1 BIOE 4710/5710 – Bone Tissue  Function, physiology and composition of bone tissue cortical trabecular  Biomechanics of bone tissue mechanical properties viscoelasticity  Textbook: Skeletal Tissue Mechanics, (Martin RB et al.)

2 Bone: Structural Hierarchy

3 Bone: Composition  collagen + water + mineral + proteoglycans + noncollagenous proteins  mineral: bioapatite Ca 10 (PO 4 ) 6-x (OH) 2-y (CO 3 ) x+y  6 x 0 and 2 y 0  substitutions include HPO 4, CO 3, Mg, Fl rod or plate shaped (5x5x40 nm)  proteoglycans decorin biglycan

4 Bone: Composition

5

6  proteoglycans may control mineralization decorin  collagen fibrillogenesis  protein core-GAG biglycan  interaction with collagen ?  noncollagenous proteins osteocalcin, osteonectin, osteopontin osteocalcin abundant  chemoattractant for bone cells  suppresses excess mineralization

7 Bone: Trabecular vs. Cortical

8 Bone: Trabecular Bone  Trabecular bone (a.k.a. cancellous or spongy bone) found in cuboidal bones, flat bones and the ends of long bones range of porosity 75%-95% interconnected pores filled with marrow

9 Bone: Trabecular Bone  Trabecular bone (cont:) formed by organization of plate- and rod-like struts called trabeculae trabeculae are about 200 m thick.

10 Bone: Cortical Bone  Cortical bone (a.k.a. compact bone) shafts of long bones shell around cuboidal bones porosity 5-10%  Haversian canal aligned with the long axis of bone contains capillaries and nerves 50 m in diameter  Volkmann’s canal transverse canals connecting Haversian canals contains blood vessels  Resorption cavities temporary spaces created by osteoclasts 200 m in diameter

11 Bone: Cortical Bone

12 Bone: Cortical Bone  Cortical bone (cont) types of cortical bone  lamellar parallel layers of lamellae mineralized collagen fibers are parallel within each lamella direction of fibers may alternate between adjacent lamellae  woven bone quickly formed poorly organized, fibers are more or less randomly arranged more mineralized than lamellar weaker than mineralized

13 Bone: Primary and secondary  primary bone: laid down on existing bone surface circumferential lamellar  lamellae are parallel to bone surface  primary osteons around blood vessels

14 Bone: Primary and secondary  primary bone: (cont) plexiform  construction of a trabecular network followed by filling in the gaps  mixture of woven and lamellar bone  large and fast growing animals (cows)

15 Bone: Primary and secondary  secondary bone: results from resorption and replacement of existing bone with lamellar bone (remodeling) cortical bone: secondary tissue consists of cylindrical structures called “secondary osteons” or “Haversian systems”  200 m in diameter  16 concentric cylindrical lamellae  outer boundary “cement line”

16 Bone: Primary and secondary

17 Bone: Primary and secondary  secondary bone: ( cont) trabecular bone:  remodeling produces trenches on the existing surfaces  filling of these trenches create “trabecular packets”

18 Bone: Modeling and remodeling  modeling customized the shape of bones in accordance with mechanical needs  metaphyseal modeling to reduce bone diameter during growth  diaphyseal modeling to increase bone diameter addition of bone on the periosteum resorption of bone at endosteum

19 Bone: Modeling and remodeling  modeling (cont) customized the shape of bones in accordance with mechanical needs  diaphyseal modeling to alter curvature cross section drifts sideways relative to the ends of the bone  modeling of flat bones resorption on the inner surface and formation on the outer surface of cranial bone to accommodate the growth in size of brain

20 Bone: Modeling and remodeling  remodeling removes older bone and replaces with new bone prevents accumulation of fatigue damage draws calcium from bones to be used metabolically elsewhere fine tunes mechanical properties accomplished by teams of about 10 osteoclasts and several hundred osteoblasts that work together in “basic multicellular units” (BMUs)

21 Bone: Modeling and remodeling

22 Bone: Modeling and remodeling

23 Bone: Modeling and remodeling  remodeling (cont.) three stages in BMU’s lifetime (ARF)  Activation  Resorption  Formation resorption in the form of a tunnel or ditch about 200 m in diameter at a rate of 40 m/day mesenchymal cells differentiate into osteoblasts

24 Bone: Modeling and remodeling  remodeling (cont.) osteoblasts fill the tunnel with osteoid tissue at a rate of 0.5 m/day resorption lasts for 3 weeks remodeling sequence lasts for 4 months BMU’s replace 5% of cortical bone and 25% of trabecular bone each year

25 Bone: Modeling and remodeling

26 Bone: Modeling and remodeling

27 Bone: Modeling and remodeling  modeling-remodeling: differences action of osteoclasts and osteblasts are independent in modeling and coupled in remodeling modeling results in change of bone’s size, shape or both whereas remodeling does not effect size or shape usually rate of modeling reduced after maturation, remodeling occurs throughout life modeling is continuous and prolonged whereas remodeling is episodic

28 Bone: Strength of cortical bone

29 Bone: Strength of cortical bone  determinants of osteonal bone mechanical properties porosity  holes weaken structures  voids in bone range from a few to several hundred micrometers  Schaffler and Burr (1988) (up to 31% porosity) E = 33.9 (1-p) 10.9, p:porosity, E:modulus  Currey (1988) (up to 7.8% porosity) E = 23.4 (1-p) 5.74

30 Bone: Strength of cortical bone

31 Bone: Strength of cortical bone  determinants of osteonal bone mechanical properties (cont) mineralization  amount of mineral per volume of bone matrix (specific mineralization)  amount of mineral per unit volume of whole bone (volumetric mineralization, affected by porosity)  Schaffler and Burr (1988) E = 89.1 A 3.91 A: percent ash by mass

32 Bone: Strength of cortical bone  determinants of osteonal bone mechanical properties (cont) density  apparent density: mass per unit bulk volume (function of porosity and mineralization)  Carter and Hayes (1977) : strain rate, E: modulus d: density apparent density of cortical bone g/cm 3 histologic architecture  osteonal density  amount of primary lamellar bone collagen fiber organization

33 Bone: Strength of cortical bone

34 Bone: Strength of cortical bone  determinants of osteonal bone mechanical properties (cont) fatigue damage rate of deformation  osteoid tissue  fluid flow within interconnected spaces  cement lines  energy absorption capacity optimized in the range of s -1

35 Bone: Strength of cortical bone

36 Bone: Strength of Cancellous Bone

37 Bone: Strength of Cancellous Bone  determinants of cancellous bone mechanical properties apparent density  apparent density of trabecular bone g/cm 3  the relationship given by Carter and Hayes (1977) applies to trabecular bone trabecular density mean trabecular thickness

38 Bone: Strength of Cancellous Bone  determinants of cancellous bone mechanical properties trabecular orientation (mean intercept length)

39 Bone: Viscoelastic models  Sedlin (1965) three-parameter solid a frictional element to account for plastic deformation  Bargren et al. (1974) Kelvin is good enough for physiological rates  Laird and Kingsbury (1973) three-parameter solid cannot model the dependency on frequency

40 Bone: Fatigue properties