Characterisation of time-dependent mechanical behaviour of trabecular bone and its constituents

Trabecular bone is a porous composite material which consists of a mineral phase (mainly hydroxyapatite), organic phase (mostly type I collagen) and water assembled into a complex, hierarchical structure. In biomechanical modelling, its mechanical response to loads is generally assumed to be instantaneous, i.e. it is treated as a time-independent material. It is, however, recognised that the response of trabecular bone to loads is time-dependent. Study of this time-dependent behaviour is important in several contexts such as: to understand energy dissipation ability of bone; to understand the age-related non-traumatic fractures; to predict implant loosening due to cyclic loading; to understand progressive vertebral deformity; and for pre-clinical evaluation of total joint replacement. To investigate time-dependent behaviour, bovine trabecular bone samples were subjected to compressive loading, creep, unloading and recovery at multiple load levels (corresponding to apparent strain of 2,000-25,000 με). The results show that: the time-dependent behaviour of trabecular bone comprises of both recoverable and irrecoverable strains; the strain response is nonlinearly related to applied load levels; and the response is associated with bone volume fraction. It was found that bone with low porosity demonstrates elastic stiffening followed by elastic softening, while elastic softening is demonstrated by porous bone at relatively low loads. Linear, nonlinear viscoelastic and nonlinear viscoelastic-viscoplastic constitutive models were developed to predict trabecular bone’s time-dependent behaviour. Nonlinear viscoelastic constitutive model was found to predict the recovery behaviour well, while nonlinear viscoelastic-viscoplastic model predicts the full creep-recovery behaviour reasonably well. Depending on the requirements all these models can be used to incorporate time-dependent behaviour in finite element models. To evaluate the contribution of the key constituents of trabecular bone and its microstructure, tests were conducted on demineralised and deproteinised samples. Reversed cyclic loading experiments (tension to compression) were conducted on demineralised trabecular bone samples. It was found that demineralised bone exhibits asymmetric mechanical response - elastic stiffening in tension and softening in compression. This tension to compression transition was found to be smooth. Tensile multiple-load-creep-unload-recovery experiments on demineralised trabecular samples show irrecoverable strain (or residual strain) even at the low stress levels. Demineralised trabecular bone samples demonstrate elastic stiffening with increasing load levels in tension, and their time-dependent behaviour is nonlinear with respect to applied loads . Nonlinear viscoelastic constitutive model was developed which can predict its recovery behaviour well. Experiments on deproteinised samples showed that their modulus and strength are reasonably well related to bone volume fraction. The study considers an application of time-dependent behaviour of trabecular bone. Time-dependent properties are assigned to trabecular bone in a bone-screw system, in which the screw is subjected to cyclic loading. It is found that separation between bone and the screw at the interface can increase with increasing number of cycles which can accentuate loosening. The relative larger deformation occurs when this system to be loaded at the higher loading frequency. The deformation at the bone-screw interface is related to trabecular bone’s bone volume fraction; screws in a more porous bone are at a higher risk of loosening

Prediction of vertebral strength in vitro by spinal bone densitometry and calcaneal ultrasound

Spinal bone mineral density (BMD) measurements and calcaneal ultrasound were compared in terms of their ability to predict the strength of the third lumbar vertebral body using specimens from 62 adult cadavers (28 females, 34 males), BMD was measured using dual X-ray absorptiometry (DXA) in both vertebra and calcaneus. Quantitative computed tomography (QCT) was used to determine trabecular BMD, cortical BMD, cortical area, and total cross-sectional area (CSA) of the vertebral body, Bone velocity (BV) and broadband ultrasonic attenuation (BUA) were measured in the right calcaneus. Vertebral strength was determined by uniaxial compressive testing, Vertebral ultimate load was best correlated with DXA-determined vertebral BMD (r(2) = 0.64), Of the QCT parameters, the best correlation with strength,vas obtained using the product of trabecular BMD and CSA (r(2) = 0.61), For vertebral ultimate stress, however, the best correlation was observed with QCT-measured trabecular BMD (r(2) = 0.51); the correlation with DXA-determined BMD was slightly poorer (r(2) = 0.44), Calcaneal ultrasound correlated only weakly with both ultimate load and stress with correlation coefficients (r(2)) of 0.10-0.17, as did calcaneal BMD (r(2) = 0.18), Both spinal DXA and spinal QCT were significantly (p < 0.001) better predictors of L3 ultimate load and stress than were either calcaneal ultrasound or calcaneal DXA. Multiple regression analysis revealed that calcaneal ultrasound did not significantly improve the predictive ability of either DXA or QCT for L3 ultimate load or stress, Calcaneal DXA BMD, bone velocity, and BUA correlated well with each other (r(2) = 0.67-0.76), but were only modestly correlated with the DXA and QCT measurements of the vertebra. These data indicate that spinal DXA and spinal QCT provide comparable prediction of vertebral strength, but that a substantial proportion (typically 40%) of the variability in vertebral strength is unaccounted for by BMD measurements, Ultrasonic measurements at the calcaneus are poor predictors of vertebral strength in vitro, and ultrasound does not add predictive information independently of BMD, These findings contrast with emerging clinical data, suggesting that calcaneal ultrasound may be a valuable predictor of vertebral fracture risk in vivo, A possible explanation for this apparent discrepancy between in vivo and in vitro findings could be that current clinical ultrasound measurements at the calcaneus reflect factors that are related to fracture risk but not associated with bone fragility

Aging changes in vertebral morphometry

We analyzed the vertebral morphometry of healthy premenopausal women and their changes with age and menopause in order to better define the reference population for the clinical and epidemiological evaluation of vertebral fractures. Vertebral morphometry has been performed on lateral thoracic and lumbar spine films from 50 premenopausal and 76 postmenopausal normal women, age range 39-74 years. Vertebral heights and the anterior height/posterior height ratio are significantly lower in postmenopausal compared with premenopausal women. Vertebral anterior height decreases about 1.5 mm/year, whereas middle and posterior height decreases about 1.3 and 1.2/mm year, respectively. A statistically significant reduction of vertebral heights by around 1 mm/vertebra was observed in postmenopausal (n = 16) compared with premenopausal women (n = 20) of the same age (P < 0.05). The results demonstrate that vertebral heights are lower with advancing age and menopause and that the vertebral heights difference in elderly people is not only the consequence of a cohort effect. The results also contribute to better defining the reference population to be chosen for evaluating vertebral deformation

Non Destructive Characterization of Cortical Bone MicroDamage by Nonlinear Resonant Ultrasound Spectroscopy

The objective of the study was to evaluate the ability of a nonlinear ultrasound technique, the so-called nonlinear resonant ultrasound spectroscopy (NRUS) technique, for detecting early microdamage accumulation in cortical bone induced by four-point bending fatigue. Small parallelepiped beam-shaped human cortical bone specimens were subjected to cyclic four-point bending fatigue in several steps. The specimens were prepared to control damage localization during four-point bending fatigue cycling and to unambiguously identify resonant modes for NRUS measurements. NRUS measurements were achieved to follow the evolution of the nonlinear hysteretic elastic behavior during fatigue-induced damage. After each fatigue step, a small number of specimens was removed from the protocol and set apart to quantitatively assess the microcrack number density and length using synchrotron radiation micro-computed tomography (SR-µCT). The results showed a significant effect of damage steps on the nonlinear hysteretic elastic behavior. No significant change in the overall length of microcracks was observed in damaged regions compared to the load-free control regions. Only an increased number of shortest microcracks, those in the lowest quartile, was noticed. This was suggestive of newly formed microcracks during the early phases of damage accumulation. The variation of nonlinear hysteretic elastic behavior was significantly correlated to the variation of the density of short microcracks. Our results suggest that the nonlinear hysteretic elastic behavior is sensitive to early bone microdamage. Therefore NRUS technique can be used to monitor fatigue microdamage progression in in vitro experiments.BONUS_07BLAN019

Finite element analysis of idealised unit cell cancellous structure based on morphological indices of cancellous bone

Human bones can be categorised into one of two types—the compact cortical and the porous cancellous. Whilst the cortical is a solid structure macroscopically, the structure of cancellous bone is highly complex with plate-like and strut-like structures of various sizes and shapes depending on the anatomical site. Reconstructing the actual structure of cancellous bone for defect filling is highly unfeasible. However, the complex structure can be simplified into an idealised structure with similar properties. In this study, two idealised architectures were developed based on morphological indices of cancellous bone: the tetrakaidecahedral and the prismatic. The two architectures were further subdivided into two types of microstructure, the first consists of struts only and the second consists of a combination of plates and struts. The microstructures were transformed into finite element models and displacement boundary condition was applied to all four idealised cancellous models with periodic boundary conditions. Eight unit cells extracted from the actual cancellous bone obtained from micro-computed tomography were also analysed with the same boundary conditions. Young’s modulus values were calculated and comparison was made between the idealised and real cancellous structures. Results showed that all models with a combination of plates and struts have higher rigidity compared to the one with struts only. Values of Young’s modulus from eight unit cells of cancellous bone varied from 42 to 479 MPa with an average of 234 MPa. The prismatic architecture with plates and rods closely resemble the average stiffness of a unit cell of cancellous bone