AMER. ZOOL., 24:5-12 (1984)
Comparative Mechanical Properties and Histology of Bone1
JOHN CURREY
Department of Biology, University of York,
York, Y01 5DD, England
SYNOPSIS. Different bone tissues differ in their amounts of porosity, mineralization,
reconstruction, and preferred orientation. All these have important effects on mechanical
properties. Very porous, cancellous bone is always weaker and more compliant than
compact bone on a weight for weight basis, yet it occurs in places where its energyabsorbing ability, or its low density, is advantageous. Bone varies considerably in its mineralization, and such variations have quite disproportionate effects on mechanical properties. These variations can be shown to be adaptive. In particular, there must always be
a compromise between stiffness and resistance to fracture; these two properties run contrary to each other. The reason for secondary remodeling is an unresolved problem,
though in a few places the role of such remodeling in changing the grain of the bone is
clearly mechanically adaptive. The mechanical properties of non-mammalian bone are
obscure, and as the histology of such bone is often quite different from that of mammalian
bone, we are no doubt in for some surprises when the mechanical properties of nonmammalian bone are discovered.
canaliculi, blood channels, and erosion
Bone material can vary in a number of spaces. On the other hand, cancellous bone
ways that have important effects on its can have all degrees of porosity, from being
mechanical properties. Some of this vari- effectively absent to being effectively comation is adaptive. Some, as far as we can pact bone. It is noticeable, however, that
tell, is not. I intend to show what this vari- there is usually a fairly clear morphological
distinction between compact and cancelation is, and how it is, or is not adaptive.
There are four variables of importance lous bone—the one does not usually grade
whose effects are not impossibly difficult to into the other.
There have been many studies of canquantify, though they do tend to be corcellous
bone, but the important ones here
related with each other, and this produces
are those of Carter and his associates (Carproblems. They are:
ter and Hayes, 1976, 1977; Carter et al,
1980). They have shown that over a wide
a) Porosity
range of values Young's modulus oc pit and
b) Mineralization
strength oc p2, where p is the bulk density,
c) Reconstruction
that is the density with the spaces between
d) Orientation
the boney struts being counted as part of
I shall first show the magnitude of their the volume but not adding the mass. This
effects, and then discuss the adaptive—or relationship holds for both tension and
compression. The variation in values of p
otherwise—reasons for them.
are such that there are very great variaPorosity
tions in the values of strength and Young's
modulus.
Carter and Hayes (1977) found
No bone is completely solid except, perhaps, that of some teleost fish which con- compressive strength varying between 2
tains neither bone cells nor blood channels. and 200 MPa, and Young's modulus
However, compact bone does not often between 20 and 20,000 MPa. Cancellous
have more than a few percent of porosity, bone is such an obvious feature of most
the cavities being those for blood cells, their bones that such wide variation in mechanical properties must be explained. It is
interesting that theoretical and experi1
From the Symposium on Biomechanics presented mentally determined values in foams with
at the Annual Meeting of the American Society of interconnecting cavities, which is what in
Zoologists, 27-30 December 1982, at Louisville, Ken- effect cancellous bone is, show that both
tucky.
INTRODUCTION
JOHN CURREY
40r
o°
°
200
whale bulla
30
0
20
100
tortoise
10
crocodile//'
/deer
antler
10
Young's modulus (GPa)
0L
40
60
Ash(%)
80
20
FIG. 2. Relationship between bending strength and
Young's modulus. These points represent specimens
of deer's antler, cow's femur, Galapagos tortoise's
femur and crocodile's nasal.
FIG. 1. Relationship between Young's modulus and
the ash content of different types of bone. The continuous lines enclose individual points, which are not
shown.
the values of highest Young's modulus.
Work of fracture, which is a measure of
the toughness of bone, rises to a maximum
at about 59% mineral (Fig. 4), and then
strength and modulus should follow a falls rapidly. Note that the range of minsquared power relationship to density (Gib- eralization over which great changes in
son and Ashby, 1982).
mechanical properties take place is quite
small; a ninefold increase in modulus takes
Mineralization
place as the mineralization increases from
Although the variation in mineralization 48% to 71%.
of bone is not as great as that of porosity,
the mechanical effects are nearly as profound. Figure 1 shows variation of Young's
modulus of elasticity of compact bone with
the amount of mineralization, as deter- frachre
mined by ashing. It must be admitted that lOOOJnT ,
the lower values for mineralization or ash,
below about 50%, probably have some
cross-talk from porosity as in these bones
the vascular channels are rather large. Figure 2 shows the relationship between
Young's modulus and bending strength.
Figure 3 shows the relationship between FIG. 3. Relationship between three mechanical
the three important mechanical variables, properties. It is not possible to test both work of fracture and bending strength of the same specimen.
and includes the very highly mineralized Therefore
these values were taken from specimens
whale tympanic bulla. Young's modulus close to each other in the bone, which also barely
increases monotonically with mineral, as differed in their Young's modulus. The letter in the
we have seen, and bending strength in- circle denotes the species, w: Fin whale bulla; b: Cow's
femur; t: Galapagos tortoise femur; m: Muntjac deer
creases with Young's modulus except for antler;
d: Red deer antler; c: Crocodile nasal.
2
MECHANICAL PROPERTIES OF BONE
Orientation
Some bone is extremely anisotropic.
Table 1, derived from Reilly and Burstein's work, shows this for mammalian
compact bone. Particularly striking is the
work done in fracturing a specimen in tension. This seven- to tenfold reduction is
produced both by a reduction in the stress
at fracture and also by a great reduction
in strain at fracture. Specimens loaded in
a direction at right angles to the long axis
to the bone are very brittle.
Many of the variations seen in bone are,
of course adaptive. I shall consider the
adaptive differences first, leaving until later
the more awkward cases of apparantly unadaptive features.
oo
O
CO
o
o
o
o
o o
0
4
oo
8
o o
12
16
Young's modulus (GPa)
FIG. 4. Relationship between work of fracture and
Young's modulus. Points represent the same range of
species as in Figure 2.
POROUS BONE
Cancellous bone is very porous bone, and
is fairly easy to explain. In mammals' and
birds' skeletons, cancellous bone is found
mainly in three characteristic places: (a)
under the articulations in synovial joints;
(b) all through the length of bones that are
short relative to their length (such as wrist
bones and vertebral centra); (c) in flat bones
which are much longer in two dimensions
than in the third (such as the bones of the
pelvis, and the scapula).
An important point to get clear is that
although a block of cancellous bone is
lighter than a block of compact bone it
usually requires a greater mass of cancellous bone to produce a particular stiffness
or strength. For instance, consider compressive strength. If a piece of bone is
required to carry a compressive load of P
newtons over a short distance L (a short
distance avoids the complications of buck-
Reconstruction
Compact bone, particularly that of mammals, often undergoes internal reconstruction, leading to the formation of secondary
osteons, another name for which is Haversian systems. The effect of this on mechanical properties is nothing like as important
as that of the previously discussed variables. What is interesting about reconstruction is that it seems to be mechanically
deleterious (Currey, 1959, 1975; Reilly and
Burstein, 1975; Carter and Hayes, 1976;
Saha, 1982). This is true of properties measured under both static and dynamic loading, and of toughness. Completely primary, unreconstructed bone, is about one
and a half times as strong as reconstructed
bone. The effect on Young's modulus is
rather small.
TABLE 1. Anisotropy of the mechanical properties of compact bone '
Species
Histology:
Direction of loading relative to grain
Young's modulus/GPa
Tensile strength/MPa
Ultimate tensile strain
Yield tensile strain
Work to fracture (arbitrary units)
Derived from Reilly and Burstein (1975).
Man
Haversian
Parallel
17.5
148
0.031
0.007
75
Cow
Fibrolamellar
Normal
11.5
49
0.007
0.004
10
Parallel
26.5
167
0.033
0.006
100
Normal
11.0
55
0.007
0.005
10
8
JOHN CURREY
ling), the cross sectional area of the bone
required will be P/S where S is the compressive strength.
The total mass will be pLP/S
Now as we saw above S oc p2
Therefore mass is proportional to
LP/p; as L and P are fixed
Mass is proportional to 1/p
Therefore the mass required is inversely
proportional to the density, so if mass is to
be minimized, density should be maximized.
It can be shown that for various loading
systems, and possible failure modes, cancellous bone is never superior to compact
bone, and is usually inferior, on a mechanical property per mass basis. The situation
is even worse if the mass of mechanically
useless fat in the interstices of the cancellous bone is taken into account. If all this
is so, then at first sight it seems strange that
cancellous bone should be adaptive, yet it
is a frequent constituent of bones. I think
that the mechanical function of cancellous
bone is rather different in the three kinds
of places in which it is found.
Cancellous bone under synovial joints
The bone forming half of a synovial joint
has a thin layer of cartilage overlying a very
thin layer of subchondral bone. Beneath
this are struts of cancellous bone leading
the loads from the often expanded ends of
the bone to the compact bone of the shaft.
If the compact cortical bone were merely
continued round under the cartilage, and
there were no cancellous bone underlying
it, it would be carrying the load in bending,
and would therefore have to be quite thick
if the contours of the joint surface were
not to distort under load. But, if the bone
were thick, there would be a different difficulty. Synovial cartilage is weak and very
compliant. If the cartilage were sandwiched between two layers of rigid bone,
then when the joint was loaded in impact
during locomotion the energy distribution
would be such that the cartilage would be
squashed. Cancellous bone, being much
more compliant, will absorb much of the
energy of the impact, and so spare the cartilage, yet will also deform as a whole, and
keep the shape of the end of the bone fairly
constant, so allowing the correct amount
of congruity between the surfaces. This
solution is also slightly lighter than a structure made of solid bone.
Short wide bones
Bones like vertebral centra and wrist
bones often consist of a thin shell of compact bone surrounding the cancellous bone
which stretches right along the length of
the bone. The design criterion to be met
here is that loads must be transmitted over
the length of the bone. There must, presumably, be some limit to the distortion
allowed, and the structure should be as light
as possible. One solution to satisfy these
criteria would be a box. (Assume, initially,
that the side walls are rigid, and distortion
comes from flexure of the end walls, the
"lid.") Another solution would be an
entirely cancellous bone. Clearly, the wider
the bone the more a box lid will deflect for
a given load because it is being loaded over
a greater span, so the deflection as a proportion of the length of the bone will be
greater. So, if the deflection is to be kept
to some particular value, the lid of the box
must become thicker and thicker as the
bone gets wider. The cancellous bone, on
the other hand, is not affected by the width,
each part of the cross section bearing its
own share of the load, and deflecting
accordingly. Figure 5 shows the results of
calculations. It shows that, for a particular
set of reasonable constraints the cancellous
bone solution is lighter than the box solution when the ratio of breadth to depth is
1.5. This is at least in the region in which
we do see one solution changing over to
another, though the point of changeover
comes when the bones are somewhat too
flat. If we allowed the sidewalls of the box
solution to deflect, then the changeover
would approach even more closely the situation found in real bones.
Sandwich bones
Bones such as the ilium are classical sandwich structures. Two sheets of compact
bone are separated by a cancellous filling.
The cortices bear the bending load; one is
in tension, the other in compression. The
MECHANICAL PROPERTIES OF BONE
to
to
S
|.8h
.05
Breadth/Length
FIG. 5. Comparison of the box solution and the cancellous bone solution. A cylindrical bone is loaded
with a uniform stress on two opposite faces. The solid
lines show the relative mass of the box solution having
the same maximum deflection as the cancellous bone
solution, whose mass is taken as unity. The sidewalls
are considered completely stiff. The lower curve
assumes the lid fixed firmly to the sidewalls; the upper
curve assumes the lid is simply supported by the sidewalls. The pictures at the ends of the wavy lines show
the appearance of half the bone, the marrow cavity
being represented by dots.
filling keeps the cortices apart, so ensuring
that the second moment of area remains
large, and preventing the cortices from
buckling. The filling also has to bear some
shear stresses. Again it is possible, by making some simplifying assumptions, to calculate the relative masses of various solutions to this problem. The results are shown
in Figure 6. There are two variables; the
proportion of the depth occupied by cancellous bone, and the density (or porosity)
of the cancellous bone. (In the previous
section the density of the cancellous bone
was uniquely determined by the allowable
strain.) There is again some, though not
spectacular, saving in mass by adopting a
sandwich construction, and the total proportion of the depth occupied by cancellous bone does agree quite well with what
is found in mammals generally.
In both the sandwich bone and the short
bone, the potential saving in mass would
be much greater if there were no mechanically useless fat to add to the mass of the
cancellous bone.
0
.2
.4
.6
.8
Cancellous proportion of depth
FIG. 6. Weight of sandwich bone relative to a solid
plate of the same stiffness. Abscissa: proportion of the
depth of the sandwich occupied by cancellous bone.
Dotted lines: assuming no marrow; continuous lines:
assuming marrow present. The numbers on the lines
refer to the porosity. (A porosity of unity means that
the cancellous bone is absent, and the sandwich has
no filling except marrow.)
Minimum weight frameworks
So far I have talked about cancellous
bone merely as a uniform lump that obeyed
two power laws: strength oc p2, Young's
modulus <x p3. In fact it is often obviously
exquisitely adapted to the stresses falling
on it. It is possible to generate, mathematically, so-called minimum weight frameworks which are, as the name suggests,
frameworks that will bear a particular load
with the minimum weight possible. Figure
7 shows a minimum weight cantilever, and
a cross section of the ilium of a horse. The
correspondence of the two structures is
seductive, and shows that the reconstruction mechanism in cancellous bone is accurately responsive to the stresses falling on
the bones. (Proving that this is so is, in fact,
rather difficult.)
MINERALIZATION
The compact bone of mammals shows a
great range of mechanical properties, and
these seem to be produced mainly by dif-
10
JOHN CURREY
Fie. 7. Above: a mathematically generated minimum weight cantilever, supported at A and B, and
loaded at its free end at C. The continuous lines represent parts of the framework loaded in compression,
the interrupted lines those parts loaded in tension.
Below: cross section of part of the ilium of a horse.
This is a flat plate sandwich structure. The main part
of the pelvis is around B. The ilium is loaded by adductor muscles near its free end A.
ferences in mineralization. The most
heavily mineralized bone I know is the tympanic bulla of the whale. This has a high
modulus of elasticity (31 GPa) and a derisible work of fracture and bending
strength. However the high modulus is
adaptive, because it increases the input
impedance of the otic bone, and prevents
the sound from reaching the inner ear
except via the tympanic membrane. Isolating the ear is very important for marine
mammals because the body in water is
almost transparent to sound and the usual
cues for locating the direction of sound are
therefore vague (Currey, 1979).
The mineralization of the antlers of deer
is rather variable, ranging from quite low
values in some specimens of red deer to
values in muntjac nearly as high as those
in cow's femora. The monotonic increase
shown in the relationship between Young's
modulus and mineralization is not shown
by the bending strength or work of fracture. It would be fascinating to know what
bending strengths bone could achieve with
somewhat higher values of mineralization
than the most highly mineralized cow bones
shown here. Unfortunately, there are no
natural experiments intermediate between
the cow's bone and the bulla to tell us. The
bulla has given up the struggle to be strong,
in the pursuit of stiffness. The adaptive
reason for the upper limit on bending
strength is that, at the highest strength, the
toughness as shown by the work of fracture
is declining rapidly. Natural selection has
balanced the competing needs for stiffness
and strength, which go together, with that
for toughness. The balance achieved is different in the cow and in the red deer. For
the deer the more important feature is the
resistance to impact, because the antler is
used in fighting, and the toughness can
achieve very high values. For the cow's
femur, locomotory efficiency is needed, and
therefore stiffness becomes relatively more
important. The red deer antler shows considerable variation in all four of the properties we measured, and indeed some values for work of fracture are quite low.
These different properties seem to vary
regionally over the antler, and I am not
yet sure of the significance of this variation.
The muntjac antler is not used seriously
for fighting (Chapman, 1981) and its properties are intermediate between those of
red deer and cow bone, but the work of
fracture is not as high as one would expect
from a bone with such a relatively low
Young's modulus.
Finally, the bone with the consistently
highest values for work of fracture was the
femur of the Galapagos Tortoise Geochelone elephantopus. The mineralization was
at the upper end of the range seen in red
deer. Unfortunately, we have essentially no
data about the mechanical properties of
reptile bone, so we do not know whether
the Galapagos Tortoise is typical of reptiles, or whether reptiles show a similar
range of values to that of mammals.
Whether the high work of fracture of the
tortoise, with the corresponding low value
of Young's modulus, is adaptive is difficult
to say. Tortoises are not notable for fast
locomotion, but Galapagos Tortoises are
notoriously clumsy. For a very long-lived
MECHANICAL PROPERTIES OF BONE
11
animal, the selection pressures on not
breaking a bone may be considerable.
HISTOLOGY, RECONSTRUCTION,
AND ANISOTROPY
There is a great range of histological
types of bone, but we know extremely little
about the mechanical properties of the different types. We do know in mammalian
bone that the Haversian bone, which
replaces by reconstruction the primary
fibrolamellar bone is weaker and less stiff
than the primary bone. It is not really clear
why this should be so, indeed what we know
of fracture processes in bone might make
us guess that Haversian bone would be
stronger than primary bone, because it looks,
superficially anyhow, more like a composite material. Probably its weakness has to
do with the insertion of tubes of bone of
lower Young's modulus in pre-existing
bone.
What is interesting about Haversian bone
is why it should form at all. Various reasons
have been produced, from a need to take
calcium from the bone to the need to prevent the bone from becoming over-mineralized. All these non-mechanical explanations would seem to fall down because
of peculiar distribution of Haversian remodelling. For instance, why should a homeostatic mechanism, involving a reduction in
strength of the bone, proceed with great
vigor in healthy young Americans, who can
rarely be short of calcium in their diet, yet
be absent in the bones of small wild rodents
who must often undergo great fluctuations
in calcium intake? The mechanical explanations would not seem to fare much better. Secondary remodeling takes place more
vigorously towards the marrow cavity than
towards the subperiosteal side, yet the
greatest stresses, and therefore the greatest likelihood of microfracture, will be near
the subperiosteal surface. Also, as shown
in Figure 8, Haversian remodeling occurs
remarkably symmetrically in paired bones,
rather as if a program of reconstruction
were being carried out. It stretches the
imagination to think that these symmetrically arranged reconstruction events are
FIG. 8. Paired sections of a tibia of a cat, to show
symmetry of remodeling. Fine stippling: Haversian
bone; plain: Primary bone; black splodges: Haversian
systems actively forming.
taking out symmetrically placed microfractures.
One instance in which remodeling may
be mechanically adaptive is when Haversian remodelling occurs when the grain of
the bone is changed. Both primary bone
and Haversian bone are very anisotropic
(Table 1). Bones can grow only by accretion, and therefore bone that was originally well-oriented can be found in a position where it is loaded at a large angle to
its grain, which makes it weak. This is particularly likely to occur under muscle insertions and here, indeed, Haversian remodeling is very common. Remodeling also
occurs actively in compact coarse-cancellous bone. This is bone produced by the
filling in of cancellous bone that was originally at the ends of long bones, but which
becomes incorporated into the main shaft
during growth. Compact coarse-cancellous
bone has a low bending strength, is rather
compliant, and has a low work of fracture.
This weakness must be caused by the almost
random distribution of the grain of the
bone. The replacement of this jumble of
fossilized trabeculae by adaptively oriented
Haversian systems, which themselves are
weaker than a neatly produced fibrolamellar bone is a classic case of making the
best of a bad job.
Biewener (1982) has shown that the bone
of small mammals, of body mass in the
region 0.1 to 1 kg, has bending strengths
very similar to that of cows and humans.
12
JOHN CURREY
It may well be that the other mechanical
properties will be similar too. At the
moment we are almost totally ignorant of
the mechanical properties of non-mammalian bone. There are good indications
that at least some birds' bones are similar
mechanically to mammalian bones (Biewener, 1982), but good information about the
reptiles and anamniotes is lacking. The histology of these bones is often rather different from that of mammals and birds.
For instance, the bone of Geochelone, with
its very high work of fracture, seems mainly
to consist of compact coarse cancellous
bone, which in mammals has a rather low
work of fracture. Much reptile bone consists of very fine textured circumferential
lamellae; most teleost fish have acellular
bone, and so on.
When the mechanical properties of these
bony types are determined we shall probably be in for some surprises. However, I
would be very surprised if it were not possible, in the end, to show that the mechanical properties, and the histology that produces them, are mainly determined by the
selective balance between stiffness, and
resistance to fracture. These two properties are both important, yet require contrary design features in the bone material.
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with body size?J. Exp. Biol. 98:289-301.
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Carter, D. R., G. H. Schwab, and D. M. Spengler.
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