6 research outputs found
Linear viscoelasticity - bone volume fraction relationships of bovine trabecular bone
Trabecular bone has been previously recognized as time-dependent (viscoelastic) material, but the relationships of its viscoelastic behaviour with bone volume fraction (BV/TV) have not been investigated so far. Therefore, the aim of the present study was to quantify the time-dependent viscoelastic behaviour of trabecular bone and relate it to BV/TV. Uniaxial compressive creep experiments were performed on cylindrical bovine trabecular bone samples ([Formula: see text] ) at loads corresponding to physiological strain level of 2000 [Formula: see text] . We assumed that the bone behaves in a linear viscoelastic manner at this low strain level and the corresponding linear viscoelastic parameters were estimated by fitting a generalized Kelvin–Voigt rheological model to the experimental creep strain response. Strong and significant power law relationships ([Formula: see text] ) were found between time-dependent creep compliance function and BV/TV of the bone. These BV/TV-based material properties can be used in finite element models involving trabecular bone to predict time-dependent response. For users’ convenience, the creep compliance functions were also converted to relaxation functions by using numerical interconversion methods and similar power law relationships were reported between time-dependent relaxation modulus function and BV/TV
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