: Deformation before Failure

  11. Bone is a Composite Material Chicken wing bones: some baked in oven, denatured protein, only mineral left brittle some soaked in vinegar, removed mineral, leaving only collagen  ductile (rubbery)

  12. Bone mechanics • Depend on • Type of loading • Compression, tension, & shear • Duration, frequency, number of repetitions • Bone density • Compact vs. Cancellousbone • Age/gender, use/disuse

  13. Tension (longer and thinner) Unloaded Compression (shorter and fatter) Bending (tension & compression) Torsion (primarily shear) Shear (parallel load) N&F Fig 1-10

  14. Bending: Tension + Compression Compression Tension

  15. Mechanical properties of bone: Stress-strain relationship • Stress = F / A • Strain = ∆L / L F ∆L L

  16. Stress-strain for compact bone loaded in tension • Elastic: no permanent deformation • Plastic: permanent deformation • Yield point: strain where plastic range begins • Ultimate strain/stress: fracture occurs Ultimate strain Yield point Elastic Plastic 150 Stress (MPa) 3 0.7 Strain (%)

  17. Compact bone vs. tendon/ligament in tension Bone E = 17 GPa Ult. stress = 150 MPa Stress (MPa) Tendon/ligament E = 1.5 GPa Ult. stress = 100 MPa 150 100 yield yield 0 0 0.7 3 6 9 Strain (%)

  18. Tendon vs. bone strain in running • Achilles tendon • strain ~ 6% (vs. 8%) • Tibia • Strain ~ 0.07% (vs. 0.7%)

  19. Compact bone in compression & tensionsame modulus, but different yield points Stress (MPa) Stress (MPa) Compression Tension 190 150 ult. strain yield 1 2.6 3 0.7 Strain (%) Strain (%)

  20. Ultimate stress of compact bone • Compression: ~190 MPa • Tension: ~150 MPa • Shear: ~ 65 MPa

  21. Bone mechanics • Depend on • Type of loading • Compression, tension, & shear • Duration, frequency, number of repetitions • Bone density • Compact vs. Cancellousbone • Age/gender, use/disuse

  22. Compact vs. cancellous bone in compression (effects of density) 200 Compact (r = 1.8 gm/cm3) Stress (MPa) 100 Cancellous (r = 0.9 gm/cm3) Cancellous (r = 0.3 gm/cm3) 0 20 15 0 5 10 Strain (%)

  23. Bone density effects on ultimate strength 100 Compact Ultimate compressive stress (MPa) 10 Strength µr2 Cancellous 1 0.1 0.2 0.5 1 2 Density (g / cm3)

  24. Broken Back? A smokejumper (mass = 70 kg) hits the ground with 25x body weight. If the load is concentrated on the facet joints, which have an area of 1 cm2, will they break? (F = mass x g; g = 9.81 m/s2) • Yes • No • It depends …

  25. Bone mechanics • Depend on • Type of loading • Compression, tension, & shear • Duration, frequency, number of repetitions • Bone density • Compact vs. Cancellousbone • Age/gender, use/disuse

  26. Failure Modes • Single load/high stress • Tensile fractures usually induced by rigorous muscle contractions • Compression fractures induced by impacts • Most fractures involve bending, torsional, or combined loads • Multiple loads (repetitive)/low stress

  27. Repetitive loading: Tension • # of repetitions important • Running: • SF = 1.3 strides/s • ~ 2 hours of running • 10,000 strides • But bone repairs during recovery 150 Fracture stress (MPa) 60 100 10,000 1,000 Repetitions

  28. Bone remodelling • Bone remodelling is dependent upon mechanical loading • Wolffe’s Law (1892) • Bone laid down where needed • Resorbed where not needed • bone response is site specific, not general • bone responds to high loads and impact loading • trabecular bone lost most rapidly during unloading (bed rest, spaceflight etc.)

  29. Repetitive Loads -> Fatigue • Number of repetitions important • Time between repetitions is important • Muscle fatigue increases stress on bones • Bone cannot repair rapidly enough

  30. Peak bone stress on anteromedial surface of tibia • Walk (1.4 m/s): Peak values • compression: 2 MPa • tension: 3 - 4 MPa • Run (2.2 m/s): Peak values • compression: 3 MPa • tension: 11-12 MPa Ultimate stresses C: 190 MPa T: 150 MPa See N&F, Fig. 1-30

  31. Lifting a box Calculate how much force in the back extensor muscles is needed when lifting a 1 kg box with the arms outstretched (r = 30 cm), compared to when the arms are beside the body (r = 5 cm). The muscle’s effort arm: (reffort = 5cm).

  32. Lifting a box Calculate how much force in the back extensor muscles is needed when lifting a 1 kg box with the arms outstretched (r = 30 cm), compared to when the arms are beside the body (r = 5 cm). • 6 times less force • 6 times more force • the same force • 150 times more • I don’t understand

  33. Vertebra Surface Area • Vertebral bodies are the primary weight-bearing components of the spine • Progressive increase in vertebral size (area) from cervical region to the lumbar region • Variation serves a functional purpose: • Stress-reduction

  34. Bone mechanics • Depend on • Type of loading • Compression, tension, & shear • Duration, frequency, number of repetitions • Bone density • Compact vs. Cancellousbone • Age/gender, use/disuse

  35. Aging: reduced bone density/quality • Greater porosity in compact & cancellous bone • Compact bone tensile strength • Age 20: 140 MPa • Age 80: 120 Mpa • So most of the problem is with density in cancellous bone (less dense, not poor quality) • Geometry changes as well Data from Burstein et al.

  36. Can Exercise Help? • cross sectional studies indicate + • highest BMD in weight lifters • BMD proportional to body weight • Higher tibia BMD and CSA in runners • prospective training studies, modest +

  37. Bone mechanics • Depend on • Type of loading • Compression, tension, & shear • Duration, frequency, number of repetitions • Bone density • Compact vs. Cancellousbone • Age/gender, use/disuse

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