Proc IMechE Part H:
J Engineering in Medicine
? IMechE 2012
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Design and validation of bending test
method for characterization of
miniature pediatric cortical bone
Carolyne I Albert1,2, John Jameson1and Gerald Harris1,2
Osteogenesis imperfecta is a genetic disorder of bone fragility; however, the effects of this disorder on bone material
properties are not well understood. No study has yet measured bone material strength in humans with osteogenesis
imperfecta. Small bone specimens are often extracted during routine fracture surgeries in children with osteogenesis
imperfecta. These specimens could provide valuable insight into the effects of osteogenesis imperfecta on bone material
strength; however, their small size poses a challenge to their mechanical characterization. In this study, a validated minia-
ture three-point bending test is described that enables measurement of the flexural material properties of pediatric cor-
tical osteotomy specimens as small as 5mm in length. This method was validated extensively using bovine bone, and the
effect of span/depth aspect ratio (5 vs 6) on the measured flexural properties was examined. The method provided rea-
sonable results for both Young’s modulus and flexural strength in bovine bone. With a span/depth ratio of 6, the median
longitudinal modulus and flexural strength results were 16.1 (range: 14.4–19.3)GPa and 251 (range: 219–293)MPa,
respectively. Finally, the pilot results from two osteotomy specimens from children with osteogenesis imperfecta are pre-
sented. These results provide the first measures of bone material strength in this patient population.
Material properties, flexural, osteogenesis imperfecta, pediatric, bone
Date received: 10 May 2012; accepted: 12 September 2012
Osteogenesis imperfecta (OI), or brittle bone disease, is
a genetic disorder of bone fragility. This fragility is
attributed to a combination of bone mass deficiency
and compromised material properties. No data, how-
ever, is yet available to describe bone material strength
in OI. Small bone fragments that are routinely extracted
during fracture repair and corrective osteotomy proce-
dures in young individuals with OI could be useful for
bone material characterization. Unfortunately, their
small size, that is, often not more than 5mm in length,
renders these fragments unsuitable for typical mechani-
cal characterization protocols, which require machined
bone specimens that are a few centimeters long.1–5In
fact, few studies6,7have explored the material behavior
of pediatric bones in general, due to a scarcity of speci-
mens available for testing. For this reason, a validated
and appropriately sized test method enabling the mea-
surement of material strength of miniature bone
specimens could be useful in characterizing pediatric
bones, such as those from children with brittle bones.
The characterization of OI bone material and struc-
tural behavior can provide valuable insight toward
improved care for children with this disorder. For
example, finite element models have been developed to
assess stress distribution and fracture risk in OI during
daily activities.8,9These models could be useful in the
development of treatment strategies to reduce fracture
occurrence in individuals with OI; however, the ability
1Orthopaedic and Rehabilitation Engineering Center, Department of
Biomedical Engineering, Marquette University, Milwaukee, WI, USA
2Shriners Hospitals for Children, Chicago, IL, USA
Carolyne I Albert, Orthopaedic and Rehabilitation Engineering Center,
Marquette University, PO Box 1881, 735 N. 17th Street, ASF Suite 105,
Milwaukee, WI 53201-1881, USA.
of these models to assess fracture risk remains hindered
by a shortage of bone material property data in OI.
The most considerable challenge in mechanical char-
acterization of pediatric osteotomy bone fragments is
their small size, that is, often as small as 5mm in length.
Previously described techniques that are suitable for
characterizing the mechanical properties of these minia-
ture bone specimens include nanoindentation10–13and
micromechanical tests.14–16Each of these techniques
presents unique advantages and limitations.
During nanoindentation, a diamond-tip indenter is
compressed into the surface of a polished specimen to
measure local material properties, specifically, Young’s
modulus and hardness. The small scale of the indents,
that is, typically a few hundred nanometers deep and a
few microns wide,11,13,17enables measurement of bone
material properties within osteonal bone or individual
local measurements that vary considerably within a sin-
gle specimen,18–21and it does not offer a direct measure
of material strength.
A few studies have characterized flexural bone mate-
rial properties using ‘‘microspecimens’’ (e.g. machined
beams 120mm 3 120mm 3 1.5mm in size).14–16The
described approach could be suitable for testing minia-
ture osteotomy specimens. These microspecimens, how-
ever, are thinner than the diameter of a typical single
secondary osteon, and they are therefore too small to
capture the heterogeneous microstructure and composi-
tion of cortical bone. Moreover, the elastic modulus esti-
mates obtained for adult human cortical bone using
microspecimens, that is, 5–7GPa,14–16tend to be much
lower than the generally accepted values, that is, typically
15–20GPa.4,22The size-dependency of human cortical
bone elastic modulus measurements in bending was
examined for beam depths (thicknesses) between 100 and
1000mm, with a fixed span/depth aspect ratio of 10.16A
beam depth of approximately 560mm or greater pro-
vided a more or less constant modulus result of 15GPa,
whereas this measure decreased for beam depths less
than 320mm. A depth of 560mm would be appropriate
for characterizing pediatric osteotomy specimens. With
this specimen depth, a span/depth aspect ratio of 10
would require a span length of 5.6mm. Unfortunately,
the surgical pediatric bone specimens that have been col-
lected to date are often not greater than 5mm in length;
therefore, a maximum span length of 4mm would be
more appropriate for their characterization.
The objectives of this study are to describe a vali-
dated three-point bending test method suitable for mea-
surement of the elastic modulus, yield stress, yield
strain, and flexural strength, of small cortical osteot-
omy specimens obtained by routine surgery. The valida-
tion of the test method was performed with 39 beam
specimens of bovine bone having two span/depth aspect
ratios, 5 and 6, and two orientations, that is, parallel
and perpendicular to the long bone axis. The method
was further validated with acrylic beam specimens.
Finally, the described method was used to measure
flexural bone material properties of cortical osteotomy
specimens obtained from two children with OI.
A three-point bending apparatus was designed to char-
acterize the mechanical properties of miniature beams
of cortical bone, approximately 5mm in length. The
potential sources of error were investigated carefully, in
light of the small scale of the specimens and that of
their maximum deflections during testing. A multistage
approach was taken to validate the test setup, including
validating load and deflection measurement, identifying
and minimizing potential sources of experimental error,
and assessing the effectiveness of the setup in measur-
ing the modulus of elasticity (E), yield strength (sy),
yield strain (ey), and flexural strength (sfm) of bone
Jig design and testing system
A custom-designed, three-point bending jig was built
for this study (Figure 1). The loading nose and supports
consisted of 1/16-in (1.6mm) diameter stainless steel
pins that were fixed into grooves machined in upper
and lower aluminum platens using cyanoacrylate. A
constant bottom span length (L) of 4mm (actual mea-
surement 3.973mm) was chosen to accommodate the
length of pediatric osteotomy specimens that were col-
lected as part of another study. The jig was mounted
onto an electromechanical testing system (Model 3345;
Instron?, Norwood, MA) with a 50-N capacity load
cell (Model 2519-102; Instron).
The following potential sources of experimental
error were identified: load measurement error, displace-
ment measurement error, and misalignment between
the loading nose and supports. Special care was taken
to address these sources of error as follows:
(a) Misalignment between the loading nose and sup-
ports: The top and bottom platens were aligned
using four stainless steel dowel pins 1/16-in
(1.6mm) diameter, which were removed prior to
testing (Figure 1). These alignment pins helped to
ensure that the loading nose was parallel to and
centered between the supports for a symmetrical
Load measurement error: The load cell calibration
was verified using calibrated weights (Christian
Becker Inc., New York). The slope of load mea-
sured versus load applied was 0.9999 (R2= 1.0),
indicating a load measurement error of approxi-
Displacement measurement error: With the electro-
Instron?), crosshead displacement is measured by
a built-in encoder. The displacement measured by
the built-in encoder provides a combined measure
of beam specimen deflection and deformation
106Proc IMechE Part H: J Engineering in Medicine 227(2)
occurring within the load frame, load cell, mount-
ing base, and three-point bending jig, that is, the
loading nose, supports, and platens (Figure 1).
Thus, the use of the encoder displacement as a
measure of midspan beam deflection would result
in compounded errors from each of these compo-
nents. To reduce this source of error, an external
linear variable differential transformer (LVDT;
Model 2601; Instron?) was incorporated in the
jig design. The displacement measured by the
external LVDT includes deformation within the
platens (platens 2 and 3), loading nose, and sup-
ports, but does not include any deformation
occurring within the load frame, load cell, and
mounting base (Figure 1). The calibration of the
LVDT was verified using gage blocks (Hoke
Measurement Systems Inc., Bloomfield, CT),
while the sensor was mounted onto the jig. The
slope of LVDT measurement versus gage block
thickness was 0.9980 (R2= 1.0), indicating an
In the original jig design, the loading nose and sup-
ports were 1/32-in (0.8mm) diameter stainless steel
pins. The compliance of the platens, loading nose and
supports, based on the load cell and external LVDT
measurements, was assessed using a stiff ‘‘dummy
specimen’’ (a 7/32-in stainless steel Allen key). With
these thinner pins, the compliance was not constant
but instead increased nonlinearly with increasing
load. This problem was resolved once these pins were
replaced with thicker ones having a 1/16-in (1.6mm)
diameter. The final compliance of the platen and 1/
16-in (1.6mm) diameter loading nose and supports,
based on the load cell and external LVDT measure-
ments, was 0.06mm/N.
Validation of the three-point bending setup with
bovine cortical bone
A cross-section of cortical bone was harvested from the
midfemoral diaphysis of a 1-year-old female cow.
Miniature rectangular cortical beams were obtained
from this cross-section using a diamond saw (IsoMet?
Low Speed Saw; Buehler?, Lake Bluff, IL) and a 0.3-
mm-thick blade. First, the cross-sections were cut into
slices, each having a thickness approximately equal to
the desired beam depth. The beams were then obtained
from these bone slices (Figure 2). The following precau-
tions were taken while cutting the beam specimen. The
diamond saw blade was thinner in the periphery, which
caused thickness variations in the machined part. More
specifically, the last corner of the bone slice to be cut
by the diamond saw had a larger thickness than the
other regions of the slice (e.g. in one slice, that differ-
ence was 27%). The region having higher thickness
than the rest of the slice was identified, marked with a
permanent marker, and excluded when machining
beams from the slice. The thickness was found to be
relatively even within the remaining regions of the
slice (after the last-cut thicker corner was removed),
with variations of 1%–2%. Each beam was machined
such that its depth was equivalent to the thickness of
the slice. Finally, when machining the beams from the
bone slices, the slices were gripped onto a 1/4-in-thick
acrylic backing to prevent bending of the slice during
Three groups of specimens were tested: T1, L1, and
L2, each having 13 beam specimens, n = 13 (Table 1).
In group T1, the beam specimens were machined such
Figure 1. Diagram of three-point bending test setup. The three-point bending jig was mounted on an electromechanical materials
testing machine, and the upper and lower platens were aligned using four dowel pins. Deflection was measured with an externally
mounted LVDT. (a) Front view of the three-point bending test assembly (not drawn to scale). (b) Top view of the lower platen
showing the bottom two rollers and the location of the four alignment pins.
Albert et al.107
that the long beam axis was transverse to the long axis
of the femoral diaphysis, whereas in groups L1 and L2,
the beam long axis was oriented parallel to the diaphy-
seal long axis (Figure 2). The beams were at least 5mm
in length and approximately 1mm in width (w). A
beam depth (d) of approximately 650mm (L/d ratio of
approximately 6) was used for groups T1 and L1. For
group L2, d was approximately 800mm (L/d ratio of
approximately 5). The beam w and d measurements
were obtained with a digital micrometer (Model 293-
340; Mitutoyo Corporation, Kanagawa, Japan). These
measurements are shown in Table 1.
The loading was applied using Bluehill 2 Software
(Instron?) in flexural loading mode. The loading con-
sisted of five cycles of preconditioning followed by a
ramp to failure. The preconditioning cycles were
applied at a crosshead displacement rate of 0.3mm/min
( \15MPa) for group T1 and 0.05–2.0N ( \30MPa)
for groups L1 and L2. The ramp to failure was applied
in displacement control, using the external LVDT to
control the displacement rate. The LVDT displacement
rate was 2 (groups L1 and T1) and 1.7mm/min (group
L2), which resulted in strain rates of 0.8%/s–1.0%/s
for all specimens. The specimens were kept hydrated
during the test using a drop of normal saline, which
was held in place by surface tension.
The force and displacement data were sampled at
100 Hz throughout the test. The flexural stress and
strain were obtained from the load and LVDT displa-
cement data using the following beam equations
3 F L
2 w d2
6 d d
where I is the cross-sectional moment of inertia of the
beam; w and d are the beam specimen width and depth,
respectively (Figure 2); L is the span between the sup-
ports; F is the applied load; d is the beam deflection at
midspan (displacement measured by the LVDT); and
sfand efare the calculated maximum tensile stress and
strain at midspan, respectively.
The following material properties were calculated
from the stress–strain curve obtained during the displa-
cement ramp to failure. The yield strength (sy) and yield
strain (ey) were determined using the 0.2% strain offset
method (Figure 3). The flexural strength (sfm) was
defined as the maximum stress on the stress–strain curve.
The energy absorbed to failure was estimated as the area
under the stress–strain curve. The modulus of elasticity
(E) was determined using the following equation
4 w d3
where m is the slope of the straight part of the load–
displacement curve. For groups L1 and L2, E was
Figure 2. Anatomical orientation and flexural loading configuration for the longitudinal and transverse beams. Dimensions shown
are specimen width (w), depth (d), and span length (L).
Table 1. Beam dimensions and anatomical orientation for each
group of bovine bone specimens (median (range)).
w (mm)d (mm)
w: beam specimen width; d: beam specimen depth.
108 Proc IMechE Part H: J Engineering in Medicine 227(2)
calculated over a load range equivalent to stresses of
50–100MPa, while for group T1, it was calculated
within the equivalent stress range of 20–30MPa.
The flexural properties were compared between
groups L1 and T1, and between groups L1 and L2
using Mann–Whitney U tests, with a significance level
of 0.05. A nonparametric method was chosen because
the normality assumption was rejected in one of the
variables (ey) for group T1, based on the Wilks–Shapiro
test. For the sake of uniformity, nonparametric statisti-
cal approach was used consistently for all analyses, and
the median and ranges were reported for all variables.
Validation of the three-point bending setup with
The three beams of acrylic were prepared using the
same specimen preparation methods as described for
the bone specimens. Each beam was tested twice non-
destructively, up to a maximum bending stress of
approximately 35MPa. The elastic modulus was
obtained from the straight part of the stress–strain
curve, that is, between stresses of 10 and 35MPa.
Pilot study—osteotomy specimens from two children
Under Institutional Review Board (IRB) approval and
informed consent, two bone specimens were obtained
from children with OI during routine osteotomy proce-
dures (IRB #10101309 from Rush University Medical
Center and #HR-2167 from Marquette University).
Specimen ‘‘OI-I’’ was obtained from the right humeral
diaphysis of an 11-year-old girl with OI type I (mild
form of the disorder), and specimen ‘‘OI-III’’ from the
Figure 3. Typical curves for (a) load–displacement and (b) flexural stress–strain data obtained from longitudinal (black) and
transverse (gray) beam specimens. Yield strength (sy) and wield strain (ey) were calculated using the 0.2% strain offset method.
Flexural strength (sfm) was determined as the maximum stress on the flexural stress–strain curve.
Albert et al. 109
right femoral diaphysis of an 8-year-old female with OI
type III (severe form). The specimens were prepared into
small beams using the same methods as described for the
bovine bone specimens. The specimen OI-I, however, was
too small to grip directly with the diamond saw chuck,
and therefore, this specimen was affixed onto a wood man-
drel using cyanoacrylate prior to cutting. These human
bone specimens were oriented such that the long beam axis
was parallel to the estimated long bone axis (based on the
curvature of the periosteal surface). Their dimensions
(Table 2) were roughly the same as those in bovine group
L1, and they were subjected to the same test methods as
described previously for that group.
stress–strain curves for typical longitudinal and trans-
verse bovine bone specimens are shown in Figure 3.
The stress–strain curves for the beams of OI bone are
presented in Figure 4. The flexural material properties
for the acrylic, bovine bone and human OI bone speci-
mens are presented in Table 3.
For the beams of bovine bone, the orientation (T1
vs. L1) had a significant effect on all measured flexural
properties (p\0.001). The median E was 60% lower
in the transverse beams (group T1) than in the longitu-
dinal beams of equivalent dimensions (group L1).
Similarly, the medians sy, ey, sfm, and energy to failure
were 69%, 25%, 77%, and 95% lower, respectively, for
the transverse beams than for the longitudinal ones.
When comparing results from groups L1 vs. L2, the
following observations were made. There was no signif-
icant difference in E between these two groups (p =
0.069). However, the beam depth had a significant
effect on sy, ey, sfmand energy to failure (p\0.001).
The median results for sy, ey, sfm, and energy to failure
were 69%, 19%, 19%, and 96% higher for specimens in
group L2 than for those in group L1, respectively.
load–displacementcurves and corresponding
In this study, a validated three-point bending test setup
is described that enables measuring flexural bone mate-
rial properties of small cortical osteotomy specimens.
The test method was validated using miniature beams
of acrylic, as well as beams of bovine cortical bone
Table 3. Cortical bone modulus (E), flexural strength (sfm), yield strength (sy), yield strain (ey), and energy absorbed to failure
measured for the bovine and pediatric OI bone, and acrylic beams (median (range)).
ey(%) Energy to
Mild OI (OI-I)
Severe OI (OI-III)
*p \ 0.001 compared to group T1.
**p = 0.069 compared to group L1.
***p \ 0.001 compared to group L1.
Figure 4. Stress–strain data curves for the OI bone specimens.
The three beams obtained from the individual with mild OI
(specimen OI-I) are shown as dashed lines, while the nine beams
obtained from the individual with severe OI (specimen OI-III)
are shown as solid lines.
Table 2. Description of the pediatric OI bone specimens (median (range)).
OI severity Age Anatomic siteBeam orientation Number
w (mm)d (mm)
Type I (mild)
Type III (severe)
OI-I: osteogenesis imperfecta type I; OI-III: osteogenesis imperfecta type III.
110Proc IMechE Part H: J Engineering in Medicine 227(2)
oriented longitudinally and transversely relative to the
long axis of the femur diaphysis. Finally, a pilot study
of osteotomy specimens from children with OI was per-
formed, providing the first data for bone material
strength in this patient population.
Three point bending tests are a common tool used
to characterize bonematerial
Nonetheless, these bending tests entail a number of lim-
itations. For example, local deformation of the speci-
men is likely to occur at the points of contact with the
loading nose and supports due to stress concentrations.
This local deformation can result in an overestimation
of beam deflection at midspan, and thus underestima-
tion of E. Fracture is assumed to occur at the midpoint
between the supports, which may not be exactly true.
Furthermore, the beam theory used to derive stresses
and strains from the load–displacement data assumes
linear elastic behavior throughout the test. This
assumption, however, does not hold true beyond the
point of yield. For this reason, bending test results tend
to overestimate ultimate material strength. A more in-
depth discussion of this phenomenon can be found in
previous works.26,27To emphasize its distinction from
ultimate tensile strength, the maximum stress value in
strength,’’28‘‘bending strength,’’1‘‘modulus of rup-
ture,’’29,30or ‘‘computed ultimate bending strength.’’2
In this article, this value is reported as flexural strength.
Similarly, the energy to failure was calculated for each
bone specimen as the area under the flexural stress–
strain curve up to the point of fracture. Due to overes-
timation of stress in the post-yield region, the energy to
failure results presented in this study thus represent
estimates rather than accurate values.
A minimum span/depth aspect ratio of 8 has been
recommended for measuring the flexural properties of
ceramic materials (ASTM C674). For bone, E has been
found to decrease with decreasing span/depth ratio
when that ratio was below 15, while it was roughly con-
stant for ratio over 20.31As mentioned earlier, due to
the small size of our previously collected pediatric bone
specimens, a maximum span length of 4mm was
deemed appropriate for characterizing those specimens.
With this chosen span length, beam depths of 500 and
266mm would be required in order to obtain span/
depth ratios of 8 and 15, respectively. As discussed ear-
lier, the beam depths above 560mm (i.e. span/length
ratios of 5 and 6) were selected for our specimens on
the basis of decreased E values reported with smaller
beam depths.16This minimum depth value, being two
or three times the size of a secondary osteon, also
ensures a certain amount of heterogeneity in micro-
structure within the specimens. Nonetheless, it should
be acknowledged that the relatively small span/depth
aspect ratios used in this study may have resulted in
some error due to shear deformation within the
In spite of the abovementioned limitations, the meth-
ods described in this article yielded reasonable results
for acrylic as well as bovine bone. For acrylic, E was
within 3% of the expected value of 3.2MPa.33The
longitudinal E values for bovine bone (groups L1 and
L2) were of similar magnitude to those reported in
another bending study that characterized larger bovine
specimens (10mm 3 4mm 3 80mm), that is, 18.6 6
1.2GPa.25Similarly, the longitudinal sfmresults were
within the range of value reported in other studies of
larger bovine bone specimens in bending, that is, 170–
In this study, beam depth did not have a significant
effect on longitudinal E. There was no significant differ-
ence in E between groups L1 and L2, having specimen
depths of 636–659mm (span/depth ratio of 6) and 803–
815mm (ratio of 5), respectively. This observation was
similar to that of a previous study of human cortical
bone, in which a more or less constant E was reported
for beam depths greater than 560mm, with a constant
span/depth ratio of 10.16Beam depth, however, had sig-
nificant effects on sy, efy, and sfm, all of which were
higher for the thicker specimens (group L2) than for the
thinner ones (L1).
Micromechanical bending studies of human bone,14–16
with specimen depths ranging from 50 to 200mm,
reported much lower E (by 50%–75%) than typical val-
ues for larger adult human cortical bone specimens (15–
20GPa).4,22This size-related phenomenon has not yet
been explained, however, it was suggested that the lower
E reported in micromechanical bending tests may be
attributed to stress concentrations and inhomogeneities
in microspecimens caused by Haversian canals and cana-
liculi.34The methods described in this article, however,
did not result in such underestimation of E, but provided
values similar to those reported for larger bovine bone
The methods described in this article were used to
characterize two osteotomy specimens from children
with OI. For these specimens, E was lower than values
previously obtained by nanoindentation for children
with severe OI (9–22)GPa.10–13,18The moduli mea-
sured by nanoindentation, however, do not take into
account specimen porosity, and a substantial amount
of cortical porosity was apparent in our specimens by
visual inspection. Such cortical porosity has also been
observed histologically in iliac biopsies from children
with OI.35In the pediatric OI specimens observed in
this study, the flexural properties were lower than pre-
viously published values for adult cortical bone, for
example, 11–20GPa for E, 194 (21)MPa for sfm, and
154 (13)MPa for sy.4,22,23Little normal pediatric data,
unfortunately, is available for comparison with the
flexural properties measured in this study. One study
characterized flexural properties in cadaveric bones
from children and adults.6It was found that E and sfm
were lower in pediatric than in adult bones. The E val-
ues reported in that study (79–162GPa, when combin-
ing specimens of all ages), however, were consistently
much higher than the generally accepted range for
adult human bones. The flexural strength for the two
Albert et al.111
OI pediatric bone specimens were lower than the value
previously reported for a ‘‘normal’’ 8-year-old girl
(190MPa).6This apparent decreased flexural strength
in the pediatric OI bone specimens may be the result of
In this study, the beams obtained from the individ-
ual with severe OI (specimen OI-III) absorbed less
energy to failure than did those obtained from the
individual with mild OI (specimen OI-I). Nonetheless,
a certain amount of variability was seen within each
OI osteotomy specimen (Table 3 and Figure 4), and
in light of the small sample size in this pilot study
(one specimen with each mild and severe OI), a larger
study is needed to draw definitive conclusions regard-
ing the effects of OI severity on bone material
In conclusion, this study describes a validated three-
point bending test method with a span of 4mm suitable
to characterize the material behavior of miniature bone
specimens such as those obtained during osteotomy
procedures. This method provided reasonable E, sy,
and sfmresults for bovine bone. The results for sy, and
sfm, however, were sensitive to the span/depth aspect
ratio. For that reason, this parameter should be consid-
ered when comparing bone properties measured with
the presented method. Two specimens obtained from
children with OI were also characterized in a pilot
study, providing the first ever data for flexural and
yield strength for this patient population. Finally, the
flexural test setup described in this article can be used
to characterize miniature bone specimens, such as those
obtained during routine osteotomy procedures, which
can lead to improved understanding of bone disorders
such as OI.
The contents of this article were developed under a
grant from the Department of Education, NIDRR
grant H133E100007. However, these contents do not
necessarily represent the policy of the Department of
Education, and you should not assume endorsement by
the Federal Government.
The authors wish to thank Thomas Silman, Ray
Hamilton, and Dave Gibas from the Discovery
Learning Laboratory at Marquette University for their
help in designing and machining the testing apparatus.
We are also grateful to Dr. Peter Smith, Pediatric
Surgeon at Shriners Hospitals for Children, Chicago,
for his support and for providing the pediatric bone
specimens used in this study, as well as to Ms Kathy
Reiners, Motion Analysis Laboratory Coordinator at
Shriners Hospitals for Children, Chicago, for her assis-
tance with collection and handling of those specimens.
Conflict of interest
The authors report no conflicts of interest. This work
was supported by the U.S. Department of Education
NIDRR grant H133P080005.
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beam specimen depth
modulus of elasticity
cross-sectional moment of inertia of the
span length between the supports
slope of load–displacement curve in the
linear elastic region
beam specimen width
beam deflection at midspan
maximum tensile strain at midspan
maximum tensile stress at midspan
Albert et al.113