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
Haversian canal

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
Tendon:
E (tendon or ligament) = Pa
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
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

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

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

12. 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)

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

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

16. Bending: Tension + Compression

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

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

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

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

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

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

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

24. 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) 20 5 10 15
Strain (%)

25. Bone density effects on ultimate strength
100
Compact
Ultimate
compressive
stress
(MPa) 10
Strength µ r2
Cancellous 1
0.1
0.2
0.5 1 2
Density (g / cm3)

26. 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 …

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

28. 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

29. 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
1,000
10,000
Repetitions

30. 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.)

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

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

33. 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).

34. 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

35. 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

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

37. 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.

38. 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 +

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