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The tensile properties of single osteons.

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The Tensile Properties of Single Osteons '
ANTONIO ASCENZI AND ERMANNO BONUCCI
Institute of Morbid Anatomy, University of Pisn,
Pisa, Italy
ABSTRACT
The ultimate tensile strength and modulus of elasticity of individual
osteons from human and ox compact bone were determined with a specially designed
microwave extensimeter. The results were related to the degree of calcifkation and the
orientation of collagen fiber-bundles in successive lamellae of the osteons. The following conclusions were made: (1) When osteon specimens are dried, their tensile strength
and modulus of elasticity increase, while their percent elongation under tension falls.
(2) In the osteon samples tested wet, the degree of calcification induces an increase in
the modulus of elasticity with additional amounts of calcium salts. (3) The modulus
of elasticity in tension of the organic matrix corresponds to that of collagen. ( 4 ) In
the osteons having a marked longitudinal arrangement of bundles of fibers in successive lamellae, the ultimate tensile strength and modulus of elasticity seem greater and
the percentage elongation under tension seems lower than i n osteons whose bundles
in successive lainellae change through an angle of about 90". ( 5 ) The tensile properties of osteons seem independent of the age of the subject. ( 6 ) Human and ox osteons
reveal the same tensile behavior. (7) The tensile stress-strain curves show that, even
at the level of single osteons, bone behaves like a complex material, which, according
to Sedlin, can be represented by a Hooke body linked in series to a Kelvin body.
In the last two decades, there has been
an increased interest in problems concerned with the mechanical properties of
bone (cf. Evans, '57; Sedlin, '65).
At the present time, the lack of any
quantitative studies of the micromechanical properties of isolated osteons has induced us to investigate the tensile strength
of samples obtained by dissection from
Haversian systems. In a previous paper,
the results of research on the ultimate tensile strength of the same units were given
(Ascenzi and Bonucci, '64). The aim of
this paper is to present the definitive results of a quantitative investigation of the
tensile deformation of single osteons from
human and ox femoral shafts using a specially designed microwave extensimeter.2
MATERIALS AND METHODS
As discussed in a previous paper (Ascenzi and Bonucci, '64), it appears very
difficult at the present time to isolate samples corresponding to a whole osteon in
order to test tensile properties. For this
reason, the present tensile strength studies
were made on samples corresponding
to portions of longitudinally sectioned
osteons.
Longitudinal sections, 20-50 p in thickness, were prepared from femoral shafts
ANAT. REC., 158: 375-386.
by grinding them on glass plates. Special
care was taken to avoid heating the material. The samples were taken from longitudinally sectioned osteons using the dissection technique described by Ascenzi and
Fabry ('59) and Ascenzi and Bonucci ('64).
With this technique it was easy to prepare
samples of the desired shape (fig. l a ) .
A region with parallel sides was isolated
from the middle portion of half a longitudinally sectioned osteon, as seen in figure
la. The ends of the sample fitted into
square lugs in the tensile apparatus to
assure a good fixation. The isolated middle
portion of the sample had a length of 0.40.6 mm corresponding to the distance between the jaws of the tensile apparatus.
The cross-sectional area of the sample
at the middle was used in calculating the
ultimate tensile strength and the modulus
of elasticity. The thickness of the sample
was determined by mounting it edgewise
under the microscope and measuring the
thickness with an eyepiece micrometer.
The samples were tested in a wet and a
dry state, respectively, to determine the
1 This work was supported by a grant of the National
2The paper reporting the partial and preliminary
results of this investigation was presented at the Joints
and Bones Symposium he!d in Wiesbaden, Germany,
on August 11, 1965, dunng the VIII International
Congress of Anatomists.
Research Council of Italy.
375
3 76
ANTONIO ASCENZI AND ERMANNO BONUCCI
Fig. 1 ( a ) A specimen ready to be tested.
Polarizing microscope. % 50. ( b ) Osteon sample
having a longitudinal spiral course of fiber bundles i n successive lamellae. ( c ) Osteon samples
with fiber bundles changing direction i n successive lamellae through an angle of 90”. Polarizing
microscope. x 100.
influence of moisture on their tensile
strength. The cross-sectional areas of both
wet and dry samples were measured.
The tested osteons revealed some structural peculiarities in the degree of calcification and in the structure of the matrix
with respect to the orientation of the collagen fiber bundles. The degree of calcification was determined by microradiography. The osteons tested were those
containing the least amount of apatite,
i.e., those at the initial stage of calcification; and those having the maximum
amount of apatite. The latter osteons, although sometimes referred to as “fully
calcified osteons” in this paper, have, in
fact, a slightly lower apatite content than
interosteonic lamellae, the only kind of
bone which can properly be considered
fully calcified.
Osteons with two types of fiber bundle
orientation were chosen. In the first type,
the fibers had a marked longitudinal spiral
course with the pitch of the spiral changing so slightly that the angle of the fibers
in one lamella was practically the same as
that of the fibers of the next lamella. Under
polarized light, osteons of this type appeared uniformly bright in longitudinal
section (fig. l b ) . In the second type, the
fibers i n one lamella formed a n angle of
nearly 90” with the fibers of the next one
(fibers ran alternately). Under polarized
light, these osteons revealed a n alternation
of dark and bright lamellae in longitudinal
section (fig. l c ) .
Some samples were decalcified i n a versene solution buffered to pH 7. At regular
intervals, the decalcification was checked
by measuring the increase in birefringence
(cf. Ascenzi and Bonucci, ’61). The minimum time required for decalcification averaged about two hours and 30 minutes.
The samples were subjected to a direct
tensile force parallel with their longitudinal axis. For this purpose, the ends of
each specimen were fixed in specially designed jaws, the upper one of which was
fixed. A thin nylon thread was attached
to the lower jaw and charged with 1 gm
loads. The elongations of the osteon were
recorded with a specially designed microwave extensimeter (see later). As soon as
the length of a n osteon, produced by the
addition of a load, became constant, additional weights were added. Difficulties
were encountered in applying this method
when the stress had passed the elastic
limit. In this case, it was difficult to decide
when a new equilibrium had been reached.
I n practice, therefore, more weights were
added when the speed of elongation produced by each successive increase in stress
had slackened considerably.
To avoid any torsion of the sample, particular care was taken to ensure that the
tensile force was applied strictly along the
longitudinal axis. All the measurements
were performed at a temperature of ca.
20°C.
The material used in this research was
obtained from the femoral shafts of oxen
and from a young and a n old man, 30 and
80 years of age, respectively. So f a r as is
known, no pathological bones were included in the material. The total number
of prepared osteons was 140, of which 23
were discarded as unsuitable for measurement. The remaining 117 units consisted
of 21 ox osteons and 96 human osteons.
Some osteons were dried at room temperature while others were put in saline solution or in distilled water.
The microwave extensimeter used for
measuring variations in length of the osteons subjected to tensile stress is based
on cavity and pulse techniques, the prin-
377
TENSILE PROPERTIES OF SINGLE OSTEONS
ciples of which may be summarized as
follows :
Let h and D be the height and the diameter, respectively, of a metallic cylinder
whose cavity functions as a resonator for
electromagnetic waves. The resonance frequency f o of this cavity will depend on h, D
and the configuration of the electromagnetic field inside its cavity (mode). If the
type of configuration chosen is that commonly indicated by “Teolzmode” the following relation holds (cf. Montgomery, ’47)
fo2
=
-;: (
CYLINDRICAL
-4
APPENDAGE
UPPER JLW WITH ITS SCREW
_________
SAMPLE
SCREW R I N G
-
~
LOWER JAW WITH I T S SCREW
NYLON
TH
C2
--)
1.488 + h2
C being the velocity of light in a vacuum.
Any variation in the height ( h ) of the
cavity produces a variation in the resonance frequency. By measuring this variation it is possible to deduce, by using equation ( l ), the corresponding variation of h.
Figure 2 is a diagram of the apparatus
used for measuring the elongation of the
osteon specimens subjected to tensile stress.
The upper end of a specimen is fixed in one
jaw and the lower end in another jaw supporting a disc of Plexiglas whose lower
metallized surface forms the upper plane
of the cylindrical cavity. The disc, which
may roll into the vertically orientated cavity, has a very thin nylon thread attached
to its center. The thread extends through
the long axis of the cavity and comes out
through a small hole at the center of the
lower fixed end of the apparatus. When
traction is applied to the thread by attaching some weights to it, the osteon sample
elongates, thus causing the upper plane of
the cylindrical cavity to fall and decrease
the height of the cavity. Because the elongation of the sample (AZ) and the reduction in the height of the cavity (-Al) are
of exactly the same magnitude, any change
in the length of the sample is easily deduced from the corresponding variation in
the resonance frequency of the cavity. If
AZ is very small compared with the height
( h ) of the cavity, equation (2) gives the
corresponding fractional change in the
resonance frequency
Of course, the problem is that of measuring small fractional changes in the resonance frequency of a ca.vity. For this pur-
WEIGHTS
-~
.
&
Fig. 2
meter.
Diagram of the cavity used as extensi-
pose a pulse technique was used which has
the advantage of being relatively simple
and assuring high sensitivity and accuracy
by the elimination of all spurious effects.
For more detailed information about the
technique, see Battaglia, Bruin and GOZzini (’58) and Ascenzi, Bonucci and Checcucci (’66).
A block diagram and a photograph of
our apparatus are given in figures 3 and 4,
respectively.
With this apparatus, measurements of
variations in length of a single sample
were accurate to within 1 % . A greater
accuracy was not necessary because the
3 A s will appear evident later, the Teoin mode was
chosen because: ( a ) the functlonlng of the cavity m
this mode does not require electrical contact between
the lateral and the end walls of the cavity, so that the
height of the cylinder can be varied; (b) the presence
of a dielectric thread running along the axis of the
cylinder (see later) does not disturb the functioning
of the cavity, because for Teolnmodes the electric field
is null along the axis.
3 78
ANTONIO ASCENZI AND E R M A N N O BONUCCI
geometrical dimensions (length and sec- breaking point are shown in table 1. Two
tion) of the osteonic sample (see Ascenzi sets of values are given for the ultimate
and Bonucci, '61, '64) could not be meas- tensile strength: ( 1 ) the values we obured with a greater degree of accuracy.
tained in the present investigation alone
and ( 2 ) a combination of these values
RESULTS
with those from our earlier investigation
Of the results discussed here, those on using the same method but without the
ultimate tensile strength, modulus of elas- extensimeter (Ascenzi and Bonucci, '64).
ticity, and percentage elongation at the
A unified conspectus of the stress-strain
curves recorded from various types of
osteon samples, kept in four different conditions, from the cadaver of a 30-year-old
man are shown in figure 5. For each of
1
$,)KLYSTRON
these conditions, a representative curve
was chosen that most closely corresponded
to the means of all individually recorded
curves. To allow direct comparisons between single sets of recorded curves, the
tensile strength is expressed in gm/vZ of
section (ordinates) and the tensile strain
as percentage elongation with respect to the
original length of the sample (abscissae).
Figure 5a is the diagram for osteon 19
which closely corresponds to the means of
Fig. 3 The block diagram of the extensimeter. seven stress-strain curves of air-dried
Fig. 4 Photograph showing some details of the apparatus. a, Klystron; b, cavity used as extensimeter; c, transmission cavity.
TENSILE PROPERTIES O F SINGLE OSTEONS
379
of calcium salts. The fiber bundles had a
marked longitudinal spiral course in successive lamellae. These curves also approximate a straight line, as did the curves
of osteons with the maximum degree of
(v
calcification (cf. fig. 5a). However, the
uppermost points of these curves show
more deviation from a straight line before
L
Q,
failure of the bone. Student’s t test ren
vealed no significant differences between
the modulus of elasticity (203,900 iE
cn 0 . 0 1
76,400 kg/cmz) and the ultimate tensile
I
strengths of these osteons and those of the
ul
fully calcified ones. The mean of the presv)
ent results is 19.33 -C 2.88 kg/mm8 and
aJ
those for the combined results 20.38 2
L
.L2.62 kg/mm”. The percentage elongation
v)
at the breaking point (4.42
1.41) is increased.
Figure 5c is a plot for osteon 36 which
closely corresponds to the means of the
tensile strain values for 12 wet osteons
0with the maximum amount of calcium salts
0
2
4
6
8 1 0 1 2
and fiber bundles with a marked longituOy0 e l o n g a t i o n
dinal spiral course in successive lamellae.
These curves show an elastic range like
Fig. 5 Diagrams closely corresponding to the
means of four sets of stress-strain curves recorded that of the corresponding dry osteons.
for osteons having a very marked longitudinal
However, the proportional limit is only
spiral course of fiber bundles i n successive lamel- about half the breaking stress because the
lae, taken from a man of 30. (a) Air-dried and
fully calcified osteon 19. ( b ) Air-dried osteon 13 samples elongate more, near the breaking
at the initial stage of calcification. ( c ) Wet and point. Beyond this proportional limit, each
fully calcified osteon 36. ( d ) Wet osteon 135 at additional increment in stress causes excesthe initial stage of calcification. To make dia- sive yielding and permanent plastic degrams clearer only a few experimental values are
formation of the specimen. In both the
plotted.
straight part of the curves and the deviatosteon samples with the maximum amount ing plastic region, a given stress will proof calcium salts and fiber bundles with a duce greater strains than in dry osteons.
marked longitudinal spiral course in suc- Consequently, the modulus of elasticity
cessive lamellae. The curves approximate (119,400 59,000 kg/cm2) and the ultia straight line up to the breaking point, mate tensile strength (12.26 1.51 kg/
indicating a proportionality between stress mm2or 11.65 i 1.74 kg/mm2 for the mean
and strain in accordance with Hooke’s Law. of the combined results) are lower than in
Only the uppermost points show a very dry bone, whilst the wet samples show a
short curve deviating from a straight line greater percentage elongation (6.84
before the breaking point. The modulus of 2.86) than dried osteons.
Figure 5d is the diagram for osteon 135.
elasticity is very high, 238,600 -C 71,200
kg/cm2. The ultimate tensile strength is It closely corresponds to the means of 12
19.73 3.26 kg/mm2 or 21.20 t 2.97 tensile stress-strain curves recorded for wet
kg/mm2 for the mean of the combined re- osteons with the least amount of calcium
sults. The percentage elongation at the and a marked longitudinal spiral course of
the fiber bundles in successive lamellae.
breaking point is 2.15 -C 0.55.
Figure 5b is the diagram for osteon 13,
4 Young’s modulus of elasticity “E” is the ratio unit
deformation. With very few exceptions,
closely corresponding to the means of six itstress/unit
is a constant for any given material up to the
tensile stress-strain curves recorded for air- elastic limit, but afterwards falls. Obviously the
of elasticity reported here for osteons refers
dried osteon samples with the least amount modulus
to stress values below the elastic limit.
0.02
a
*
*
380
ANTONIO ASCENZI AND ERMANNO BONUCCI
This diagram is similar to that for fully
calcified wet osteons (fig. 5c) because i t
deviates greatly from a straight line as the
ultimate tensile strength is approached.
However, the initial portion of the curve,
which also clearly deviates from the curve
of proportionality, indicates that plasticity
begins at an early stage. Therefore, the
possibility of calculating the modulus of
elasticity or of attributing any precise
meaning to it is seriously reduced. Its
approximate value is 61,100 30,000 kg/
cm2. Student's t test showed that the ultimate tensile strength (10.65 +- 1.73 kg/
mmZor 10.95 2 1.88 kg/mmz for the mean
of the combined results) is not significantly
different from that of wet osteons at the
final stage of calcification. The percentage
elongation reaches 9.40 f 2.72.
The wet osteons were prepared by hydration of the material in saline solution or
distilled water. Contrary to the suggestion
of Currey ('59), our previous (Ascenzi and
Bonucci, '64) and present investigations
revealed no significant differences i n tensile properties between osteons rehydrated
in saline solution and those rehydrated in
distilled water.
Figure 6 shows a comparison between
the stress-strain curve of the wet fully calcified osteon 36 (a) and the tensile stress-
*
0 02,
strain curve for osteon 65, closely corresponding to the means of five decalcified
wet human osteons containing the maximum amount of calcium ( b ) . In all samples, the fiber bundles in successive lamellae had a marked longitudinal spiral course.
The modulus of elasticity appears to be
very low (10,500 3,500 kg/cm2) with an
average ultimate tensile strength of 8.53
C 1.40 kg/mm'.
The percentage elongation at the breaking point is very high
(21.90 7.15).
No significant difference is evident between these results and those recorded for
decalcified wet osteons, with the same
longitudinal spiral course of the fiber bundles i n successive lamellae and the least
amount of calcium salts. In fact, the values
from four osteons are as follows: modulus
of elasticity 14,800 2 6,200 kg/cmz; ultimate tensile strength 8.77 1.19 kg/mmz;
and percent elongation a t the breaking
point 20.62 2 5.10.
Figure 7 shows the stress-strain curves
of wet osteons from a 30-year-old m a n but
with differences in the degree of calcification and orientation of fiber bundles i n
successive lamellae. The origin of the coordinate system is transferred along the abscissae axis for each set of diagrams to
avoid the confusion which might arise from
superimposing the charts. The curve for
osteon 36 (fig. 7a) closely corresponds to
*
*
N
N
a
L
0)
a
k0Ol
a
E
m
k
0 01
n
n
u
I
n
n
L
a
.
Q)
ui
L
&
Lo
0
0
(I
0
2
4
6
0
O/O
10
12
14
16
18
20
22
elongation
Fig. 6 The diagram c seen in figure 5. ( b )
Diagram recorded for osteon 65 and closely corresponding to the means of a set of stress-strain
curves from decalcified wet osteons, having the
maximum amount of calcium previously fixed
and having a very marked longitudinal spiral
course of fiber bundles in successive lamellae.
Man of 30.
1
3
0
1
3
0
1
3
0
1
3
5
7
4
11
elongation
Fig. 7 Diagrams closely corresponding to the
means of four sets of stress-strain curves recorded
for osteons taken from a man of 30. ( a ) ( c )
Diagrams already reported in figure 5 (charts c,
d ) . ( b ) Wet and fully calcified osteon 41 with
fiber bundles running alternately in such a way
that their direction i n successive lamellae changes
through a n angle of 90". ( d ) Wet osteon 47 a t
initial stage of calcification and with fiber bundles running alternately in successive Iamellae.
381
TENSILE PROPERTIES OF SINGLE OSTEONS
the means of a set of 12 diagrams for fully
calcified osteons in which the fiber bundles
of successive lamellae had a marked longitudinal spiral course. The curve for osteon
41 (fig. 7b) closely corresponds to the
means for nine fully calcified osteons but
with fiber bundles running alternately in
successive lamellae. These curves show a
clear deviation from the curves of proportionality, thus indicating that plasticity begins at an early stage. Consequently, it is
not easy to determine the limit of elasticity
and any attempt to evaluate the modulus
of elasticity appears to be unreliable. It is
probably something like 55,900 26,100
kg/mm2 with the ultimate tensile strength
dropping to 10.39 1.71 kg/mm2 or 9.59
_c 1.55 kg/mm2 for the mean of the combined results.
Similar results are shown in figure 7c for
wet osteons in the initial stage of calcification and with fiber bundles in successive
lamellae having a marked longitudinal
spiral course. Figure 7d illustrates the
curve recorded for osteon 47. It closely
corresponds to the means for six osteons
with the same degree of calcification as
those in figure 7c but with fiber bundles
running at an angle of 90" in successive
lamellae alternately. The modulus of elasticity is probably 44,700 i- 19,700 kg/cm'.
The ultimate tensile strength drops to 9.06
2 1.48 kg/mmz.
A comparison was made of the tensile
properties of osteons from an adult (30
years of age) and an old man (80 years of
age). Two types of wet osteons from the
old man were analyzed : ( 1) osteons whose
fiber bundles in successive lamellae had a
marked longitudinal spiral course and ( 2 )
osteons in which the bundles of fibers of
one lamella formed an approximate angle
of 90" with the fiber bundles of the next
lamella. Osteons at both the initial and
final stages of calcification were studied.
No significant differences were found between the ranges covered by tensile stressstrain curves for eight wet and fully calcified osteons obtained from an 80-year-old
man (fig. 8b) and similar osteons obtained
from a 30-year-old man (fig. 8a). In the
osteons from both individuals the fiber buiidles of successive lamellae formed an angle
of 90". The osteons from the old man had
a modulus of elasticity averaging 62,100 2
*
*
(u
ao.01
I
dr
Q.
a
1
b
E
0
I
v)
v)
Q,
L
.L,
a
0
0
I
I
2
4
6
8
10
V0 e l o n g a t i o n
Fig. 8 ( a ) This is the same diagram as that
seen in figure 7 (chart b). ( b ) Diagram recorded
for osteon 66 and closely corresponding to the
means of a set of 14 stress-strain curves plotted
from wet fully calcified osteons with fiber bundles
running alternately in successive lamellae. Man
of 80.
35,800 kg/cm2 and an ultimate tensile
strength averaging 8.82 i- 0.85 kg/mm' or
9.41 -t 1.24 kg/mm2 for the mean of the
combined results. The percentage elongation at the breaking point was 8.23 -I 3.45.
Other groups of osteon samples showed
fairly similar results (table 1).
The results obtained for ox osteons (fig.
9 ) are exactly comparable to those for human osteons. Stress-strain curves were recorded for both dry and wet osteons ha.ving
a marked longitudinal spiral course of the
fiber bundles in successive lamellae.
Figure 9a was recorded for osteon 83
and closely corresponds to the means for
five dried, fully calcified osteon samples.
The modulus of elasticity averaged 180,700
2 19,400 kg/cm*; the ultimate tensile
strength 20.90 2 1.15 kg/mm2 or 21.28 5
1.83 kg/mm2 for the mean of the combined
results; and the percentage elongation 3.45
2 0.38.
Figure 9b was recorded for osteon 93
and closely corresponds to the means for
five dried-osteons at the initial stage of
ossification. The modulus of elasticity is
133,400 24,400 kg/cm'; the ultimate
tensile strength 19.49 F 1.94 or 20.60 -C
2.74 kg/mmz; and the percentage elongation 9.32 2 1.18.
Figure 9c was recorded for osteon 97
and closely corresponds to the means for
20.90C 1.15
19.49k 1.94
12.12C0.74
11.28t0.48
5
5
5
6
dry
dry
wet
wet
OL and FC
OL and LDC
OL and FC
OL and LDC
14
8
wet
wet
180,700f 19,400
133,400*24,400
149,600*28,700
54,600i.12,300
3.4520.38
9.322 1.18
8.30f 1.10
11.14i1.41
108,700t39,100
7.68 k 2.39
49,30Ot33,300
10.50k2.54
62,100~35,aoo 8.2323.45
39,600C 7,300
14.2823.28
10.91& 0.81
9.472 1.26
8.8220.85
8.60C0.69
wet
2.152055
4.42f 1.41
6.84 2 2.86
9.40 t 2.72
10.2924.03
9.802 0.92
21.902 7.15
20.6225.10
%
238,600 t 71,200
203,900 t 76,400
119,000C 59,000
61,lOOC 30,000
55,900 C 26,100
44,700 2 19,700
10,500-C 3,500
14,800 C 6,200
kg/cmz
kg/mm2
Elongation
at breaking
point
19.73t 3.26
19.33-+ 2.88
12.26? 1.51
10.652 1.73
10.39-C1.71
9.06 k 1.48
8.532 1.40
8.77k 1.19
E
Present results
UTS
8
5
7
6
12
12
9
6
5
4
No.
wet
dry
dry
wet
wet
wet
wet
wet ( d )
wet ( d )
State of
samples
OL and FC
OL and LDC
OCD and FC
OCD and LDC
OL and FC
OL and LDC
OL and FC
OL and LDC
OCD and FC
OCD and LDC
OL and FC
OL and LDC
Types of
osteons
measured osteons
22
15
21
21
28
18
24
16
32
23
22
No.
21.28 +- 1.83
20.60zk2.74
12.042 1.54
11.25C1.79
9.41&1.24
10.96 0.92
*
21.20C2.97
20.38 2 2.62
11.65k 1.74
10.952 1.88
9.592 1.55
kg/mmz
UTS
Combined results
of
N~ number of measured osteons; OL, osteons whose fiber bundles had a longitudinal course with the angles of fibers i n successive lamellae practically
the &&e. OCD osteons whose fiber bundles in successive lamellae formed an angle of 90'; LDC, osteons at lowest degree of calcification; FC, fully calcified
OSteons; 8, decklcsed. The young subject in the present investigation was aged 30 years; in the previous investigation, 20 years.
2-year-old ox
80-year-old man
Young man of
20 and 30
Individuals
and age
Average values of the ultimate tensile strength (UTS), modulus of elasticity ( E ) , % elongation at breaking-point for each set
TABLE 1
B
5
3
W
8
4
E
?rl
M
ti9
2
%n
8
0
P
TENSILE PROPERTIES OF SINGLE OSTEONS
383
:-I
0.01
In
ul
al
1
0
2
4
Oy0
6
8
I
I
I
1 0 1 2 1 4
elongation
Fig. 9 Diagrams closely corresponding to the
means of four sets of stress-strain curves recorded
for ox osteons having a very marked longitudinal
spiral course of fiber bundles in successive lamellae. ( a ) Air-dried and fully calcified osteon 83.
( b ) Air-dried osteon 93 at the initial stage of
calcification. ( c ) Wet and fully calcified osteon
97. ( d ) Wet osteon 101 at the initial stage of
calcification.
five wet fully calcified osteon samples. The
modulus of elasticity averaged 149,600 2
28,700 kg/cm2; the ultimate tensile
strength 12.12 2 0.74 or 12.04 2 1.54 kg/
mm2; and the percentage elongation 8.30
c1.10.
Figure 9d was recorded for osteon 101
and closely corresponds to the means for
six wet osteon samples at the initial stage
of ossification. The modulus of elasticity
was 54,OO 12,300 kg/cm2; the ultimate
tensile strength 11.28 ? 0.48 or 11.25 2
1.79 kg/mm2; and the percentage elongation averaged 11.14 1.41.
Finally, a careful examination of the
fractures of all the tested osteons (fig. 10)
showed that the break area may include
some osteocyte cavities, but there is no
demonstrable relationship between the
number of intersected osteocytes, on the
one hand, and the cross-section and ulti-
*
*
Fig. 10 A series of break ends of tested 0steons. Polarizing microscope. X 100.
mate tensile strength of the specimen, on
the other.
DISCUSSION
In discussing the results furnished by
the present investigation, it may be useful
to attempt a comparison between the tensile behavior of single osteons and the
tensile behavior of bone samples of macroscopic size.
Our results with samples taken from isolated osteons with a marked longitudinal
arrangement of fiber bundles in successive
lamellae show that the tensile curve for dry
bone approximates a straight line, as previously reported by Wertheim (1847), Hallerman ('34), Marique ('45) and Evans
and Lebow ('51) for macroscopic specimens. However, for the osteon samples,
the stress-strain curve deviates very slightly
from a straight line immediately before the
breaking point. This deviation is somewhat
clearer in osteons at the initial stage of
calcification than in fully calcified ones.
This result does not allow us to consider
dry osteons as entirely elastic as was for-
384
ANTONIO ASCENZI A N D ERMANNO BONUCCI
merly believed, especially by Hallerman,
for macroscopic bone samples. On the
other hand, there is some similarity between our data and those reported by
Dempster and Liddicoat (’52), who also
showed that Hooke’s Law is not strictly respected. As the breaking point is approached, the elongation of the sample is
somewhat higher than one would expect.
In any case, it should be emphasized that
the samples prepared from single osteons
are not entirely representative of all the
structures present in compact bone. For
instance, the interosteonic cementing zone
is lacking.
There is no significant difference between the modulus of elasticity of dry, fully
calcified osteons and the modulus of elasticity of dry osteons at the initial stage of
calcification. An impressive similarity exists between our values and those of Rauber
(1876), Manque (’45), Evans and Lebow
(’51) and Dempster and Liddicoat (’52).
The influence of moisture on the tensile
properties of osteons is indicated by the
difference in the shape of stress-strain
curves from wet and dry samples. If one
considers units having a marked longitudinal arrangement of the fiber bundles in
successive lamellae, the curve shows an
elastic range like that of the dry osteon.
But, as the samples elongate further toward
the breaking point, the proportionality between stress and strain ends at a proportional limit about half the breaking stress.
Beyond this proportional limit, each additional increment in stress causes excessive
yielding and permanent plastic deformation. Nevertheless, the transition from
elastic to plastic deformation occurs gradually, rather than abruptly, so that, regardless of how accurately the modulus of
elasticity is calculated, it is still an approximation. This explains the high standard
deviation of the mean obtained for the
modulus of elasticity. The behavior of the
tensile stress-strain curves shows that,
even at the level of single osteons, bone
behaves like a complex material. According to Sedlin (’65) and Sedlin and Sonnerup (’65), bone can be represented by a
Hooke body linked in series to a Hooke and
a Newton body, which are linked in parallel (Kelvin body).
The percentage elongation under tension
reveals a significant difference between dry
and wet osteon specimens, the latter being
subject to a greater elongation.
There is a very close correspondence between these results and the curves recorded
from macroscopic bone specimens (cf.
Dempster and Liddicoat, ’52; Evans and
Lebow, ’51). Moreover, our previous (cf.
Ascenzi and Bonucci, ’64) and present observations furnish evidence that the ultimate tensile strength of osteons, both at
the initial and final stages of calcification,
is significantly greater in dry tested samples
than in wet ones.
If the values obtained by Evans and Lebow (’51) for the percentage elongation
under tension were calculated applying the
same procedure used by us, i.e., multiplying by 100 the ratio “initial length/total
elongation at the breaking point,” one must
conclude that the percentage elongation of
the osteons is somewhat greater than that
obtained from macroscopic bone samples.
Both dry and wet osteons show that the
amount of calcium salts plays an essential
role in the elasticity of bone tissue. In dry
osteons, at the initial stage of ossification,
the stress-strain curve deviates much more
from the straight line than it does in dry
fully calcified osteons, thus revealing a
greater plastic range. On the other hand,
the curve obtained from wet osteons at the
initial stage of ossification is similar to
that for fully calcified wet osteons; however, the initial portion shows a clear deviation from the straight line of proportionality which indicates that plasticity
begins at an early stage. These data clearly
indicate that the elasticity of bone tissue
is a function of the amount of calcium
salts, i.e., the hydroxyapatite crystallites
present in the bone. The lower the calcium
content, the higher is the plasticity of the
tissue (see also Currey, ’62). In accordance with the present results, the stressstrain curves recorded for decalcified osteons indicate a sharp drop in elasticity.
An important point to be considered is
the close similarity between stress-strain
curves recorded for human and for ox osteons. This finding agrees with the view
of Ascenzi and Bonucci (’61), that, with
regard to optical properties (birefringence),
no essential difference exists between bone
TENSILE PROPERTIES O F SINGLE OSTEONS
units of the two mammalian species. The
investigations of Rowland, Jowsey and
Marshall ('59), which show that differences in the amount of calcium salts cannot
be demonstrated in human and ox osteons,
also provide indirect support for this view.
As previously reported, the tensile properties of human organic matrix (ossein),
prepared both from osteons with the lowest
degree of calcification and from fully calcified osteons, do not reveal any significant
differences. These results appear to agree
with those published by Strandh ('60) who
has furnished chemical evidence that variations in the amount of ossein are not demonstrable during the calcification of osteons. Moreover, it must be pointed out
that there is a very close correspondence
between t e modulus of elasticity of decalcified o teons with the lowest and highest degree of calcification. In the former,
the modulus of elasticity is 10,500 2 3,500
kg/cm2 and in the latter 14,800 t 6,200
kg/cmz. These values agree with those for
the modulus of elasticity of collagen which
is about 200,000 lb/in2, i.e., 14,061 kg/cm'
(cf. Currey, '62).
The values given for the ultimate tensile
strength of decalcified osteons are not comparable with those reported in our previous
paper (Ascenzi and Bonucci, '64) because
in the present investigation we were able to
measure the section of the samples directly
on decalcified material.
The differences between the stress-strain
curves recorded for osteons having longitudinally orientated fibers and osteons in
which the fiber bundles run alternately,
changing their direction in successive lamellae through an angle of go", suggest that
the latter have a lower modulus of elasticity
than the former. Besides, the ultimate tensile strength of osteons in which the fiber
bundles run alternately, changing their
direction in successive lamellae is significantly lower than in osteons having longitudinally orientated fibers. Consequently,
the percentage elongation increases. These
results appear to correspond with Maj and
Toajari's investigations (see Maj and Toajari, '37a, '37b; Toajari, '37) revealing that,
in the specimens with the greatest breaking load, the majority of the collagen fibers
are lontzitudinallv orientated. In this connectionr it should be noted that, according
2
385
to Dempster and Coleman ('61), the crossgrain ultimate tensile strength of bone
is much less than the parallel-to-grain
strength.
The stress-strain curves of osteon samples from an 80-year-old man show that
for wet units there is no appreciable change
in tensile properties with advancing age.
These findings are in agreement with those
of Evans and Lebow ('51), but differ from
those of Rauber (1876) and Melick and
Miller ('661, who reported a decrease in
tensile strength of bone with advancing
age. In conclusion, our results suggest
that the quality of osteons is unchanged
even in advanced old age.
ACKNOWLEDGMENTS
The authors are deeply grateful to Prof.
F. Gaynor Evans, Department of Anatomy,
The University of Michigan, Ann Arbor,
Michigan, U.S.A., for his help with this
manuscript.
They also wish to express their indebtedness to A. Benvenuti, G. Ciampi, F. Castellano and L. Di Baldo for technical assistance during the course of the present
investigation.
It is a pleasure to thank Springer-Verlag
for permission to publish figures 2 and 3,
which originally appeared in "Studies on
the Anatomy and Function of Bone and
Joints."
1966 F. Gaynor Evans, ed.
Springer-Verlag,Berlin - Heidelberg - New
York.
LITERATURE CITED
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osteon. Acta Anat., 44: 236-262.
1964 The ultimate tensile strength of
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Ascenzi, A., E. Bonucci and A. Checcucci 1966
The tensile properties of single osteons studied
using a microwave extensimeter. In: Studies
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Ascenzi, A., and C. Fabry 1959 Technique for
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139-142.
Battaglia, A., F. Bruin and A. Gozzini 1958
Microwave apparatus for the measurement of
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1-9.
Currey, J. D. 1959 Differences in the tensile
strength of bone of different histo1oe;ical
__
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---
386
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1962 Strength of bone.
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grain. J. Appl. Physiol., 16: 355-360.
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Melick, R. A., and D. R. Miller 1966 Variations
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