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Bone Tissue Mechanics

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Bone Tissue Mechanics Bone Tissue Mechanics João Folgado Paulo R. Fernandes Instituto Superior Técnico, 2015 PART 4 and 5 Biomecânica dos Tecidos, MEBiom, IST Bone Biology Biomecânica dos Tecidos, MEBiom, IST Bone cells Bone cells: • osteoclasts (bone resorption) • osteoblasts (bone formation) • osteocytes •lining cells osteoblast canaliculi Osteocyte trabecula (in lacunae) lining cell osteoclast Biomecânica dos Tecidos, MEBiom, IST Bone Modelling vs. Remodelling osteogenesis – bone production from soft tissue (fibrosis tissue or cartilage). Bone formation in a early stage of growth. It also happens in bone healing. bone modelling – Modelling results in change of bone size and shape. The rate of modelling is greatly reduced after skeletal maturity. Involves independent actions of osteoclasts and osteoblasts. • bone remodelling – Process of replacement of “old bone” by “new bone”. It repairs damage and prevent fatigue damage. Usually does not affect size and shape. Occurs throughout life, but is also substantially reduced after growth stops. A combined action of osteoclasts and osteoblasts (BMU - Basic multicellular unit). Biomecânica dos Tecidos, MEBiom, IST Some features of bone tissue Bone Surfaces • periosteum (external surface of bone) • endosteum (internal surface of bone) • Haversian canals • Trabeculae Bone surfaces are important because is there that bone activity take place in order to renew bone tissue. Biomecânica dos Tecidos, MEBiom, IST Types of bone tissue and the shapes of bones - different shapes for bones of the same individual -Similarities between bones of different animals (we can recognize a femur, regardless of what animal it came from) - Some specific characteristics for a specie. (it is possible to identify an isolated bone as a human bone). Biomecânica dos Tecidos, MEBiom, IST Types of bone tissue: Trabecular vs. Compact bone Spongy Bone (trabecular) Compact Bone (cortical) Marrow - Compact bone – porosity 5%-10% - Trabecular bone – porosity 75%-95% Biomecânica dos Tecidos, MEBiom, IST Composition of Bone – Quantitative representation - Water - Organic Matrix (mainly collagen) - Mineral (mainly hydroxyapatite) VT=Vm+Vv ρ – apparent density V –total volume ρ ≅ T m – density of bone tissue 2.0 g/ml V – Bone matrix ρ m v – density of soft tissue in the void spaces Vv – volume of voids ≅ 1.0 g/ml ∼ Bv – volume fraction (Bv = 0 1) ρρVV+ ∼ ρ = mm vv pv – porosity (pv = 0 1) VT VV ==mv ρ =1.0 2.0gml / Bpvv , VVTT Porosity: • cortical bone → pv = 5% ~ 10% • trabecular bone → pv = 75% ~ 90% Ash fraction: ratio between the ash mass and dry mass. It is a measure of the degree of mineralization of bone tissue Biomecânica dos Tecidos, MEBiom, IST Bone is a hierarchical material Biomecânica dos Tecidos, MEBiom, IST Types of bone tissue: Lamelar vs. Woven At a refined scale we can distinguish between lamelar and woven bone. Lamelar – highly organized bone Woven – poorly organized bone Types of bone tissue: Primary vs. Secondary Primary – appears during growth (modelling) Secondary – appears due to remodelling Biomecânica dos Tecidos, MEBiom, IST Woven bone • Quickly formed, poorly organized tissue Plexiform bone •Quickly formed •“brick wall” appearence • layers of lamelar and woven bone • appears in large, fast-growing animals (cows, sheeps) Biomecânica dos Tecidos, MEBiom, IST Compact bone vs trabecular propertie Cortical trabecular Volume fraction 0.95 0.20 surface / bone volume 2.5 20 (mm2/mm3) Total bone volume 1.4×106 0.35×106 (mm3) (80%) (20%) Total internal surface 3.5×106 7.0×106 (mm2) (33%) (67%) • the surface of trabecular bone is one reason to have more bone remodelling. • This can be a consequence of a higher necessity of remodelling. • the higher remodeling rate can explain the fact of trabecular bone being less stiff. Biomecânica dos Tecidos, MEBiom, IST Cortical bone – hierarquical levels level structure dimensions 0 Solid material > 3000 μm 1 Secondary osteons (A) Ø=200 ~ 300μm Primary osteons (B) 100 – 300 μm plexiform (C) l ≈ 150 μm woven bone (D) 2 lamellae (A,B*,C*) t ≈ 3 ~ 7 μm lacunae (A,B,C,D) Ø =10~20μm max 3 – 20 μm cement lines (A) t ≈ 1 ~ 5 μm canaliculi 3 Collagen-mineral 0.06 – 0.6 μm composite (A,B,C,D) Biomecânica dos Tecidos, MEBiom, IST Primary bone – Primary osteons • primary bone is also called as immature bone • primary osteons are formed by the mineralization of cartilage • primary osteons have less lamellae than the secondary osteons. Biomecânica dos Tecidos, MEBiom, IST Secondary Cortical Bone Biomecânica dos Tecidos, MEBiom, IST Secondary Cortical Bone • The secondary osteons result from remodeling •Osteons affect the mechanical properties of cortical bone: •By the replacement of highly mineralized bone matrix with less calcified material •Increasing the porosity •Altering the collagen fibers orientation •Introduction of a cement line interface. Ø osteons = 200 ~ 300 μm Ø canal = 50 ~ 90 μm Ø vessel = 15 μm μ Ømax lacuna = 10 ~ 20 m Biomecânica dos Tecidos, MEBiom, IST BMU – Basic Multicellular Unit In compact bone the BMU works in order to create a secundary osteon Biomecânica dos Tecidos, MEBiom, IST BMU – tunneling and forming an osteon Biomecânica dos Tecidos, MEBiom, IST Cortical bone – secondary osteons Biomecânica dos Tecidos, MEBiom, IST osteons –lamellar structure •osteons are made of several lamellae Biomecânica dos Tecidos, MEBiom, IST Orientation of colagen fibers Ascenzi and Bonucci : • fibers are paralel within lamellae • different orientation between lamellae a = type T (transverse fiber orientation) b = type A (alternating) c = type L (longitudinal) Biomecânica dos Tecidos, MEBiom, IST Cortical bone structure ? 3 2 1 Biomecânica dos Tecidos, MEBiom, IST Trabecular bone • here we have trabeculae instead od osteons. • trabeculae thickness less than 200μm and length about1000μm=1mm • trabecular bone is less stiff than cortical bone. • Bone turnover is faster in trabecular bone Biomecânica dos Tecidos, MEBiom, IST Trabecular bone Biomecânica dos Tecidos, MEBiom, IST Bone remodelling on trabecular surface • remodelling on trabecular surface Biomecânica dos Tecidos, MEBiom, IST Bone remodelling on trabecular bone Biomecânica dos Tecidos, MEBiom, IST BMU activation and Turnover rate Biomecânica dos Tecidos, MEBiom, IST Material properties of cortical bone ? 3 2 1 Biomecânica dos Tecidos, MEBiom, IST Mechanical Properties - Anisotropy of Cortical Bone • The stiffness and strength for the human and bovine secondary bone are similar in the transverse direction but in the longitudinal direction the values are higher for bovine bone. •The anisotropy ratios are less in human Haversian bone than in bovine Havarsian bone. •The ultimate stress is very different for compression and tension 3 - longitudinal 2 - circunferencial • comparing the ultimate stress in the longitudinal, circumferential and radial 1 -radial directions for bovine bone the following ration were obtained: • primary bone → 3 : 1 : 0.4 • secondary bone (tension) → 3 : 1 : 0.7 • secondary bone (compression) → 3 : 1 : 1 • osteons make whole bone transversely isotropic with respect to strength Biomecânica dos Tecidos, MEBiom, IST Mechanical properties – elastic properties of bovine bone 3 - longitudinal • ultrasonic measure 2 - circunferencial 1 -radial transversalmente isotrópico C11 C12 C13 00 0 C C 00 0 11 13 C33 00 0 C = C44 00 C 0 44 1 sim. ()C − C 2 11 12 • Secondary bone present a transversely isotropic behavior • Due to bone remodeling (haversian bone) the behavior goes from orthotropic to transversely isotropic Biomecânica dos Tecidos, MEBiom, IST Mechanical properties for compact bone ? transversely isotropic C11 C12 C13 00 0 3 C11 C13 00 0 2 C33 00 0 C = C44 00 1 C 0 44 1 sim. ()C − C 2 11 12 Biomecânica dos Tecidos, MEBiom, IST example – bone with implant • usual loads do not lead to high transverse normal stresses • however, there are situations where the transverse normal stress can be high, for instance the introduction of an implant can induce this kind of stress and lead to bone failure. Biomecânica dos Tecidos, MEBiom, IST Failure criteria for orthotropic materials • for orthotropic materials (or transversely isotropic), failure criteria such as the Von Mises criterion are not adequate. • a failure criterion often used for this type of materials is the Tsai-Wu criterion. (it is applied for composite materials – laminates reinforced with fibers – it is adequate for cortical bone) • theTsai-Wu criterion says the the failure occurs when the stress level, described by the following expression, is greater or equal to 1 σ σ σ σ 2 σ 2 σ 2 F1 1+ F2 2+ F3 3+ F11( 1) + F22( 2) + F33( 3) + σ σ σ σ σ σ σ 2 σ 2 σ 2 +2F12 1 2+ 2F13 1 3+ 2F23 2 3+ F44( 4) + F55( 5) + F66( 6) =1 σ σ σ σ σ σ σ σ σ σ σ σ where 1, 2 , 3, 4, 5, 6 are the stresses 11, 22, 33, 12, 23, 13 in the material reference system, and the 12 coefficients Fi,Fij are determined experimentally Biomecânica dos Tecidos, MEBiom, IST Failure criteria for orthotropic materials How to obtain the coefficients for the Tsai-Wu criterion? Example • for instance, doing uniaxial tension and compression tests in direction 1 (direction of orthotropy) we have: σ tf σ tf 2 tension: F1 1 + F11( 1 ) =1 σ cf σ cf 2 compression: F1 1 + F11( 1 ) =1 σ tf σ cf where 1 e 1 are the ultimate values for tension and compression, respectively Solving the system for the two unknowns: σ tf σ cf σ tf σ cf F1=1/ 1 +1/ 1 F11= – 1/( 1 1 ) • similar test can be done for the remaining directions as well as shear tests to obtain the coefficients Fi e Fii • the coefficients Fij, i≠j, must be obtained by biaxial tests. Biomecânica dos Tecidos, MEBiom, IST Cortical Bone – influence of porosity Elastic Modulus: From diverse studies (Schaffler and Burr, 1988, Carter and Hayes, 1977, Rice et al., 1988) we can consider that the elastic modulus is proportional to a power of the volume fraction: Cortical bone→ E ∼ (1−p)7.4 Trabecular bone→ E ∼ (1−p)2 Cortical and trabecular bone→ E ∼ (1−p)3 Biomecânica dos Tecidos, MEBiom, IST Mechanical properties of osteons – tension test a = type T , b = type A , c = type L ε = 0.01 = 1% = 10.000 με • type L osteon have greater tensile strength and lower ultimate deformation than the type A osteons.
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