File Name: SLS1_02.DOC

EXPERIMENT SLS1 BSP2

BONE BIOMECHANICS

[PIs:]{.underline}

[Russia]{.underline}

A. V. Bakulin, Institute of Biomedical Problems, Moscow, Russia

[US]{.underline}

E. Morey-Holton, Ames Research Center, Moffett Field, California

[Introduction]{.underline}

Study of mechanical properties of mammalian bones performed previously
in Cosmos flights and ground-based simulation experiments has
demonstrated variations in bone strength and deformability during and
after exposure to microgravity \[1, 4, 5, 6, 7, 8\]. However, single
mechanical stress is only one of situations that may increase bone
injury risk. The objective of this investigation was to study mechanical
properties of rat spongy bone after space flight when exposed to
multiple repeated compression and to compare them with mineralization
parameters.

[Materials and Methods]{.underline}

The IMBP specialists were supplied with bone samples dissected from rats
flown in space for 9 days. Altogether, they received bone samples from
25 animals representing 5 groups: basal control (5 rats - BC), space
flight (5 rats - R+0), vivarium control (5 rats - C+0), flight rats
allowed to get readapted for 9 days after recovery (5 rats - R+9),
vivarium control for readaptation rats (5 rats - C+9).

Bone mechanical properties were examined using samples prepared from the
head of femur. Preliminary mechanical treatment was as follows: separate
the fragments to be taken under study by sawing in the normal direction
as related to subsequent loading and to grind them to make the cut
surface smooth.

In view of the fact that in physiological conditions the femoral head is
primarily exposed to compression, bone samples were compressed along the
direction of highest physiological loads. To provide strong restraint,
the bone samples were kept in a specially designed unit and fixed by
means of Wood\'s alloy. Bone samples were loaded using
cylindrically-shaped injectors of 1.67 mm2 in cross-section that were
moving at a speed of 1 mm/min. The stress-deformation curve was recorded
simultaneously with sample compression in every cycle.

Tests were performed by means of Instron and Tira Test machines. During
the first compression cycle every sample was stressed until the linear
stress-deformation pattern was changed; in this situation sample
deformation was 3 to 8% higher than elastic strain. After that the
injector was returned to an initial position. The subsequent compression
cycles were continued to reach the deformation level calculated
according

to the formula:

dl = (dl1\'/100) x 105,

where dl is deformation to be reached in a given loading cycle, dl1\' is
elastic strain determined in the preceding cycle of loading. After each
cycle the injector was returned to an initial position, and the
relaxation time of a sample following each cycle was 30\" to 30\". This
loading protocol was selected because: 1) it was necessary to have the
behavior of a bone sample in every subsequent cycle related to that in
the preceding cycle and 2) to provide a sufficiently large number of
loading cycles allowing adequate analysis of sample responses and a
sufficiently limited number of loading cycles in order to avoid error
induced by shifts in the sample positioning during prolonged testing.

On the basis of the resulting stress-deformation curves, the following
parameters were determined: elastic strength (δ1), elastic strain (ε1),
modulus of elasticity (E), and specific work of elastic strain (a); they
were calculated according to the formulas:

δ1 = P/S,

where S is the cross-section of the injector (1.67 mm2);

ε1= dl1/h;

where dl1 is elastic strain in mm; h is the linear height of the sample
measured prior to testing by means of a micrometer with an accuracy of
[+]{.underline} 0.01 mm;

E = δ1/ε1,

a = δ1 x dl1/2h.

In those cases when it was not easy to measure the linear portion of the
stress-deformation curve, the point of a maximum angular coefficient
(stiffness) of the sample was taken for elastic strain.

Tests were discontinued when the sample was destroyed: the destruction
time

was determined either visually or in terms of a drastic increase of
residual deformation combined with a characteristic change of the
stress-deformation curve profile.

With the help of a WLR-200 balance the samples were weighed in air and
in distilled water. Then their volume was calculated according to the
formula:

(P1 - P2)/d = V,

where P1 is the weight of a wet sample obtained in air, P2 is its weight
obtained in distilled water, and d is the specific weight of distilled
water.

Then the samples were dried and defatted in a Soxhlet apparatus. Samples
were contained in bags made of one-layered filter paper \-- one sample
per bag. The bags were labeled using a black pencil. Lipids were
extracted by a mixture of 100% ethanol and chloroform at a ratio of 4: 1
for 24 hours. After being defatted the samples in bags were air dried.
Dried and defatted samples were weighed.

Then the samples were put into 100% ethanol and kept there for
approximately

5 minutes to bring them to a constant weight. Then they were weighed
again in 100% ethanol and in air (samples soaked by 100% ethanol).

The sample volume was derived from the formula:

V2 = (P4 - P5)/d2,

where V2 is the volume of a sample, P4 is the weight of an ethanol
saturated sample in air, P5 is the weight of a sample in ethanol, and d2
is the specific weight of 100% ethanol. Porosity was calculated
according to the formula:

R = \[(P4 - P3)/(d2 x V2)\] x 100%,

where P3 is the weight of a dried defatted sample.

Then the samples were exposed to dry ashing in a muffle furnace at 600
oC (without oxidative agents) to reach a constant weight. The ash
residue was weighed,

and the volume content of the mineral component in bone, i.e., mineral
content, was calculated according to the formula:

Mm = P6/V,

where Mm is the mineral content, P6 is the weight of the ash residue,
and V is the volume of a sample \[2\].

The degree of bone mineralization was characterized by the
mineralization coefficient which was derived from the formula:

KM = P6/ (P3 - P6).

[Results and Discussion]{.underline}

Measurement data describing mineralization parameters of spongy bone are
summarized in Table 1. During the observation period the mineral content
increased

in both flight and control animals. The difference between C+0 and BC
animals was statistically significant while the difference between R+0
and BC animals was not, although the trend of changes remained the same.
The difference between C+0 and R+0 rats was statistically insignificant
but was suggestive of a tendency toward slower age-related changes of
spongy bone during space flight. Similar variations were observed during
the study of mineralization coefficient and porosity: as the age of
animals increased, the degree of bone mineralization grew and bone
porosity declined. The high rate of age-related time course variations
may point to a period of active age-related bone restructuring which
coincided with the time of the flight experiment. It should be noted
that, although bone mineralization tended to decline during flight, the
difference between R+0 and C+0 rats was not statistically significant.

Results of mechanical tests of bone samples are given in Tables 2
through 6. The tabulated data refer to strength, relative strain,
modulus of elasticity and specific work of elastic strain of bone
samples during several stress cycles. The upper line gives the results
obtained during the first stress test; in terms of the testing protocol
these data are in good agreement with the results of the elastic portion
of the strength-deformation curve obtained during single compression
test \[1\] and allows a comparison with the observations made in
previous biosatellite flight experiments.

Then the tables give results obtained from test cycles Nos. 25, 50, 75,
100, 125 and 150 which makes the data from different groups of animals
comparable. Also, the tables present data describing the most important
segments of variations of each parameter thus giving a good idea of time
course variations in general. In this case the cycle number was
calculated as the mean for each animal group and has a fractional value
and a confidence interval. The lower line presents data obtained during
the last cycle that preceded sample destruction which are averaged for 5
samples.

The results of the first test cycle give evidence that bone strength
declined after a 9-day space flight. When compared to C+0 data, elastic
strain, modulus of elasticity and specific work of elastic strain were
significantly lowered. Specific work of elastic strain was also
substantially reduced in comparison with BC rats. These findings are at
variance with the results of previous biosatellite experiments in terms
of time course variations of modulus of elasticity and elastic strain.
After biosatellite experiments of 5 to 14 days in duration, elastic
strain, as a rule, diminished, except for the Cosmos-1887 flight after
which the animals remained at 1 g for two days prior to dissection. In
some cases modulus of elasticity tended to increase \[1, 7\]. At the
same time our observations give support to previous findings suggesting
substantial decline in bone strength against the background of slight
and statistically insignificant changes in mineral content \[1, 4, 5. 6.
7\].

Time course variations in elastic strength are also illustrated in
Figure 1. Mention should be made of a significant reduction in the
number of compression cycles required to reach sample destruction in
C+0, R+0 and C+9 rats when compared to BC animals. This observation
together with a high rate of time course variations of bone
mineralization also points to the intensity of age-related bone
restructuring; in terms of time the highest intensity occurred during
flight.

In a living body, mechanical injury of bone microstructures can be
produced by very strong (extreme) mechanical effects or by repeated
cyclic (physiological) loading leading to fatigue changes in the
material. In both cases the microstructures with the highest degree of
mineralization and, consequently, with a high stiffness and low relative
strain prove to be most vulnerable. Due to this, they develop early
fatigue changes and, if they remain to be stressed, mechanical injuries.
Destruction of the most fragile and stiff microstructures diminishes the
modulus of elasticity. In this situation, variations of elastic strength
are dependent on the level of relative strain during every stress cycle
and on the ratio of the number of microstructures with a varying degree
of mineralization and, consequently, mechanical properties of bone. Time
course variations of elastic strength in C+0, R+0 and C+9 rats were
similar: peak was reached during cycles 40 to 60 and destruction
occurred during cycles 80 to 100. This suggests that the most important
part was played not by the difference in the proportion of
microstructures with various mineral content and mechanical properties
but by their different concentration which was responsible for
dissimilar bone strength. It should be noted that this conclusion can be
applied only to mineralized bone and that the amount of nonmineralized
tissue has essentially no impact on compression test results. Time
course variations of elastic strength in BC and R+9 rats was different:
peak was reached during cycles 110 to 130 and destruction occurred
during cycles 134 to 151. In this case, longer-term resistance that bone
offered to cyclic compression can be attributed to a substantial amount
of elastic and, evidently, poorly mineralized juvenile structures formed
as a result of active remodeling processes.

Time course variations in elastic strain can be characterized by its
monotonous increase with an increase in the number of loading cycles.
This was associated with the loading procedure per se and with a high
bone ability for relaxation and shape recovery after each loading cycle.
This, in turn, can be attributed to a relatively low degree of
mineralization. In the course of loading slightly noticeable residual
deformations occurred only immediately before sample destruction.
Peculiar relaxation of bone samples prior to destruction may be
responsible for a wider data scattering, i.e., an increase of the mean
error (m) when the time of sample destruction approached.

Time course variations of the modulus of elasticity are shown in Figure
2. In

the course of loading the modulus of elasticity diminished, probably,
due to the above mentioned factors.

Time course variations of specific work of elastic strain in all groups
of animals, as illustrated in Figure 3, showed a characteristic pattern:
monotonous increase in the course of loading and a sudden decrease
immediately before destruction. The causes responsible for this kind of
behavior remain unclear. It is very likely that a decrease of the
specific work during cyclic loading reflects the process of sample
destruction and, therefore, can be viewed as another indicator of
structure changes.

In summary, the 9-day flight did not produce significant changes in
mineralization parameters of rat spongy bone. The results obtained were
suggestive of only tendencies toward diminished mineralization when
compared with the age-matched controls. The exposure led to a
significant decline in mechanical properties of bone as a material;
however, this did not enhancebone fragility, and was, probably,
associated with the phenomena of \"strength degradation\" \[3\].
Analysis of repeated loading revealed substantial differences in bone
behavior after 9 days of recovery. The above changes could be produced
by a modified rate of bone remodeling. In view of this, it seems
appropriate to discuss the bone strength data in comparison with
morphometric results obtained by other investigators.

[References]{.underline}

1\. Bakulin, A.V., Oganov, V.S., Feldesz, J. Study of Rat Functional
Adaptation to Altered Mechanical Loading. Abstr. Intern. Symp. Cosmos
Biosatellites. Leningrad, 12-15 August, 1991, pp. 14-15 (in Russian).

2\. Volozhin, A.I., Didenko, I.E., Stupakov, G.P. Chemical Composition
of the Mineral Component of Vertebrae and Heel Bone of Bed Rested Men.
Kosm. Biol. Aviakosm. Med., 1981, vol. 15, No. 1, pp. 43-44 (in
Russian).

3\. Knets, J.W., Pfafrod, H.O., Saulgozis, J. Deformation and
Destruction of Hard Biological Tissues. Riga, Zinatne, 1980, 319 pp. (in
Russian).

4\. Mirolyubov, G.P., Korzhenyants, V.A., Stupakov, G.P., Volozhin,
A.I., Korolev, V.V. Bone Strength During Hypokinesia. Bull. Exper. Biol.
Med., 1975, No. 10, pp. 36-38 (in Russian).

5\. Stupakov, G.P., Volozhin, A.I., Didenko, I.E. Strength and Mineral
Composition of Man\'s Vertebrae Upon Bed Rest. Bull. Exper. Biol. Med.,
1981, vol. 91, No. 5, pp. 544-546 (in Russian).

6\. Stupakov, G.P., Volozhin, A.I., Zasypkin, V.V., Remizov, S.M.
Variations of Mechanical Properties of Rat Bones as a Result of a 19-Day
Space Flight on Cosmos-936. Mech. Composite Materials, 1980, No. 3, pp.
530-537 (in Russian).

7\. Bakulin, A.V., Ilyin, E.A., Oganov, V.S., Lebedev, V.I. The State of
Bones of Pregnant Rats During an Acute Stage of Adaptation to
Weightlessness. Proc. 2nd Intern. Conf. Space Physiology. Toulouse,
France, 20 - 22 Nov., 1985 (ESA SP-237), pp. 225-228.

8\. Spengler, D.M., Morey, E.R., Carter, D.R., Turner, R.T., Baylink, D.
Effects of Spaceflight on Structural and Material Strength of Growing
Bone. Proc. Exp. Biol. Med., 1983, vol. 174, pp. 224-228.

[Summary]{.underline}

After 9 days of flight and after 9 days of recovery mechanical
properties and mineral content of spongy bone exposed to multiple cyclic
compressions were investigated. No significant changes in mineral
content were observed; the variations indicated only a trend toward
diminished mineralization when compared to the age-matched controls.
However, mechanical properties of rat bone significantly deteriorated.
Preliminary analysis of the cyclic compression results revealed
significant differences in bone behavior 9 days after recovery. These
changes can be attributed to an increase in the number of poorly
mineralized juvenile structures in rat bones.

[Table 1]{.underline}

Mineralization Parameters of Rat Spongy Bone (Femoral Head; M/m)

  ----------------- ----------------- ----------------- -----------------
  Rat group         Mineral content   Mineralization    Porosity
                                      coefficient       

  ----------------- ----------------- ----------------- -----------------

  ----------------- ----------------- ----------------- -----------------
  n = 5             g/cubic cm        g/g               \%

  ----------------- ----------------- ----------------- -----------------

  ----------------- ----------------- ----------------- -----------------
  BC                0.368             0.828             31.2

  ----------------- ----------------- ----------------- -----------------

  ----------------- ----------------- ----------------- -----------------
                    0.008             0.028             1.8

  ----------------- ----------------- ----------------- -----------------

  ----------------- ----------------- ----------------- -----------------
  C+0               0.394\*           0.892             34.4

  ----------------- ----------------- ----------------- -----------------

  ----------------- ----------------- ----------------- -----------------
                    0.013             0.027             2.1

  ----------------- ----------------- ----------------- -----------------

  ----------------- ----------------- ----------------- -----------------
  R+0               0.378             0.850             34.1

  ----------------- ----------------- ----------------- -----------------

  ----------------- ----------------- ----------------- -----------------
                    0.009             0.043             1.8

  ----------------- ----------------- ----------------- -----------------

  ----------------- ----------------- ----------------- -----------------
  C+9               0.441\*           0.948\*           26.1\*

  ----------------- ----------------- ----------------- -----------------

  ----------------- ----------------- ----------------- -----------------
                    0.012             0.021             1.0

  ----------------- ----------------- ----------------- -----------------

  ----------------- ----------------- ----------------- -----------------
  R+9               0.459\*\*         0.977\*\*         26.5\*\*

  ----------------- ----------------- ----------------- -----------------

  ----------------- ----------------- ----------------- -----------------
                    0.012             0.020             1.5

  ----------------- ----------------- ----------------- -----------------

\*p BC \< 0.05

\*\*p R+0 \< 0.05

[Table 2]{.underline}

Mechanical Tests of Spongy Bone of BC Rats (Femoral Head; n = 5; M/m)

  -------------- -------------- -------------- -------------- --------------
  Loading cycle  Mechanical     Relative       Modulus of     Specific work
                 stress         strain         elasticity     

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 N/mm2          \%             N/mm2          N/mm2

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  1              15.10          9.54           164.2          0.76

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 2.10           1.48           18.7           0.19

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  25             21.14          15.75          136.4          1.72

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 2.29           1.26           14.9           0.24

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  29.2           22.21          16.85          131.6          1.90

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  7.4            2.48           1.05           11.1           0.30

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  50             23.45          21.10          112.2          2.48

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 2.49           0.95           12.1           0.29

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  52.2           23.59          21.55          110.2          2.54

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  3.6            2.50           0.86           13.0           0.28

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  67.1           23.11          24.91          94.8           2.86

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  0.8            1.00           2.08           12.5           0.16

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  75             22.95          27.32          85.9           3.12

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 0.95           1.92           9.2            0.20

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  86.1           23.44          29.69          79.8           3.48

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  5.7            0.89           1.76           6.0            0.24

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  100            25.22          32.57          78.3           4.12

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 1.06           1.49           6.1            0.17

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  111.2          26.66          34.91          77.0           4.63

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  1.8            1.22           1.22           6.2            0.11

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  125            25.80          37.28          70.4           4.77

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 1.69           1.70           7.2            0.22

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  132.6          25.32          38.60          66.8           4.84

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  2.7            2.15           2.18           8.2            0.34

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  150            24.62          44.40          57.5           5.36

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  10.1           4.21           3.67           12.2           0.41

  -------------- -------------- -------------- -------------- --------------

  -----------------------------------------------------------------------
  S a m pl e d e s t r u ct i o n

  -----------------------------------------------------------------------

  -------------- -------------- -------------- -------------- --------------
  151.3          21.47          44.55          55.7           4.57

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  32.6           2.18           8.14           13.7           0.59

  -------------- -------------- -------------- -------------- --------------

[Table 3]{.underline}

Mechanical Tests of Spongy Bone of C+0 Rats (Femoral Head; n = 5; M/m)

  -------------- -------------- -------------- -------------- --------------
  Loading cycle  Mechanical     Relative       Modulus of     Specific work
                 stress         strain         elasticity     

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 N/mm2          \%             N/mm2          N/mm2

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  1              21.04\*        7.75           286.9\*        0.81

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 0.71           0.79           38.7           0.08

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  17.1           28.17          10.53          272.8          1.48

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  2.5            1.46           0.65           25.5           0.10

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  25             28.31          13.58          219.3          1.92

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 1.20           0.58           16.6           0.11

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  30.7           28.41          15.77          180.7          2.24

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  2.4            0.94           0.50           7.7            0.11

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  49.3           31.86          19.87          161.0          3.16

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  1.8            0.78           0.60           7.2            0.11

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  50             31.84          19.96          160.4          3.18

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 1.04           0.77           10.6           0.07

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  59.3           31.70          21.11          152.6          3.32

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  1.2            1.29           0.93           13.9           0.03

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  66.2           29.02          24.08          120.7          3.49

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  1.5            0.74           0.33           4.3            0.07

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  75             29.60          24.99          120.7          3.67

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 1.24           0.85           9.6            0.08

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  78.7           29.85          25.38          120.7          3.75

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  2.6            1.74           1.38           14.9           0.10

  -------------- -------------- -------------- -------------- --------------

  -----------------------------------------------------------------------
  S a m pl e d e s t r u ct i o n

  -----------------------------------------------------------------------

  -------------- -------------- -------------- -------------- --------------
  92.9\*         28.25          28.42          100.1          4.03

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  9.1            2.02           1.42           7.2            0.42

  -------------- -------------- -------------- -------------- --------------

Significant difference in the first and the last loading cycles:

\* p BC \< 0.05

\*\* p C+0 \< 0.05

[Table 4]{.underline}

Mechanical Tests of Spongy Bone of R+0 Rats (Femoral Head; n = 5; M/m)

  -------------- -------------- -------------- -------------- --------------
  Loading cycle  Mechanical     Relative       Modulus of     Specific work
                 stress         strain         elasticity     

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 N/mm2          \%             N/mm2          N/mm2

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  1              12.97\*\*      7.26           186.1\*\*      0.48\*,\*\*

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 0.53           0.90           20.7           0.07

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  18.4           18.21          11.40          163.3          1.07

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  5.5            1.92           1.48           14.7           0.23

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  25             19.64          12.77          157.8          1.30

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 1.47           1.18           11.8           0.18

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  40.7           23.04          16.02          145.0          1.85

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  2.2            1.02           0.88           9.0            0.14

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  50             23.85          18.18          133.2          2.18

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 0.81           0.83           7.8            0.11

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  57.8           24.53          20.00          123.4          2.45

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  1.8            0.60           0.78           6.7            0.09

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  69.9           23.70          22.86          104.1          2.71

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  0.9            0.28           0.70           4.5            0.06

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  75             23.32          24.02          98.2           2.80

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 0.96           0.76           6.0            0.13

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  86.5           20.96          26.51          79.3           2.77

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  4.1            1.64           0.81           7.6            0.20

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  100            22.43          29.57          76.5           3.32

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 3.12           2.92           11.9           0.86

  -------------- -------------- -------------- -------------- --------------

  -----------------------------------------------------------------------
  S a m pl e d e s t r u ct i o n

  -----------------------------------------------------------------------

  -------------- -------------- -------------- -------------- --------------
  103.6\*        19.46          30.03          65.5           2.93

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  9.3            0.52           2.01           3.9            0.23

  -------------- -------------- -------------- -------------- --------------

Significant difference in the first and the last loading cycles:

\* p BC \< 0.05

\*\* p C+0 \< 0.05

[Table 5]{.underline}

Mechanical Tests of Spongy Bone of C+9 Rats (Femoral Head; n = 5; M/m)

  -------------- -------------- -------------- -------------- --------------
  Loading cycle  Mechanical     Relative       Modulus of     Specific work
                 stress         strain         elasticity     

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 N/mm2          \%             N/mm2          N/mm2

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  1              19.91          7.00           339.0\*        0.71

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 2.56           1.49           95.5           0.19

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  24.1           29.47          13.28          257.5          1.94

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  4.0            4.85           2.48           69.7           0.47

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  25             30.01          13.40          258.0          2.01

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 4.64           2.23           53.7           0.52

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  40.2           39.24          15.37          267.2          3.05

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  3.0            4.42           1.98           37.6           0.56

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  50             39.11          17.96          235.0          3.49

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 3.35           2.17           38.9           0.42

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  58.3           39.01          20.15          207.6          3.85

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  1.7            2.29           2.36           40.3           0.28

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  72.8           34.91          24.78          151.0          4.21

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  2.4            3.24           2.45           34.3           0.18

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  75             36.52          29.02          148.7          5.11

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 20.52          17.16          81.3           3.09

  -------------- -------------- -------------- -------------- --------------

  -----------------------------------------------------------------------
  S a m pl e d e s t r u ct i o n

  -----------------------------------------------------------------------

  -------------- -------------- -------------- -------------- --------------
  85.3\*         35.91          26.53          151.2          4.65

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  12.8           2.55           4.77           32.0           0.70

  -------------- -------------- -------------- -------------- --------------

Significant difference in the first and the last loading cycles:

\* p BC \< 0.05

\*\* p C+0 \< 0.05

[Table 6]{.underline}

Mechanical Tests of Spongy Bone of R+9 Rats (Femoral Head; n = 5; M/m)

  -------------- -------------- -------------- -------------- --------------
  Loading cycle  Mechanical     Relative       Modulus of     Specific work
                 stress         strain         elasticity     

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 N/mm2          \%             N/mm2          N/mm2

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  1              17.76          6.74\*         267.4\*        0.61

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 2.18           0.53           33.1           0.10

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  7.5            20.20          9.10           225.9          0.91

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  1.3            2.56           0.43           36.3           0.10

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  25             25.48          12.90          208.9          1.63

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 2.92           0.82           37.6           0.13

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  30.3           27.07          14.04          203.8          1.85

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  3.4            3.28           1.21           39.0           0.16

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  50             34.44          18.51          191.7          3.25

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 4.14           1.23           33.2           0.38

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  57.2           37.14          20.15          187.3          3.76

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  3.3            4.99           1.26           27.5           0.61

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  74.7           32.12          23.51          136.6          3.79

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  1.0            4.98           0.70           21.0           0.62

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  75             32.12          23.51          136.6          3.79

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 4.45           0.77           18.0           0.59

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  86.7           34.36          26.97          128.1          4.63

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  2.4            3.91           0.83           15.0           0.56

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  100            29.38          31.04          95.8           4.54

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 4.72           0.79           16.0           0.74

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  103.1          28.22          31.99          88.2           4.52

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  3.3            5.53           0.76           16.9           0.91

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  125            41.13          36.22          113.6          7.47

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
                 4.11           0.81           12.3           0.72

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  126.3          41.89          36.47          115.0          7.64

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  3.8            2.69           0.87           7.7            0.53

  -------------- -------------- -------------- -------------- --------------

  -----------------------------------------------------------------------
  S a m pl e d e s t r u ct i o n

  -----------------------------------------------------------------------

  -------------- -------------- -------------- -------------- --------------
  134.9\*\*      34.04          37.78          93.6           6.44

  -------------- -------------- -------------- -------------- --------------

  -------------- -------------- -------------- -------------- --------------
  16.0           3.81           3.50           14.6           0.93

  -------------- -------------- -------------- -------------- --------------

Significant difference in the first and the last loading cycles:

\* p BC \< 0.05

\*\* p C+0 \< 0.05

![](media/image1.pct){width="7.5in" height="3.8333333333333335in"}

Figure 1. Variations in mechanical stress upon repeated loading of the
head of rat femur.

![](media/image2.pct){width="7.430555555555555in" height="4.0in"}

Figure 2. Variations in the modulus of elasticity upon repeated loading
of the head

of rat femur

![](media/image3.pct){width="7.319444444444445in"
height="3.8472222222222223in"}

Figure 3. Variations in specific work of elastic strain upon repeated
loading of the head of rat femur