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)

N&F, Fig 1-3 trabeculaeHaversian canal

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

Bone Synonyms

Compact = cortical

Cancellous = trabecular

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

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

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)

Bending: Tension + Compression

Compression

Tension

Mechanical properties of bone: Stress-strain relationship

• Stress = F / A• Strain = ∆L / L

∆L

L

F

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

• Compression: ~190 MPa• Tension: ~150 MPa• Shear: ~ 65 MPa

Ultimate stress of compact bone




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 …




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 boxCalculate 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 boxCalculate 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




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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