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Bone Biomechanics, Fall 2016, G. Rouhi
Cortical and cancellous bones• At the macroscopic level:
– Cortica l (Haversian or compact) & Cancellous (spongy or trabecular )• Porosity: 5 to 10%• Found in the shaft of long bones and forms the outer shell around cancellous bone
at the end of joint and the vertebrae• In cortical bone the main structural unit is the osteon or Haversian system- Osteons
form approximately two thirds of the cortical bone volume; the remaining one third is interstitial bone composed of the remnants of past generations of osteons and subperiosteal and subendosteal circumferential lamellae.
Bone Biomechanics, Fall 2016, G. Rouhi
Compact bone • It is a dense, solid mass with only microscopic channels; cover the outer walls of long bones• The basic structura l unit is Osteon or HS- Osteons form approximately two thirds of the cortical bone
volume; the remaining one third is interstitial bone composed of the remnants of past genera tions of osteons and subperiosteal and subendosteal circumferential lamellae.
• An Osteon: Haversian canal, osteocyte lacunae,osteocytic processes within canaliculi• Max. density: 1.9 gr/cm3 ; 80% of the skeletal mass; largely responsible for the supportive and
protective function of the skeleton
Haversian system or Osteon
Bone Biomechanics, Fall 2016, G. Rouhi
Bone Biomechanics, Fall 2016, G. Rouhi
Bone Biomechanics, Fall 2016, G. Rouhi
Compact bone A typical osteon is a hollow cylinder with the outer and inner diameters of about 200 (or 250) and 50 μm, respectively. An osteon is made up of 20 to 30 concentric lamellaeMicro-m thick., and surrounding the outer border of each osteon there is a cement line, a 1-2 μm thick layer of mineral ized matrix deficient in collagen fibers, which it is believed they act as crack stoppers when cracks are present. Surrounding the outer border of each osteon is a cement line, a 1- to 2- micro-m-thick layer of mineralized matrix deficient in collagen fibers.
Bone Biomechanics, Fall 2016, G. Rouhi
Bone Biomechanics, Fall 2016, G. Rouhi
Bone Biomechanics, Fall 2016, G. Rouhi
Bone Biomechanics, Fall 2016, G. Rouhi
Cortical boneThe lamellae of adult cortical boneappear in 3 major patterns: circularrings of lamellae (concentric lamellae)surrounding a longitudinally vascularchannel that together form a structuralcone, the Osteon or Haversian system;several layers of lamellae extendinguninterrupted around par t or all of thecircumference of the shaft to form whatis known as the circumferentiallamellae (inner and outer); angularfragments of what formerly wereconcentric or circumferential lamellaefilling the gaps between the Haversiansystems, known as the interstitiallamellae
Bone Biomechanics, Fall 2016, G. Rouhi
Anisotropy in boneOrthotropy: Cancellous bone , transversely isotropic: cortical bone
Bone Biomechanics, Fall 2016, G. Rouhi
Propert ies of cortical bone
The material properties of cortical bone depend on loading ra te, and when loaded past the yield point, cortical bone shows characteristic of plasticity, damage accumulation, creep, and fatigue
Cortical bone is transversely isotropic, meaning that it has one primary material axis (the longitudinal) and is isotropic in the plane perpendicular to this axis (the transverse plane)
The longitudinal axis is generally aligned with the diaphysealaxis of long bones
It is stiffer and stronger when loaded in L direction compared with the radial or circumferential directions
This structure efficiently resists the largely uniaxial stresses that develop along the diaphyseal axis during habitual activities such as walking and running
Bone Biomechanics, Fall 2016, G. Rouhi
Spongy bone– Basic structura l unit: a trabecula; networks of plates and rods– Porosity: 50 to 90%– The average thickness of a trabecula is 100-150 µm– Approximately 20% of the skeletal mass in the adult human skeleton
Bone Biomechanics, Fall 2016, G. Rouhi
Spongy boneTrabecualr bone is less mineralized than cortical bone, and experimental evidence
and data suggest that spongy bone is much more active in remodeling than that of cortica l bone. With ageing there ar e changes in the microarchitecture of bone. There is thinning of the cortex and of trabeculae, and a loss of connectivity, in particular of the horizontal trabeculae.
Bone Biomechanics, Fall 2016, G. Rouhi
Spongy bone– An inhomogeneous porous anisotropic structure– If the stress pattern in spongy bone is complex, then the structure of the network
of trabeculae is also complex and highly asymmetric- The symmetry depends upon the direction of applied loads
– In bones where the loading is largely uniaxial, such as the vertebrae, the trabeculae often develop a columnar structure
– The trabeculae are surrounded by marrow that is vascular and provides nutrients and waste disposal from the bone cells
– There are no blood vessels within the trabeculae, but there are vessels immediately adjacent to the tissue
Bone Biomechanics, Fall 2016, G. Rouhi
Spongy bone– SP as a cellular material: a network of rods produces open cells while one of
plates gives closed cells
– At low apparent densities the cells form an open network of rods- Open cell, rod like structures develop in regions of low stress
– As the relative density increases, structure transforms into a more closed network of plates. The plate-like is typically found in vertebrae
Bone Biomechanics, Fall 2016, G. Rouhi
Typical sites of osteoporotic frac ture
Bone Biomechanics, Fall 2016, G. Rouhi
Mechanical proper ties of cortical bone and cancellous bone tissuesBecause of a high surface-to-volume ratio, cancellous bone remodeling is more activethan cortical bone. Osteons exist in the trabeculae when the thickness of trabecula isgreater than 350 μm (e.g. the calcaneus)- it suggests that formation of osteons (bonelemellae formed around vascular channels) is a specific structural response to nutrientrequirements. At the scale of lamellae, it’d be reasonable to hypothesize thatcancellous and cortical bone tissues have similar properties
Bone Biomechanics, Fall 2016, G. Rouhi
Genera lized Hook’s lawGeneralized Hook’s law:
123131
312323
231212
33333
2
233322
1
133311
3
322233
22222
1
122211
3
311133
2
211122
11111
1,1,1
1,,
,1,
,,1
GC
GC
GC
EC
EC
EC
EC
EC
EC
EC
EC
EC
12
123131
232323
231212
33333
2
233322
1
233311
3
312233
22222
1
122211
3
311133
2
211122
11111
22,1,1
1,,
,1,
,,1
EC
GC
GC
EC
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E22CCC
E1CC,
ECCCCCC,
E1C
313123231212
333322222211113311222233332233111111
Orthotropic (9)
Transversely isotropic (5) Isotropic (2)
Bone Biomechanics, Fall 2016, G. Rouhi
Influence of bone geometry on biomechan ical behavior• In tension and compression, area of cross-section
• In bending, both the cross-sectional area and distribution of bone tissue around the neutral axis, as well as the length of the bone
• A larger moment of inertia results in a stronger and stiffer bone
• In torsion, polar moment of inertia (J ), the larger J, the stronger and stiffer bone
• In the process of fracture healing, there is callus formation (why), when bone heals completely, it will take the original size
• The immediate effect of drilling a hole and inserting a screw in a rab bit femur was a 74% decrease in energy storage capacity!
• Clinically, the surgical removal of a piece of bone can greatly weaken the bone, particularly in torsion.
Bone Biomechanics, Fall 2016, G. Rouhi
Mechanical behavior of bone
• Mechanical behavior of bone is affected by:– its mechanical properties– its geometric characteristics– the loading mode applied – direction of loading– ra te of loading– frequency of loading
Bone Biomechanics, Fall 2016, G. Rouhi
Mater ial properties of cortica l boneMaterial constants
Bone Biomechanics, Fall 2016, G. Rouhi
Material prop erties of cortical boneMaterial constants
Cortical bone can withstand greater stress in compression than in tension, and greater stress in tension than shear Cortical bone has a re latively high strength to modulus ratio, it’s a high performance material, especially in compression
Bone Biomechanics, Fall 2016, G. Rouhi
Typical stress strain behavior for human cortical bone
Human cortical bone exhibits an initial LE behavior, a marked yield point, and failure at a relatively low strain level
Bone Biomechanics, Fall 2016, G. Rouhi
Viscoelasticity• A Viscoelastic material is one in which:
– Hystersis is seen in the Stress-Strain curve, – Stress Relaxation occurs, – Creep occurs.
Hystersis Stress RelaxationCreep
Bone Biomechanics, Fall 2016, G. Rouhi
Viscoelasticity of cortical boneCortical bone is a VE material. Its modulus and strength increase as the ra te of loading is increased . Over a six-order-of-magnitude increase in strain ra te, modulus only changes by a factor of 2, and strength by a factor of 3. Thus for the majority of physiological activities, which tend to occur in a re latively narrow range of strain rates (0.01 to 1 percent of strain per second) cortical bone can be reasonably assumed to behave elastically. However the increased stiffness and strength properties and the tendency toward more brittle behavior are important in high strain ra te situation such as high speed trauma, and perhaps during falls
Bone Biomechanics, Fall 2016, G. Rouhi
Fatigue, creep, and viscoelasticityCortical bone shows fatigue and creep and has a grea ter resistance to failure in these modes in compression than tension. If the fatigue and creep properties were obtained from devitalized bone specimens, then the fatigue life values are lower bounds on the in vivo fatigue life. Thus, it’s unlikely that high cycle (low stress) fatigue failures occurs in vivo, since the resulting fatigue damage would be healed biologically before large enough cracks can develop that would cause fracture. But, low cycle fatigue (stress fractures) can occur when higher levels of repetitive stresses are applied over shorter time intervals
FatigueCreep
Bone Biomechanics, Fall 2016, G. Rouhi
Fatigue, creep,…When cortical bone is loaded beyond its yield point, unloaded and reloaded, its modulus is reduced. This is evidence of damage, something that does not occur in metals where the modulus after plastic yielding is the same as the initial modulus. As the surrounding bone matrix permanently deforms and sustains damage, cells may be altered and a biological response may be induced, which encourages the bone cells to repa ir the damage done to the bone matrix
Bone Biomechanics, Fall 2016, G. Rouhi
Tensile vs. compressive strengthStress-strain behavior for compressive andtensile loading of bovine (left) and humanvertebra l (right) trabecular bone
By contrast to the large post-yield regionthat exists for compression, the post-yieldregion for tensile loading is small
Loading was stopped at 3% strain, butfractures occurred ear lier for the tensilespecimens as denoted by the X
For high stiffness specimens, the spongybone is markedly stronger in compression,whereas for lower stiffness specimens, thebone has about the same strength in tensionand compression
Strength-density relationThe precise relationship between the ultimate stress of trabecular bone vs. apparent density or volume fraction remains an open question
The most common relation used is from the early work of Cater and Hayes (J. Bone Joint Surg., 1977, 59A, 954-962):
where σult is ultimate stress (in MPa), ρ is apparent density (in g/cm3) and ε dot is strain ra te (in s-1).
Statistical analysis of litera ture data for only trabecular bone but from many sites subsequently found that a squared relationship worked best, supporting the power law model
For human bone, the reported strength-density relationships do not vary tremendously across site
Bone Biomechanics, Fall 2016, G. Rouhi
0.062
68ult
Bone Biomechanics, Fall 2016, G. Rouhi
Bone surfaces
Free surfaces: Endosteum, periosteum, trabeculae, and Haversian canals
Cancellous bone surface contributes more than 61% of the total bone surface
The mean trabecular surface to volume ra tio is 8 times greater that in CB
Bone surfaces: resorp tion (OCs), formation (OBs), or quiscent (BLc)
Bone Biomechanics, Fall 2016, G. Rouhi
How do bone cells sense mechanical stimuli?Hypothesis: osteocytes act as sensors.
Different mechanisms:1. Direct stimulation (strain,…),2. Fatigue damage,3. Fluid flow.
Deficiencies in the present models: e.g., …. signal sent by an osteocyte decays exponentially, Nature, 2000.
Rouhi, et al., 2006a, To be submitted.
How do bone cells sense mechanical stimuli?
Bone Biomechanics, Fall 2016, G. Rouhi
Suggested texts
• D.L. Bartel, D.T. Davy and T.M. Keaveney, Orthopaedic Biomechanics, Mechanics and Design in Musculoskeletal Systems, Prentice Hall, 2006.
• M. Nordin and V.H. Frankel, Basic Biomechanics of the Musculoskeletal System, 3rd edition, Lippincott Williams & Wilkins, 2001.
• S.C. Cowin, Bone Mechanics Handbook, 2nd Edition, CRC Press, 2001.
• R.B. Martin and D.B. Burr, Structure, Function, and Adaptation of Compact Bone, Raven Press, 1989.
• D.R Carter and G.S. Beaupre, Skeletal Function and Form, Mechanobiology of Skeletal Development, Again, and Regeneration, Cambridge University Press , 2001.