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: Structural Hierarchy

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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

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Bone: Composition

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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 vs. Cortical

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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

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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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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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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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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

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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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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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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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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

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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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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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Bone: Fatigue properties

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1 BIOE 4710/5710 – Bone Tissue Function, physiology and composition of bone tissue cortical trabecular Biomechanics of bone tissue mechanical properties