From Tension to Compression: Asymmetric Mechanical Behaviour of Trabecular Bone’s Organic Phase
From Tension to Compression: Asymmetric Mechanical Behaviour of Trabecular Bone's Organic Phase
SHUQIAO XIE 1 2
ROBERT J. WALLACE 0 1
ANTHONY CALLANAN 1 2
PANKAJ PANKAJ 1
0 Orthopaedics and Trauma, The University of Edinburgh , Chancellor's Building, Edinburgh EH16 4SB , UK
1 ing, Institute for Bioengineering, The University of Edinburgh , Faraday Building, The King's Buildings, Edinburgh EH9 3DW , UK. Electronic mail:
2 School of Engineering, Institute for Bioengineering, The University of Edinburgh , Faraday Building, The King's Buildings, Edinburgh EH9 3DW , UK
-Trabecular bone is a cellular composite material comprising primarily of mineral and organic phases with their content ratio known to change with age. Therefore, the contribution of bone constituents on bone's mechanical behaviour, in tension and compression, at varying load levels and with changing porosity (which increases with age) is of great interest, but remains unknown. We investigated the mechanical response of demineralised bone by subjecting a set of bone samples to fully reversed cyclic tension-compression loads with varying magnitudes. We show that the tension to compression response of the organic phase of trabecular bone is asymmetric; it stiffens in tension and undergoes stiffness reduction in compression. Our results indicate that demineralised trabecular bone struts experience inelastic buckling under compression which causes irreversible damage, while irreversible strains due to microcracking are less visible in tension. We also identified that the values of this asymmetric mechanical response is associated to the original bone volume ratio (BV/TV).
Demineralised bone; Inelastic buckling; Stiffness reduction; Bone volume ratio
With increasing ageing population, which is known
to cause deteriorated bone quality, understanding the
mechanical response of bone to loads has assumed
increased importance. Bone is subjected to a wide
range of loading regimes that include tension,
compression and shear. Evaluation of the mechanical
behaviour of bone has been the subject of numerous
studies in which its elastic properties,22,36 its yielding
and post elastic behaviour,2,26,39 its time dependent
response to loading8,29,30,49 and its response to cyclic
and fatigue loading11,12,17,19,44 have been considered.
For trabecular bone, it is now recognised that its
elastic moduli can be reasonably well predicted from
the bone volume to total volume ratio (BV/TV) and
indices of its microarchitecture such as mean intercept
length and star volume distribution fabric
tensors36,43,50; and its elastic limit in the strain space is
fairly isotropic and largely independent of BV/TV.3,26
A few studies have used cyclic loading to understand
the fatigue behaviour of cortical11,12,17 and trabecular
bone,19,44 however apart from few studies,11,12 all
others have been in either only in tension17 or only in
compression.19,44 A few trabecular bone studies19,44
have also successfully related its strain response under
cyclic loading to indices of bone micro-structure.
Bone is a composite material which comprises of a
mineral phase (mainly carbonated hydroxyapatite),
organic phase (mostly type I collagen) and water
assembled into a complex, hierarchical structure.16,48
Mechanically collagen and mineral play very different
roles—the elastic modulus of collagen is much lower
than that of the hydroxyapatite, but the former is three
orders of magnitude tougher.38 While the mineral
provides the stiffness, it is much more brittle than the
collagen. Therefore mineral-collagen ratio (known to
increase with age in humans1) has a role in the
mechanical behaviour of trabecular bone. For
example, evaluation of elastic modulus of bone from
different species has shown that it increases with mineral
content.18 Tests conducted on demineralised compact
bovine humeral diaphyseal bone samples show that
they had an elastic modulus of around 600 MPa9;
untreated cortical bone (extracted samples without any
chemical treatment) on the other hand is reported to
have an elastic modulus in excess of 6 GPa.18 Study of
the mechanical behaviour of bone’s constituents,
therefore, is important in several contexts. Firstly the
mechanical behaviour of the constituents helps in the
understanding of the bone behaviour as a
composite.9,20,28 This in conjunction with changing mineral
collagen ratio and porosity with age gains significant
importance.28 The effect of the contribution of bone
constituents is not only on its elastic modulus9 but also
on its strength,15 and its behaviour under cyclic
loads.35 Secondly, it has been suggested that data on
the mechanical properties of collagen has clinical
relevance in the early stages of fracture repair before bone
mineralisation occurs.9 Thirdly, though not considered
in this study, the two main constituents of bone are
known to play very different roles in its
To evaluate the mechanical behaviour of the
organic phase, a number of previous studies have
undertaken mechanical tests on demineralised bone;
almost all of which have been on cortical
bone.7,9,10,14,34,35 Evaluation of elastic modulus and
strength through monotonically increasing loading in
tension9,10,14 or compression34 has been the focus of
most studies. Bone and consequently its constituents
are subjected to cyclic loading.44 Novitskaya et al.,
conducted cyclic loading tests on demineralised
cortical bone in three different directions and showed that
cortical bone has anisotropic cyclic behaviour with
larger energy dissipation in transverse directions.35
Loading cycles in this cited study were confined to
compression although the contribution of the organic
phase to tension has been noted to be much more
significant.10 Studies conducted on the mechanical
behaviour of demineralised trabecular bone are
limited, confined to monotonic loading in compression
and generally conducted with an aim to evaluate elastic
modulus and strength.15 These limited studies indicate
that there is considerable gap in understanding the
mechanical behaviour of the organic phase of bone
under cyclic loading at different load levels.
This study aims to analyse the mechanical
behaviour of demineralised trabecular bone in tension and
compression using a novel experimental protocol.
Firstly it aims to evaluate the response due to fully
reversed cyclic loading to examine how samples behave
in tension and compression. Such tests have not been
previously conducted for demineralised bone and are
rare even for untreated bone.11,12 Secondly it aims to
evaluate how the cyclic response varies with
application of different load levels. Few tests conducted on
untreated bone (and limited to compression) have
shown that the response varies with load level.44 Lastly
by undertaking a micro-CT (lCT) of samples prior to
demineralisation this study aims to consider how the
response is influenced by the original BV/TV of
trabecular bone. Our hypothesis is that the mechanical
behaviour of demineralised trabecular bone has
tension compression asymmetry, varies with load levels
and is associated with its porosity.
MATERIALS AND METHODS
Fresh proximal tibia, from bovine (under 30 months
old when slaughtered), were obtained from a local
abattoir and stored at 2 20 C until utilised. The
bones were allowed to thaw at room temperature
before bone cores were extracted along its principal axis,
using diamond coring tools (Starlite, Rosement, IL,
USA). A low speed rotating saw (Buehler, Germany)
was used to create parallel sections and to trim growth
plates if they were present. All coring and cutting were
conducted in a water bath to avoid excessive heat
generation. The cylindrical bone samples (n = 5) had
a diameter of 10.6 ± 0.1 mm and mean height of
22.1 ± 0.7 mm.
Bone marrow was removed from each sample using
a dental water jet (Interplak, Conair) with tap water at
room temperature.27 All the samples were then
centrifuged at 2000 r.p.m for 2 h to remove any residual
marrow.41 All the samples were scanned using lCT
scanner (Skyscan 1172, Bruker, Kontich, Belgium) at a
resolution of 17.22 lm and the system’s software was
used to evaluate bone volume to total volume ratio
(BV/TV) of the bone, which was found to be in the
range 21–32%. Scanning parameters used were: source
voltage 54 kV, current 185 lA, exposure 885 ms with a
0.5 mm aluminium filter between X-ray source and the
sample. The image quality was improved by using two
After scanning, demineralisation was conducted by
submerging samples in 20 ml 0.6 N hydrochloric acid
(HCl) at room temperature assisted by a racking
system. The solution was changed daily31 for 2 weeks
after which the completeness of demineralisation was
verified using lCT scanning. All samples in this study
were found to be fully demineralised in 2 weeks. It
should be noted that although EDTA solution has
been previously used to demineralise bone, we used
HCl because the process is much quicker and has been
employed successfully in previous studies.10,13,15,16
Samples were fixed into end-caps (Fig. 1a) using
bone cement (Simplex, Stryker, UK) with the
assistance of a custom made alignment tool in order to
minimise end-artefacts during testing.23 The effective
length (19.1 ± 0.7 mm) of each sample was calculated
as the length of the sample between the end-caps plus
half the length of the sample embedded within the
endcaps.23 Each sample was placed in an epoxy tube filled
with PBS to ensure that they remained hydrated at all
stages of mechanical testing.
Each sample was subjected to reversible cyclic
loading by means of an Instron material testing
machine (50 N load cell, Model 3367). Samples were
subjected to 5 loading cycles varying from tension to
compression to the same axial force amplitude after
which the load level was increased (Fig. 1b). Five load
levels were selected: 0.2, 0.4, 0.6, 0.8 and 1.0 N
(corresponding to average axial stress varying from 2.27 to
11.33 kPa). The choice of 5 cycles at each load level
was based on preliminary tests, which showed that
most variation in strain (or displacement) response
occurred in the first five cycles, after which this
variation was very small. Our preliminary tests also showed
that initiating the first cycle in tension or compression
made little difference to the strain response. Cyclic
loads were applied under strain control, i.e., the strain
was slowly increased till the required load level was
achieved. A very slow 0.1%/s strain-based loading rate
was used to minimise the heat generation (e.g.,
demineralised samples took from 1 to 11 s to attain a load
of 0.2 N).
The stress–strain curves for the first cycle at the
lowest load level (0.2 N) and the highest load level
(1.0 N) are shown in Figs. 2a and 2b, respectively. It is
apparent that the resulting strain response is associated
with the sample’s original BV/TV; samples with higher
BV/TV experience much lower strain in comparison to
the more porous samples. For example, the sample
with BV/TV = 32% experienced only 0.14% strain in
tension compared to 0.82% strain observed for sample
with BV/TV = 21% (Fig. 2a). Comparing tension
(taken as positive) and compression for the first load
cycle, it can be seen that the differences in axial strain
magnitude is small for samples with higher BV/TV and
the difference increases with increasing porosity and
with increasing load level (Fig. 2b). It is clear that the
mechanical behaviour of demineralised trabecular
bone is strongly dependent on its original BV/TV.
This trend is consistent for all cycles and at all load
levels. This is illustrated in Figs. 2c and 2d which show
the cyclic loading history for two typical samples; the
insets show load application. For clarity, only the first
and fifth cycles for each load level are shown.
Comparing Figs. 2c and 2d, it is apparent that the higher
BV/TV sample experiences lower strains at the same
load level (i.e., it is stiffer) for both tension and
compression. Nonlinearity of the stress–strain response is
also more pronounced for the lower BV/TV sample.
This BV/TV dependence was observed with all the
Another apparent observation from the shape of the
curves in Fig. 2 is that the demineralised samples
become stiffer with increasing stress in tension and
exhibit stiffness reduction with increasing stress in
compression; this was observed at all load levels, in all
cycles and for all tested samples. More importantly,
the transition from tension to compression is smooth
for every load level (Figs. 2c and 2d); this was observed
for all the samples tested. Further examination of the
loading and unloading curves in compression indicates
that buckling is not entirely elastic. Figure 2 clearly
indicates that the original BV/TV plays an important
role in the cyclic response of demineralised trabecular
bone. It is important to note that all samples were
extracted in the same direction, from similar
anatomical site, from cattle of about the same age and
employing the same demineralisation process i.e. by
using HCl solution.
To further evaluate the cyclic response we examined
ratcheting strain and dissipated strain energy density in
tension (DSEDT) and compression (DSEDC), as shown
in Fig. 3, for all load levels and for all samples. We also
considered the secant moduli, defined as four different
slopes for one complete cycle of loading and unloading in
tension and compression as shown in Fig. 3. Ratcheting
strain can be defined as the average of peak strain in
tension etpeak taken as positive and compression ecpeak
taken as negative at the same load level (Fig. 3). A
nonzero ratcheting strain only occurs when the mechanical
properties in tension and compression are different.40
We first considered the most porous sample (with BV/
TV of 21%) for demonstrating the variation in
ratcheting strain (er) in different cycles and at different load
levels (Fig. 4a). Ratcheting strain was consistently
negative, which implies that the demineralised samples
experience larger strain in compression than in tension
at the same load level (Fig. 4a). Even for this most
porous sample the ratcheting strain only increases
marginally with increasing cycle number; while the
increase with load level is nonlinear and much more
significant. Next we considered the ratcheting strain for all
five samples in the first load cycle for all load levels. As
expected, the magnitude of ratcheting strains is much
larger for samples with lower BV/TV (Fig. 4b). Also the
ratcheting strains are consistently negative and their
magnitude increases rapidly with load level (Fig. 4)
indicating that the organic phase has a much better load
bearing capability in tension without significant
additional strains than in compression.
BV/TV = 21%
BV/TV = 23%
BV/TV = 25%
BV/TV = 29%
BV/TV = 32%
DSEDT and DSEDC were calculated by integrating
corresponding areas, as discussed and the results are
shown in Fig. 5 for the first cycle for each load level.
Both DSEDT and DSEDC increase with increasing
load levels, and dissipated strain energy values and
their rate of change increases with decreasing BV/TV
(Fig. 5). Energy dissipation in compression was found
to be consistently higher than in tension. This is
because the samples experience not only lower strains in
tension but also because tensile strains do not have
large irreversible component. On the other hand, in
compression the samples experience large strains and
these include relatively large irreversible strains due to
inelastic buckling of collagen struts.
As discussed, four secant moduli were evaluated
(Fig. 6): Eltoading, Etunloading, Eloading and Eunloading. These
are illustrated for samples with the largest and smallest
BV/TV in Fig. 6. As expected, the porous sample has
smaller secant moduli in comparison to the denser
sample (i.e. Eltoading ¼ 0:28 MPa for BV/TV = 21%
compared with 1.66 MPa for BV/TV = 32%). The
unloading modulus is always higher than the loading
modulus in both tension and compression. With
increasing load level Etunloading remains almost constant,
while Eloading decreases slightly. In contrast to tension,
Eloading and Eunloading both decrease dramatically with
increasing load level. This interesting trend, followed
by all the samples, indicates that while compression
leads to significant irreversible strain with increasing
load in the demineralised microstructure of bone, this
is relatively small in tension.
This study considered fully reversible
tension–compression cyclic loading tests on five demineralised
trabecular bone samples with BV/TV ranging from 21 to
32%. Samples were subjected to five different load
levels (0.2 to 1 N at 0.2 N interval denoted as load level
1–5), and five cycles were applied at each load level.
The asymmetric responses of the organic phase of
trabecular bone were found when it loaded cyclically
from tension to compression. The study shows
demineralised trabecular microstructure stiffens in tension
and undergoes stiffness reduction in compression. The
trend of the asymmetric mechanical response is
associated to the original BV/TV.
In previous studies the shape of loading curve in
compression for untreated trabecular bone have shown
a reduced load carrying capacity with increasing
load21,25,32 but unloading demonstrates that much of
this is due to irrecoverable plastic strain.24,33,37 It is
perhaps not improper to infer that this is due to the
damage and failure of the mineral phase. Stiffness
reduction in compression has been previously observed
for demineralised cortical bone.35 For trabecular bone,
however, the stiffness reduction is likely to be
accentuated due to elastic and inelastic buckling of
demineralised trabecular struts. Previous tests in tension on
demineralised cortical bone have shown stiffening with
load increase,9,14 similar to what was observed in this
study. For untreated bone, however, it is stiffness
reduction (rather than stiffness increase) that has been
previously observed in tension as well,25 which can be
attributed to failure of the mineral-collagen interface.
To the best of our knowledge, there have been no
previous tests on demineralised bone, cortical or
trabecular that have considered fully reversible cyclic
loading. However, similar compression-softening and
stretch-stiffening have been previously observed in
semi-flexible biopolymers45 where it has been suggested
that this asymmetric response in tension and
compression is caused by the bending and/or buckling
stress in fibres under compression, force for which is
much lower than the load required for straightening
and stretching. This behaviour is akin to a rectangular
steel frame braced along one diagonal and subjected to
shear.5 When the diagonal brace is in tension the
deformation of the frame is limited but when it is in
compression its inelastic buckling results in larger
deformation and residual deformations.
Observed irreversible strain, we believe, is due to
inelastic buckling in compression as stated above and
has implications for old/osteoporotic bone. Ageing
bone not only leads to reduction in BV/TV but also
relative increase in mineral to collagen ratio.1
Consequently there is increased reliance on the limited
organic phase to provide ductility; our tests show that the
demand to sustain increasing magnitudes of strain by
the organic phase increases dramatically in
compression with decreasing BV/TV. At the macro scale the
behaviour of bone in tension and its fracture toughness
have been seen as key to bone fracture46 while our
study indicates that possible failure due to inelastic
trabecular buckling in compression needs greater
consideration. Mineral deposition increases the elastic
modulus of bone and hence the buckling load, however
once bucking is initiated (which is more likely in low
BV/TV bone) then it is likely to be inelastic due to
limited contribution of mineral in tension. Buckling
has been previously proposed as the probable cause of
failure for vertebral trabecular bone.4,42 Our study
demonstrated that this buckling of trabeculae could be
initiated from organic phase of trabecular bone. This
study also shows that the possibility of hip fractures in
the elderly occurring due to normal physiological
activities, such as level walking, resulting in the
individual falling down (rather than the fracture being
caused by a fall) does exist.47
A few studies have attempted to develop predictive
models of the mechanical behaviour of bone based on
the properties of the mineral, organic phase and their
interaction at either the solid phase level20 or in terms
of demineralised and deproteinised macro level.28
These cited studies have been limited to the prediction
of elastic properties and have not distinguished
between compression and tension. Our study can help
take these predictive models forward. It is important to
note that many of the findings in this study were only
made possible by the novel experimental protocol
which permitted evaluation of demineralised samples
at different load levels and in both tension and
Our work suffers from a number of limitations.
Firstly, all the tests were conducted at room
temperature; creep behaviour has been reported to be
temperature dependent.6 Secondly, the stress–strain
responses were measured directly from the machine
rather than using extensometer, but the aim of the
paper is to compare the trends—response to reversible
cyclic loading from tension to compression and across
samples with different BV/TV prior to
demineralisation. Lastly, since we only considered a limited number
of samples, a statistical analysis that considers the
influence of different variables was not possible. These
trends, we believe, are real despite the limitations.
This study, we believe, makes several important
contributions. Firstly it develops a novel experimental
protocol that can evaluate the mechanical response of
materials under cyclic loads that range from tension to
compression and are of varying magnitudes. The study
will help in the development of composite models from
the mechanical response of its constituents. We have
shown that the behaviour of the organic phase of
trabecular bone has tension–compression asymmetry
and varies with load levels and porosity. Interestingly,
the transition from tension to compression is found to
be smooth for all load levels. Collagen struts stiffen in
tension while they undergo inelastic bucking in
compression. These findings may explain, at least partially,
the reasons for non-traumatic fractures in the elderly
as increasing bone porosity and reduced collagen to
mineral ratio will result in higher risk of buckling
We grateful acknowledge the financial support of
EPSRC [Grant EP/K036939/1].
CONFLICT OF INTEREST
The authors confirm that there is no conflict of
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