The relative effects of collagen fiber orientation, porosity, density, and mineralization on bone strength

J. Bi,mwc~ics

Vol. 22, No. 5. PP. 419-426,

Printed in Gnat

1989. Q

Britain

0021-9290/89 163.00 + .oO t989 Maxwell Pergamon Macmillan plc

THE RELATIVE EFFECTS OF COLLAGEN FIBER ORIENTATION, POROSITY, DENSITY, AND MINERALIZATION ON BONE STRENGTH R. B. MARTIN and J. ISHIDA The Orthopaedic Research Laboratories, University of California at Davis, Davis, CA 95616, U.S.A. Abstract-This investigation determined the relative importance of collagen fiber o~entation, porosity, density, and mineralization in determining the tensile strength of bovine cortical bone. Thirty-nine specimens were tested for failure stress and the values of eight histologic and compositional parameters: collagen fiber orientation, wet and dry apparent density, percent mineralization of the bone matrix, and several components of porosity (Haversian canals, Volkmann’s canals, and plexiform vascular spaces). Linear regression analysis showed that collagen fiber orientation was consistently the single best predictor of strength. Mineralization of the bone matrix was generally a poor predictor of strength. Density and porosity ranked between these variables in importance. M~tiple regression equations containing all significantly correlated variables achieved correlation coefficients of 0.607 for plexiform bone and 0.881 for osteonal bone. Also, separate analysis of plexiform and osteonal specimens showed that the latter group was weaker even though it was less porous, apparently because it had collagen fibers which were less longitudinally oriented. This study suggests it is feasible to develop better empirical formulae for the prediction of cortical bone strength than are currently available if a variety of variables is introduced. Additional data are needed to confirm these results.

INTRODUCTION

Many previous investigations have addressed the relationship between the histology of cortical bone and its mechanical properties (Ascenxi and Bonucci, 1964, 1967; Evans and Bang, 1967; Carter and Spengler, 1978; Currey, 1959; HBrt et al., 1965; Reilly and Burstein, 1974). Bone can be described by several microstructural and compositional variables, including density, porosity, mineral or calcium content, collagen fiber orientation, anisotropy, and histologic type. While some investigators have suggested linear or power laws between one or more microstructural variables and mechanical properties, others merely state that such features as secondary osteons significantly affect strength or stiffness. Cortical bone develops in two stages. The first stage, called primary bone, consists of numerous circumferential lamellae laid down parallel to the outer surface of the bone. Scattered through these lamellae are primary osteons containing the bone’s vascular supply. Some primary bone, termed ‘plexiform’, is more rapidly formed and contains layers of wovenfibered bone. Cow bone, frequentfy used to study mechanical properties because of its size and availability, is of this type. Katz and Yoon (1974) observed that bovine primary bone consists of parallel laminar fibers and is orthotropic in its elastic properties. primary bone later remodefs to secondary osteonal bone or Haversian bone. Ascenzi and Bonucci (1967) observed that secondary osteons have varying internal

Received infinulform 22 December 1987. &*I22:5-B

structures which produce different appearances in polarized light. They categorized these osteonal structures into three types according to whether the collagen fibers are p~ominately lon~tu~n~ (nearly parallel to the osteonal and bone axes), circumferential, or alternating. The first two of these types appear dark and bright, respectively, in plane polarized light. Investigating the relationship between mechanical properties and fiber orientation in single osteons, Ascenxi and Bonucci (1967) concluded that osteons containing mostly lon~tudinally oriented collagen fibers have a higher tensile strength than those containing many circumferentially oriented fibers. The mechanical properties of bone are also functions of its mineral content. Vose and Kubala (1959) concluded that bending strength increases as percent mineral content increases. Ascenxi and Bonucci (1967, 1968) also found that the tensile strength of segments of single osteons was greater when they were fully mineralized. Another parameter of cortical bone is density. Carter and Hayes (1976) concluded that the compressive strength and stiffness of bone are power functions of apparent density. Although the relationships between these variables and mechanical properties have been studied individually, there are apparently no published studies which have attempted to simultaneously determine the relative importance of all of these parameters. Therefore, this investi~tion was designed to examine the relative effects of collagen fiber orientation, porosity, density and mineralization on the tensile strength of primary and secondary bovine bone, and to determine which variable is the best single predictor of strength. 419

R. B.

420

MARTIN

and J.

ISHIDA

METHODS

The midshaft of a bovine femur was cut perpendicular to the long axis of the bone into 4.5 cm segments with a band saw. Each of these shaft segments was then cut parallel to the long axis of the bone into four specimens. Thirty-nine of these specimens were milled into 4.5 x 1.8 x 0.5 cm slabs as shown in Fig. 1. A l/2 in. radius mill was used to mill the gage length to a width of 0.5 cm in the middle third of the specimen. The specimens were stored in cold mammalian saline until tested.

J

5xsx5mm segment for density and mineralization

/@ -H

CdCUlHiOlU

100 micron thick histological cross-section

Tensile testing

An Instron Model 1122 materials testing machine was used at a crosshead speed of 10 mm min- i. Before testing, the cross-sectional dimensions were measured and recorded. With these measurements and the load deformation curve, tensile strength was calculated as the stress at failure. Histology

After mechanical testing, a 100 P thick cross-section was prepared using an Isomet low speed saw (Buehler Ltd). The section was cut as close as possible to the fracture site (see Fig. 2) and stained in a fast green FCF/orange stain for 12 h, followed by a basic Fuchson/Celestine blue stain for 1 h. Next, the section was differentiated in 1% acetic acid in 70% ethanol; dehydrated in an ethanol series, cleared in xylene; and mounted on a glass slide. Fiber orientation

An Olympus Vanox model microscope with light meter and plane polarizing filters above and below the stage was used. An Olympus EMM-6 model light

Jrll

Fig. 1. The dimensions of the tension test specimens are shown in centimeters, except for the radius of the gage length fillet, which was determined by the l/2 in. milling tool.

--r4

Fig. 2. The locations of the histologic cross-section and the density/mineralization specimen are shown relative to the fracture site.

meter was used to obtain a voltage proportional to the average light intensity of the field of view. The lower (analyzer) filter was rotated to produce bright and dark fields. The light intensity of the bright field without the presence of a bone section was standardized at 2 V. The light intensity of the stained cross-section in the bright field (V,) was found to be dependent upon staining and porosity. The dark field light intensity (IQ was governed by staining, porosity, and the birefringence of the collagen fibers. We defined a ‘longitudinal structure index’, LSI = VJV,, as an approximate measure of the degree of longitudinal collagen fiber orientation for each specimen. Since staining and porosity had similar effects in both fields (staining reduced and porosity increased the light intensity), forming a ratio of the bright and dark field light measurements tended to cancel the effects of variations in these variables. The LSI was measured at 4 standardized sites on the section, and the average LSI of the specimen was recorded. Figure 3 shows the appearance of the plexiform and osteonal specimens in ordinary and polarized light. Porosity

Working at a magnification of 10x with an eyepiece reticule grid and an Olympus BH-2 model microscope, porosity was estimated by point counting. The grid contained 121 points; the fraction of these points falling upon void spaces was defined as the porosity of the field. Figure 3 shows the typical appearance of void spaces in plexiform and osteonal

421

423

Tensile strength of bovine cortical bone

bone. Three components of porosity were measured: Haversian canal porosity (POR H), Volkmann’s canal porosity (POR V), and the porosity of the vascular channels characteristic of plexiform bone (POR P). Smaller voids (e.g. osteocyte lacunae) were not included in the measurement. The total of the three components of porosity (POR T) was also recorded. These variables were measured for nine different fields on each section, and the specimen averages were recorded. Wet and dry density

Adjacent to the histologic section, a 5 mm length of the tensile specimen was cut for density determinations; see Fig. 2. After the volume of this segment was calculated from its dimensions, it was blotted dry, weighed, and the wet density (WET DEN) was calculated. The segment was then vacuum-dried at 100°C for 24 h, weighed, and the dry density (DRY DEN) was calculated. Mineralization

Finally, the segment was ashed at 800°C in a muffled furnace for 48 h. The ashed segment was weighed, and the ashed weight was divided by the dry weight to obtain the percent mineralization of the bone matrix (% MIN). Analysis

The specimens were divided into three groups according to their bone structure as revealed by the histologic section-plexiform bone, osteonal bone, or mixed (specimens which consisted of both plexiform and osteonal bone). The mean and variance of each variable was determined for each group, and a oneway analysis of variance was used to test for differences between the groups. In addition, a stepwise multiple regression analysis was conducted between tensile strength and the eight independent histo-compositional variables (LSI, POR T, POR V, POR H, POR P, WET DEN, DRY DEN, %MIN). This

analysis was done for the entire sample of specimens, and for each histologic group. In all cases, the criterion for significance was PXO.05. RESULTS

One osteonal specimen was eliminated from the analysis because of its unusually high tensile strength: 169 MPa. Since this specimen’s strength was more than three standard deviations larger than the mean of the remaining osteonal specimens, and more than two standard deviations larger than the mean of the plexiform specimens, it was felt that this deletion would give a better representation of the osteonal specimens. Tables 1 and 2 show the means and standard deviations of tensile strength and the independent variables for the entire sample, and for the three histologic groups: plexiform, osteonal, and mixed. The means of the plexiform specimens are generally higher than those of the osteonal specimens, and the means of the mixed specimens fall above or between the plexiform and osteonal means. Osteonal specimens were significantly weaker than plexiform specimens. They also were less porous, more dense (in the wet state), and had fewer longitudinally oriented collagen fibers. The differences between groups were not statistically significant for % MIN and dry density. Table 1. Means and standard deviations for all the specimens Strength, MPa

106+26 0.0142&0.014 0.0237 _+0.020 0.0506 * 0.047 0.088 1 kO.020 1.80+0.14 2.01+0.14 18.3& 6.3 0.699 + 0.029 39

Haversian porosity Volkmann’s porosity Plexiform porosity Total porosity Dry density, g cc-’ Wet density, g cc- ’ LSI % Min (g/g) No. specimens

Table 2. Effects of histologic type

Strength, MPat Haversian porosity$ Volkmann’s porosityj Plexiform porosity Total porosityf Dry density, g cc-‘* Wet density, g cc- I* LSIT % Min (g/g)* No. specimens

Plexiform

Osteonal

Mixed

115+26

87.4* 13 0.0282 k 0.010 0.0400+0.012

112*20 0.0148 f 0.007 0.0270 + 0.014 0.0506 f 0.026 0.0924~0.014 1.85+0.042 2.02 + 0.044 22.0 * 5.9 0.696 kO.029 10

0.0062~0.014 0.0972 k 0.024 0.103 kO.014 1.82f0.07 2.03 ; 0.037 20.6 k 5.2 0.711* 0.023 15

0.0680* 0.008 1.73+0.23 1.97kO.24 13.3k4.5 0.692 + 0.031 13

*No significant difference between groups. tNo significant difference between plexiform and mixed groups. Significant difference between plexiform and osteonal groups and between osteonal and mixed group (P < 0.05). ISignificant difference between all groups (P < 0.05).

424

R. B. MARTINand J. ISHIDA Table 3. Relative importance of the predictors of failure strength All

Plexiform

Osteonal

Mixed

LsI*

LsI*

LSI*

POR C

(R= 0.489, P = 0.002)

(R= 0.490, P = 0.002)

(R=0.628, P=O.O21)

(R=0.00628, P=O.SlO)

DRY DEN* WET DEN* POR C* POR P* POR H* % MIN* POR T

DRY DEN* WET DEN* POR T* POR P* % MIN* POR C*

POR T’ DRY DEN* WET DEN* POR C % MIN POR H

POR P POR T POR H WET DEN % MIN LSI DRY DEN

* = Significant predictor.

Table 4. Multiple regression equations for tensile strength Type

bone

of

All

Plexiform

Strength=0.150+0.0013 LSI-0.627 -0.556 Pv 0.333 Pp R=0.607, P=O.O317 Strength=0.145+0.0013

Ph

LSI

+0.0559 Pv +0.282 Pp -0.610 Pt -0.135 Dw +0.156 Dd -0.495 %M

LSI

-0.769 Pt -0.092 Dw +O.OlO Dd

R = 0.607, P = 0.032 Osteonal

Strength=0.127+0.0015 R=0.841, P=O.O28

Mixed

No significant equation

-0.136 Dw +0.156 Dd -0.0051 %M

LSI = Longitudinal structure index; Pn = Haversian porosity; Pt = Total porosity; %M = Percent mineralization; Pv = Volkmann’s porosity; Pp = Plexiform porosity; Dw = Wet density; Dd = Dry density.

Table 3 shows the results of the stepwise multiple regression analysis. The best predictor of strength was defined as the last independent variable to be eliminated during the stepwise regression. Conversely, the least useful predictor was the first variable to be eliminated during the regression. The variables marked with asterisks are those which achieved significance at some point during the stepwise regression analysis. The correlation coefficient (R)and P-values displayed in Table 3 are those of the best predictor, i.e. the results of the last step in the regression analysis. LSI was the best single predictor of tensile strength when all the specimens are considered. If one considers only osteonal bone, LSI was again the best predictor, with an even better correlation coefficient (R= 0.63). On the other hand, for purely plexiform bone, LSI correlated less well with strength (R=0.49). In the specimens of mixed histologic structure, LSI was never a significant predictor of stress. In fact, none of the histo-compositional variables achieved significance in the mixed bone specimens. Dry and wet density were the second and third best predictors of strength for the entire sample and for the plexiform group. In osteonal bone, the density variables ranked behind POR T, but were again signifi-

cant predictors. Percent mineralization ranked consistently low as a correlate of tensile strength in all three bone structure groups. Multiple regression equations in which only the significant independent variables appear are shown in Table 4. In the analysis, it was found that once significance was achieved, removal of another variable decreased the correlation coefficient. Thus, these equations represent the best empirical predictors of tensile strength for the experimental sample reported here. If one considers only osteonal bone, a multiple correlation 0.841 is obtained for the strength equation, which includes only four factors: LSI, total porosity, and wet and dry density. The strength equation for plexiform bone involves all seven variables. Since none of the independent variables achieved significance in the mixed histologic structure group, a strength equation is not shown for these specimens. DlSCUSSlON

The results in Table 1 reinforce the conclusion (Carter et al., 1976) that Haversian remodeling weakens bone structure, causing plexiform bone to have a larger tensile strength than osteonal bone. This reduc-

Tensile strength of bovine cortical bone

tion in strength has previously been attributed to (a) increased porosity, (b) increased numbers of cement line interfaces, or (c) reduced mineralization (Carter and Spengler, 1978). The present study suggests that porosity and mineralization are less important than collagen fiber orientation in reducing the strength of osteonal bone. Bovine plexiform bone which has not been significantly remodeled has relatively more longitudinally oriented collagen fibers than osteonal bone, as shown by its higher LSI index. This is usually readily apparent when viewing the two types of structure in polarized light under the microscope (see Fig. 3). The classification of osteons into structural types (longitudinal fibers, circumferential fibers, and both orientations in alternating lamellae) based upon their appearance in polarized light (Ascenzi and Bonucci, 1968) has been confirmed in large measure by Frasca et al. (1977,1978). However, these authors showed that the differences between bright, dark, and intermediate osteons are not absolute but more a matter of degree. All three types seem to contain many longitudinal fibers, but there is a lack of circumferential and oblique fibers in dark osteons. The classification of osteons based upon birefringence has also been criticised because the birefringence pattern can change as one moves along its length, and as the direction of the osteon axis changes (Black et al., 1974). Nevertheless, the work of Frasca and colleagues confirmed that bright osteons contain a greater proportion of longitudinal fibers than do dark osteons. In the present study, osteons were not categorized into such Ascenzian types; rather, the overall orientation of collagen fibers in the bone tissue was assessed using the birefringence technique. This method is consistent with the interpretation of Frasca’s group, and yielded a correlation between longitudinal fiber orientation and tensile strength for bone tissue which was similar to that for individual osteons. This may indicate that collagen fiber orientation is an important determinant of the tensile strength of bone, or it could mean only that both birefringence and strength correlate with a third governing variable. Although LSI was the best predictor of tensile strength for both plexiform and osteonal bone, the correlation was better in osteonal bone. Plexiform bone contains a preponderance of longitudinally oriented collagen fibers; its LSI values are relatively less variable. Haversian bone is more heterogeneous and contains a variety of fiber orientations; therefore, its LSI values spread over a larger range, providing a more distinct correlation. There are few reports in the literature relating cortical bone strength to its collagen fiber orientation. Vincentelli and Evans (1971) obtained correlation coefficients between tensile strength and numbers of light and dark osteons in human bone which were similar to the LSI correlations reported here: 0.443 for dark osteons and - 0.487 for light osteons. Evans and Vincentelli (1974) obtained lower correlations (R less

425

than 0.240) between compressive strength and the numbers of light and dark osteons; in this case porosity gave a much higher correlation (R = 0.655). In addition to LSI, wet and dry density proved to be significant predictors of strength. However, wet and dry density were highly correlated to each other (R=0.945), and these two variables are clearly redundant. Also, density is in general a function of both the porosity and mineralization of bone tissue. This may explain why density has been found to be a good predictor of strength and elastic modulus when a wide variety of bone types is studied (Carter and Hayes, 1976; Currey, 1984). Perhaps the reason this variable had better predictive value in those studies than the current one is that they produced a broader range of density values, giving a greater opportunity for a high correlation. The present results are in concert with work showing that the tissue birefringence of human femoral cross-sections is not randomly distributed, but corresponds to stress patterns (Portigliatti Barbos et al., 1983). That is, more longitudinally oriented fibers are located in the lateral-anterior cortex (which is placed in tension during gait) than in the medial-posterior cortex (which is compressed in gait). While our results were influenced by the presence of plexiform bone, which does not occur in humans, nevertheless, both studies suggest that bone with more longitudinally oriented collagen fibers is better suited to support tensile stress. Vose and Kubala (1959) obtained a high correlation (R = 0.94) between the bending stress at failure and Xray determined ash content of the human femur midshaft. It should be pointed out that this method of measuring ‘mineralization’ also depended upon porosity. In this study, relative to density and fiber orientation, percent mineralization proved overall to be the poorest correlate of strength of the variables examined. Again, this may have been because mineralization varied over a very narrow range of values, so there was little possibility for a high correlation. It appears that the stiffness of cortical bone can be better predicted by histo-compositional variables than can strength. Schaffler (1985) studied the relationship between the tensile elastic modulus of bovine cortical bone and density (not significant), ash content (R=0.69), the inverse square root of porosity (R = -0.84) and fraction osteonal bone (R=0.82). These individual correlations are clearly much higher than those reported here for tensile strength. The high correlation (R =0.91) obtained by Currey (1984) between density, calcium content, and tensile elastic modulus of cortical bone from a variety of species supports this hypothesis. The relatively poor correlation between mineralization and strength reported here raises the question of the usefulness of quantitative CT scans as a means of estimating the mechanical properties of a bone in situ. Fortunately, the present results probably do not apply to that problem. It must be remembered that CT scan

426

IL%.

MARTIN

results are usually directed at assessing trabecular bone for the effects of osteoporosis. In that case, the CT numbers are primarily- a function of porosity rather than variations in miner~ization of the bone matrix. Also, in that case the orientation of trabecular structure may influence strength more than collagen fiber o~enta~~on. Clearfy, this study does not contain sufRcient data to provide dependable empirical formulae for the estimation of tensile strength of bovine cortical bone, much less cortical bone in general. Nor is the development of such equations necessarily just a matter of entering the number of specimens. It is jrn~~ant to know how much the variability depends upon observer and instrument idiosvncracies. animal-to-anima1 variation, the specific bone(e.g. tibia or femur), the species, and pathologic changes (e.g. Paget’s disease). Another factor which is probabi~ important is the pro~~sity for primary bone in some species to be plexiform (as in this ex~~ment) or circumferential hnnellar (as in human& For these reasons, it is important that this work be repeated. In summary, the results of this study suggest that the m~hanical properties of cortical bone can be better predicted if a variety of histological variables is used, and that collagen fiber orientation is at least as impo~a~t as density, porosity, and minera~~ation in determining tensile strength. ~c&~w~e~~e~~~s-~e authors are grateful to David Heitter and Neil Sharkey for their technical assistance with this work, REFERENCES Ascenzi, A. and Bonucci, B. (1964) The uhimate tensile strength of single osteons. Actu enatom, S#t,160-183. Ascenzi, A. and Bonucci, E. (1967)The tensile properties of single osteons. An&m. Rec. 1% 375-386. Ascend, A. and Bonucci, E. (1968)The compressive properties of single osteons. Artatom,Rec. M&377-392. Black, J., Mattson, R. and Korostoff, E. (1974) Waversian osteons: size, distribution, internal structure, and orientation. J. biomed. Mater, Res. 8, 299-319.

and 3. ISHIRA

Carter, D. R. and Hayes, W. C. (1976) Bone compressive st~ngt~ the in~uen~ of density and strain rate. Science 194,1174-1176. Carter, D. R., Hayes, W. C. and Schurman, D. J. (1976) Fatigue life of compact hone-II. Effectsof microstructure and density. j. %~~~c~u~jes9, 21l-218. Carter, D. R. and Spender, D. M. (1978)Mechanic& properties end com~sition of cortical bone. Cl&t.~r~~~~~. Relat. Res. 135, 192-217. Currey, J. (1959)Differencesin the tensile strength of bone of different histological types. J. Anat. 98, 87-95. Currey, J. (1984) Tfie ~ec~u~~cu~ Adaptations of Bones. Princeton University Press, New Jersey. Evans, F. G. and Bang, S. (1967) Differences and relationships between the physical properties and the microscopic structure of human femoral, tibiai, and fibular cortical bone. Am. J. Anat. 120.7948. Evans, F. G. and Vincentetii, R. (1974) Relations of the compressive properties of humad co&al bone to histological structure and allocation. J. %j~~c~~ics ‘&l-10. Frasca, P., Harper, R. A. and Katz, J. L. (1977)Collagen fiber orientations in human secondary osteons. Acta anatom. 9f&, l-13. Frasca, P., Harper, R. A. and Katz, J. L. (1978)Mineral and collagen fiber o~entation in human secondary osteons. J. dental. Res. 57, 526-533. H&t, J., Kucera, P,, Vavra, M. and Voleuik, V. (1965) Comparison of the mechanical properties of both the primary and Haversian bone tissue. Aeta awtom. 61, 412-423. Katz, J. L. and Yoon, H. S. (1974) The structure and anisotropic mechanical properties of bone. IEEE Trans. biomecf.Engng 31, 12. Portigliatti Barbos, M., Bianco, P. and Ascenzi, A. (1983) Distribution of osteonic and interstitial components in the human femoral shaft with reference to structure, caicification, and mechan~~l properties. Acta stop. 115, 178-186. Reilly, D. and Burstein, A, H. (1974)The mechanic& propertiei of cortical bone. .J. %oneJr Surg. 56-A, lOO&-1021. Schafher,M. B. (1985)Stiffnessand fat&e of comoact hone at physiological strains and strain rates. Dissertation, Mor8anto~, WV. Vincentelli, R. and Evans, F. G. (1971) Relations among mechanical properties, collagen fibers, and calcification in adult human &t&al bone. 2. Bi~~c~i~s

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Vase, G. P. and Kubaht, A. L. (1959)Bone strength and its re~at~oashipto X-ray dete~in~ ash content. bud BioI. 31,261-270.