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Tendon

Tendon. Tendon. Outline: Function Structure Mechanical Properties Significance to movement. Function. Connect muscle to bone, but are not rigid Are quite stretchy Passive but important

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Tendon

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  1. Tendon

  2. Tendon • Outline: • Function • Structure • Mechanical Properties • Significance to movement

  3. Function • Connect muscle to bone, but are not rigid • Are quite stretchy • Passive but important • Not just rigid, passive structural links b/n muscle and bone, but also affect movement through the overall function of the muscle-tendon-unit. • Function: • transmit muscle force and slide during movement • Store elastic energy Tendon properties affect force transmitted from muscle to bone

  4. Structure • Primarily collagen : a structural protein • Collagen fibril -> fascicle->tendon • Bad blood supply -> slow to heal

  5. Parallel bundles of collagen fibers • Resist stretching along long axis of tendon • Sufficiently flexible

  6. Tendon • Outline: • Function • Structure • Mechanical Properties • Significance to movement

  7. Mechanical Properties • Many experiments on isolated tendons • Show same mechanical property across different tendons

  8. Force Linear region Toe region Displacement (Dx) Tendon or ligament • “J-shaped” • Stiffness (k) = slope • units = N/m • Stiffness: force required to stretch tendon/ligament by a unit distance • Force per change in length • Hooke’s Law • F=kx • F=elastic force • x=amount of stretch • k=stiffness

  9. Tendons/ligaments are viscoelastic • Purely elastic materials • force-displacement relationship does NOT depend on velocity of stretch or time held at a length or load • Viscoelastic materials • force-displacement relationship DOES depend on: • Velocity of stretching • Time held at a given length or load Think of other materials that are viscoelastic?

  10. Tendons are viscoelastic • Nonlinear response • Hysteresis • Velocity dependent loading • Creep • Load relaxation

  11. Force Linear region Toe region Displacement (Dx) Viscoelasticity trait #1: Nonlinear Response • “J-shaped” • Stiffness (k) = slope • units = N/m • Stiffness: force required to stretch tendon/ligament by a unit distance • Force per change in length • Hooke’s Law • F=kx • F=elastic force • x=amount of stretch • k=stiffness

  12. Force Stretch Recoil Displacement (x) Viscoelasticity trait #2: Hysteresis (Stretch & recoil: ) • Hysteresis: Force vs. displacement different for stretch & recoil

  13. Viscoelasticity trait #3: velocity dependent stiffness Fast stretch Slow stretch Force At faster stretching velocities: 1. More force needed to rupture tendon Displacement From Wainwright et al. (1976). “Mechanical design in organisms”.

  14. Displacement Time Viscoelasticity trait #4: Creep • Stretched with a constant force & displacement measured • Length increases with time

  15. Viscoelasticity trait #5: Load relaxation • Specimen held at a constant length & force measured Force Time 2-10 min ( N & F, Fig 3-10)

  16. Elastic energy • Stretch: mechanical work done on tendon/ligament equals elastic energy storage • Area under force - displacement curve Force Displacement Elastic energy stored during stretch

  17. Viscoelasticity trait #3: velocity dependent stiffness Fast stretch Slow stretch Force At faster stretching velocities: 1. More force needed to rupture tendon 2. More energy is stored Displacement From Wainwright et al. (1976). “Mechanical design in organisms”.

  18. Elastic energy • Stretch: mechanical work done on tendon/ligament equals elastic energy storage • Area under force - displacement curve • Recoil: material returns some (most) of energy stored elastically during stretch

  19. Force Displacement Elastic energy returned during recoil Mechanical energy stored & returned by tendon/ligament Force Displacement Elastic energy stored during stretch

  20. Force Displacement Larger hysteresis loop -greater energy loss• Hysteresis: indicates“viscoelasticity” For normal stretches, 90-95% of the elastic energy stored in tendons & ligaments is returned Energy lost

  21. Elastic energy • Stretch: mechanical work done on tendon/ligament equals elastic energy storage • Area under force - displacement curve (x,F) Area = ½ Fx ½ kx ½ kx2 A & B A & C Force Displacement Elastic energy stored during stretch

  22. Achilles elastic energy storage during stance phase of run Example of important equations: Uelastic = 0.5 k (DL)2 F = kDL Known: kAchilles= 260 kN/m F = 4700 N Uelastic = ? A)2.34 B)42120 C) 42 D)0.042 E) None of the above FAchilles Fg

  23. Strain • Can measure length change in terms of mm • But more useful as % of original length, so can compare tendons of different lengths • Strain (e) = L-Lo/Lo • L: current length • Lo:original length • ‘stretchiness’

  24. Stress • Because tendons have different thickness, want to normalize force as well • Thicker tendons need more force and vice versa • So normalize by area • Stress (s)=Force/Area

  25. Stress/Strain (s/e) • By normalizing stress and strain, can now compare properties of materials of different sizes and shapes, regardless of absolute shape • Measure intrinsic tendon properties

  26. Stress/Strain Relation for Tendon/Ligament Plastic region Stress s(MN/m2) syield sfailure 100 Elastic region Failure (rupture) Toe region Injury E s e 8% Strain e

  27. Stress (MN/m2) 70 Stretch 35 Recoil 0 5 2.5 0 Strain (%) Stress vs. Strain for tendon/ligament • Similar for all mammalian tendons & ligaments • Elastic modulus: slope • E=stress/strain, =s/e • units of Pascals (N/m2), same as stress • kPa, Mpa, GPa

  28. Compare the stiffness of a rubber band and a block of soft wood A) rubber band is more stiff B) rubber band is less stiff C) stiffness is similar D) Not enough information

  29. Can compare different materials easily Tendon E = 1 GPa Soft wood (pine) E = 0.6 GPa Passive muscle E = 10kPa Rubber E = 20kPa Bone E= 20 GPa Walnut E= 15 Gpa Diamond E= 1000 Gpa JelloE = 1Pa

  30. Stress vs. strain: material not geometry Two important definitions: Stress = F / A F = force; A = cross-sect. area Units = N / m2 = Pa Strain (%) = (displacement / rest length) • 100 = (DL / L) • 100

  31. Stiffness vs. Elastic Modulus • Elastic Modulus (a.k.a. “Young’s Modulus”) • Slope of stress-strain relationship • a material property • Stiffness • Slope of force-displacement relationship • depends on : • material (modulus) & geometry • Structural property

  32. Stress/Strain vs Force/Length • Material property vs. structural property • Stress/Strain ind of geometry • Force/Length (stiffness) depends on geometry.

  33. Geometry effects • Stress = Elastic modulus • Strain • F / A = E • ∆L / L • Force = Stiffness • displacement • F = k∆L • Combine (1) & (2) to find: k = EA/L • E: similar in all tendons/ligaments A or L causesk

  34. Extending the stress-strain relationship to injurious loads for tendon/ligament Plastic region Stress (MN/m2) 100 Elastic region Failure (rupture) Injury 8% Strain

  35. Stress/Strain vs Force/Length • Material property vs. structural property • Stress/Strain ind of geometry • Force/Length (stiffness) depends on geometry.

  36. Tendon strain • Achilles tendon during running: ~ 6% • close to strain where injury occurs (~ 8%) • Wrist extensor due to muscle force (P0): ~ 2%

  37. Tendon • Outline: • Function • Structure • Mechanical Properties • Significance to movement

  38. We need tendons with different stiffnesses for different functions.How is this accomplished? Possibilities: • different material properties • different geometry (architecture)

  39. High force vs. versus fine control • Muscles in arm/hand demand fine control • precision more important than energy Slinky vs. rope

  40. Ankle extensor tendon vs. wrist extensor tendon Achilles • Wrist extensor • k = 15 kN/m • F (muscle) = 60 N • DL = F / k = 0.004 m • Achilles tendon • k = 260 kN/m • F (muscle) = 4.7 kN • DL = F / k = 0.018 m Force Wrist ext. Displacement

  41. Basis for tendon stiffness variation? • different material properties? • different geometry (architecture)?

  42. Achilles tendon vs. wrist extensor tendon • Achilles tendon vs. wrist ext. tendon • k: 17 times greater • Geometric differences? • A: 30 times greater • L: 1.75 times longer k = EA/L E ~ 1.5 GN / m2

  43. Useful tendon equations F = k L Elastic Energy = 0.5 k (L)2 Elastic Energy = 1/2 F L k = A/L  elastic modulus = stress/strain ~ 1.5 x 109 N/m2 for tendon stress = F/A strain = L/L 10,000 cm2 = 1 m2

  44. Human Tendons Compared E = 1.5 x 109 N/m2 for both tendons wrist Achilles L = 0.17 m L = 0.29m A = 1.67 x 10-6 m2 A = 0.00005 m2 k = EA/L = 15 kN/mk = EA/L = 260 kN/m elongation for 60N load? elongation for 4,700N load? L = F/k = 0.004m F/k = 0.018m Strain? = L/L = 0.004 / 0.17 = 2.4% = 0.018 / 0.29 = 6.2%

  45. Problem Solving Approach • Write down what is given • Write down what you need to find • Write down the equations you will use • Show work! • Step by step

  46. Practice Problem Design a wrist extensor tendon that when loaded with 60N of force will undergo the same %strain (6.2%) as the Achilles tendon. (Given L, determine A) L=0.17 m

  47. Practice Problem If the wrist extensor tendon in the example had a cross sectional area = to the Achilles tendon example, what would be the absolute length change with a load of 60 N? Given: Aachilles= 0.00005 m2; Lwrist= 0.17m

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