Viscoelastic properties of copper deficient chick bone

J Biamechonics Vol 12, pp. 197-203 Pergamon Press 1979. Printed m Great Britain

VISCOELASTIC PROPERTIES OF COPPER DEFICIENT CHICK BONE* RKHAIW

S.

RKGINSI,

ANTHONY G.

CAKTWKIGHT$

and Rotre~r B.

Department of Orthopaedicst and the Department University of California, Davis, California,

RWKI:K$

of Nutrition:, U.S.A.

and Department

of Mechanical Engineerin& University Guildford, Surrey, England

of Surrey,

Abstract Chickens fed copper deficient diets from birth produce a bone with increased collagen solubility. This, in turn, is related to the decrease in the cross-links in the collagen. The decreased cross-links in the collagen alter the mechanical properties of bone so that it exhibits an increase in its stress relaxation and a decrease in its tolerance to deformation. The above information was obtained by studying whole chick tibias subjected to stress relaxation experiments in torsion, followed by torsional tests to failure.

INTRODUCTION Copper is a necessary metal for many biological systems ; for example, in mollusks and arthropods, it is required for the respiratory pigment hemocyanin (Storer et al., 1972) which is analogous to the ironcontaining pigment hemoglobin in mammalian systems. The cytochrome oxidase systems also require copper for proper function (Carnes, 1968). In connective tissue, copper is a necessary metal for lysyl oxidase, an enzyme participating in the formation of intra and intermolecular cross-links in collagen and elastin. Such cross-links help provide additional stability and, in most instances, decreases the solubility of the collagen and elastin fibers (Fietzek et al., 1976). The effects of copper deficiency on bone have been described in several species, including the chicken (Underwood, 1971; Carlton et al., 1974; Rucker et al., 1975, 1977). The bone changes consist of increased fragility, especially in the epiphyseal and metaphyseal area, but cellular morphology and mineralization of cortical bone do not seem to be affected by the lack of dietary copper. The mechanical properties of bone are also affected by insufficient dietary copper. Rucker et al. (1975, 1977) has reported changes in the physical properties of bone from copper deficient chicks which suggests alteration of the viscoelastic properties of bone due to copper deficiency. Viscoelastic properties of materials may be examined by a number of different techniques (Alkonis et ul., 1972; Fietzek ef al., 1976) and several investigators (McElhaney, 1966; Sammarco et al., 1971; Sedlin, 1965a. b) have investigated these properties in bone.

* Received

30 January

1978.

I/ Rapid repair material. Meadway Dental Supplies, Ltd., 4 Way, Old Woking, Surrey, England. When tested within the parameters of these experiments, the potting material did not demonstrate any stress relaxation. Manor

Basically, it involves deforming the material and examining the force required to maintain the deformation. In viscoelastic material, the force should decrease with time. Assuming collagen represents a major viscoelastic element of bone, alterations in the structural properties of collagen should cause changes in the stress relaxation times. In view of the effects of copper deficiency on collagen cross-linking and the physical properties of bone, a study of stress relaxation times of the tibia from copper deficient chicks seemed appropriate. After the initial stress relaxation tests were done, attempts to create artificial cross-links in the collagen, using formaldehyde and sodium borohydride (NaBH,), were carried out. Formaldehyde treatment followed by NaBH, reduction results in the formation of reduced aldimine and aldo-derived cross-links in collagen (Bailey, 1968a, b; Balian et (II., 1969).

MATERIALS AND METHODS

White Leghorn chickens, from the day of hatching, were fed copper deficient or copper supplemented (25 ppm) skim milk diets (Appendix A) for 20 days. The group fed the diet containing 25 ppm of copper (supplemented as CuSO,) served as controls and their intake was restricted to that of the copper deficient birds. The basic diet contained less than one ppm of copper. At 20 days, the animals were sacrificed and the tibias collected for study. The control and test animals were paired by body weight, as bone strength and some changes in bone morphology are known to be related to body weight (Saville, 1976; Rucker er al., 1975). The tibias were placed in saline containing 100 units of penicillin and 0.5 mg streptomycin per 20 ml and stored at -20°C. Just prior to testing the bones were thawed, the epiphyses and periosteum removed and each end of the bone potted in methylmetacrylate. I/ 197

198

RICHARD S. RIGGINS,ANTHONY G. CAR-WRIGHT

and

ROBERTB. RUCKER

Table I. Some parameters measured

on the bone specimens. D indicates the copper deficient bones and C indicates the controls. The values are the mean f standard error. There are no significant differences between the deficient animals and their controls. Two estimates for outside diameter and cortical thickness were taken for each bone when possible Number of determinations

Mean (m)

Standard error (m)

Length out of pot

D C

18 16

2.2 x lo-* 2.0 x 1o-2

5.2 x 1o-3 5.0 x lo-’

Outside diameter

D C

36 32

2.48 x 10-s 2.37 x lO-3

5.7 x lo-5 3.3 x lo-5

Cortical thickness

D C

31 30

3.54 x lo+ 3.48 x lO-4

1.2 x 1o-s 1.2 x 1o-5

Polar moment inertia rn+

D C

12 12

1.18 x 10-i’ 1.13 x lo-‘2

5.7 x lo-t4 6.8 x lo-i4

The bones were kept moist with a phosphate buffered saline, pH 7.2, at all times. The geometry of the specimen can be seen in Fig. 1 and the average measurements taken with a micrometer and calipers can be found in Table 1. For cortical thickness, two measurements were taken with the micrometer on fragments of bone from the midshaft, after the bone was fractured. Outside diameters were measured with the caliper at midshaft, Two measurements were taken, 90” apart. The testing apparatus was a modification of the Tecquipment* torsional testing machine. A stainless steel shim 0.06 x 1.3 x 5.0 cm, on which two wire foil strain gauges were cemented?, converted the torque to an electrical signal which was recorded on an x-y plotter& The degree of rotation was converted to an electrical signal by a simple carbon track potentiometer. A constant temperature was maintained by a continuous and voluminous irrigation of the bone with phosphate buffered saline, pH 7.2. A constant temperature waterbath was used to maintain the desired temperature and the solution was recirculated with an impulse pump. The machine was statically calibrated using analytical weights and a dial gauge to measure the degree of rotation. The stress relaxation experiments were performed by placing the bone in the machine and allowing the temperature to stabilize (approximately 15 min) at 38°C. A step input of 0.041 Nm was applied to the bone and the torque required to maintain the deformity was recorded over a 30min period. It required 1-2sec to apply the initial torque. The following experiments were done. After the initial stress relaxation experiments, one tibia of the pair was soaked ‘24 hr in 0.1 molar formaldehyde solution followed by 8 hr in a 5 mg/ml NaBH, solution, buffered * Sam L. Denison and Son, Ltd., Hunslet Foundry, Leeds 10, England. t Gauge type EA-06-5OOBH-120 Micro Measurements, Romulus, Michigan, U.S.A. # X-Y Recorder 26OOA3.Bryan’s Southern Instruments, Ltd., Willow Lane, Mitcham, Surrey, England.

in an isotonic phosphate solution, pH 8.6. The corresponding member of the pair served as a control and was treated for a similar period in isotonic phosphate buffer, pH 8.6. The stress relaxation experiments were then repeated. Finally, after allowing the bones to stabilize 48-72 hr at SC, they were tested to failure. Torque was applied at a constant rate of 0.04 rad set-‘. The choice of 38°C in the stress relaxation experiments was based on prior investigations. The effects of strain rate on the elastic modulus of bone is well known (McElhaney, 1966; Sammarco et al., 1971; Sedlin et al., 1965a, b), but the effects of temperature has been less explored. From theoretical considerations of viscoelastic material, the elastic modulus should be temperature dependent, as well as strain rate dependent. Subsequently, the effects of temperature on the stress relaxation of chick tibia was evaluated using the normal bone from three-week-old chickens. Temperatures of 2, 25 or 40°C were examined using eight bones from four chickens, beginning at 2” and progressing to 40°C. From these results, 38°C was selected as the appropriate temperature for the experiments (see Results).

k2.12cmj

Distal /...... -.i

Proximal 7”. .........._

3wk. old Chick Tibia Epiphyses Removed

Fig. 1. Diagram of a specimen of bone with the mean values for the parameters measured (see Table 1) not to scale.

199

Properties of copper deficient chick bone r

0.10

isi

MAXWELL

BODY

0 ?

b

Fig. 2. Maxwell body. E, represents the spring constant q represents the dashpot constant.

and

+

’

The simplest linear viscoelastic model for a stress relaxation experiment is the Maxwell body (Fig. 2). The stress at any time (I) for a Maxwell body subjected to a constant strain is f o,e-7,

(5 =

0.05

I

I

I

I

1

I

I

0

5

IO

15

20

25

30

TIME

(minutes1

Fig. 3. Graph of time (1) vs -In u/a0 for chick tibia. gO = initial torque (stress) and o = torque (stress) and any time t. The plot assumes chick tibia responds as a simple Maxwell body to a stress relaxation experiment which, if true. the plot should have been linear.

(1)

where u = stress, go = initial stress

et al., 1976). Rearranging equation logarithms of both sides yields:

and

_,,“=f Qo

T = relaxation time defined as the proportionality constant between the stress-strain moduli of the spring and the dashpot.

72

E'

r

I

‘5

A plot of in(a/a,) against t should be linear with a slope of l/r. Such was not the case for the bone samples examined (Fig. 3); however, by solving the equation for

where q is the stress-strain proportionality constant of the viscous elements (the dashpot) and E is the stress-strain proportionality constant for the elastic elements (the spring) (Aklonis et al., 1972 ; Wainwright

9.2

1 and taking the

1

7=---f

lna QO

. LEFT TIEIA 0 RIGHT TIBIA

4.6* 0

2.3

4.6

6.9

Log 1 Fig. 4. Graph where

of -log

relaxation

time (7) vs log time (t) for chick tibia

TZ-----

t

In” 00 The data from both the right and left tibia of a copper deficient animal have been plotted showing linearity of the data when expressed in this form. B = torque at any time (t), bO = initial torque.

the

RICHARDS. RIGGINS,ANTHONY G. CARTWRIGHTand ROBERTB. RUCKER

200

Table 2. Stress relaxation values from log-log plots of relaxation time (T) vs time (t). Values are for the mean f the standard error. Within groups, significant differences exist between values not having the same letter in the superscript. P values can be found in the text. Numbers in parentheses represent the number of observations, whereas the letters in parentheses refer to the formulae in the text. Test A represents those bones treated with buffered (pH 8.6) 0.1 M formaldehyde and NaBH,, whereas the Test B designates bone treated only with buffer (pH 8.6)

throughout the incubation period (see text)

Initial Tests Intercepts (f) Slopes (6)

Control

Copper deficient

155 k 17”.*(12) 0.581 k 0.018’(12)

203 f 28”(12) 0.513 k 0.024’(12)

187 k 23”.b(6) 0 .533 + - 0.024’*‘+(6)

184 + 5Pb(6) 0.556 f 0.021’~‘(6)

195 f 47”.b(6) 0.526 f 0.029d(6)

120 + 32b(6) 0.561 k 0.02Yd(6)

Test A

Intercepts (f) Slopes (b) Test B

Intercepts (_f) Slopes (b)

and plotting

log T against log f, a straight line was (Fig. 4). As a result, relaxation times were calculated for each test using torque values (a) at times 60,250,500, 1000 and 1500 sec. The log T was plotted against log t and the slope and intercepts were determined by the method of least squares (Dixon et al., 1969). The mean values for the slope and intercepts for each group were then computed after this procedure (Table 2). For statistical analysis, the differences between paired animals and, when appropriate, between tibias obtained

from the same animal, were tested against a null hypothesis using the student t test (Dixon et al., 1969). Generally, this gave the same results as would have

been obtained if the mean values of the various groups had been tested against each other ; however, by using paired data, the statistical precision was increased and a number of theoretical disadvantages were eliminated.

RESULTS

Temperature

Increasing temperature caused an increase in stress relaxation over the temperature tested. Figure 5 shows the plot of the log relaxation time vs log time, which linearized the results for analysis. The difference between the intercepts at 40 and 3°C is significant (p < 0.025) and between 25 and 3°C (p < 0.005) but not between 25 and 40°C. The slopes did not differ. Stress relaxation time - copper dqjicient and control chicks

Significant differences exist between stress relaxation times of the control chick tibias (C) and corresponding tibias from copper deficient chicks (0). Figure 6 shows the percentage of the initial torque vs time for the control and copper deficient bones. Table 2 (initial tests) gives the computed mean values and standard error for the slopes and intercepts when the data is linearized by plotting on log-log paper. The data are based on twenty-four observations using twelve chicks. The difference between the slopes was significant (p < O.Ol), but the difference between the intercepts was not significant. I

0

3.75

_I

7.5

Log t Fig. 5. Graph of the log relaxation time (T)vs log time (t) for three. different temperatures. The differences between the intercepts 40 and 3°C (p < 0.025) and 25 and 3°C (p i 0.05) are significant but not the differences between 25 and 40°C. The slopes are identical.

Stress relaxation times and art$cial cross-links No significant differences were noted between stress relaxation of the copper deficient chick tibias treated with formaldehyde and NaBH, and their corresponding controls (test A - Table 2). However, there was a significant decrease in the value of the intercept (p < 0.005) in the copper deficient group after incubation

Properties

STRESS

of copper

deficient

201

chick bone

RELAXATION

STRAIN

RATE

0.04

RADIANS

set-’ ,086

-CONTROL ---COPPER

DEFICIENT

IO.6

DEFORMATION

13.8

RADIANS

144

19.3

me1

85 Fig. 7. Graphs of the mean values for torque vs deformation until failure at 0.04rad SE-‘. There is no significant difference between the modulus of rigidity (slope) or the torques at yield or at fracture. The differences between the deformation at yield and at fracture were significant at p < 0.05.

80

I

I

IO

5

I

I

I

I

15

20

25

30

TIMECminutes)

Fig. 6. Stress relaxation in copper deficient chick tibias and tibias from control animals. The ordinate represents the percentage of initial torque remaining at any specific time. The two curves are significantly different.

in phosphate buffer, pH 8.6 (initial test vs B-Table 2). The copper supplemented control group showed a decrease in the slope @ < 0.025) after incubation in

buffer at pH 8.6 (initial test vs test B - Table 2). Tests to failure

When a continuously increasing torque was applied at a rate of 0.04 rad set- I until failure, differences in yield point, ultimate strength, torsional rigidity and

energy absorption to fracture could be evaluated (Fig. 7). Although there was no significant difference between copper deficient bones and control bones for the values of torsional rigidity, torque at yield and ultimate torque, deformation or strain at yield and at failure was significantly greater for the tibias from the control animals (p < 0.05 both values, Table 3). Additional parameters

The mean body weight for the chickens was 112g, with a standard error of 4.5 g. There was no difference in the mean body weights of the two groups, as the copper deficient and control chickens were paired and matched by body weight. The mean value and standard error for the length of bone tested, its outside diameter at midshaft and the cortical thickness, can be found in Table 1. The polar moment

Table 3. Table of values for yield deformations

and torques as well as ultimate values and moduli of rigidity. Values represent the mean k standard error and numbers in parentheses represent the number of bones. Within groups, significant differences exist between numbers not having the same letter superscript. Test A is the group treated with formaldehyde and NaBH,, whereas Control B were treated with the buffer only Control

Copper

deficient

_.____ Yie&de~rmations Control

(rad/m)

B

Yield torque (Nm) Test A Control B Ultimate deformation Test A Control B Ultimate torque Test A Control B

14 f 1.0(6) 13.8 f 0.60(S)

11.4 f 1.5(7)b 10.6 + 0.60(B)*

0.067 f 0.0050(6) 0.076 + 0.0073(6)”

0.085 f 0.0049(6) 0.071 * 0.0054(B)

(rad/m) 18 + 1.0(5)“.b 19 + 1.0(6)

16 _+ 1.7(6)“,* 14.4 + 1.0(8)b

0.085 + 0.006(6) 0.088 i O.COS(6)

0.10 + O.OlO(6) 0.086 + 0.007(B)

2.58 + 0.23(6) 2.34 + 0.21(6)

2.83 _+ 0.36(6) 2.53 f 0.25(B)

(,Nm)

Modulus of rigidity Test A Control B

(GNmm2)

202

RICHARD S.

RIGGINS, ANTHONY G. CARTWRIGHT and

of inertia is also found in Table 1. These values incorrectly assume a uniform hollow tube, but the error in this assumption is considered to be small.

DISCUSSION

Copper is a necessary metal for the enzyme lysyl oxidase (Harris et al., 1974) which, in turn, is felt to play an important role in collagen cross-linking (O’Dell, 1976). Rucker et al. (1975) has investigated the effect of copper deficiency in chick bone and reported an increase in bone collagen solubility, which is attributed to a reduction in the collagen cross-links. Ash content and total collagen of the bone remains unaffected by the lack of dietary copper. Since cortical bone from copper deficient chicks does not exhibit cellular changes (Carhon et al., 1964), or changes in its mineralization (Carlton et al., 1964; Rucker et al., 1975), it may be concluded that changes in mechanical properties of the tibia from copper deficient chicks are probably related to altered collagen cross-linking. Similar conclusions have been drawn by Bailey (1968a) and by Rigby (1959) on the relationship of collagen cross-linking and the mechanical properties of tendon. Failure of collagen to cross-link properly has definite effects on the mechanical properties of bone. Such bone exhibits an increase in the flow characteristics, as measured by the stress relaxation experiments. The force required to maintain a fixed deformity decreased much more rapidly in chicken bone with cross-link deficient collagen (Fig. 6). Furthermore, when these deficient bones were taken to failure with moderately rapid strain rates, they appear more brittle and lack the toughness of normal bone (Fig. 7). Although increased brittleness and increased flow may seem incompatible, if one considers crack propagation in bone to be similar to crack propagation in other composite materials, the apparent conflict may be resolved. If the collagen fiber provides some resistance to the propagation of the crack as it attempts to progress through bone, then the loss of the collagen’s integrity and its increased flow characteristics would offer less resistance to the crack and the material would appear more brittle. Furthermore, strains in the elastic region; if briefly applied, could be borne chiefly by the mineral component and would be unaffected by changes in the collagen cross-linking. Over the longer periods of strain observed in stress relaxation experiments, effects in the collagen would become more apparent as the visco-elastic nature of the bone could be observed. *Recently, Robins and Bailey (1977) have shown

that sodium cyanoborohydride circumvents some of the problems which occurred in our study in that this form of borohydride allows for reduction at lower pH. We hope to reevaluate this section of the report substituting cyanoborohydride for sodium borohydride.

ROBERT B. RUCKER

The creation of artificial cross-links in collagen have been reported by several investigators (Bailey, 1968a, b; Balian et al., 1969; Rucker et al., 1975). Rucker et al. (1975) reported that artificially induced cross-links in copper deficient chick bone restored some degree of toughness to the bone, allowing it to withstand greater deformation with a rapidly applied torque. In view of these observations, it was assumed that the stress relaxation behavior would also be influenced by formaldehyde treatment followed by sodium borohydride reduction. However, the magnitude of the changes effected by chemical modification of the bone collagen proved to be insufficient for statistical significance. The bone from copper deficient chicks appeared to have decreased stress relaxation after chemical modification. The opposite effect was observed in the control bone. Also, merely incubating bone in phosphate buffer at a high pH appeared to have as much effect as did the reaction with formaldehyde and sodium borohydride. Several factors may have compromised this portion of the study. The choice of conditions for chemical modification was based on the relative reactivity of sodium borohydride. Sodium borohydride reacts rapidly with water at a low pH, but under alkaline conditions, sodium borohydride is a very effective reducing agent. Unfortunately, the tensile properties of collagen can also be modified in an alkaline environment (Bailey, 1968b). Under certain conditions, sodium borohydride has also been reported to cause peptide bond cleavage (Paz et al., 1970). We had hoped that such side reactions and modifications in chick bone collagen would not be significant, but our results would indicate that this was not the case*. Nevertheless, this study clearly demonstrates differences between bone from copper deficient and copper supplemented chicks, even following attempts at chemical modifications as shown by the final experiments in which the bone was taken to failure (Figs. 6 and 7). Using the Maxwell body (Fig. 2) as a model and considering the results of this investigation, an equation can be formulated that adequately describes the stress relaxation behavior of the chick tibia tested in torsion. From equation (1) which represents a Maxwell body under constant strain : t u = bee

(1)

1

and 1

The plot of log such a graph:

5 vs

log r is a straight line (Fig. 4). From

iOgT=Li+biogt,

where A is the intercept and T =

where f is the antilogarithm

b

is the slope:

ftb, of A.

Properties

Substituting

equation

(3) into

equation

of copper

(1) gives:

0 = aOe-filb

which

is the empirical

solution

for T at any

time

t in

seconds in the stress relaxation experiments using torsion on whole chick tibia. Values for 6 and fare found in Table 2. Equation (4) adequately represents the experimental data for times between 60 and 18OOsec. For times earlier than 60 set, the experimental apparatus was not sufficiently precise to evaluate the stress relaxation times. It took 1-2sec to apply the step input, so t = 0 and u0 were imprecise and relaxation times close to t = 0 may have contained large errors. These errors would become progressively smaller as the time from I = 0 increased. Beyond 1800 set, stress relaxation times were not examined and extension of equation (4) below 609~ and beyond 1800~ will require more data in these areas. Acknowledgements - Supported in part by: Public Services Fellowship 1 F32 AM05650-01 and Public Services Grant PHS AM 15278-04.

Health Health

REFERENCES

Aklonis, J. J., Macknight. W. J. L. and Stein, M. (1972) Introducrion to Polymer Vtscoelusticity. Wiley, New York. Bailey, A. J. (1968a) Intermediate labile intermolecular crosslinks in collagen fibers. Biochim. biophys. Acta 160, 44-453. Bailey, A. J. (1968b) The nature of collagen. Vol. 26B. Extracellular and support structures. In Comprehensire Biochemistrv (Edited bv Florkin. M. and Stotz. E. H.).., _ DD. _ 297-423. Elsevier, Barking. Balian, G. A., Bowes, J. H. and Cater, C. W. (1969) Stabilization of cross-links in collagen by borohydride reduction. Biochim. biophys. Acta 181, 331-333. Carlton, W. W. and Henderson, W. (1964) Lesions in experimental copper deficiency in chickens. Acian Dis. 8, 48855. Games, W. H. (1968) Copper and connective tissue metabolism. In International Reviews of Connectiue Tissue Disense (Edited by Hall, D. A.), Vol. 4, pp. 197-232. Academic Press, New York. Dixon, W. J. and Massey, F. J., Jr. (1969) Introduction to Statistical Analysis, 3rd Edn. McGraw-Hill, New York. Fietzek, P. P. and Kuhn, K. (1976) The primary structure of collagen. Int. Reo. Connect. Tissue Res. 7, l-60. Harris, E. D.,Gonnerman, W. A., Savage, J. E. and O’Dell, B. L. (1974) Connective tissue amine oxidase. II. Purification and partial characterization of lysyl oxidase from chick aorta. Biochim. biophys. Actu 341, 332-344. McElhaney, J. H. (1966) Dynamic response of bone and muscle tissue. J. appf. Phxsioi. 21, 1231-1236. O’Dell, B. L. (1976) Biochemistry of copper. Med. C/ins. N. Am. 60, 687-703. Paz, M. A., Henderson, E., Rombauer, R., Abrash, L., Blumenfeld, 0. 0. and Gallop, P. M. (1970) Alpha amino alcohols as products of a reactive side reaction of denatured collagen with sodium borohydride. Biochemistry 9,2123-2127.

deficient

203

chick bone

Rigby, B. J., Hirari, N., Spikes, J. D. and Eyring, H. (1959)The mechanical properties of rat tail tendon. J. qen. Phrsiol. 43, 2655283. Robins, S. P. and Bailey, A. J. (1977) Characterization of the products ofreduction of skin tendon and bone with sodium cyanoborohydride. Biochem. J. 163, 339- 346. Rucker, R. B., Riggins, R. S., Laughlin, R., Chan, M. M..Chen, M. and Tom, K. (1975) Etfects of nutritional copper deficiency on the biomechanical properties of bone and arterial elastin metabolism in the chick. J. Nutr. 105, 106221070. Rucker, R. B., Murray, J. and Riggins. R. S. ( 1977) Nutritional copper deficiency and penicillamine administration. Some effects on bone collagen and arterial elastin cross-linkmg. Adl;. exp. Med. Biol. (B)86, 619-647. Sammarco,G. J., Burstein, A. H., Davis, W. L. and Frankel, V. H. (1971) The biomechanics of torsional fractures: The effect of loading on ultimate properties. J. Biomech. 4, 113-117. Saville, P. D. (1967) Water fluoridation effect on bone fragility and skeletal calcium content in the rat. .I. Nurr. 91, 353-357. Sedlin, E. D. (1965a) A rheological model for cortical bone : A study of the physical properties of human femoral samples. Acta orthop. stand. 36 (Suppl. 83), l-77. Sedlin, E. D. and Sonncrup, L. (1965b) Rheological considerations in the physical properties of bone. In Culctfied Tissues (Edited by Fleish, H.. Blackwood, H. J. J. and Owen, M.), pp. 98-101. Springer, Berlin. Storer, T. I., Asinger, R. L., Stebbins, R. C. and Nybakken, J. W. (1972) General Zoology. 5th Edn, p. 149. McGraw-Hill, New York. Underwood, E. J. (1971) Truce Elements in Human und Animal Nutrition. 3rd Edn Chapter 3. Academic Press, New York. Wainwright, S. A., Biggs, W. D., Currey, J. D. and Gosline, J. M. (1976) Mechanical Design in Organisms. Edward Arnold, London.

APPENDIX

Experimental

A

diet Skim milk Corn Oil Cerelose D-L Methionine L-Arginine Glycine

69.07, 5.0;; 24.Ou, 0.57; 0.5”” 1.O”,,

Minerul mix. 20 g per kg of diet Vitumin mix 10 g per kg of diet Copper is added as CuSO,, 25 ppm to control Mineral

diet.

mix

Adjusted of diet:

with cerelose so that 2”/, in this diet gave as g/Kg

CaHPO,. 2H,O, 10; FeSO,. 0.308 ; KCI, 3 ; NaCL, 1.

7H,O,

0.264:

MnSO,,

Vitamin mix Adjusted with cerelose so that 17; in this diet gave as g/kg of diet: Biotin, 0.03; B,,, 0.0003; Ca pantothanate, 20; choline chloride, 900; Folacin, 4; menadione, 1; Nicotinic acid, 50; pyridoxine, 8 ; Thiamin HCI, 24; DL tocopheryl acetate, 110; retinoi, 1.5; Vitamin D,, 5,ooO (I.U.).