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Viscoelastic Properties of Bone Tissue
- 1. BIOE 3200 Fall 2015 BIOE 3200 - Fall 2015
- 2. Identify tissue structures and components that contribute and/or explain viscoelastic properties for different biologic materials ◦ These slides focus on bone ◦ In class we will focus on ligament BIOE 3200 - Fall 2015
- 3. σ= f(ε, ἐ); E = f(ε, ἐ) Strain rate in daily activities increases as activity becomes more strenuous ◦ Slow walking ~ 0.001/sec ◦ Brisk walking ~ 0.01/sec For typical daily activities, E changes by ~15% ◦ Slow running ~ 0.03/sec ◦ Fast running ~ 0.06/sec We can estimate the % change in bone strength for brisk walking versus slow walking BIOE 3200 - Fall 2015 Loaded slower Loaded faster
- 4. Graph of bone strain over time for adult human cortical bone in tension shows… ◦ Bone will continue to deform if under constant stress for an extended period of time ◦ If loaded for long enough time, cortical bone will break at a stress well below yield and ultimate strengths. ◦ Creep without fracture: permanent deformation (viscoplastic behavior) BIOE 3200 - Fall 2015
- 5. As loading rate increases by 6 orders of magnitude: ◦ Modulus (E) increases by a factor of 2 ◦ Strength (σ) increases by a factors of 3 BIOE 3200 - Fall 2015
- 6. BIOE 3200 - Fall 2015
- 7. BIOE 3200 - Fall 2015
- 8. BIOE 3200 - Fall 2015 From Orthopaedic Biomechanics, Bartel, Davy and Keaveny (2006).
- 9. BIOE 3200 - Fall 2015 Bone tissue: ◦ Mineral phase (70% by weight) Calcium phosphate (hydroxyapatite) Calcium carbonate ◦ Organic matrix (20% by weight) with cells embedded Type I collagen (90%) Other glycoproteins and glycosaminoglycans (10%) ◦ Water (10% by weight)
- 10. BIOE 3200 - Fall 2015 Consider effects of factors such as strain rate, structure, and level of osteoporosis for, say, a 90 year old compared to a 20 year old.
Editor's Notes
- Strain rates in bone often reported as microstrain/sec Activities: Jump from 2 stairs =~ slow running; falling from standing height =~ fast running See review article by Yang et al. 2011, “What do we currently know from in vivo bone strain measurements in humans?”, J Musculoskelet Neuronal Interact 2011; 11(1):8-20 At very high strain rates, cortical bone exhibits ductile to brittle transition as strain rate increases
- On the strain versus time graph, with primary, secondary and tertiary stages (similar phases as many engineering materials); bone will continue to deform under constant stress over extended period of time - Primary stage: specimen strain continues after loading and creep (increase in strain) rate gradually decreases. - Secondary stage: lower, nearly constant creep rate - Tertiary stage: increase in creep rate just before creep fracture Creep mechanisms not well understood, but they are different for tensile and compressive loading (resistance to creep fracture is greater for compressive than for tensile loading). Osteon pullout is common for tensile loading, and fractures tend to cross through osteons for compressive loading.
- This demonstrates the strain rate dependence of bone
- Under compression, trabecular bone has a long plateau (yield) – trabeculae crush, fill in spaces, so little change in stress with large deformation. Bone properties depend on apparent density 𝝆: ratio of the mass of the bone tissue to the bulk volume of the specimen (bone as a whole organ), including volume of vascular pore spaces. 𝝆app for trabecular ranges from ~0.1 g/cm3 for elderly spine, ~0.3 g/cm3 for tibia, up to ~0.5 g/cm3 for proximal femur (load-bearing). Decreases with age after maturity at about 2%/year
- Modulus doesn’t change significantly but strength is reduced at a rate of about 2 % per year. Tensile ultimate strain decreases by about 10% per decade, from 5% in 20’s to < 1% in 80’s. Old bone is more brittle than young bone, therefore energy to fracture (area under stress-strain curve before fracture) is much less.
- Bone tissue is remarkably resilient and adaptable, as shown by Wolff’s Law. But adaptation of bone is also controlled by cellular mechanisms, which change with age. Individual osteocytes are thought to communicate with each other and the bone surface lining cells via a network of their dendritic connections (Hazenberg, Taylor and Lee, 2007). During bone loading the osteocytes are thought to measure the strains induced by applied loads. When a force is applied to bone tissue it will undergo deformation. This deformation will cause fluid to move within the bone matrix. The figure shows compression loading along the long axis of a long bone such as the femur or tibia. The compression load will cause deformation of the bone tissue and movement of fluid. Reference: Hazenberg JG, Taylor D, and Lee TC. The role of osteocytes and bone microstructure in preventing osteoporotic fractures. Osteoporos Int 18: 1-8, 2007.