Time Dependent Behaviour of Trabecular Bone at Multiple Load Levels
Time Dependent Behaviour of Trabecular Bone at Multiple Load Levels
A. HAMISH R. W. SIMPSON 0 1
PANKAJ PANKAJ 1
0 Department of Orthopaedics, The University of Edinburgh , Chancellor's Building, Edinburgh EH16 4SB , UK
1 engineering, School of Engineering, The University of Edinburgh , King's Buildings, Edinburgh EH9 3DW , UK. Electronic mail:
2 Institute for Bioengineering, School of Engineering, The University of Edinburgh , King's Buildings, Edinburgh EH9 3DW , UK
-The deformation of bone when subjected to loads is not instantaneous but varies with time. To investigate this time-dependent behaviour sixteen bovine trabecular bone specimens were subjected to compressive loading, creep, unloading and recovery at multiple load levels corresponding to apparent strains of 2000-25,000 le. We found that: the time-dependent response of trabecular bone comprises of both recoverable and irrecoverable strains; the strain response is nonlinearly related to applied load levels; and the response is linked to bone volume fraction. Although majority of strain is recovered after the load-creep-unloadrecovery cycle some residual strain always exists. The analysis of results indicates that trabecular bone becomes stiffer initially and then experiences stiffness degradation with the increasing load levels. Steady state creep rate was found to be dependent on applied stress level and bone volume fraction with a power law relationship.
Creep-recovery; Viscoelastic; Bone volume fraction; Steady state creep rate; Creep compliance
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Trabecular bone, a composite cellular material with
hierarchical structure, is generally treated as
time-independent in biomechanical models.24 But in reality its
response to mechanical loads is known to be
time-dependent.5,13,19,23,29 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,26
to predict implant loosening due to cyclic load,30 to
understand progressive vertebral deformity,25 and
preclinical evaluation of total joint replacements.30
Consequently, trabecular bone’s time-dependent behaviour
has great clinical relevance, but it has received
relatively little attention.
A few studies have attempted to relate the creep
behaviour with micro-architecture of bone. Kim et al.
conducted one cycle of load-creep-unload-recovery
experiments in which they applied a load
corresponding to 2000le and found that the samples with thinner
trabeculae and greater connectivity were associated
with increased logarithmic creep rate.13 Novitskaya
et al. reported the changes in micro-architectural
indices evaluated from micro computed tomography
(lCT) before and after the creep; the study found that
creep induced changes in trabecular separation and
structural model index.23 Novitskaya et al. also found
that the steady state creep rate was higher and the final
creep strain was larger for samples with low bone
volume fraction (BV/TV) (or apparent density).23
BV/TV or apparent density have been extensively
employed to evaluate the time-independent stiffness of
bone,11,14 which is then used in subject-specific
models.33 Similar relationships between BV/TV and
timedependent response will permit their application in
computational simulations where modelling
time-dependent behaviour is important e.g., implant
loosening. These relationships need to be considered at
multiple loads to incorporate any load-level
dependence. Manda et al. conducted creep experiments at a
single load level (corresponding to a small apparent
strain of 2000 le) and reported the relationships
between BV/TV and linear viscoelasticity for
trabecular bone.19
Previous studies have shown that under static
conditions (or very slow strain rates) the strain in trabecular
bone increases non-linearly with applied loads.10,16,17,21
However, time dependent behaviour with changing load
levels has received limited attention. A few previous
studies have considered multiple load levels but
different loads were applied to different specimens i.e., each
specimen was subjected to a single load level.4,5,20
Bowman et al. found a strong power law relationship
between the steady state creep rate and the applied
stress level, but when they included apparent density
into the relation, the fit did not improve, in fact the r2
value decreased.5 Also, Moore et al. related steady state
creep rate to applied stress level, but this study also
conducted cyclic loading tests on each sample at a single
stress level.20 Multiple load levels were considered by
one recent study in which a mathematical model for the
recoverable (or elastic) strain18 with respect to load
levels was developed; however, while this study alluded to
BV/TV relationship with nonlinear viscoelasticity it did
not develop it.
In summary, previous studies have shown that
under static loading trabecular bone has a non-linear
stress–strain behaviour and its time-independent
e (...truncated)