1 BIOE 4710/5710 – Bone Tissue Function, physiology and composition of bone tissue cortical trabecular Biomechanics of bone tissue mechanical properties.
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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.)
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Bone: Composition
collagen + water + mineral + proteoglycans + noncollagenous proteins
mineral: bioapatite Ca10 (PO4)6-x (OH)2-y(CO3)x+y
6 x 0 and 2 y 0 substitutions include HPO4, CO3, Mg, Fl
rod or plate shaped (5x5x40 nm) proteoglycans
decorin biglycan
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Bone: Composition
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
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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
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Bone: Trabecular Bone
Trabecular bone (cont:) formed by organization of plate- and rod-like
struts called trabeculae trabeculae are about 200 m thick.
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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
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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
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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
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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)
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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”
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Bone: Primary and secondary
secondary bone: (cont) trabecular bone:
remodeling produces trenches on the existing surfaces
filling of these trenches create “trabecular packets”
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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
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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
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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)
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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
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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
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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
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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
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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 A3.91
A: percent ash by mass
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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 1.8-2.0 g/cm3
histologic architecture osteonal density amount of primary lamellar bone
collagen fiber organization
E 3790 0 .06 d 3
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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 0.01-0.1 s-1
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Bone: Strength of Cancellous Bone
determinants of cancellous bone mechanical properties apparent density
apparent density of trabecular bone 1.0-1.4 g/cm3
the relationship given by Carter and Hayes (1977) applies to trabecular bone
trabecular density mean trabecular thickness
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Bone: Strength of Cancellous Bone
determinants of cancellous bone mechanical properties trabecular
orientation (mean intercept length)
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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
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