Abstract
Trabecular bone is a multiscale hierarchical composite material that is known to display time-dependant properties. However, most biomechanical models treat this material as time independent. Time-dependant properties, such as creep and relaxation, are thought to play an important role in many clinically relevant orthopaedic issues: implant loosening, vertebral collapse, and non-traumatic fractures. In this study compressive multiple-load-creep-unload-recovery (MLCUR) tests were applied to human trabecular bone specimens.
15 female femoral heads were harvested, with full ethical approval and patient consent, at the time of total hip replacement. Central cores were extracted and cut parallel under constant irrigation. Specimens were embedded in end caps using surgical cement, an epoxy tube was secured around the end caps and filled with phosphate buffered saline (PBS) to ensure the specimens remained hydrated throughout. Embedded samples were scanned by microCT (SkyScan 1172, Bruker) at a resolution of 17µm to determine microarchitecture. Bone volume fraction (BVF) was used to represent microarchitecture. Specimens had an effective length of 16.37mm (±1.90SD) with diameter of 8.08mm (±0.05SD), and BVF of 19.22% (±5.61SD).
The compressive MLCUR tests were conducted at 5 strain levels, 2000µε, 4000µε, 6000µε, 8000µε and 10000µε. At each strain level, the load required to maintain each strain was held for 200s (creep) then unloaded to 1N for 600s (recovery). The instantaneous, creep, unloading and recovered strains can be easily obtained from the strain-time curves. Stress-strain plots revealed the Young's modulus. Data was modelled using line of best fit with appropriate curve fitting. R2 values were used to indicate association. Mechanical testing demonstrated the expected time independent relationship between BVF and stiffness: higher stiffness was found for specimen with higher BVF and this was consistent for all strain levels.
Creep strain was found to depend on instantaneous strain and BVF. At low levels of instantaneous strain, there was a greater amount of creep strain in low BVF samples (R2 = 0.524). This relationship was no longer apparent at higher strain levels (R2 = 0.058). Residual strain also depended on the applied instantaneous strain and BVF: at low levels of strain, residual strain was similar with all BVF (R2 = 0.108) and at high levels of strain, residual strain was greater in low BVF samples (R2 = 0.319). The amount of instantaneous strain applied to each sample is constant, variations in stiffness result in different applied loads. In low BVF bone, the stiffness is also low, therefore the stress required to reach designed strain is also lower: yet, there is more creep and less recovery.
We have demonstrated that even at loads below recognised yield levels, time-dependence affects the mechanical response and residual strain is present. In cases of low BVF, deflection due to creep, and increased irrecoverable strain could have clinically relevant consequences, such as implant loosening and vertebral collapse. The role of time-dependant properties of bone is seldom considered. This data could be developed into a constitutive model allowing these time-dependant behaviours to be incorporated in finite element modelling, leading to better predictions of implant loosening, especially for lower quality bone.
