The mechanical behaviour of cancellous bone

Cancellous bone has a cellular structure: it is made up of a connected network of rods and plates. Because of this, its mechanical behaviour is similar to that of other cellular materials such as polymeric foams. A recent study on the mechanisms of deformation in such materials has led to an understanding of how their mechanical properties depend on their relative density, cell wall properties and cell geometry. In this paper, the results of this previous study are applied to cancellous bone in an attempt to further understand its mechanical behaviour. The results of the analysis agree reasonably well with experimental data available in the literature.     

Finite element prediction of fatigue damage growth in cancellous bone

Cyclic stresses applied to bones generate fatigue damage that affects the bone stiffness and its elastic modulus. This paper proposes a finite element model for the prediction of fatigue damage accumulation and failure in cancellous bone at continuum scale. The model is based on continuum damage mechanics and incorporates crack closure effects in compression. The propagation of the cracks is completely simulated throughout the damaged area. In this case, the stiffness of the broken element is reduced by 98% to ensure no stress-carrying capacities of completely damaged elements. Once a crack is initiated, the propagation direction is simulated by the propagation of the broken elements of the mesh. The proposed model suggests that damage evolves over a real physical time variable (cycles). In order to reduce the computation time, the integration of the damage growth rate is based on the cycle blocks approach. In this approach, the real number of cycles is reduced (divided) into equivalent blocks of cycles. Damage accumulation is computed over the cycle blocks and then extrapolated over the corresponding real cycles. The results show a clear difference between local tensile and compressive stresses on damage accumulation. Incorporating stiffness reduction also produces a redistribution of the peak stresses in the damaged region, which results in a delay in damage fracture.     

Anisotropy and inhomogeneity of the trabecular structure can describe the mechanical strength of osteoarthritic cancellous bone

Osteoarthritic cancellous bone was studied to investigate the development of this pathology, and the functional changes it induces in the bone. In order to predict how the morphological alterations of the tissue induced by the pathology can change the mechanical properties of the structure, two different strategies have been used in the literature: (1) emphasising the influence of structural anisotropy; (2) stressing the highly inhomogeneous characteristics of cancellous bone. The aim of the present study was to verify the theory that mechanical strength of osteoarthritic cancellous bone depends both on tissue anisotropy and inhomogeneity.Twenty-five specimens were extracted from osteoarthritic femoral heads, along selected directions, and analysed by means of a microtomograph. The same specimens were mechanically tested in compression to determine the mechanical strength. The most representative structural parameters, confirmed by a stepwise analysis, were used to define four models to describe the measured mechanical strength. The models were applied neglecting (global analysis) or considering (local analysis) tissue inhomogeneities to verify whether the correlation with ultimate stress could be improved.The coefficient of determination increased from 0.53, considering only bone volume fraction, up to 0.88, combining it with off-axis angle and normalised eigenvalue. A further improvement was found performing a local analysis (R²=0.90), which corresponded to a decrease of 17% in the residual error.The proposed approach of considering both tissue anisotropy and inhomogeneity improved the accuracy in predicting the mechanical behaviour of cancellous bone tissue and should be suitable for more general loading conditions.     

Age-dependent fatigue behaviour of human cortical bone

Despite a general understanding that bone quality contributes to skeletal fragility, very little information exits on the age-dependent fatigue behavior of human bone. In this study four-point bending fatigue tests were conducted on aging bone in conjunction with the analysis of stiffness loss and preliminary investigation of nanoindentation based measurements of local tissue stiffness and histological evaluation of resultant tensile and compressive damage to identify the damage mechanism responsible for the increase in age-related bone fragility. The results obtained show that there is an exponential decrease in fatigue life with age, and old bone exhibits different modulus degradation profiles than young bone. In addition, this study provides preliminary evidence indicating that during fatigue loading, younger bone formed diffuse damage, lost local tissue stiffness on the tensile side. Older bone, in contrast, formed linear microcracks lost local tissue stiffness on the compressive side. Thus, the propensity of aging human bone to form more linear microcracks than diffuse damage may be a significant contributor to bone quality, and age related fragility in bone.     

Viscoelastic behaviour and failure of bovine cancellous bone under constant strain rate

A programme has been established to characterize the long-term behaviour of cancellous bone. Fresh bovine cancellous specimens of dimensions 10 x 10 x 10 mm3 and 10 x 40 x 3.6 mm3 were manufactured and used within the testing programme. Results published in the literature indicate that the long-term behaviour of cancellous bone is well described by a power law, which is a very similar response of typical polymers. So far, dynamic mechanical tests (DMA) in three-point bending, under frequencies between 0.01 and 100 Hz at room temperature, confirmed the published results in a qualitative way. Nevertheless, the measured dimensionless damping, tan delta, was slightly higher than the values reported in the literature for the compact bone. The relaxation curves were obtained from dynamic tests and confirmed that bone relaxation modulus can be described by a power law function of time. Tests under constant compression strain rate were performed at four different strain rates: 0.15/s, 0.015/s, 0.0015/s and 0.00015/s and strain rate dependent behaviour was observed. An average elastic bending modulus of 300 MPa was obtained.     

The mechanical behaviour of intracondylar cancellous bone of the femur at different loading rates

The compressive properties of human cancellous bone of the distal intracondylar femur in its wet condition were determined. Specimens were obtained from six cadaveric femora and were tested at a strain rate of 0.002, 0.10 and 9.16 sec⁻¹. It was found that the compressive strength decreases with an increasing vertical distance from the joint. The highest compressive strength level was recorded in the posterior medial condyle. Correlations among the mechanical properties, the bulk specimen density and the bone mineral content yield (i) highly significant correlations between the compressive strength and the elastic modulus (ii) highly significant correlations between the compressive strength or the modulus of elasticity and the bulk specimen density (iii) a doubtful correlation between the compressive strength and the bone mineral content. All recorded graphs of the impact loaded specimens displayed several well defined stress peaks, unlike the graphs recorded at low loading rates. It can be concluded that upon impact loading the localized trabecular failure which is associated with each peak, does not affect the spongy bone's stress capacity in a detrimental way.     

Limitations of the continuum assumption in cancellous bone

Most existing stress analyses of the skeleton which consider cancellous bone assume that it can be modelled as a continuum. In this paper we develop a criterion for the validity of this assumption. The limitations of the continuum assumption appear in two areas: near biologic interfaces, and in areas of large stress gradients. These limitations are explored using a probabilistic line scanning model for density measurement, resulting in an estimate of density accuracy as a function of line length which is experimentally verified. Within three to five trabeculae of an interface, a continuum model is suspect. When results as predicted using continuum analyses vary by more than 20-30% over a distance spanning three to five trabeculae, the results are suspect.     

Biomechanical behaviour of cancellous bone on patellofemoral arthroplasty with Journey prosthesis: a finite element study

Isolated patellofemoral (PF) arthritis of the knee is a common cause of anterior knee pain and disability. Patellofemoral arthroplasty (PFA) is a bone conserving solution for patients with PF degeneration. Failure mechanisms of PFA include growing tibiofemoral arthritis and loosening of components. The implant loosening can be associated with bone resorption or fatigue-failure of bone by overload. This research work aims at determining the structural effects of the implantation of PF prosthesis Journey PFJ (Smith & Nephew, Inc., Memphis, TN, USA) on femoral cancellous bone. For this purpose, the finite element method is considered to perform computational simulations for different conditions, such as well-fixed and loosening scenarios. From the global results obtained, in the well-fixed scenario, a decrease in strain on cancellous bone was noticed, which can be related to bone resorption. In the loosening scenario, when the cement layer becomes inefficient, a significant increase in cancellous bone strain was observed, which can be associated with bone fatigue-failure.These strain changes suggest a weakness of the femur after PFA.     

Yield behavior of bovine cancellous bone

The compressive yield strain was measured for 61 specimens of bovine cancellous bone from three distal femora. There was no significant relationship (p = 0.08, R2 = 0.051) between yield strain and the degree of trabecular orientation. There was a significant positive correlation (p less than 0.00001, R2 = 0.319) between yield strain and structural (apparent) density and significant negative correlation (p less than 0.0025, R2 = 0.145) between yield strain and bone density. Yield strain correlated best with bone solid volume fraction Vv (epsilon y = 0.592 +2- 1.446vv, R2 = 0.337). The quantity, yield strain, is highly dependent on specific definitions of the yield point and the point of zero strain. For this study the yield point was defined by a 0.0003 offset criterion, and the point of zero strain was defined as the point where the tangent at 15 percent of yield crosses zero. The results using these definitions were compared with results using yield strain values determined by other definitions of the yield point and zero strain. The correlations between yield strain and trabecular orientation, structural density and bone density changed very little for differing definitions of yield. The results suggest that yield strain in cancellous bone is isotropic or independent of textural anisotropy, so the yield behaviour may be characterized by a maximum strain yield criterion. The results also suggest that the primary mode of yield in cancellous bone is buckling of the trabeculae.     

The fracture toughness of cancellous bone

The mechanical capacity and integrity of cancellous bone is crucial in osteoporosis, a condition which is set to become more prevalent with increasing lifespan and population sizes. The fracture toughness (FT) of cancellous bone has never been examined before and the conditions associated with the growth of a major crack through the lattice of cancellous bone, a cellular solid, may improve our understanding for structural integrity of this material. The aim of this study is to provide (i) basic data on cancellous bone FT and (ii) the experimental support for the hypothesis of Gibson, L.J., Ashby, M.F. [1997a. Chapter 10: Wood. In: Cellular Solids: Structure and Properties, second ed. Cambridge University Press, pp. 387–428; Gibson, L.J., Ashby, M.F., 1997b. Chapter 11: Cancellous Bone. In: Cellular Solids: Structure and Properties, second ed. Cambridge University Press, pp. 429–52] that the FT of cancellous bone tissue is governed by the density of the tissue to a power function of between one and two. 294 SENB and 121 DC(T) specimen were manufactured from 45 human femoral heads, 37 osteoporotic and 8 osteoarthritic, as well as 19 equine thoracic vertebrae. The samples were manufactured in two groups: the first aligned with the trabecular structure (A_∥), the second orientated at 90° to the main trabecular orientation (A_⊥). The samples were tested in either tensile or bending mode to provide values of the stress intensity factor (K). The results which were obtained show a strong and significant link between the density of the cancellous bone tissue and that the critical stress intensity values are governed by the density of the tissue to a power function of between 1 and 2 (K_Q vs. apparent density: A_⊥=1.58, A_∥=1.6). Our results provide some fundamental values for the critical stress intensity factor for cancellous bone and also support the previous hypothesis as set by Gibson, L.J., Ashby, M.F., 1997a. Chapter 10: Wood. In: Cellular Solids: Structure and Properties, second ed. Cambridge University Press, pp. 387–428; Gibson, L.J., Ashby, M.F., (1997b). Chapter 11: Cancellous Bone. In: Cellular Solids: Structure and Properties, second ed. Cambridge University Press, pp. 429–52.     

The cancellous bone multiscale morphology-elasticity relationship

The cancellous bone effective properties relations are analysed on multiscale across two aspects; properties of representative volume element on micro scale and statistical measure of trabecular trajectory orientation on mesoscale. Anisotropy of the microstructure is described across fabric tensor measure with trajectory orientation tensor as bridging scale connection. The scatter measured data (elastic modulus, trajectory orientation, apparent density) from compression test are fitted by stochastic interpolation procedure. The engineering constants of the elasticity tensor are estimated by last square fitt procedure in multidimensional space by Nelder-Mead simplex. The multiaxial failure surface in strain space is constructed and interpolated by modified super-ellipsoid.     

Transversely isotropic elasticity imaging of cancellous bone

To measure spatial variations in mechanical properties of biological materials, prior studies have typically performed mechanical tests on excised specimens of tissue. Less invasive measurements, however, are preferable in many applications, such as patient-specific modeling, disease diagnosis, and tracking of age- or damage-related degradation of mechanical properties. Elasticity imaging (elastography) is a nondestructive imaging method in which the distribution of elastic properties throughout a specimen can be reconstructed from measured strain or displacement fields. To date, most work in elasticity imaging has concerned incompressible, isotropic materials. This study presents an extension of elasticity imaging to three-dimensional, compressible, transversely isotropic materials. The formulation and solution of an inverse problem for an anisotropic tissue subjected to a combination of quasi-static loads is described, and an optimization and regularization strategy that indirectly obtains the solution to the inverse problem is presented. Several applications of transversely isotropic elasticity imaging to cancellous bone from the human vertebra are then considered. The feasibility of using isotropic elasticity imaging to obtain meaningful reconstructions of the distribution of material properties for vertebral cancellous bone from experiment is established. However, using simulation, it is shown that an isotropic reconstruction is not appropriate for anisotropic materials. It is further shown that the transversely isotropic method identifies a solution that predicts the measured displacements, reveals regions of low stiffness, and recovers all five elastic parameters with approximately 10% error. The recovery of a given elastic parameter is found to require the presence of its corresponding strain (e.g., a deformation that generates ??? is necessary to reconstruct C????), and the application of regularization is shown to improve accuracy. Finally, the effects of noise on reconstruction quality is demonstrated and a signal-to-noise ratio (SNR) of 40 dB is identified as a reasonable threshold for obtaining accurate reconstructions from experimental data. This study demonstrates that given an appropriate set of displacement fields, level of regularization, and signal strength, the transversely isotropic method can recover the relative magnitudes of all five elastic parameters without an independent measurement of stress. The quality of the reconstructions improves with increasing contrast, magnitude of deformation, and asymmetry in the distributions of material properties, indicating that elasticity imaging of cancellous bone could be a useful tool in laboratory studies to monitor the progression of damage and disease in this tissue.     

Use of the cylinder osteotome for cancellous bone grafting

An instrument is described for removing iliac crest cancellous bone grafts under local anesthesia. The device has widespread applications for plastic and orthopedic surgery. The convenience of obtaining bone grafts with this device broadens the use of bone-grafting techniques in patients in whom the need for bone graft is unexpected.     

Tensile and compressive properties of cancellous bone

The relationship between the mechanical properties of trabecular bone in tension and compression was investigated by non-destructive testing of the same specimens in tension and compression, followed by random allocation to a destructive test in either tension or compression. There was no difference between Young's modulus in tension and compression, and there was a strong positive correlation between the values (R = 0.97). Strength, ultimate strain and work to failure was significantly higher in tensile testing than in compressive testing.     

Post-yield relaxation behavior of bovine cancellous bone

Relaxation studies were conducted on specimens of bovine cancellous bone at post-yield strains. Stress and strain were measured for 1000 s and the relaxation modulus was determined. Fifteen cylindrical, cancellous bone specimens were removed from one bovine femur in the anterior–posterior direction. The relaxation modulus was found to be a function of strain. Therefore cancellous bone is non-linearly viscoelastic/viscoplastic in the plastic region. A power law regression was fit to the relaxation modulus data. The multiplicative constant was found to be statistically related through a power law relationship to both strain (p<0.0005) and apparent density (p<0.0005) while the power coefficient was found to be related through a power law relationship, E(t, ε)=A(ε)t^?n(ε), to strain (p<0.0005), but not apparent density.     

Alfacalcidol restores cancellous bone in ovariectomized rats

Active vitamin D metabolites have been demonstrated to reduce vertebral and hip fractures in elderly patients. A number of in vitro and in vivo pre-clinical studies have suggested that vitamin D may effectively stimulate osteoblastic activity and exert an anabolic effect on bone. The current study was designed to further explore the ability of an active vitamin D analog to restore bone in a skeletal site with established osteopenia in ovariectomized (OVX) rats. Female Sprague Dawley rats at five months of age and 8 weeks after sham ovariectomy or ovariectomy were randomly divided into 7 groups with 10 per group. At the beginning of the treatments, one group of sham-operated rats and one group of OVX rats were sacrificed to serve as baseline controls. Another group of sham-operated rats and one group of OVX rats were treated with vehicle for 4 weeks. The OVX rats in the remaining groups were treated with alfacalcidol at 0.05, 0.1 or 0.2 microg/kg/d by daily oral gavage, 5 days/week for 4 weeks. As expected, estrogen depletion caused high bone turnover and cancellous bone loss in lumbar vertebra of OVX rats. Alfacalcidol treatment at 0.1 or 0.2 but not 0.05 microg/kg/d increased serum calcium and phosphorus in OVX rats as compared with vehicle treatment. In addition, serum parathyroid hormone was suppressed, whereas serum osteocalcin was increased by alfacalcidol at all dose levels. Furthermore, histomorphometric data of 2nd lumbar vertebral body revealed that cancellous bone volume in OVX rats treated with alfacalcidol at 0.1 or 0.2 microg/kg/d was increased to the level of sham-operated rats treated with vehicle. This increment in cancellous bone mass was accompanied by increases in trabecular number and thickness and a decrease in trabecular separation. Moreover, osteoclast surface and number were significantly decreased, whereas bone formation variables such as mineralizing surface and bone formation rate were significantly increased in alfacalcidol- treated OVX rats compared with those of vehicle-treated OVX rats. Finally, a linear regression analysis showed that alfacalcidol treatment dose-dependently altered most of the variables measured in the current study. In conclusion, alfacalcidol completely restores cancellous bone by stimulating bone formation and suppressing bone resorption in lumbar vertebra of OVX rats when the treatment is started at an early phase of osteopenia. The evidence of increased bone formation by alfacalcidol treatments further supports the notion that active vitamin D metabolites or their analogs may exert anabolic effects on bone.