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) trabeculae Haversian canal N&F, Fig 1-3 Haversian 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 Tendon: E (tendon or ligament) = 1.5 109 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

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

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)

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 Bone density Compression, tension, & shear Duration, frequency, number of repetitions Bone density Compact vs. Cancellous bone Age/gender, use/disuse

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

Bending: Tension + Compression

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

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 (%)

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 (%)

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

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 (%)

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

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

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 (%)

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)

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 …

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

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 # 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

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 Ultimate stresses C: 190 MPa T: 150 MPa See N&F, Fig. 1-30

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). 6 times less force 6 times more force the same force 150 times more 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 Bone density 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 +

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