The Tensile Properties of Single Osteons ' ANTONIO ASCENZI AND ERMANNO BONUCCI Institute of Morbid Anatomy, University of Pisn, Pisa, Italy ABSTRACT The ultimate tensile strength and modulus of elasticity of individual osteons from human and ox compact bone were determined with a specially designed microwave extensimeter. The results were related to the degree of calcifkation and the orientation of collagen fiber-bundles in successive lamellae of the osteons. The following conclusions were made: (1) When osteon specimens are dried, their tensile strength and modulus of elasticity increase, while their percent elongation under tension falls. (2) In the osteon samples tested wet, the degree of calcification induces an increase in the modulus of elasticity with additional amounts of calcium salts. (3) The modulus of elasticity in tension of the organic matrix corresponds to that of collagen. ( 4 ) In the osteons having a marked longitudinal arrangement of bundles of fibers in successive lamellae, the ultimate tensile strength and modulus of elasticity seem greater and the percentage elongation under tension seems lower than i n osteons whose bundles in successive lainellae change through an angle of about 90". ( 5 ) The tensile properties of osteons seem independent of the age of the subject. ( 6 ) Human and ox osteons reveal the same tensile behavior. (7) The tensile stress-strain curves show that, even at the level of single osteons, bone behaves like a complex material, which, according to Sedlin, can be represented by a Hooke body linked in series to a Kelvin body. In the last two decades, there has been an increased interest in problems concerned with the mechanical properties of bone (cf. Evans, '57; Sedlin, '65). At the present time, the lack of any quantitative studies of the micromechanical properties of isolated osteons has induced us to investigate the tensile strength of samples obtained by dissection from Haversian systems. In a previous paper, the results of research on the ultimate tensile strength of the same units were given (Ascenzi and Bonucci, '64). The aim of this paper is to present the definitive results of a quantitative investigation of the tensile deformation of single osteons from human and ox femoral shafts using a specially designed microwave extensimeter.2 MATERIALS AND METHODS As discussed in a previous paper (Ascenzi and Bonucci, '64), it appears very difficult at the present time to isolate samples corresponding to a whole osteon in order to test tensile properties. For this reason, the present tensile strength studies were made on samples corresponding to portions of longitudinally sectioned osteons. Longitudinal sections, 20-50 p in thickness, were prepared from femoral shafts ANAT. REC., 158: 375-386. by grinding them on glass plates. Special care was taken to avoid heating the material. The samples were taken from longitudinally sectioned osteons using the dissection technique described by Ascenzi and Fabry ('59) and Ascenzi and Bonucci ('64). With this technique it was easy to prepare samples of the desired shape (fig. l a ) . A region with parallel sides was isolated from the middle portion of half a longitudinally sectioned osteon, as seen in figure la. The ends of the sample fitted into square lugs in the tensile apparatus to assure a good fixation. The isolated middle portion of the sample had a length of 0.40.6 mm corresponding to the distance between the jaws of the tensile apparatus. The cross-sectional area of the sample at the middle was used in calculating the ultimate tensile strength and the modulus of elasticity. The thickness of the sample was determined by mounting it edgewise under the microscope and measuring the thickness with an eyepiece micrometer. The samples were tested in a wet and a dry state, respectively, to determine the 1 This work was supported by a grant of the National 2The paper reporting the partial and preliminary results of this investigation was presented at the Joints and Bones Symposium he!d in Wiesbaden, Germany, on August 11, 1965, dunng the VIII International Congress of Anatomists. Research Council of Italy. 375 3 76 ANTONIO ASCENZI AND ERMANNO BONUCCI Fig. 1 ( a ) A specimen ready to be tested. Polarizing microscope. % 50. ( b ) Osteon sample having a longitudinal spiral course of fiber bundles i n successive lamellae. ( c ) Osteon samples with fiber bundles changing direction i n successive lamellae through an angle of 90”. Polarizing microscope. x 100. influence of moisture on their tensile strength. The cross-sectional areas of both wet and dry samples were measured. The tested osteons revealed some structural peculiarities in the degree of calcification and in the structure of the matrix with respect to the orientation of the collagen fiber bundles. The degree of calcification was determined by microradiography. The osteons tested were those containing the least amount of apatite, i.e., those at the initial stage of calcification; and those having the maximum amount of apatite. The latter osteons, although sometimes referred to as “fully calcified osteons” in this paper, have, in fact, a slightly lower apatite content than interosteonic lamellae, the only kind of bone which can properly be considered fully calcified. Osteons with two types of fiber bundle orientation were chosen. In the first type, the fibers had a marked longitudinal spiral course with the pitch of the spiral changing so slightly that the angle of the fibers in one lamella was practically the same as that of the fibers of the next lamella. Under polarized light, osteons of this type appeared uniformly bright in longitudinal section (fig. l b ) . In the second type, the fibers i n one lamella formed a n angle of nearly 90” with the fibers of the next one (fibers ran alternately). Under polarized light, these osteons revealed a n alternation of dark and bright lamellae in longitudinal section (fig. l c ) . Some samples were decalcified i n a versene solution buffered to pH 7. At regular intervals, the decalcification was checked by measuring the increase in birefringence (cf. Ascenzi and Bonucci, ’61). The minimum time required for decalcification averaged about two hours and 30 minutes. The samples were subjected to a direct tensile force parallel with their longitudinal axis. For this purpose, the ends of each specimen were fixed in specially designed jaws, the upper one of which was fixed. A thin nylon thread was attached to the lower jaw and charged with 1 gm loads. The elongations of the osteon were recorded with a specially designed microwave extensimeter (see later). As soon as the length of a n osteon, produced by the addition of a load, became constant, additional weights were added. Difficulties were encountered in applying this method when the stress had passed the elastic limit. In this case, it was difficult to decide when a new equilibrium had been reached. I n practice, therefore, more weights were added when the speed of elongation produced by each successive increase in stress had slackened considerably. To avoid any torsion of the sample, particular care was taken to ensure that the tensile force was applied strictly along the longitudinal axis. All the measurements were performed at a temperature of ca. 20°C. The material used in this research was obtained from the femoral shafts of oxen and from a young and a n old man, 30 and 80 years of age, respectively. So f a r as is known, no pathological bones were included in the material. The total number of prepared osteons was 140, of which 23 were discarded as unsuitable for measurement. The remaining 117 units consisted of 21 ox osteons and 96 human osteons. Some osteons were dried at room temperature while others were put in saline solution or in distilled water. The microwave extensimeter used for measuring variations in length of the osteons subjected to tensile stress is based on cavity and pulse techniques, the prin- 377 TENSILE PROPERTIES OF SINGLE OSTEONS ciples of which may be summarized as follows : Let h and D be the height and the diameter, respectively, of a metallic cylinder whose cavity functions as a resonator for electromagnetic waves. The resonance frequency f o of this cavity will depend on h, D and the configuration of the electromagnetic field inside its cavity (mode). If the type of configuration chosen is that commonly indicated by “Teolzmode” the following relation holds (cf. Montgomery, ’47) fo2 = -;: ( CYLINDRICAL -4 APPENDAGE UPPER JLW WITH ITS SCREW _________ SAMPLE SCREW R I N G - ~ LOWER JAW WITH I T S SCREW NYLON TH C2 --) 1.488 + h2 C being the velocity of light in a vacuum. Any variation in the height ( h ) of the cavity produces a variation in the resonance frequency. By measuring this variation it is possible to deduce, by using equation ( l ), the corresponding variation of h. Figure 2 is a diagram of the apparatus used for measuring the elongation of the osteon specimens subjected to tensile stress. The upper end of a specimen is fixed in one jaw and the lower end in another jaw supporting a disc of Plexiglas whose lower metallized surface forms the upper plane of the cylindrical cavity. The disc, which may roll into the vertically orientated cavity, has a very thin nylon thread attached to its center. The thread extends through the long axis of the cavity and comes out through a small hole at the center of the lower fixed end of the apparatus. When traction is applied to the thread by attaching some weights to it, the osteon sample elongates, thus causing the upper plane of the cylindrical cavity to fall and decrease the height of the cavity. Because the elongation of the sample (AZ) and the reduction in the height of the cavity (-Al) are of exactly the same magnitude, any change in the length of the sample is easily deduced from the corresponding variation in the resonance frequency of the cavity. If AZ is very small compared with the height ( h ) of the cavity, equation (2) gives the corresponding fractional change in the resonance frequency Of course, the problem is that of measuring small fractional changes in the resonance frequency of a ca.vity. For this pur- WEIGHTS -~ . & Fig. 2 meter. Diagram of the cavity used as extensi- pose a pulse technique was used which has the advantage of being relatively simple and assuring high sensitivity and accuracy by the elimination of all spurious effects. For more detailed information about the technique, see Battaglia, Bruin and GOZzini (’58) and Ascenzi, Bonucci and Checcucci (’66). A block diagram and a photograph of our apparatus are given in figures 3 and 4, respectively. With this apparatus, measurements of variations in length of a single sample were accurate to within 1 % . A greater accuracy was not necessary because the 3 A s will appear evident later, the Teoin mode was chosen because: ( a ) the functlonlng of the cavity m this mode does not require electrical contact between the lateral and the end walls of the cavity, so that the height of the cylinder can be varied; (b) the presence of a dielectric thread running along the axis of the cylinder (see later) does not disturb the functioning of the cavity, because for Teolnmodes the electric field is null along the axis. 3 78 ANTONIO ASCENZI AND E R M A N N O BONUCCI geometrical dimensions (length and sec- breaking point are shown in table 1. Two tion) of the osteonic sample (see Ascenzi sets of values are given for the ultimate and Bonucci, '61, '64) could not be meas- tensile strength: ( 1 ) the values we obured with a greater degree of accuracy. tained in the present investigation alone and ( 2 ) a combination of these values RESULTS with those from our earlier investigation Of the results discussed here, those on using the same method but without the ultimate tensile strength, modulus of elas- extensimeter (Ascenzi and Bonucci, '64). ticity, and percentage elongation at the A unified conspectus of the stress-strain curves recorded from various types of osteon samples, kept in four different conditions, from the cadaver of a 30-year-old man are shown in figure 5. For each of 1 $,)KLYSTRON these conditions, a representative curve was chosen that most closely corresponded to the means of all individually recorded curves. To allow direct comparisons between single sets of recorded curves, the tensile strength is expressed in gm/vZ of section (ordinates) and the tensile strain as percentage elongation with respect to the original length of the sample (abscissae). Figure 5a is the diagram for osteon 19 which closely corresponds to the means of Fig. 3 The block diagram of the extensimeter. seven stress-strain curves of air-dried Fig. 4 Photograph showing some details of the apparatus. a, Klystron; b, cavity used as extensimeter; c, transmission cavity. TENSILE PROPERTIES O F SINGLE OSTEONS 379 of calcium salts. The fiber bundles had a marked longitudinal spiral course in successive lamellae. These curves also approximate a straight line, as did the curves of osteons with the maximum degree of (v calcification (cf. fig. 5a). However, the uppermost points of these curves show more deviation from a straight line before L Q, failure of the bone. Student’s t test ren vealed no significant differences between the modulus of elasticity (203,900 iE cn 0 . 0 1 76,400 kg/cmz) and the ultimate tensile I strengths of these osteons and those of the ul fully calcified ones. The mean of the presv) ent results is 19.33 -C 2.88 kg/mm8 and aJ those for the combined results 20.38 2 L .L2.62 kg/mm”. The percentage elongation v) at the breaking point (4.42 1.41) is increased. Figure 5c is a plot for osteon 36 which closely corresponds to the means of the tensile strain values for 12 wet osteons 0with the maximum amount of calcium salts 0 2 4 6 8 1 0 1 2 and fiber bundles with a marked longituOy0 e l o n g a t i o n dinal spiral course in successive lamellae. These curves show an elastic range like Fig. 5 Diagrams closely corresponding to the means of four sets of stress-strain curves recorded that of the corresponding dry osteons. for osteons having a very marked longitudinal However, the proportional limit is only spiral course of fiber bundles i n successive lamel- about half the breaking stress because the lae, taken from a man of 30. (a) Air-dried and fully calcified osteon 19. ( b ) Air-dried osteon 13 samples elongate more, near the breaking at the initial stage of calcification. ( c ) Wet and point. Beyond this proportional limit, each fully calcified osteon 36. ( d ) Wet osteon 135 at additional increment in stress causes excesthe initial stage of calcification. To make dia- sive yielding and permanent plastic degrams clearer only a few experimental values are formation of the specimen. In both the plotted. straight part of the curves and the deviatosteon samples with the maximum amount ing plastic region, a given stress will proof calcium salts and fiber bundles with a duce greater strains than in dry osteons. marked longitudinal spiral course in suc- Consequently, the modulus of elasticity cessive lamellae. The curves approximate (119,400 59,000 kg/cm2) and the ultia straight line up to the breaking point, mate tensile strength (12.26 1.51 kg/ indicating a proportionality between stress mm2or 11.65 i 1.74 kg/mm2 for the mean and strain in accordance with Hooke’s Law. of the combined results) are lower than in Only the uppermost points show a very dry bone, whilst the wet samples show a short curve deviating from a straight line greater percentage elongation (6.84 before the breaking point. The modulus of 2.86) than dried osteons. Figure 5d is the diagram for osteon 135. elasticity is very high, 238,600 -C 71,200 kg/cm2. The ultimate tensile strength is It closely corresponds to the means of 12 19.73 3.26 kg/mm2 or 21.20 t 2.97 tensile stress-strain curves recorded for wet kg/mm2 for the mean of the combined re- osteons with the least amount of calcium sults. The percentage elongation at the and a marked longitudinal spiral course of the fiber bundles in successive lamellae. breaking point is 2.15 -C 0.55. Figure 5b is the diagram for osteon 13, 4 Young’s modulus of elasticity “E” is the ratio unit deformation. With very few exceptions, closely corresponding to the means of six itstress/unit is a constant for any given material up to the tensile stress-strain curves recorded for air- elastic limit, but afterwards falls. Obviously the of elasticity reported here for osteons refers dried osteon samples with the least amount modulus to stress values below the elastic limit. 0.02 a * * 380 ANTONIO ASCENZI AND ERMANNO BONUCCI This diagram is similar to that for fully calcified wet osteons (fig. 5c) because i t deviates greatly from a straight line as the ultimate tensile strength is approached. However, the initial portion of the curve, which also clearly deviates from the curve of proportionality, indicates that plasticity begins at an early stage. Therefore, the possibility of calculating the modulus of elasticity or of attributing any precise meaning to it is seriously reduced. Its approximate value is 61,100 30,000 kg/ cm2. Student's t test showed that the ultimate tensile strength (10.65 +- 1.73 kg/ mmZor 10.95 2 1.88 kg/mmz for the mean of the combined results) is not significantly different from that of wet osteons at the final stage of calcification. The percentage elongation reaches 9.40 f 2.72. The wet osteons were prepared by hydration of the material in saline solution or distilled water. Contrary to the suggestion of Currey ('59), our previous (Ascenzi and Bonucci, '64) and present investigations revealed no significant differences i n tensile properties between osteons rehydrated in saline solution and those rehydrated in distilled water. Figure 6 shows a comparison between the stress-strain curve of the wet fully calcified osteon 36 (a) and the tensile stress- * 0 02, strain curve for osteon 65, closely corresponding to the means of five decalcified wet human osteons containing the maximum amount of calcium ( b ) . In all samples, the fiber bundles in successive lamellae had a marked longitudinal spiral course. The modulus of elasticity appears to be very low (10,500 3,500 kg/cm2) with an average ultimate tensile strength of 8.53 C 1.40 kg/mm'. The percentage elongation at the breaking point is very high (21.90 7.15). No significant difference is evident between these results and those recorded for decalcified wet osteons, with the same longitudinal spiral course of the fiber bundles i n successive lamellae and the least amount of calcium salts. In fact, the values from four osteons are as follows: modulus of elasticity 14,800 2 6,200 kg/cmz; ultimate tensile strength 8.77 1.19 kg/mmz; and percent elongation a t the breaking point 20.62 2 5.10. Figure 7 shows the stress-strain curves of wet osteons from a 30-year-old m a n but with differences in the degree of calcification and orientation of fiber bundles i n successive lamellae. The origin of the coordinate system is transferred along the abscissae axis for each set of diagrams to avoid the confusion which might arise from superimposing the charts. The curve for osteon 36 (fig. 7a) closely corresponds to * * N N a L 0) a k0Ol a E m k 0 01 n n u I n n L a . Q) ui L & Lo 0 0 (I 0 2 4 6 0 O/O 10 12 14 16 18 20 22 elongation Fig. 6 The diagram c seen in figure 5. ( b ) Diagram recorded for osteon 65 and closely corresponding to the means of a set of stress-strain curves from decalcified wet osteons, having the maximum amount of calcium previously fixed and having a very marked longitudinal spiral course of fiber bundles in successive lamellae. Man of 30. 1 3 0 1 3 0 1 3 0 1 3 5 7 4 11 elongation Fig. 7 Diagrams closely corresponding to the means of four sets of stress-strain curves recorded for osteons taken from a man of 30. ( a ) ( c ) Diagrams already reported in figure 5 (charts c, d ) . ( b ) Wet and fully calcified osteon 41 with fiber bundles running alternately in such a way that their direction i n successive lamellae changes through a n angle of 90". ( d ) Wet osteon 47 a t initial stage of calcification and with fiber bundles running alternately in successive Iamellae. 381 TENSILE PROPERTIES OF SINGLE OSTEONS the means of a set of 12 diagrams for fully calcified osteons in which the fiber bundles of successive lamellae had a marked longitudinal spiral course. The curve for osteon 41 (fig. 7b) closely corresponds to the means for nine fully calcified osteons but with fiber bundles running alternately in successive lamellae. These curves show a clear deviation from the curves of proportionality, thus indicating that plasticity begins at an early stage. Consequently, it is not easy to determine the limit of elasticity and any attempt to evaluate the modulus of elasticity appears to be unreliable. It is probably something like 55,900 26,100 kg/mm2 with the ultimate tensile strength dropping to 10.39 1.71 kg/mm2 or 9.59 _c 1.55 kg/mm2 for the mean of the combined results. Similar results are shown in figure 7c for wet osteons in the initial stage of calcification and with fiber bundles in successive lamellae having a marked longitudinal spiral course. Figure 7d illustrates the curve recorded for osteon 47. It closely corresponds to the means for six osteons with the same degree of calcification as those in figure 7c but with fiber bundles running at an angle of 90" in successive lamellae alternately. The modulus of elasticity is probably 44,700 i- 19,700 kg/cm'. The ultimate tensile strength drops to 9.06 2 1.48 kg/mmz. A comparison was made of the tensile properties of osteons from an adult (30 years of age) and an old man (80 years of age). Two types of wet osteons from the old man were analyzed : ( 1) osteons whose fiber bundles in successive lamellae had a marked longitudinal spiral course and ( 2 ) osteons in which the bundles of fibers of one lamella formed an approximate angle of 90" with the fiber bundles of the next lamella. Osteons at both the initial and final stages of calcification were studied. No significant differences were found between the ranges covered by tensile stressstrain curves for eight wet and fully calcified osteons obtained from an 80-year-old man (fig. 8b) and similar osteons obtained from a 30-year-old man (fig. 8a). In the osteons from both individuals the fiber buiidles of successive lamellae formed an angle of 90". The osteons from the old man had a modulus of elasticity averaging 62,100 2 * * (u ao.01 I dr Q. a 1 b E 0 I v) v) Q, L .L, a 0 0 I I 2 4 6 8 10 V0 e l o n g a t i o n Fig. 8 ( a ) This is the same diagram as that seen in figure 7 (chart b). ( b ) Diagram recorded for osteon 66 and closely corresponding to the means of a set of 14 stress-strain curves plotted from wet fully calcified osteons with fiber bundles running alternately in successive lamellae. Man of 80. 35,800 kg/cm2 and an ultimate tensile strength averaging 8.82 i- 0.85 kg/mm' or 9.41 -t 1.24 kg/mm2 for the mean of the combined results. The percentage elongation at the breaking point was 8.23 -I 3.45. Other groups of osteon samples showed fairly similar results (table 1). The results obtained for ox osteons (fig. 9 ) are exactly comparable to those for human osteons. Stress-strain curves were recorded for both dry and wet osteons ha.ving a marked longitudinal spiral course of the fiber bundles in successive lamellae. Figure 9a was recorded for osteon 83 and closely corresponds to the means for five dried, fully calcified osteon samples. The modulus of elasticity averaged 180,700 2 19,400 kg/cm*; the ultimate tensile strength 20.90 2 1.15 kg/mm2 or 21.28 5 1.83 kg/mm2 for the mean of the combined results; and the percentage elongation 3.45 2 0.38. Figure 9b was recorded for osteon 93 and closely corresponds to the means for five dried-osteons at the initial stage of ossification. The modulus of elasticity is 133,400 24,400 kg/cm'; the ultimate tensile strength 19.49 F 1.94 or 20.60 -C 2.74 kg/mmz; and the percentage elongation 9.32 2 1.18. Figure 9c was recorded for osteon 97 and closely corresponds to the means for 20.90C 1.15 19.49k 1.94 12.12C0.74 11.28t0.48 5 5 5 6 dry dry wet wet OL and FC OL and LDC OL and FC OL and LDC 14 8 wet wet 180,700f 19,400 133,400*24,400 149,600*28,700 54,600i.12,300 3.4520.38 9.322 1.18 8.30f 1.10 11.14i1.41 108,700t39,100 7.68 k 2.39 49,30Ot33,300 10.50k2.54 62,100~35,aoo 8.2323.45 39,600C 7,300 14.2823.28 10.91& 0.81 9.472 1.26 8.8220.85 8.60C0.69 wet 2.152055 4.42f 1.41 6.84 2 2.86 9.40 t 2.72 10.2924.03 9.802 0.92 21.902 7.15 20.6225.10 % 238,600 t 71,200 203,900 t 76,400 119,000C 59,000 61,lOOC 30,000 55,900 C 26,100 44,700 2 19,700 10,500-C 3,500 14,800 C 6,200 kg/cmz kg/mm2 Elongation at breaking point 19.73t 3.26 19.33-+ 2.88 12.26? 1.51 10.652 1.73 10.39-C1.71 9.06 k 1.48 8.532 1.40 8.77k 1.19 E Present results UTS 8 5 7 6 12 12 9 6 5 4 No. wet dry dry wet wet wet wet wet ( d ) wet ( d ) State of samples OL and FC OL and LDC OCD and FC OCD and LDC OL and FC OL and LDC OL and FC OL and LDC OCD and FC OCD and LDC OL and FC OL and LDC Types of osteons measured osteons 22 15 21 21 28 18 24 16 32 23 22 No. 21.28 +- 1.83 20.60zk2.74 12.042 1.54 11.25C1.79 9.41&1.24 10.96 0.92 * 21.20C2.97 20.38 2 2.62 11.65k 1.74 10.952 1.88 9.592 1.55 kg/mmz UTS Combined results of N~ number of measured osteons; OL, osteons whose fiber bundles had a longitudinal course with the angles of fibers i n successive lamellae practically the &&e. OCD osteons whose fiber bundles in successive lamellae formed an angle of 90'; LDC, osteons at lowest degree of calcification; FC, fully calcified OSteons; 8, decklcsed. The young subject in the present investigation was aged 30 years; in the previous investigation, 20 years. 2-year-old ox 80-year-old man Young man of 20 and 30 Individuals and age Average values of the ultimate tensile strength (UTS), modulus of elasticity ( E ) , % elongation at breaking-point for each set TABLE 1 B 5 3 W 8 4 E ?rl M ti9 2 %n 8 0 P TENSILE PROPERTIES OF SINGLE OSTEONS 383 :-I 0.01 In ul al 1 0 2 4 Oy0 6 8 I I I 1 0 1 2 1 4 elongation Fig. 9 Diagrams closely corresponding to the means of four sets of stress-strain curves recorded for ox osteons having a very marked longitudinal spiral course of fiber bundles in successive lamellae. ( a ) Air-dried and fully calcified osteon 83. ( b ) Air-dried osteon 93 at the initial stage of calcification. ( c ) Wet and fully calcified osteon 97. ( d ) Wet osteon 101 at the initial stage of calcification. five wet fully calcified osteon samples. The modulus of elasticity averaged 149,600 2 28,700 kg/cm2; the ultimate tensile strength 12.12 2 0.74 or 12.04 2 1.54 kg/ mm2; and the percentage elongation 8.30 c1.10. Figure 9d was recorded for osteon 101 and closely corresponds to the means for six wet osteon samples at the initial stage of ossification. The modulus of elasticity was 54,OO 12,300 kg/cm2; the ultimate tensile strength 11.28 ? 0.48 or 11.25 2 1.79 kg/mm2; and the percentage elongation averaged 11.14 1.41. Finally, a careful examination of the fractures of all the tested osteons (fig. 10) showed that the break area may include some osteocyte cavities, but there is no demonstrable relationship between the number of intersected osteocytes, on the one hand, and the cross-section and ulti- * * Fig. 10 A series of break ends of tested 0steons. Polarizing microscope. X 100. mate tensile strength of the specimen, on the other. DISCUSSION In discussing the results furnished by the present investigation, it may be useful to attempt a comparison between the tensile behavior of single osteons and the tensile behavior of bone samples of macroscopic size. Our results with samples taken from isolated osteons with a marked longitudinal arrangement of fiber bundles in successive lamellae show that the tensile curve for dry bone approximates a straight line, as previously reported by Wertheim (1847), Hallerman ('34), Marique ('45) and Evans and Lebow ('51) for macroscopic specimens. However, for the osteon samples, the stress-strain curve deviates very slightly from a straight line immediately before the breaking point. This deviation is somewhat clearer in osteons at the initial stage of calcification than in fully calcified ones. This result does not allow us to consider dry osteons as entirely elastic as was for- 384 ANTONIO ASCENZI A N D ERMANNO BONUCCI merly believed, especially by Hallerman, for macroscopic bone samples. On the other hand, there is some similarity between our data and those reported by Dempster and Liddicoat (’52), who also showed that Hooke’s Law is not strictly respected. As the breaking point is approached, the elongation of the sample is somewhat higher than one would expect. In any case, it should be emphasized that the samples prepared from single osteons are not entirely representative of all the structures present in compact bone. For instance, the interosteonic cementing zone is lacking. There is no significant difference between the modulus of elasticity of dry, fully calcified osteons and the modulus of elasticity of dry osteons at the initial stage of calcification. An impressive similarity exists between our values and those of Rauber (1876), Manque (’45), Evans and Lebow (’51) and Dempster and Liddicoat (’52). The influence of moisture on the tensile properties of osteons is indicated by the difference in the shape of stress-strain curves from wet and dry samples. If one considers units having a marked longitudinal arrangement of the fiber bundles in successive lamellae, the curve shows an elastic range like that of the dry osteon. But, as the samples elongate further toward the breaking point, the proportionality between stress and strain ends at a proportional limit about half the breaking stress. Beyond this proportional limit, each additional increment in stress causes excessive yielding and permanent plastic deformation. Nevertheless, the transition from elastic to plastic deformation occurs gradually, rather than abruptly, so that, regardless of how accurately the modulus of elasticity is calculated, it is still an approximation. This explains the high standard deviation of the mean obtained for the modulus of elasticity. The behavior of the tensile stress-strain curves shows that, even at the level of single osteons, bone behaves like a complex material. According to Sedlin (’65) and Sedlin and Sonnerup (’65), bone can be represented by a Hooke body linked in series to a Hooke and a Newton body, which are linked in parallel (Kelvin body). The percentage elongation under tension reveals a significant difference between dry and wet osteon specimens, the latter being subject to a greater elongation. There is a very close correspondence between these results and the curves recorded from macroscopic bone specimens (cf. Dempster and Liddicoat, ’52; Evans and Lebow, ’51). Moreover, our previous (cf. Ascenzi and Bonucci, ’64) and present observations furnish evidence that the ultimate tensile strength of osteons, both at the initial and final stages of calcification, is significantly greater in dry tested samples than in wet ones. If the values obtained by Evans and Lebow (’51) for the percentage elongation under tension were calculated applying the same procedure used by us, i.e., multiplying by 100 the ratio “initial length/total elongation at the breaking point,” one must conclude that the percentage elongation of the osteons is somewhat greater than that obtained from macroscopic bone samples. Both dry and wet osteons show that the amount of calcium salts plays an essential role in the elasticity of bone tissue. In dry osteons, at the initial stage of ossification, the stress-strain curve deviates much more from the straight line than it does in dry fully calcified osteons, thus revealing a greater plastic range. On the other hand, the curve obtained from wet osteons at the initial stage of ossification is similar to that for fully calcified wet osteons; however, the initial portion shows a clear deviation from the straight line of proportionality which indicates that plasticity begins at an early stage. These data clearly indicate that the elasticity of bone tissue is a function of the amount of calcium salts, i.e., the hydroxyapatite crystallites present in the bone. The lower the calcium content, the higher is the plasticity of the tissue (see also Currey, ’62). In accordance with the present results, the stressstrain curves recorded for decalcified osteons indicate a sharp drop in elasticity. An important point to be considered is the close similarity between stress-strain curves recorded for human and for ox osteons. This finding agrees with the view of Ascenzi and Bonucci (’61), that, with regard to optical properties (birefringence), no essential difference exists between bone TENSILE PROPERTIES O F SINGLE OSTEONS units of the two mammalian species. The investigations of Rowland, Jowsey and Marshall ('59), which show that differences in the amount of calcium salts cannot be demonstrated in human and ox osteons, also provide indirect support for this view. As previously reported, the tensile properties of human organic matrix (ossein), prepared both from osteons with the lowest degree of calcification and from fully calcified osteons, do not reveal any significant differences. These results appear to agree with those published by Strandh ('60) who has furnished chemical evidence that variations in the amount of ossein are not demonstrable during the calcification of osteons. Moreover, it must be pointed out that there is a very close correspondence between t e modulus of elasticity of decalcified o teons with the lowest and highest degree of calcification. In the former, the modulus of elasticity is 10,500 2 3,500 kg/cm2 and in the latter 14,800 t 6,200 kg/cmz. These values agree with those for the modulus of elasticity of collagen which is about 200,000 lb/in2, i.e., 14,061 kg/cm' (cf. Currey, '62). The values given for the ultimate tensile strength of decalcified osteons are not comparable with those reported in our previous paper (Ascenzi and Bonucci, '64) because in the present investigation we were able to measure the section of the samples directly on decalcified material. The differences between the stress-strain curves recorded for osteons having longitudinally orientated fibers and osteons in which the fiber bundles run alternately, changing their direction in successive lamellae through an angle of go", suggest that the latter have a lower modulus of elasticity than the former. Besides, the ultimate tensile strength of osteons in which the fiber bundles run alternately, changing their direction in successive lamellae is significantly lower than in osteons having longitudinally orientated fibers. Consequently, the percentage elongation increases. These results appear to correspond with Maj and Toajari's investigations (see Maj and Toajari, '37a, '37b; Toajari, '37) revealing that, in the specimens with the greatest breaking load, the majority of the collagen fibers are lontzitudinallv orientated. In this connectionr it should be noted that, according 2 385 to Dempster and Coleman ('61), the crossgrain ultimate tensile strength of bone is much less than the parallel-to-grain strength. The stress-strain curves of osteon samples from an 80-year-old man show that for wet units there is no appreciable change in tensile properties with advancing age. These findings are in agreement with those of Evans and Lebow ('51), but differ from those of Rauber (1876) and Melick and Miller ('661, who reported a decrease in tensile strength of bone with advancing age. In conclusion, our results suggest that the quality of osteons is unchanged even in advanced old age. ACKNOWLEDGMENTS The authors are deeply grateful to Prof. F. Gaynor Evans, Department of Anatomy, The University of Michigan, Ann Arbor, Michigan, U.S.A., for his help with this manuscript. They also wish to express their indebtedness to A. Benvenuti, G. Ciampi, F. Castellano and L. Di Baldo for technical assistance during the course of the present investigation. It is a pleasure to thank Springer-Verlag for permission to publish figures 2 and 3, which originally appeared in "Studies on the Anatomy and Function of Bone and Joints." 1966 F. Gaynor Evans, ed. Springer-Verlag,Berlin - Heidelberg - New York. LITERATURE CITED Ascenzi, A., and E. Bonucci 1961 A quantitative investigation of the birefringence of the osteon. Acta Anat., 44: 236-262. 1964 The ultimate tensile strength of single osteons. Acta Anat., 5%: 160-183. Ascenzi, A., E. Bonucci and A. Checcucci 1966 The tensile properties of single osteons studied using a microwave extensimeter. In: Studies on the Anatomy and Function of Bone and Joints. F. G. Evans, ed. Springer-Verlag. Heidelberg, pp. 121-141. Ascenzi, A., and C. Fabry 1959 Technique for dissection and measurement of refractive index of osteons. J. Biophys. Biochem. Cytol., 6: 139-142. Battaglia, A., F. Bruin and A. 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