Skeleton = support structure against gravity

Transcription

1 Skeleton = support structure against gravity xylem bone chitin

2 Bone Vandruff

3 Bone (Currey, 2002) different levels of organization

4 Bone composite material: calcium phospate cristals collagen non collagenous proteins water cells blood vessels matrix mineralization of turkey leg tendon crystals are platelet shaped

5 Bone (Currey, 2002) 1) Structure & types of bone Molecular hydroxyapatite [Ca 10 (PO 4 ) 6 (OH) 2 ] Type I Collagen

6 1) Structure & types of bone Cellular * Bone lining cells = periosteum * Osteoblasts (derived from BLC) lay down collagen matrix osteocyte * Osteocytes (derived from osteoblasts) cells in the body of the bone communicate through canaliculi * Osteoclasts (derived from precursor cells in blood) destroy bone

7 1) Structure & types of bone Woven bone laid down quickly in embryonic stage + repair (>4µ / day) random orientation of collagen highly mineralized yet porous Lamellar bone laid down slowly (<1µ / day) arranged in sheets of alternating thickness lower degree of mineralization

8 1) Structure & types of bone Haversian bone (= secondary osteons)

9 1) Structure & types of bone Fibrolamellar bone * alternate deposition of woven and lamellar bone * strong and quick

10 1) Structure & types of bone primary vs. secondary

11 1) Structure & types of bone compact vs. cancellous (trabecular) compact is solid with only spaces for osteocytes cancellous bone = large spaces

12 Darwin s finch beaks

13 Structure & types of bone

14 2) Mechanical properties principal role of bone is being stiff (raideur) so it can transmit forces and movement, strength (load before breaking) is of secondary importance

15 2) Mechanical properties Strain (déformation) Deformation under load (F) causes deformation ΔL/L or ΔB/B = normal strains denoted as ε (in %) Strain of 0.01 (10%) = µε Shear (cisaillement) strain is denoted as γ (angle in radians) In biological materials ε typically < 0.005; γ < 0.1 γ

16 Loads producing strain * compression = compressive strain * torsion = shear strain * tension = tensile strain * bending (flexion) = tensile, shear and compressive strains

17 2) Mechanical properties Stress (contrainte mécanique) = Intensity of force acting across a plane, in Pa = Nm 2 F zx and F zy = shear forces, depend on angle of F with the plane F zz /A = normal stress = (F cos θ) / (A/cos θ) = (F cos 2 θ) / A F zx /A & F zy /A= shear stresses = F sin θ / (A/cos θ) = (F cos θ sin θ) / A

18 Load deformation curves tensile testing of bone: deformation ~ load plastic deformation brittle (fragile) material: postyield energy low tough (résistant) material: postyield energy high E = Young s modulus (Pa = Nm 2 ); for bone typically GPa

19 Isotropy vs. anisotropy: If mechanical properties are the same in all directions: isotropy E = σ/ε G = τ/γ σ: normal stress τ: shear stress E = 2G (1 + ν) Young s modulus (module): E Shear modulus: G Poisson ratio: v Poisson effect: stretch in one direction leads to shrinking in all others

20 Isotropy vs. anisotropy: Bone is anisotropic! If orthotropic symmetry holds (= three perpendicular planes of symmetry) then: mechanical behavior is described by 3 Young s moduli (E) 3 shear moduli (G) 6 Poisson ratios (ν) stress hysteresis Bone has viscoelastic properties: i.e. E is strain rate dependent (i.e. hysteresis) Strain rate = strain / time strain

21 Bone is anisotropic in fracture

22 2) Mechanical properties fatigue défaillance mécanique structures failing under loads lower than failure stress failure due to stress concentration repeated loading results in cracking

23 Creep (résistance à la déformation) failure at load which does not typically produce failure if loaded only briefly material is loaded and kept at a given stress and time is recorded Human femur Log (t) = Log (σ) Compression Human femur Log (t) = Log (σ) tension Bos ulna Log (t) = Log (σ) tension Antler base Log (t) = Log (σ) tension Antler tip Log (t) = Log (σ) tension Bos cancellous bone Log (t) = Log (σ) Compression σ in Mpa

24 Mechanical properties how to measure in vitro digital speckle particle interferometry ultrasound three point bending

25 In vivo Implant strain gauges (jauges de contrainte) on the bone (resistance ~ deformation)

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27 Mechanical properties

28 Variation in bone composition strength = résistance Property antler femur Bulla Work of fracture (Jm 2 ) Bending strength (MPa) Young's modulus (GPa) Mineral content (% ash) Density (103 kgm 3 ) mineral content & organic content vary consequences for mechanical properties

29 Mineral volume fraction has an important effect on mechanical properties

30 Bending strength vs. Young s modulus very high mineral content, very brittle

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32 Mechanical behavior of cancellous bone horse cervical vertebra perpendicular arrangement of trabeculae ideal to minimise stress

33 Trabecular orientation? horse thoracic vertebra spinous process principal stress trajectories in a cantilever beam

34 Braced (entretoisées) structures no rigidity rigid braced b, bending stress; t, tensile stress, c, compressive stress

35 Cancellous bone absorbs energy compressive loading

36 Impact loading and load transfer load must be transmitted to bone cortex without local buckling but high local stresses must be avoided solution: trabecular bone transfers load to cortex while minimizing stress and buckling

37 3) Adaptation of bone Shape varies in relation to function A, B, C = dog; D = deer

38 The shapes of long bones distortion (Z) must be limited when bone of length (L) is subjected to bending moments (M) Z = ML 2 /8EI with I = second moment of area (moment quadratique) bending of a beam results in change in length In all fibers except those in the neutral plane cross section has a second moment of area I = Σ y 2 δ area about the neutral axis I is dependent on axis of loading

39 The shapes of beams If we want to minimize mass: ρla = ρl Σ in δ area (ρ = density) thus ratio of mass to I is ρla/i = ρl Σ δ area / Σ y 2 δ area thus, to minimize mass, area should be far away from neutral axis If I greater then area is smaller and less mass needed to limit deflection Ideal: two sheets if neutral axis is M M If axis m m then cube. If variable then hollow cylinder!

40 How hollow should bones be? ideal = thin wall, but possibility of buckling! alligator bending moment causing buckling = ERt 2 area needed to prevent buckling = (R/t) 1/3 If R >> t then mass must increase Camel Pteranodon

41 Bone adaptation to load intact ulna cut 3 months later strain during walking

42 3) Adaptation of bone environment (e.g. aquatic)

43 4) bone muscle interactions Tendons Sharpey s fibres

44 4) bone tendon interactions Sesamoids

45 4) bone bone interactions Cartilage

46 4) bone bone interactions Articulations

47 The shape of articulations low strength surfaces like bone cannot bear load over small surface area thus: large articulations chitin is high strength surface and thus articulations can be small and have greater curvature

48 5) Safety factors and loading facteur de sécurité how much should bones be over designed? breakage can be common in animals! (up to 30%) G = cost of growth; U = cost of use; F = cost of failure V = variability of loading P, pterodactyl; S, stag antler; T, terrestrial animal long bone; G, Gibbon long bone

49 5) scaling & shape allometry vs isometry isometry: A ~ L 2, M ~ L 3 allometry = non geometric scaling Galileo, 1638 elastic similarity : maintain elastic deformation at different sizes (McMahon)

50 TP dissection et modélisation dissection des muscles adducteurs (m. masseter, m. temporalis, m. pterygoideus) carnivore (chien) vs. herbivore (mouton) temporalis temporalis masseter masseter

51 Musculature du chien m. temporalis m. masseter m. pterygoideus

52 Chien

53 Ahhh la Vache

54 Vache

55 TP dissection et modélisation mesurer le poids des muscles (densité de 1.06 g/cm 3 ), longueur de fibres, angle de pennation qui donnent la force théorique maximale (stress ± 30N/cm 2 ). Force = PCSA * cos α

56 TP dissection et modélisation calcul des forces de morsure et les forces dans l articulation (+ orientation) en utilisant l hypthèse de l equilibrium statique: Σ M = 0 et M = r * F; M bite = (M mass + M temp + M pter ) Σ F ext = 0, Fx joint = (Fx bite + Fx mass + Fx temp + Fx pter ) et Fx joint = (Fy bite + Fy mass + Fy temp + Fy pter )

57 TP dissection et modélisation comparaison entre les différentes espèces, évaluation de la structure et orientation de l articulation.