Bone Stiffness Predicts Strength Similarly for Human
Vertebral Cancellous Bone in Compression and for
Cortical Bone in Tension
D. P. FYHRIE and D. VASHISHTH
Bone and Joint Center, Henry Ford Hospital, Detroit, MI, USA
The yield strength and ultimate strength of cortical and
cancellous bone tissue are very highly correlated to bone
stiffness. For samples of human vertebral cancellous bone in
compression and for bovine cortical bone in tension, the
coefficient of determination (r
) for regression between ulti-
mate strength and stiffness was 0.89 and 0.92, and between
yield strength and stiffness it was 0.94 and 0.93, respectively.
The slope of the regression for human vertebral cancellous
bone ultimate strength predicted by stiffness was not statis-
tically different from similar regressions for cortical bone in
tension in either a bovine sample or in published data from
multiple species. We believe that the observed correlation
results from the evolutionary need to build sufficiently strong
bones using cells that are sensitive to deformation and that
directly control bone stiffness, but not strength. The practical
significance of this work is that an in vivo estimate of bone
stiffness (e.g., from ultrasound measurement) may be a sur-
rogate for bone strength. (Bone 26:169–173; 2000) © 2000
by Elsevier Science Inc. All rights reserved.
Key Words: Strength; Stiffness; Yield strain; Cortical bone;
Cancellous bone; Adaptation.
The correspondence of bone strength to functional need is a
significant part of the adaptation of a species to its environment.
For survival, bones must be strong enough to survive normal
activities but not so oversized that to build and carry them is in
itself a risk.
Despite the adaptive significance of appropriately
strong bones, it is not generally possible to determine structural
strength without either an actual fracture test or a complex,
structural-level failure analysis. As a consequence, it is unlikely
that bone strength as a property is under direct biological control
by a cellular level mechanism.
There is good evidence that bone cells respond to the tissue
deformation and fluid flow caused by applied loads.
is widely believed that the cellular response to bone deformation
is what closes the loop in control of bone mass, and that bone
deformation (strain) is an epigenetic signal for the creation of
appropriately sized bones.
However, it is stiffness, not
strength, that determines the deformation of bone tissue. There-
fore, if bone strength is to be controlled by bone cells, a strong
correspondence between stiffness and strength would be ex-
pected. Materials in general do not have such a correspondence.
If one exists for bone, it would suggest a biological linkage
between the properties.
There is strong evidence for a correlation between yield
strength and stiffness
and between ultimate strength and
for cancellous bone. The correlation be-
tween yield strength and stiffness for multiple test axes
consistent with an hypothesis that the yield strain of cancellous
bone is uniform and isotropic.
However, it has been recently
demonstrated that the yield strain of cancellous bone in compres-
sion is not uniform,
invalidating at least the strongest form of
that hypothesis. Relationships similar to those for cancellous
bone exist between the yield strength or ultimate strength and
stiffness of cortical bone.
Despite these powerful observa-
tions, complete understanding of the interrelationship between
the parameters that measure the pre- and postyield mechanical
properties of bone has not been established.
Our previous research on bone mechanical properties in-
cluded the observation that human vertebral cancellous bone
ultimate strength correlates with stiffness.
The aim of the
current study was to extend this line of research and to determine
how well bone stiffness predicts yield strength, yield strain,
ultimate stress, and ultimate strain for both cortical and cancel-
lous tissue. As will be demonstrated, the mechanical properties
of human vertebral cancellous bone in compression and cortical
bone in tension are related in similar ways; yield strength and
ultimate strength are highly correlated to bone stiffness by a
relationship that is the same for both vertebral cancellous and
habitually loaded cortical bone.
Materials and Methods
Bovine bone (18 months of age; bilateral tibia and femur) and
five adult human vertebral cancellous bones with no known
history of bone disease (49 to 88 years of age; females; L3 and
L4 vertebrae) were obtained and frozen at Ϫ20°C with soft tissue
attachments. The mid-diaphysis of the bovine tibia and femurs
were subsequently cleaned and cut into 8-cm-long strips of
cortical bone oriented along the long axis of the bone. These
strips were turned on a lathe (Emco Compact 5; Maier Co.,
Austria) into cylindrical dumbbell specimens of 15-mm-gage
length and 3-mm-gage section diameter (fillet radius ϭ 24 mm;
grip section diameter ϭ 5 mm). The specimens were stored in
saline at Ϫ20°C until testing.
Address for correspondence and reprints: David P. Fyhrie, Ph.D., Bone
and Joint Center, Henry Ford Hospital, 2799 W. Grand Boulevard,
Detroit, MI 48202. E-mail: firstname.lastname@example.org
Bone Vol. 26, No. 2
© 2000 by Elsevier Science Inc. 8756-3282/00/$20.00
All rights reserved. PII S8756-3282(99)00246-X