Material properties of cortical bone

Transcription

1 Material constants Material properties of cortical bone

2 Material constants Material properties of cortical bone Cortical bone can withstand greater stress in compression than in tension, and greater stress in tension than shear Cortical bone has a relatively high strength to modulus ratio, it s a high performance material, especially in compression

3 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

4 Bone cells Osteoclasts, osteoblasts, osteocytes, and bone lining cells

5 Osteoclasts Osteoclasts: Bone resorbing cells; form a ruffled border when resorbing bone; proton pumps

6 Osteoblasts Osteoblasts: bone forming cells Two stages: first, matrix formation (osteoid), then mineralization The OB becomes a flat bone lining cell, or an osteocyte, or undergo apoptosis

7 Osteocytes Mechanosenors, most abundant cell type in mature bone (ten times more osteocytes than osteoblasts in normal human bone); Most of the OCs lie within 150µm of a blood vessel; celluelr density of OCs within 1 mm 3 Osteocyes Cell processes Osteocytes may have up to 80 cell processes (and therefore, 80 canaliculi) and via these processes they keep contact with other osteocytes in the deeper layers of bone as well as the surface cells Mechanosenors, react quickly to mechanical stimuli in vivo; Extremely sensitive to fluid shear stresses in vitro

8 Osteocytes How Aging, do loss bone of estrogen, cells loading sense is known mechanical to stimuli? increase osteocyte apoptosis Empty and hypermineralization lacunae of cortical bone have been consistently observed in aged individuals and old dogs.152 The loss of osteocytes has been postulated to be the result of increased mean age of cortical bone and vascular degeneration or vascular disease leading to osteonecrosis Different mechanisms: Direct stimulation (strain, ), Fatigue damage, Fluid flow The osteocytes may (1) stabilize bone mineral that controls the efflux of calcium ions; (2) detect microdamage; and (3) respond to the amount and distribution of strain within bone tissue that influence adaptive modeling and remodeling behavior through cell cell interaction

9 Bone lining cells When OBs are not active, they are flattened, elongated cells covering quiescent surfaces of bone Surface density of BLCs: 19 cells/mm bone surface perimeter, decreases with age 3D networks of BLCs and OCs sense the shapes of bone and its reaction to MS, and transmit these sensations as signals to the bone surface Gap junctions are seen between adjacent bone-lining cells and between bone-lining cells and osteocytes. The surface density of bone-lining cells is about 19 cells/mm bone surface perimeter in young adult dogs, and decreases somewhat with age. They do become active osteoblasts but their fate is not known. They may return to the stem cell or preosteoblast pool and/or apoptose. Both the prolific capacity and differentiation potential of bone-lining cells under normal physiological condition is poorly understood.

10 Typical stress strain behavior for human cortical bone Unlike the ultimate stresses, which are higher in compression, ultimate strains are higher in tension for longitudinal loading. These strains can be up to 5% in young adults and fall to less than 1% in the very elderly; cortical bone becomes more brittle with aging In contrast to its longitudinal tensile behavior, cortical bone is relatively brittle in tension for transverse loading and brittle in compression for all loading directions Cortical bone is weakest when loaded transversely in tension and is also weak in shear When large IMNs are driven too far during surgery into the femoral diaphysis and produce circumferential stresses, it can be quite dangerous)

11 Typical stress strain behavior for human cortical bone Cortical bone: Is stiffer in the longitudinal direction (osteon s direction) Is stronger in compression than in tension Modulus is the same in T and C Is relatively ductile for longitudinal tension, but is brittle in all other loading modes Cortical porosity can vary from less than 5% to almost 30% and is positively correlated with age because the bone becomes more porous with aging In cortical bone, the preferred orientation is determined by the generally parallel assembly of the osteons, whereas in trabecular bone it s determined by a predominant alignment of the plates and rods

12 Heterogeneity in cortical bone In may be necessary in some cases to account for the heterogeneity that can arise from variations in microstructural parameters such as porosity. For instance, for stem stress analysis in bone-implant systems using composite beam theory, since the modulus of the metal is much greater than that of the cortical bone, 20% variations in the modulus of the cortical bone will not affect substantially the calculated stem stresses. However, if there is no implant and the focus is on bone stress, e.g. in a study of bone fracture mechanics, errors in the assumed material properties of the bone become more important

13 Aging and disease Aging and disease also affect the mechanical properties of cortical bone. Modulus varies little with age, but tensile ultimate strength decreases at a greater rate. Most importantly, tensile ultimate strain decreases by about 10% per decade, from a high of almost 5% strain at age yrs to a low of less than 1% strain beyond about 80yrs. Thus, old bone is more brittle than young bone. The energy to fracture is much less for old bone than for younger bone

14 Fatigue, creep, and viscoelasticity Cortical bone shows fatigue and creep and has a greater 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 Fatigue Creep

15 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 repair the damage done to the bone matrix

16 Viscoelasticity of cortical bone Cortical bone is a VE material. Its modulus and strength increase as the rate of loading is increased. Over a six-order-of-magnitude increase in strain rate, 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 relatively 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 rate situation such as high speed trauma, and perhaps during falls

17 Trabecular bone Mechanical behavior at the continuum level of the whole specimen- the apparent properties as opposed to those at the level of individual trabeculae- the tissue properties For instance: apparent vs. tissue modulus for trabecular bone for the whole specimen and trabecular hard tissue & the apparent vs. tissue yield strains Strength refers to the stress at which the specimen fails It has been argued that at least 5 trabecular characteristic dimensions should exist in the specimen for continuum behavior to be manifested (J. Biomech., 21, , 1988)- in other words, test specimen should not be less than about 5mm in any dimensions It s essential to appreciate the heterogeneity (non-homogeneity) in volume fraction and architecture of spongy bone

18 On-axis and off-axis properties On-axis: when loading is along the main trabecular orientation & Off-axis: when loading is oblique to the main trabecular orientation On-axis elastic and strength properties are considered as the inherent material properties, since off-axis properties depend on both the on-axis properties and the angles of alignment between the on- and off-axis coordinate systems All constitutive relations should be written in the principal material coordinate system, so-called on-axis configuration The strength of trabecualr bone depends on volume fraction, architecture, and tissue material properties Since volume fraction and architecture depend so much on anatomic site, species, age and pathologies such as OP, there is considerable variation in trabecualr bone failure stresses

19 What s the strength of trabecular bone? The compressive strength anisotropy ratio = Longitudinal compressive strength Transverse compressive For human vertebral bone, it increases from about 2.1 at age 20 to 3.4 at age 70 strength The strength anisotopy ratio varies from about 2 to 10 across a typical range of densities, being higher for lower density bone Trabecualr strength is heterogenous, anisotropic, and asymmetric (different between tension and compression)

20 Tensile vs. compressive strength Stress-strain behavior for compressive and tensile loading of bovine (left) and human vertebral (right) trabecular bone By contrast to the large post-yield region that exists for compression, the post-yield region for tensile loading is small Loading was stopped at 3% strain, but fractures occurred earlier for the tensile specimens as denoted by the X For high stiffness specimens, the spongy bone is markedly stronger in compression, whereas for lower stiffness specimens, the bone has about the same strength in tension and compression

21 Ultimate stress vs. age Age related reductions in compressive strength of human femoral and vertebral trabecular bone

22 Uniform yield strain Compressive and tensile yield strains vs. human anatomic site for spongy bone specimens tested on-axis. Compressive yield strains were always greater than tensile yield strains. For higher density spongy bone, comp. and tensile values are about 0.8 and 0.6 percent, respectively. For lower density bone, such as in the vertebral body, comp yield strains are lower at about 0.7 percent, due presumably to underlying large deformation bending or buckling-type failure mechanisms of the individual trabeculae that can occur when the density is low No dependence on density, at most only a weak correlation!

23 Failure criterion The multi-axial failure behavior of trabecular bone is an important aspect of its in vivo failure behavior, because failure usually occurs during some type of trauma where loads will be multiaxial or oblique to the principal material direction. For the failure analysis, a criterion based on maximum strains should be used. Such a criterion is advantageous because it is relatively independent of variations in apparent density, at least within an anatomic site, and is also isotropic. The criterion works as follows: Strains for any state of loading are converted into principal strains. When the principal strain exceeds the maximum allowable on-axis uniaxial strains, then failure is assumed to occur. Note that despite this yield strain criterion being both homogenous and isotropic, strength remains asymmetric, since yield strains are lower in tension than compression

24 Strength-density relation The 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, ): ult where σult is ultimate stress (in MPa), ρ is apparent density (in g/cm 3 ) and ε dot is strain rate (in s -1 ). Statistical analysis of literature 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

25 Strength-density relation Differences in architecture that occur for the different density ranges do have an effect on the strength-density relationship For example, if the on-axis strength-density relation for human vertebral bone, which has a mostly rod-type architecture, is extended to sites of higher density such as the bovine tibia, which is very plate-like, substantial errors can result For multiple sites, care must be taken to avoid extrapolation errors. In such circumstances, it appears that a power law model, fit to experimental data, is most appropriate. Even so, it s recommended to use a site specific model, if available, for those situations where analysis is confined to a single site

26 Suggested texts D.L. Bartel, D.T. Davy and T.M. Keaveney, Orthopaedic Biomechanics, Mechanics and Design in Musculoskeletal Systems, Prentice Hall, S.C. Cowin, Bone Mechanics Handbook, 2nd Edition, CRC Press, R.B. Martin and D.B. Burr, Structure, Function, and Adaptation of Compact Bone, Raven Press, D.R Carter and G.S. Beaupre, Skeletal Function and Form, Mechanobiology of Skeletal Development, Again, and Regeneration, Cambridge University Press, 2001.