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Some mechanical properties of goose femoral cortical bone
I
Bmmechhwrcs
Vol.
16. No
8. pp. 577-589.
oo?I -9?90
1983 c
Pnnted I” Grew Bnmn
SOME MECHANICAL
PROPERTIES OF GOOSE CORTICAL BONE
83 13.00
1983 Per&mm
+
M)
Press Ltd
FEMORAL
G. B. MCALISTER* and D. D. MOYLE Department of Interdisciplinary Studies, Clemson University. Clemson, SC 29631. U.S.A Abstract-The ultimate compressive strength and modulus of elasticity of femoral cortical bone from adult geese (Anser anser), were determined by sex and by quadrant by compressing small right circular cylinders which were 2.4 mm in height and 0.8 mm in diameter. The average ultimate compressive strength was 183 k29 MPa. The average modulus of elasticity was 13.2k3.4 GPa. The bending strength and bending modulus of elasticity were determined by a three point bend test on rectangular prisms which had the approximate dimensions 0.75 mm x 0.75 mm x 25 mm. The average bending strength was 263 + 44 MPa while the average bending modulus was 19.6+ 3.1 GPa. The calcium content was determined by atomic absorption spectrophotometry and no correlation was found with the mechanical properties. The histology of the cortical bone was examined both quantitatively and qualitatively. A unique type of Haversian bone is described. Goose bone was found to be morphologically similar to adolescent human bone and to have mechanical properties similar to those of adult human bone.
INTRODUCTION The study of the mechanical properties of bone has been an area of interest to investigators for many years. It has not been until recently, though, that recognition of the many variables involved in the testing of bone has occurred. The papers by Sedlin (1965) and Sedlin and Hirsch (1966) have been important in emphasizing the many factors which must be controlled in bone property experiments. Of particular importance are the histological microstructure of the bone tissue, the postmortem time of testing, the method of preservation and the mechanical strain rate. The mechanical properties and histological structure of bone taken from different animals have been studied for several reasons. First for the acquisition of mechanical property data from bone containing a variety of histological types and various degrees of mineralization. This type of information may lead to clarification of some structure-property relationships which can provide a basis for future research. A second reason for measuring the mechanical properties of non-human bone is for comparison with human data for the purpose of providing a quantitative basis for the selection of animal models to be used in orthopedic research. The domestic goose has been largely ignored as a possible candidate for an animal model, despite its bipedal nature and its advantages of low cost and easy maintenance. A previous study in this department (Wroblewski, 1980) has shown the goose to respond Receiced
23 September
1982; in revised form 18 January
1983. *Present address: Chesebrough-Pond’s Inc., Research Laboratories, Trumbull Industrial Park, Trumbull, CT 06611, U.S.A.
well to orthopedic surgery and to exhibit the same type of hip prosthesis failure modes that occur in man. The present study has examined the mechanical strength and elasticity of goose femoral cortical bone as well as the histological microstructure, and compares them to published values on human bone. EXPERIMENTAL PROCEDURE Bone procurement
Adult geese (Anser anser) were obtained from local farmers in the early summer so as to ensure that the previous egg laying season had ended. The egg laying season is over at the end of March and the authors believe that sufficient time had elapsed so that seasonal bone remodelling did not affect the results for female geese. The effects of diet and egglaying on the mechanical properties and morphology of female goose bone are curently under study in this laboratory. All mechanical testing was completed before the following egg laying season began. All of the geese were at least twelve months old at the time ofacquisition. The males and females were housed in separate cages and were fed a commercially available scratch feed. Immediately upon sacrifice, both femora were excised and wrapped in saline-soaked gauze pads. They were then sealed in plastic bags and frozen at - 22°C. The bones were put in the freezer within 30 min after sacrifice, and were mechanically tested within three weeks. Specimen preparation Compression specimens. Upon removal from the freezer, the gauze pads were removed and the bones were soaked in iced saline. Throughout the preparation procedure, the femora were repeatedly immersed in the iced saline to prevent dehydration. A slice
577
G. B. MCALISTER and D. D. MOYLE
578
2.4 mm thick was cut from the midpoint of the shaft, and two slices each 1 mm thick were cut on either side, one proximally, and one distally. The sectioning scheme is shown in Fig. 1. The thinner sections were stored in 10% buffered formalin for later use, while the thicker slice was kept in iced saline and served as the source for the compression samples.
LL::pJ:pq III
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III
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Fig. 1. Sectioning scheme for compression tested specimens.
The compression samples were right circular cylinders, 2.4 mm in height and 0.8 mm in diameter. One sample was cored from each quadrant as shown in Fig. 2. This very small sample size was necessary because of the thin cortex (l-l.5 mm).
Figure 4 is a scanning electron microscope (SEM), photograph of a whole compression cylinder. The coring bit was fashioned from a 19 gauge hypodermic needle. Both ends of the needle were cut off with a dimond saw, and an ‘x’ was filed into one end for cutting teeth. The samples were pushed out of the bit with a small piece of wire. Care was exercised so as not to damage the cylinders while removing them from the bit. The preparation time was approximately one hour per bone. Three point bend samples. The bones for the bend test were maintained in the same manner already described for the compression samples. Longitudinal sections approximately 1.0 mm square and 25.0 mm long were cut from the medial and lateral quadrants while being continuously irrigated with a physiological saline solution. Using a hand held polishing jig, the endosteal, periosteal and one of the other surfaces were polished on wet 320 grit silicon sandpaper. Irrigation was provided by tap water. The final dimensions of each bend test sample were approximately 0.75 mm x 0.75 mm x 25 mm. The exact dimensions were measured and recorded for use in the calculations. As with the compression samples, the bend test samples were stored in iced saline until testing. Preparation time was about one hour per bone. Compression test
0
]
+
o-
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Fig. 2. Transverse section of femur showing regional location of compression tested cylinders.
Goose femoral bone is rather underdeveloped histologically, with only a few small Haversian systems (50 pm diameter). Figure 3 is a reflected light photomicrograph of a polished surface of one of the compression cylinders. This figure shows that each structural element represents less than 10% of the specimen diameter and each is present in sufficient number to allow measurement of the average material property under investigation. The histology of goose femoral bone will be discussed in greater detail later. The bone was irrigated with cold water while a miniature drill press was used to core the samples. The specimens were visually inspected for dimensional accuracy, and were stored in iced saline until testing.
Uniaxial compression tests were performed on right circular cylinders of cortical bone taken from the midshafts of both femora of male and female geese. The cylinders were cored along the longitudinal axis of the bone and were taken from each of the four quadrants-anterior, medial, posterior and lateral. They were loaded axially to fracture on.an Instron Dynamic Testing Machine at a low strain rate (0.0013~-~). This strain rate was chosen to be consistent with a previous study in this laboratory (McDermott, 1981). A strip chart recorder provided a record of load vs time of deflection. The fractured specimens were stored in 107; buffered formalin for later use. The ultimate compressive strength and the compressive modulus of elasticity were calculated from the strip chart recordings of each test. The strength was determined at the point of maximum load before failure occurred. The load divided by the crosssectional area of the cylinder is the maximum stress, or ultimate compressive strength. The compressive modulus of elasticity was calculated from the slope of the linear portion of the load vs time of deflection curve. The compliance of the testing machine was measured to be 4.00 x 10-e m N- ‘, and was taken into account in the calculations. Three point bend test
Rectangular prisms were tested in a three point bending configuration in order to obtain the bending strength (modulus of rupture), and the bending modulus of elasticity. The load was applied centrally
Fig. 3. Polished surface of compression cylinder. (Reflected light microscopy, 100X).
579
Fig. 4. SEM photograph
of whole compression
580
cylinder, (27X).
Fig. 6. Woven fiber bone (Males). (Polarized light, 200X).
Fig. 7. Plexiform arrangement of vascular canals. (Microradiograph, 65X). 581.
Fi8.8. Circumferential fiber pattern (Females). (Polarized light, .65X).
582
Fig. 9. Osteonal remodeling. (Polarized light, 200X).
583
585
Some mechanical properties of goose femoral cortical bone
between cylindrical roller supports via an Instron Dynamic Testing Machine. The stroke rate was adjusted so that the strain rate in the extreme outer fibers was 0.0013s-’ in order to be consistent with the compression tests. All specimens were tested to failure, with the strip chart recording providing a record of load vs time of deflection. The fractured specimens were stored in 100, buffered formalin for later use. It was assumed that a symmetrical elastic behavior in tension and compression was present, and also that failure would occur in tension. Although neither assumption is necessarily correct for bone, such assumptions aid in the reduction of test results, and are suitable for comparison purposes (Simkin and Robin, 1978). Four point bending has usually been the test preferred by materials scientists because if the opposite faces are parallel, and the edges make 90” angles, there are no shear stresses between the center rollers, and the lower face is in pure tension. This permits the bone to fracture at its weakest point rather than at some predetermined point as occurs in three point bending. However, the very small sample size (0.75 mm x 0.75 mm x 25 mm) forced the use of a three point bend test in this study. The shear stresses due to three point bending have a parabolic distribution over the cross section, being at a maximum at the neutral axis and zero at the extreme fibers. Therefore, if failure of the specimen occurs because of failure of the extreme outer fibers, as assumed, the shear stresses should have no effect on the bending moment at failure. Simkin and Robin (1978) have shown that the effect of the shear forces on the modulus of elasticity is negligible for slender beams. For relatively small specimens, then, it can be assumed that results from a three point bend test can be realistically compared to results from a four point bend test. The bending strength and bending modulus of elasticity were calculated from the strip chart record of each bend test. For a rectangular prism in three point bending the bending stress (strength) of the outer fibers is 3PL d=m where P = maximum load reached before failure, L = the distance between end supports and b and h are the breadth and height of the specimen cross section, respectively. The bending modulus of elasticity was calculated from the linear portion of the load versus time of deflection curve for each bend test. The compliance of the testing machine was negligible since the maximum load attained was only about 1.5 lb in all cases. For a rectangular prism in three point bending, the modulus of elasticity (E) is: EC-
PL3 4bh36
where 6 is the deflection of the neutral axis, and the other variables are the same as above. Weight-percent calcium determination
Pieces approximately 5-7 mm long taken from the bend samples near the fracture site and whole compression samples were used for weight-percent calcium determinations. The samples were removed from the 100,; buffered formaiin and soaked in distilled water for 24 hr to remove any formalin precipitates. The water was changed periodically. They were then soaked in 99 “/ ethanol overnight. The samples were dried in a 60°C oven for several hours until a constant weight was obtained. The bone specimens were then decalcified in a 10,; nitric acid solution for two days. Calcium concentration was determined on a Perkin Elmer Model 403 Atomic Absorption Spectrophotometer. The final dilutions contained lo,, lanthanum oxide to prevent calcium interference. RESULTS Macromeasurements
The cortex thickness and total length of the femur from the proximal tip of the trochanter to the articulating surface of the lateral condyle were measured. The means, standard deviations (SD.), and number of observations (N) for the cortex thickness are listed by sex and by quadrant in Table 1. Table 1. Cortex thickness (mm) Quadrant Anterior Medial Posterior Lateral
Quadrant Anterior Medial Posterior Lateral
Females S.D. Mean 1.26 1.26 1.02 1.21
+0.23 kO.21 kO.21 +0.22
Males Mean S.D. 1.55 1.49 1.35 1.48
kO.36 +0.35 kO.41 +0.37
N 20 20 19 20
N 18 18 18 18
An analysis of variance was first performed to determine where significant differences between means existed. Paired t-tests were then performed by the Bonferroni approach (Neter and Wasserman, 1974) to determine if the differences were significant at the 95 ‘:” confidence level. All of the results which follow were tested for significant differences using this same method. In both the males and females, the posterior quadrant was significantly thinner than any of the other quadrants. The males had a significantly thicker cortex than the females. The average length of the male femur was 85 f 4 mm, while the female femur averaged 8 1 f 3 mm.
G. B. MCALISTER and D. D. MOYLE
586
Both femora from ten male and ten female geese were measured. Mechanical properties Compression test. The means, standard deviations (SD.) and the number of observations (IV) for the ultimate compressive strength are listed by sex and by quadrant in Table 2. In the females only, the strength of the anterior quadrant was found to be significantly less than the strength of the other quadrants at the 95 % confidence level. No significant differences were found between the two sexes.
Table 2.
Quadrant Anterior Medial Posterior Lateral
Quadrant Anterior Medial Posterior Lateral
compressive Ultimate strengths (MPa) Females Mean S.D. 164 191 203 189
20 18 9 18
Males Mean S.D.
N
*27 *21 +21 *22
Table 4. Bending strengths (MPa) Quadrant
13 17 17 15
The means, standard deviations (S.D.) and the number of observations (N) for the compressive modulus of elasticity are listed by sex and by quadrant in Table 3.
256 283
+41 +59
15 14
Quadrant
Males Mean SD.
N
232 276
Anterior Lateral
Table 3. Compressive modulus of elasticity (GPa)
Anterior Medial Posterior Lateral Quadrant Anterior Medial Posterior Lateral
11.0 14.4 14.4 14.6
N
k3.2 k3.7 k1.5 k3.5
20 18 9 18
Males S.D. Mean
N
12.2 14.2 12.6 13.2
k3.0 k3.9 +2.8 +2.9
9 10
+17 *I7
The means, standard deviations (SD.) and the number of observations (N)lfor the bending modulus of elasticity are listed by sex and by quadrant in Table 5. The males had a significantly lower modulus in the anterior quadrant as compared to the lateral quadrant. Figure 5 shows a comparison between males and females for the bending modulus of elasticity. The females had a significantly higher modulus than the males in the anterior region. Table 5. Bending modulus of elasticity (GPa)
Anterior Lateral
Females Mean S.D.
N
k3.4 +3.4
15 14
Males Mean S.D.
N
$-1.8 k1.5
9 10
19.4 20.6
Quadrant
Females Mean S.D.
N
Anterior Lateral
Quadrant
Quadrant
Females Mean S.D.
N
+35 +33 *19 k31
171 184 186 185
the bending strength are listed by sex and by quadrant in Table 4. The anterior quadrant was significantly weaker than the lateral quadrant in both the males and the females. No significant differences were found between the sexes.
Anterior Lateral
16.9 20.7
25
T
T
T
12 17 18 16
The females had a significantly lower modulus in the anterior quadrant as compared to the other quadrants. No significant differences were detected between the two sexes. Three point bend test. The means, standard deviations (S.D.) and the number of observations (N) for
A
A
? L
L
MALES FEMALES
Fig. 5. Bending modulus of elasticity (Males vs females).
Some mechanical properties of goose femoral cortical bone Calcium content
woven fiber pattern when illuminated
The calcium content of goose femoral bone was calculated as a weight-percent calcium. The calcium contents are listed by sex and by quadrant in Table 6
and in Table 7. Table 6 is for the compression test birds, while Table 7 is for the bend test birds. The calcium content of the bone averaged 24.87; w/w and there were no significant differences between the values. No correlation was found between calcium content and any of the measured mechanical properties.
Table 6. Calcium content of compression tested birds (weight percent)
Quadrant Anterior Medial Posterior Lateral
587
Females S.D. Mean 24.6 24.8 25.4 26.2
k2.3 *1.7 k2.6 k3.4
N 20 17 9 18
Quadrant
Males Mean SD.
N
Anterior Medial Posterior Lateral
24.4 25.7 24.9 25.0
12 14 13 13
k3.6 +1.5 k2.3 k2.4
with polarized light. Figure 6 is a photomicrograph showing this pattern of woven fiber bone. The anastomosing canals exhibit a roughly symmetrical, plexiform-like arrangement as seen in Fig. 7. In the females, the fibers in this layer appear more organized in circumferential layers, and do not exhibit the ‘carpet weave’ pattern under polarized light which is seen in the males. This organized fiber pattern is seen in Fig. 8. This ring is 200-300 pm thick, and is more extensively remodeled in the posterior ridge in both sexes. The third ring is the Haversian ring, and contains primary and secondary osteons. The females show a greater number of osteons, and they are more highly visible in the microradiographs than in the males. Figure 9 shows remodelling by a secondary osteon in this ring. The Haversian layer is about 200-300 pm thick in the males, and is up to 8OOpm thick in the females. The inner circumferential lamellar ring varies from 100-200 pm in thickness. Some Haversian systems are present in this ring, as well as some large resorption cavities in the female. Volkmann canals extend through this layer from the Haversian ring to the periosteum.
DISCUSSION Table 7. Calcium content of bend tested birds (weight percent)
Quadrant Anterior Lateral
Quadrant Anterior Lateral
Females Mean S.D. 24.2 25.1
k2.1 k1.4
Males S.D. Mean 24.4 24.2
_+l.O k1.1
N 16 12 N
10 10
Qualitative histology
The goose femoral bone examined in this study contains four separate concentric rings of tissue, each distinctly different from the others. There is a well developed outer circumferential lamellar ring, an underdeveloped non-Haversian ring, a Haversian ring, and a well developed inner circumferential lamellar ring. The outer circumferential ring ranges from O-50 pm in thickness, with the thinnest area being in the posterior quadrant in the region of muscle attachment.
The lamellae are very distinct, and contain an even distribution of long, narrow lacunae. Moving endosteally, the next ring differs somewhat between the two sexes. In the males, this layer contains primary vascular bone (non-Haversian) and exhibits a
Microstructure
The bone examined in this study contains a variety of types, ranging from primary vascular bone to osteonal (Haversian) bone. Both primary and secondary osteons are present adjacent to the endosteal circumferential lamina. These systems, however, are not as distinct as those seen in the human or dog cortex. The outer cement line is quite clear, but the inner lamellae are not as obvious. Geese have a complex calcium metabolism and have an efficient conservation mechanism (Simkiss, 1975). The laying season puts a tremendous strain on the calcium reserves of the female birds, and although they produce medullary bone as a labile calcium store, it is not 100% efficient and some remodelling can be expected. The geese in this study had lived through just one laying season and remodelling was obvious, especially in the females. Presumably, older geese would show much more remodelling, and Haversian bone would become more prevalent as it replaced the non-Haversian bone. Foote (1916) describes the histology of a wild goose femur cross-section. His description indicates a more extensive arrangement of Haversian systems than seen in this study, but it is similar in that the systems are not well developed histologically. The goose femoral bone examined in this study partly resembles that found in the skeletally immature human. According to Enlow (1966), in the adolescent human there is a widespread distribution of non-
588
G. B. MCALISTERand D. D.
bone along the periosteal zones, except at the points of muscle attachment. True Haversian systems are only found in areas of muscle attachment, and in endosteal regions adjacent to an inner circumferential layer of lamellar bone. Except for the distinctness of the Haversian systems, this description fits goose femoral cortical bone very well. Haversian
Calcium content
If a hydroxyapatite-like mineral structure is assumed to be present in stoichiometric form, Ca,,(PO,),(OH),, then the 24.8% calcium content found in this study converts to 62 “/;,ash weight. This is somewhat less than the ash weight found in the dog, 67% (McDermott, 1981), and is comparable to that found in the human in the 6-30 yr age group, 63.4 % (Currey and Butler, 1975). Raveling et al. (1978), reported 30% w/w calcium in the distal half of the femurs of wild geese. They noted, however, that the distal portion contained a higher calcium component than the proximal portion. Mechanical properties
The most striking feature of the mechanical property results is the large standard deviations obtained, particularly for the compressive modulus of elasticity. The standard deviations for the compressive modulus averaged 26% of the mean, while the other standard deviations were about 16 y0 of their respective means. It is possible to attribute some of the scatter in the data to variations in machining from sample to sample although every attempt was made to keep these variations as small as possible. If it were possible to use larger specimens these variations could be further minimized although other investigators (Currey and Butler, 1975 and Reilly et al., 1974) report standard deviations on the order of 10-15 % of the means even using larger specimens. Some of the scatter may also be due to inaccuracies introduced by the testing machine, particularly in the compression tests. Since extreme care was exercised to control as many variables as possible during the handling and testing of the bones in this study, the scatter in the data is most likely due to the variation in the degree of mineralization and the porosity or fractional void volume (Wall et al., 1970). However, no statistical analysis of the variance was performed on the data to determine the extent to which these variables were responsible for the variation. This large biological variation is un-
MOYLE
avoidable and implies that a large sample population should be examined if any reliable conclusions are to be drawn from tests on bone tissue. The anterior quadrant in the females had significantly lower compressive properties than the other quadrants, and while the males showed the same trend, the differences were not significant in the males. However, 90% of the time the anterior quadrant had the lowest compressive modulus and it had the lowest compressive strength 75% of the time. This is consistent with Kenner’s (Kenner et al., 1979) results on canine femoral bone. In bending, the anterior quadrant had significantly lower mechanical values than the lateral quadrant, with the anterior bending modulus being lower 80 “/:,of the time and the anterior bending strength being lower 90% of the time. Table 8 shows the average mechanical values for goose bone and some published values for human bone. For the goose, the bending modulus is approximately 20% greater than the compressive modulus. Since bending involves compression and tension, this result implies that the tensile modulus is greater than the compressive modulus. According to calculations based on Simkin’s (Simkin and Robin, 1978) work, the tensile modulus would have to be about 25% greater than the compressive modulus in order to account for the higher bending modulus. Simkin and Robin (1978) found this same tendency for the tensile modulus of elasticity to be greater than the compressive modulus of elasticity in bovine bone, while Reilly et al. (1974) found no difference between the two moduli for human bone or for bovine bone. This discrepancy could be due to the fact that Reilly et al. (1974) tested bone samples which were predominantly one histological type, either Haversian or laminar, while the bones tested in the present study contained a variety of histological types. The variation in microstructure present in goose femoral bone could lead to different mechanical properties in pure compression and in bending. The elastic moduli and strength values for human bone shown in Table 8 are average values taken from two review articles referenced in the table. It can be seen that goose bone is very similar to human bone in all properties except the bending strength. The bending strength anomaly may be due to the greater strength of primary bone as compared to Haversian bone (Currey, 1975).
Table 8. Mechanical properties comparison: Goose vs Man Species Goose Man
WGPa) 13.2 14.42
*Reilly and Burstein, 1974. tCarter and Spengler, 1978.
WGPa) 19.6 15.7*
u,(MPa) 183 193t
a,(MPa) 263 167*
Some mechanical properties of goose femoral cortical bone CONCLUSIONS
The mechanical properties of femoral cortical bone from 33 domestic geese (Anser sp.) were measured. There were no differences in any of the mechanical properties measured between the males and the females. The femaleanterior quadrant had a significantly lower modulus and strength in compression as compared to the other quadrants. The male anterior quadrant had a significantly lower bending modulus and a lower bending strength than the latera quadrant. The elastic moduli of goose femoral cortical bone are comparable to published values on human femora, but the strengths appear to be higher. Histologically, goose femoral cortical bone contains the same structures found in adolescent human femoral cortical bone.
Acknowledgement-We thank the National Science Foundation for support of this research under the ‘Experimental Program to Stimulate Competitive Research, F. W. Cooke, principal investigator, Grant No. PRM8011451.
REFERENCES
Carter, D. R. and Spengler, D. M. (1978) Mechanical properties and composition of cortical bone. Clin. Orthop. 135, 192-217. Currey, J. D. (1975) The effects of strain rate, reconstruction and mineral content on some mechanical properties of bovine bone. J. Biomechanics 8, 81-86.
589
Currey, J. D. and Butler, G. (1975) The mechanical properties of bones in children. J. Bone Jr Surg. 57A. 81&814. Enlow, D. H. (1966) An evaluation of the use of bone histology in forensic medicine and anthropology. Studies on the Anatomy and Funcrion of Bone and Joints (Edited by Evans, F. Cl.), Springer. New York. Foote, J. S. (1916) A contribution to the comparative histology of the femur. Smithson Conrr. Knowl. 35, 1-242. Kenner. Cl. H., Taylor, L. L. and Park, J. B. (1979) Compressive strength of canine femur, J. Biomechanics 12, 519-526.
McDermott, M. K. (1981) Mechanical properties of canine femoral cortical bone. M. S. Thesis, Clemson University. Neter, J. and Wasserman, W. (1974) Applied Linear Statisricaf Models. Richard D. Irwin, Homewood. IL. Raveling, D. G., Sifri, M. and Knudsen, R. B. (1978) Seasonal variation of femur and tibiotarsus constituents in Canada geese. Condor 80, 246-248. Reilly, D. T. and Burstein, A. H. (1976) Review article-The mechanical properties of cortical bone. J. Bone Jt Surg. 56A, 100-1022. Reilly, D. R., Burstein, A. H. and Frankel, V. H. (1974) The ‘elastic modulus for bone. J. Biomechanics 7, 2?1-275. Sedlin, E. D. (1965) A rheolonical model for cortical bone. Acta orthop: S&d. Suppl. i3. Sedlin. E. D. and Hirsch, C. (1966) Factors affecting the determination of the physical properties of femoral cortical bone. Aria orthop. Scand. 37, 2948. Simkin, A. and Robin, G. (1978) The mechanical testing of bone in bending, J. Biomechanics 6, 31-39. Simkiss. K. (1975) Calcium and avian reoroduction. Aoion Physiologi, (Edited by Peaker, M.). ’ Academic Press, London. Wall, J. C., Chatterji, S. and Jeffrey, J. W. (1970) On the origin of scatter in results of human bone strength tests. Med. biol. Engng. 8, 171-180. Wroblewski, T. (1980) Experimental coxofemoral replacement hemiarthroplasty in the goose (Anser sp.). M. S. Thesis, Clemson University.
Bmmechhwrcs
Vol.
16. No
8. pp. 577-589.
oo?I -9?90
1983 c
Pnnted I” Grew Bnmn
SOME MECHANICAL
PROPERTIES OF GOOSE CORTICAL BONE
83 13.00
1983 Per&mm
+
M)
Press Ltd
FEMORAL
G. B. MCALISTER* and D. D. MOYLE Department of Interdisciplinary Studies, Clemson University. Clemson, SC 29631. U.S.A Abstract-The ultimate compressive strength and modulus of elasticity of femoral cortical bone from adult geese (Anser anser), were determined by sex and by quadrant by compressing small right circular cylinders which were 2.4 mm in height and 0.8 mm in diameter. The average ultimate compressive strength was 183 k29 MPa. The average modulus of elasticity was 13.2k3.4 GPa. The bending strength and bending modulus of elasticity were determined by a three point bend test on rectangular prisms which had the approximate dimensions 0.75 mm x 0.75 mm x 25 mm. The average bending strength was 263 + 44 MPa while the average bending modulus was 19.6+ 3.1 GPa. The calcium content was determined by atomic absorption spectrophotometry and no correlation was found with the mechanical properties. The histology of the cortical bone was examined both quantitatively and qualitatively. A unique type of Haversian bone is described. Goose bone was found to be morphologically similar to adolescent human bone and to have mechanical properties similar to those of adult human bone.
INTRODUCTION The study of the mechanical properties of bone has been an area of interest to investigators for many years. It has not been until recently, though, that recognition of the many variables involved in the testing of bone has occurred. The papers by Sedlin (1965) and Sedlin and Hirsch (1966) have been important in emphasizing the many factors which must be controlled in bone property experiments. Of particular importance are the histological microstructure of the bone tissue, the postmortem time of testing, the method of preservation and the mechanical strain rate. The mechanical properties and histological structure of bone taken from different animals have been studied for several reasons. First for the acquisition of mechanical property data from bone containing a variety of histological types and various degrees of mineralization. This type of information may lead to clarification of some structure-property relationships which can provide a basis for future research. A second reason for measuring the mechanical properties of non-human bone is for comparison with human data for the purpose of providing a quantitative basis for the selection of animal models to be used in orthopedic research. The domestic goose has been largely ignored as a possible candidate for an animal model, despite its bipedal nature and its advantages of low cost and easy maintenance. A previous study in this department (Wroblewski, 1980) has shown the goose to respond Receiced
23 September
1982; in revised form 18 January
1983. *Present address: Chesebrough-Pond’s Inc., Research Laboratories, Trumbull Industrial Park, Trumbull, CT 06611, U.S.A.
well to orthopedic surgery and to exhibit the same type of hip prosthesis failure modes that occur in man. The present study has examined the mechanical strength and elasticity of goose femoral cortical bone as well as the histological microstructure, and compares them to published values on human bone. EXPERIMENTAL PROCEDURE Bone procurement
Adult geese (Anser anser) were obtained from local farmers in the early summer so as to ensure that the previous egg laying season had ended. The egg laying season is over at the end of March and the authors believe that sufficient time had elapsed so that seasonal bone remodelling did not affect the results for female geese. The effects of diet and egglaying on the mechanical properties and morphology of female goose bone are curently under study in this laboratory. All mechanical testing was completed before the following egg laying season began. All of the geese were at least twelve months old at the time ofacquisition. The males and females were housed in separate cages and were fed a commercially available scratch feed. Immediately upon sacrifice, both femora were excised and wrapped in saline-soaked gauze pads. They were then sealed in plastic bags and frozen at - 22°C. The bones were put in the freezer within 30 min after sacrifice, and were mechanically tested within three weeks. Specimen preparation Compression specimens. Upon removal from the freezer, the gauze pads were removed and the bones were soaked in iced saline. Throughout the preparation procedure, the femora were repeatedly immersed in the iced saline to prevent dehydration. A slice
577
G. B. MCALISTER and D. D. MOYLE
578
2.4 mm thick was cut from the midpoint of the shaft, and two slices each 1 mm thick were cut on either side, one proximally, and one distally. The sectioning scheme is shown in Fig. 1. The thinner sections were stored in 10% buffered formalin for later use, while the thicker slice was kept in iced saline and served as the source for the compression samples.
LL::pJ:pq III
-II-
III
-II--
IO
IO
Fig. 1. Sectioning scheme for compression tested specimens.
The compression samples were right circular cylinders, 2.4 mm in height and 0.8 mm in diameter. One sample was cored from each quadrant as shown in Fig. 2. This very small sample size was necessary because of the thin cortex (l-l.5 mm).
Figure 4 is a scanning electron microscope (SEM), photograph of a whole compression cylinder. The coring bit was fashioned from a 19 gauge hypodermic needle. Both ends of the needle were cut off with a dimond saw, and an ‘x’ was filed into one end for cutting teeth. The samples were pushed out of the bit with a small piece of wire. Care was exercised so as not to damage the cylinders while removing them from the bit. The preparation time was approximately one hour per bone. Three point bend samples. The bones for the bend test were maintained in the same manner already described for the compression samples. Longitudinal sections approximately 1.0 mm square and 25.0 mm long were cut from the medial and lateral quadrants while being continuously irrigated with a physiological saline solution. Using a hand held polishing jig, the endosteal, periosteal and one of the other surfaces were polished on wet 320 grit silicon sandpaper. Irrigation was provided by tap water. The final dimensions of each bend test sample were approximately 0.75 mm x 0.75 mm x 25 mm. The exact dimensions were measured and recorded for use in the calculations. As with the compression samples, the bend test samples were stored in iced saline until testing. Preparation time was about one hour per bone. Compression test
0
]
+
o-
@
Fig. 2. Transverse section of femur showing regional location of compression tested cylinders.
Goose femoral bone is rather underdeveloped histologically, with only a few small Haversian systems (50 pm diameter). Figure 3 is a reflected light photomicrograph of a polished surface of one of the compression cylinders. This figure shows that each structural element represents less than 10% of the specimen diameter and each is present in sufficient number to allow measurement of the average material property under investigation. The histology of goose femoral bone will be discussed in greater detail later. The bone was irrigated with cold water while a miniature drill press was used to core the samples. The specimens were visually inspected for dimensional accuracy, and were stored in iced saline until testing.
Uniaxial compression tests were performed on right circular cylinders of cortical bone taken from the midshafts of both femora of male and female geese. The cylinders were cored along the longitudinal axis of the bone and were taken from each of the four quadrants-anterior, medial, posterior and lateral. They were loaded axially to fracture on.an Instron Dynamic Testing Machine at a low strain rate (0.0013~-~). This strain rate was chosen to be consistent with a previous study in this laboratory (McDermott, 1981). A strip chart recorder provided a record of load vs time of deflection. The fractured specimens were stored in 107; buffered formalin for later use. The ultimate compressive strength and the compressive modulus of elasticity were calculated from the strip chart recordings of each test. The strength was determined at the point of maximum load before failure occurred. The load divided by the crosssectional area of the cylinder is the maximum stress, or ultimate compressive strength. The compressive modulus of elasticity was calculated from the slope of the linear portion of the load vs time of deflection curve. The compliance of the testing machine was measured to be 4.00 x 10-e m N- ‘, and was taken into account in the calculations. Three point bend test
Rectangular prisms were tested in a three point bending configuration in order to obtain the bending strength (modulus of rupture), and the bending modulus of elasticity. The load was applied centrally
Fig. 3. Polished surface of compression cylinder. (Reflected light microscopy, 100X).
579
Fig. 4. SEM photograph
of whole compression
580
cylinder, (27X).
Fig. 6. Woven fiber bone (Males). (Polarized light, 200X).
Fig. 7. Plexiform arrangement of vascular canals. (Microradiograph, 65X). 581.
Fi8.8. Circumferential fiber pattern (Females). (Polarized light, .65X).
582
Fig. 9. Osteonal remodeling. (Polarized light, 200X).
583
585
Some mechanical properties of goose femoral cortical bone
between cylindrical roller supports via an Instron Dynamic Testing Machine. The stroke rate was adjusted so that the strain rate in the extreme outer fibers was 0.0013s-’ in order to be consistent with the compression tests. All specimens were tested to failure, with the strip chart recording providing a record of load vs time of deflection. The fractured specimens were stored in 100, buffered formalin for later use. It was assumed that a symmetrical elastic behavior in tension and compression was present, and also that failure would occur in tension. Although neither assumption is necessarily correct for bone, such assumptions aid in the reduction of test results, and are suitable for comparison purposes (Simkin and Robin, 1978). Four point bending has usually been the test preferred by materials scientists because if the opposite faces are parallel, and the edges make 90” angles, there are no shear stresses between the center rollers, and the lower face is in pure tension. This permits the bone to fracture at its weakest point rather than at some predetermined point as occurs in three point bending. However, the very small sample size (0.75 mm x 0.75 mm x 25 mm) forced the use of a three point bend test in this study. The shear stresses due to three point bending have a parabolic distribution over the cross section, being at a maximum at the neutral axis and zero at the extreme fibers. Therefore, if failure of the specimen occurs because of failure of the extreme outer fibers, as assumed, the shear stresses should have no effect on the bending moment at failure. Simkin and Robin (1978) have shown that the effect of the shear forces on the modulus of elasticity is negligible for slender beams. For relatively small specimens, then, it can be assumed that results from a three point bend test can be realistically compared to results from a four point bend test. The bending strength and bending modulus of elasticity were calculated from the strip chart record of each bend test. For a rectangular prism in three point bending the bending stress (strength) of the outer fibers is 3PL d=m where P = maximum load reached before failure, L = the distance between end supports and b and h are the breadth and height of the specimen cross section, respectively. The bending modulus of elasticity was calculated from the linear portion of the load versus time of deflection curve for each bend test. The compliance of the testing machine was negligible since the maximum load attained was only about 1.5 lb in all cases. For a rectangular prism in three point bending, the modulus of elasticity (E) is: EC-
PL3 4bh36
where 6 is the deflection of the neutral axis, and the other variables are the same as above. Weight-percent calcium determination
Pieces approximately 5-7 mm long taken from the bend samples near the fracture site and whole compression samples were used for weight-percent calcium determinations. The samples were removed from the 100,; buffered formaiin and soaked in distilled water for 24 hr to remove any formalin precipitates. The water was changed periodically. They were then soaked in 99 “/ ethanol overnight. The samples were dried in a 60°C oven for several hours until a constant weight was obtained. The bone specimens were then decalcified in a 10,; nitric acid solution for two days. Calcium concentration was determined on a Perkin Elmer Model 403 Atomic Absorption Spectrophotometer. The final dilutions contained lo,, lanthanum oxide to prevent calcium interference. RESULTS Macromeasurements
The cortex thickness and total length of the femur from the proximal tip of the trochanter to the articulating surface of the lateral condyle were measured. The means, standard deviations (SD.), and number of observations (N) for the cortex thickness are listed by sex and by quadrant in Table 1. Table 1. Cortex thickness (mm) Quadrant Anterior Medial Posterior Lateral
Quadrant Anterior Medial Posterior Lateral
Females S.D. Mean 1.26 1.26 1.02 1.21
+0.23 kO.21 kO.21 +0.22
Males Mean S.D. 1.55 1.49 1.35 1.48
kO.36 +0.35 kO.41 +0.37
N 20 20 19 20
N 18 18 18 18
An analysis of variance was first performed to determine where significant differences between means existed. Paired t-tests were then performed by the Bonferroni approach (Neter and Wasserman, 1974) to determine if the differences were significant at the 95 ‘:” confidence level. All of the results which follow were tested for significant differences using this same method. In both the males and females, the posterior quadrant was significantly thinner than any of the other quadrants. The males had a significantly thicker cortex than the females. The average length of the male femur was 85 f 4 mm, while the female femur averaged 8 1 f 3 mm.
G. B. MCALISTER and D. D. MOYLE
586
Both femora from ten male and ten female geese were measured. Mechanical properties Compression test. The means, standard deviations (SD.) and the number of observations (IV) for the ultimate compressive strength are listed by sex and by quadrant in Table 2. In the females only, the strength of the anterior quadrant was found to be significantly less than the strength of the other quadrants at the 95 % confidence level. No significant differences were found between the two sexes.
Table 2.
Quadrant Anterior Medial Posterior Lateral
Quadrant Anterior Medial Posterior Lateral
compressive Ultimate strengths (MPa) Females Mean S.D. 164 191 203 189
20 18 9 18
Males Mean S.D.
N
*27 *21 +21 *22
Table 4. Bending strengths (MPa) Quadrant
13 17 17 15
The means, standard deviations (S.D.) and the number of observations (N) for the compressive modulus of elasticity are listed by sex and by quadrant in Table 3.
256 283
+41 +59
15 14
Quadrant
Males Mean SD.
N
232 276
Anterior Lateral
Table 3. Compressive modulus of elasticity (GPa)
Anterior Medial Posterior Lateral Quadrant Anterior Medial Posterior Lateral
11.0 14.4 14.4 14.6
N
k3.2 k3.7 k1.5 k3.5
20 18 9 18
Males S.D. Mean
N
12.2 14.2 12.6 13.2
k3.0 k3.9 +2.8 +2.9
9 10
+17 *I7
The means, standard deviations (SD.) and the number of observations (N)lfor the bending modulus of elasticity are listed by sex and by quadrant in Table 5. The males had a significantly lower modulus in the anterior quadrant as compared to the lateral quadrant. Figure 5 shows a comparison between males and females for the bending modulus of elasticity. The females had a significantly higher modulus than the males in the anterior region. Table 5. Bending modulus of elasticity (GPa)
Anterior Lateral
Females Mean S.D.
N
k3.4 +3.4
15 14
Males Mean S.D.
N
$-1.8 k1.5
9 10
19.4 20.6
Quadrant
Females Mean S.D.
N
Anterior Lateral
Quadrant
Quadrant
Females Mean S.D.
N
+35 +33 *19 k31
171 184 186 185
the bending strength are listed by sex and by quadrant in Table 4. The anterior quadrant was significantly weaker than the lateral quadrant in both the males and the females. No significant differences were found between the sexes.
Anterior Lateral
16.9 20.7
25
T
T
T
12 17 18 16
The females had a significantly lower modulus in the anterior quadrant as compared to the other quadrants. No significant differences were detected between the two sexes. Three point bend test. The means, standard deviations (S.D.) and the number of observations (N) for
A
A
? L
L
MALES FEMALES
Fig. 5. Bending modulus of elasticity (Males vs females).
Some mechanical properties of goose femoral cortical bone Calcium content
woven fiber pattern when illuminated
The calcium content of goose femoral bone was calculated as a weight-percent calcium. The calcium contents are listed by sex and by quadrant in Table 6
and in Table 7. Table 6 is for the compression test birds, while Table 7 is for the bend test birds. The calcium content of the bone averaged 24.87; w/w and there were no significant differences between the values. No correlation was found between calcium content and any of the measured mechanical properties.
Table 6. Calcium content of compression tested birds (weight percent)
Quadrant Anterior Medial Posterior Lateral
587
Females S.D. Mean 24.6 24.8 25.4 26.2
k2.3 *1.7 k2.6 k3.4
N 20 17 9 18
Quadrant
Males Mean SD.
N
Anterior Medial Posterior Lateral
24.4 25.7 24.9 25.0
12 14 13 13
k3.6 +1.5 k2.3 k2.4
with polarized light. Figure 6 is a photomicrograph showing this pattern of woven fiber bone. The anastomosing canals exhibit a roughly symmetrical, plexiform-like arrangement as seen in Fig. 7. In the females, the fibers in this layer appear more organized in circumferential layers, and do not exhibit the ‘carpet weave’ pattern under polarized light which is seen in the males. This organized fiber pattern is seen in Fig. 8. This ring is 200-300 pm thick, and is more extensively remodeled in the posterior ridge in both sexes. The third ring is the Haversian ring, and contains primary and secondary osteons. The females show a greater number of osteons, and they are more highly visible in the microradiographs than in the males. Figure 9 shows remodelling by a secondary osteon in this ring. The Haversian layer is about 200-300 pm thick in the males, and is up to 8OOpm thick in the females. The inner circumferential lamellar ring varies from 100-200 pm in thickness. Some Haversian systems are present in this ring, as well as some large resorption cavities in the female. Volkmann canals extend through this layer from the Haversian ring to the periosteum.
DISCUSSION Table 7. Calcium content of bend tested birds (weight percent)
Quadrant Anterior Lateral
Quadrant Anterior Lateral
Females Mean S.D. 24.2 25.1
k2.1 k1.4
Males S.D. Mean 24.4 24.2
_+l.O k1.1
N 16 12 N
10 10
Qualitative histology
The goose femoral bone examined in this study contains four separate concentric rings of tissue, each distinctly different from the others. There is a well developed outer circumferential lamellar ring, an underdeveloped non-Haversian ring, a Haversian ring, and a well developed inner circumferential lamellar ring. The outer circumferential ring ranges from O-50 pm in thickness, with the thinnest area being in the posterior quadrant in the region of muscle attachment.
The lamellae are very distinct, and contain an even distribution of long, narrow lacunae. Moving endosteally, the next ring differs somewhat between the two sexes. In the males, this layer contains primary vascular bone (non-Haversian) and exhibits a
Microstructure
The bone examined in this study contains a variety of types, ranging from primary vascular bone to osteonal (Haversian) bone. Both primary and secondary osteons are present adjacent to the endosteal circumferential lamina. These systems, however, are not as distinct as those seen in the human or dog cortex. The outer cement line is quite clear, but the inner lamellae are not as obvious. Geese have a complex calcium metabolism and have an efficient conservation mechanism (Simkiss, 1975). The laying season puts a tremendous strain on the calcium reserves of the female birds, and although they produce medullary bone as a labile calcium store, it is not 100% efficient and some remodelling can be expected. The geese in this study had lived through just one laying season and remodelling was obvious, especially in the females. Presumably, older geese would show much more remodelling, and Haversian bone would become more prevalent as it replaced the non-Haversian bone. Foote (1916) describes the histology of a wild goose femur cross-section. His description indicates a more extensive arrangement of Haversian systems than seen in this study, but it is similar in that the systems are not well developed histologically. The goose femoral bone examined in this study partly resembles that found in the skeletally immature human. According to Enlow (1966), in the adolescent human there is a widespread distribution of non-
588
G. B. MCALISTERand D. D.
bone along the periosteal zones, except at the points of muscle attachment. True Haversian systems are only found in areas of muscle attachment, and in endosteal regions adjacent to an inner circumferential layer of lamellar bone. Except for the distinctness of the Haversian systems, this description fits goose femoral cortical bone very well. Haversian
Calcium content
If a hydroxyapatite-like mineral structure is assumed to be present in stoichiometric form, Ca,,(PO,),(OH),, then the 24.8% calcium content found in this study converts to 62 “/;,ash weight. This is somewhat less than the ash weight found in the dog, 67% (McDermott, 1981), and is comparable to that found in the human in the 6-30 yr age group, 63.4 % (Currey and Butler, 1975). Raveling et al. (1978), reported 30% w/w calcium in the distal half of the femurs of wild geese. They noted, however, that the distal portion contained a higher calcium component than the proximal portion. Mechanical properties
The most striking feature of the mechanical property results is the large standard deviations obtained, particularly for the compressive modulus of elasticity. The standard deviations for the compressive modulus averaged 26% of the mean, while the other standard deviations were about 16 y0 of their respective means. It is possible to attribute some of the scatter in the data to variations in machining from sample to sample although every attempt was made to keep these variations as small as possible. If it were possible to use larger specimens these variations could be further minimized although other investigators (Currey and Butler, 1975 and Reilly et al., 1974) report standard deviations on the order of 10-15 % of the means even using larger specimens. Some of the scatter may also be due to inaccuracies introduced by the testing machine, particularly in the compression tests. Since extreme care was exercised to control as many variables as possible during the handling and testing of the bones in this study, the scatter in the data is most likely due to the variation in the degree of mineralization and the porosity or fractional void volume (Wall et al., 1970). However, no statistical analysis of the variance was performed on the data to determine the extent to which these variables were responsible for the variation. This large biological variation is un-
MOYLE
avoidable and implies that a large sample population should be examined if any reliable conclusions are to be drawn from tests on bone tissue. The anterior quadrant in the females had significantly lower compressive properties than the other quadrants, and while the males showed the same trend, the differences were not significant in the males. However, 90% of the time the anterior quadrant had the lowest compressive modulus and it had the lowest compressive strength 75% of the time. This is consistent with Kenner’s (Kenner et al., 1979) results on canine femoral bone. In bending, the anterior quadrant had significantly lower mechanical values than the lateral quadrant, with the anterior bending modulus being lower 80 “/:,of the time and the anterior bending strength being lower 90% of the time. Table 8 shows the average mechanical values for goose bone and some published values for human bone. For the goose, the bending modulus is approximately 20% greater than the compressive modulus. Since bending involves compression and tension, this result implies that the tensile modulus is greater than the compressive modulus. According to calculations based on Simkin’s (Simkin and Robin, 1978) work, the tensile modulus would have to be about 25% greater than the compressive modulus in order to account for the higher bending modulus. Simkin and Robin (1978) found this same tendency for the tensile modulus of elasticity to be greater than the compressive modulus of elasticity in bovine bone, while Reilly et al. (1974) found no difference between the two moduli for human bone or for bovine bone. This discrepancy could be due to the fact that Reilly et al. (1974) tested bone samples which were predominantly one histological type, either Haversian or laminar, while the bones tested in the present study contained a variety of histological types. The variation in microstructure present in goose femoral bone could lead to different mechanical properties in pure compression and in bending. The elastic moduli and strength values for human bone shown in Table 8 are average values taken from two review articles referenced in the table. It can be seen that goose bone is very similar to human bone in all properties except the bending strength. The bending strength anomaly may be due to the greater strength of primary bone as compared to Haversian bone (Currey, 1975).
Table 8. Mechanical properties comparison: Goose vs Man Species Goose Man
WGPa) 13.2 14.42
*Reilly and Burstein, 1974. tCarter and Spengler, 1978.
WGPa) 19.6 15.7*
u,(MPa) 183 193t
a,(MPa) 263 167*
Some mechanical properties of goose femoral cortical bone CONCLUSIONS
The mechanical properties of femoral cortical bone from 33 domestic geese (Anser sp.) were measured. There were no differences in any of the mechanical properties measured between the males and the females. The femaleanterior quadrant had a significantly lower modulus and strength in compression as compared to the other quadrants. The male anterior quadrant had a significantly lower bending modulus and a lower bending strength than the latera quadrant. The elastic moduli of goose femoral cortical bone are comparable to published values on human femora, but the strengths appear to be higher. Histologically, goose femoral cortical bone contains the same structures found in adolescent human femoral cortical bone.
Acknowledgement-We thank the National Science Foundation for support of this research under the ‘Experimental Program to Stimulate Competitive Research, F. W. Cooke, principal investigator, Grant No. PRM8011451.
REFERENCES
Carter, D. R. and Spengler, D. M. (1978) Mechanical properties and composition of cortical bone. Clin. Orthop. 135, 192-217. Currey, J. D. (1975) The effects of strain rate, reconstruction and mineral content on some mechanical properties of bovine bone. J. Biomechanics 8, 81-86.
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Currey, J. D. and Butler, G. (1975) The mechanical properties of bones in children. J. Bone Jr Surg. 57A. 81&814. Enlow, D. H. (1966) An evaluation of the use of bone histology in forensic medicine and anthropology. Studies on the Anatomy and Funcrion of Bone and Joints (Edited by Evans, F. Cl.), Springer. New York. Foote, J. S. (1916) A contribution to the comparative histology of the femur. Smithson Conrr. Knowl. 35, 1-242. Kenner. Cl. H., Taylor, L. L. and Park, J. B. (1979) Compressive strength of canine femur, J. Biomechanics 12, 519-526.
McDermott, M. K. (1981) Mechanical properties of canine femoral cortical bone. M. S. Thesis, Clemson University. Neter, J. and Wasserman, W. (1974) Applied Linear Statisricaf Models. Richard D. Irwin, Homewood. IL. Raveling, D. G., Sifri, M. and Knudsen, R. B. (1978) Seasonal variation of femur and tibiotarsus constituents in Canada geese. Condor 80, 246-248. Reilly, D. T. and Burstein, A. H. (1976) Review article-The mechanical properties of cortical bone. J. Bone Jt Surg. 56A, 100-1022. Reilly, D. R., Burstein, A. H. and Frankel, V. H. (1974) The ‘elastic modulus for bone. J. Biomechanics 7, 2?1-275. Sedlin, E. D. (1965) A rheolonical model for cortical bone. Acta orthop: S&d. Suppl. i3. Sedlin. E. D. and Hirsch, C. (1966) Factors affecting the determination of the physical properties of femoral cortical bone. Aria orthop. Scand. 37, 2948. Simkin, A. and Robin, G. (1978) The mechanical testing of bone in bending, J. Biomechanics 6, 31-39. Simkiss. K. (1975) Calcium and avian reoroduction. Aoion Physiologi, (Edited by Peaker, M.). ’ Academic Press, London. Wall, J. C., Chatterji, S. and Jeffrey, J. W. (1970) On the origin of scatter in results of human bone strength tests. Med. biol. Engng. 8, 171-180. Wroblewski, T. (1980) Experimental coxofemoral replacement hemiarthroplasty in the goose (Anser sp.). M. S. Thesis, Clemson University.