Cortical and cancellous bones - Amirkabir University of ...bme2.aut.ac.ir/odbl/images/courses/Bonebiomech-P1_Part2.pdf · Cortical and cancellous bones • At the macroscopic level:

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.


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




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.





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


Anisotropy in boneOrthotropy: Cancellous bone , transversely isotropic: cortical bone


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


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


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.


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


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


Typical sites of osteoporotic frac ture


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


Genera lized Hook’s lawGeneralized Hook’s law:

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Orthotropic (9)

Transversely isotropic (5) Isotropic (2)


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.


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


Mater ial properties of cortica l boneMaterial constants


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


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


Viscoelasticity• A Viscoelastic material is one in which:

– Hystersis is seen in the Stress-Strain curve, – Stress Relaxation occurs, – Creep occurs.

Hystersis Stress RelaxationCreep


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


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


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


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


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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)


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?


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.

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Cortical and cancellous bones - Amirkabir University of ...bme2.aut.ac.ir/odbl/images/courses/Bonebiomech-P1_Part2.pdf · Cortical and cancellous bones • At the macroscopic level: