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
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
Definitions
• Load (N)• Deformation (mm)• Stress (N/m2; Pa)• Strain (mm/mm; mm/mm*100%)• Stiffness (N/m)• Elastic Modulus (Pa)
Tissue Mechanics:Equations and Values
Force = F = kDLStress = F / AStrain = ∆L / LElastic modulus = E =Stress/StrainStiffness = k = EA / LElastic energy = 0.5k(DL)2 Elastic energy = 0.5 F DL10,000 cm2 = 1 m2
Tendon:E (tendon or ligament) = 1.5 109 PaTendon safe limits:Stress (Ultimate strength) = 100 MPaStrain = 8% strain
Bone:E (bone) = 17 x 109 PaBone safe limits: Tension = 150 MPa stress, 0.7% strainCompression = 190 Mpa stress, 1% strain
Bone is a Composite Material
One phase: mineral (strong and brittle)
Other phase: collagen (weak and ductile)
Strong vs Weak: Ultimate Stress
Ductile vs Brittle: Deformation before Failure
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)
Bone mechanics• Depend on
– Type of loading• Compression, tension, & shear• Duration, frequency, number of repetitions
– Bone density• Compact vs. Cancellous bone• Age/gender, use/disuse
Tension (longer and thinner)
Compression (shorter and fatter)
Bending(tension &compression)
Shear (parallel load)
Unloaded
N&F Fig 1-10
Torsion (primarily shear)
Stress-strain for compact bone loaded in tension
3 0.7Strain (%)
150Stress(MPa)
Yield point
Elastic Plastic
Ultimatestrain • Elastic: no permanent
deformation• Plastic: permanent
deformation• Yield point: strain where
plastic range begins• Ultimate strain/stress:
fracture occurs
Compact bone vs. tendon/ligament in tension
3
BoneE = 17 GPaUlt. stress = 150 MPa
0.7Strain (%)
150
Stress(MPa)
100
00 6 9
Tendon/ligamentE = 1.5 GPaUlt. stress = 100 MPa
yield yield
Tendon vs. bone strain in running
• Achilles tendon– strain ~ 6% (vs. 8%)
• Tibia– Strain ~ 0.07% (vs. 0.7%)
Compact bone in compression & tensionsame modulus, but different yield points
Stress(MPa)
Strain (%)
Compression
190
1 2.6 3
Tension
0.7Strain (%)
150
Stress(MPa)
yieldult.strain
Bone mechanics• Depend on
– Type of loading• Compression, tension, & shear• Duration, frequency, number of repetitions
– Bone density• Compact vs. Cancellous bone• Age/gender, use/disuse
Compact vs. cancellous bone in compression (effects of density)
Stress(MPa)
Strain (%)
200
5 10
Compact (r = 1.8 gm/cm3)
100
Cancellous (r = 0.9 gm/cm3)
Cancellous (r = 0.3 gm/cm3)0
15 200
Bone density effects on ultimate strength
Density (g / cm3)0.1 0.2 0.5 1 2
1
10
100Ultimate
compressivestress(MPa) Strength µ r2
Cancellous
Compact
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)
A)Yes
B) No
C) It depends …
Bone mechanics• Depend on
– Type of loading• Compression, tension, & shear• Duration, frequency, number of repetitions
– Bone density• Compact vs. Cancellous bone• Age/gender, use/disuse
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
Repetitive loading: Tension
Fracturestress(MPa)
150
60
100 1,000 10,000Repetitions
• # of repetitions important
• Running:– SF = 1.3 strides/s
• ~ 2 hours of running– 10,000 strides– But bone repairs
during recovery
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.)
Repetitive Loads -> Fatigue
• Number of repetitions important
• Time between repetitions is important
• Muscle fatigue increases stress on bones
• Bone cannot repair rapidly enough
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
See N&F,Fig. 1-30
Ultimate stressesC: 190 MPaT: 150 MPa
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).
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).
A) 6 times less force
B) 6 times more force
C) the same force
D) 150 times more
E) I don’t understand
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
Bone mechanics• Depend on
– Type of loading• Compression, tension, & shear• Duration, frequency, number of repetitions
– Bone density• Compact vs. Cancellous bone• Age/gender, use/disuse
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.
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 +
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