JBJS | Age-Related Changes in the Compressive Strength of Cancellous Bone. The Relative Importance of Changes in Density and Trabecular Architecture*

The Journal of Bone & Joint Surgery, Volume 79, Issue 3

Articles | March 01, 1997

Age-Related Changes in the Compressive Strength of Cancellous Bone. The Relative Importance of Changes in Density and Trabecular Architecture*

RICHARD W. McCALDEN, M.D., M. PHIL., F.R.C.S.(C)†; JOSEPH A. McGEOUGH, PH.D., D.SC.‡; CHARLES M. COURT-BROWN, M.B., CH.B., M.D.§, EDINBURGH, SCOTLAND

View Disclosures and Other Information

Investigation performed at the Departments of Orthopaedic Surgery and Mechanical Engineering, University of Edinburgh, Edinburgh

The Journal of Bone & Joint Surgery. 1997; 79:421-7

5 Recommendations (Recommend) | 3 Comments | Saved by 3 Users Save Case

text A A A

Abstract

Compressive testing to failure in the weight-bearing axis was done on 255 specimens of cancellous bone that had been machined from forty-four femora from human cadavera. The donors had ranged in age from twenty to 102 years at the time of death. After mechanical testing, the apparent density and trabecular architecture were determined.Linear regression analysis showed that the compressive strength decreased by 8.5 per cent each decade (p < 0.001). Apparent density and volume fraction also decreased significantly with age (p < 0.001). Histomorphometric analysis demonstrated that the surface-to-volume ratio and the mean separation of the trabecular plate increased with age, whereas the mean thickness and connectivity of the trabecular plate decreased.Both bivariate and multivariate analyses demonstrated that age-related changes in apparent density played an important role in the decrease in mechanical strength, accounting for a 92 per cent reduction. Microstructural changes were highly correlated with apparent density and therefore had little independent effect. Thus, similar to the situation with cortical bone, the quantitative changes in aging cancellous-bone tissue, rather than the qualitative changes, influenced the mechanical competence of the bone.CLINICAL RELEVANCE: This study provides information concerning the difference in the properties of human cancellous bone as a function of age. Because of the importance of changes in apparent density, non-invasive means can be used to estimate the mechanical properties of cancellous bone in vivo. Thus, it may be possible to predict the risk of fracture and to explain further some aspects of the mechanics of fracture in the elderly.

Figures in this Article

Introduction

Introduction | Materials and Methods | Results | Discussion | References

Age-related changes in the mechanical behavior of bone, coupled with increasing life expectancy, may be responsible for the increased prevalence of fractures in the elderly^5,27. A better appreciation of the effects of aging on the mechanical properties of bone is critical to an understanding of the risks and mechanics of fracture and is desirable for the design of more effective forms of skeletal and endoprosthetic implants for the elderly.

Although changes in mineralization of the trabeculae have little effect^2,17, apparent density and trabecular architecture strongly influence the mechanical properties of cancellous-bone tissue^{9,14,17,21,33}. The effect of age-related changes in cancellous-bone tissue on the mechanical properties is not clear. In general, changes in the mechanical properties, density, and architecture that are associated with aging have been addressed as separate issues^{6,28,31,35,40}. It has been proposed that age-related changes in the mechanical properties depend not only on changes in density but also on changes in the trabecular architecture, but we are not aware of any experimental data that support this.

The purpose of the current study was to examine age-related changes in the compressive strength of human cancellous bone in a weight-bearing portion of the femur and to relate these mechanical changes to concurrent changes in the tissue. In particular, we sought to determine the relative importance of changes in tissue density and trabecular architecture to changes in mechanical strength.

*No benefits in any form have been received or will be received from a commercial party related directly or indirectly to the subject of this article. Funds were received in total or partial support of the research or clinical study presented in this article. The funding source was Action Research for the Crippled Child.

†Department of Orthopaedic Surgery, University of Western Ontario, 345 Westminster Avenue, London, Ontario N6C 4V3, Canada. Please address requests for reprints to Dr. McCalden.

‡Department of Mechanical Engineering, University of Edinburgh, The King's Buildings, Edinburgh EH9 3JL, Scotland, United Kingdom.

§Department of Orthopaedic Surgery, University of Edinburgh, Frogston Road West, Edinburgh EH10 7ED, Scotland, United Kingdom.

†Department of Orthopaedic Surgery, University of Western Ontario, 345 Westminster Avenue, London, Ontario N6C 4V3, Canada. Please address requests for reprints to Dr. McCalden.

‡Department of Mechanical Engineering, University of Edinburgh, The King's Buildings, Edinburgh EH9 3JL, Scotland, United Kingdom.

§Department of Orthopaedic Surgery, University of Edinburgh, Frogston Road West, Edinburgh EH10 7ED, Scotland, United Kingdom.

View Larger

TABLE I BIVARIATE REGRESSION ANALYSIS FOR STRENGTH AND APPARENT DENSITY OF CANCELLOUS BONE

*The r² value represents the amount of variation in strength explained by changes in apparent density.

Data	R²Value^*
Mean bone data
Linear model: strength = -5.649 + 0.0356 density	0.94
Power model: log strength = -3.723 + 1.784 log density	0.94
Individual-specimen data
Linear model: strength = -5.555 + 0.0353 density	0.87
Power model: log strength = -3.64 + 1.748 log density	0.87
Position-1 data
Linear model: strength = -7.168 + 0.04 density	0.92
Power model: log strength = -4.123 + 1.934 log density	0.91

Add to My JBJS

TABLE I BIVARIATE REGRESSION ANALYSIS FOR STRENGTH AND APPARENT DENSITY OF CANCELLOUS BONE

*The r² value represents the amount of variation in strength explained by changes in apparent density.

Data	R²Value^*
Mean bone data
Linear model: strength = -5.649 + 0.0356 density	0.94
Power model: log strength = -3.723 + 1.784 log density	0.94
Individual-specimen data
Linear model: strength = -5.555 + 0.0353 density	0.87
Power model: log strength = -3.64 + 1.748 log density	0.87
Position-1 data
Linear model: strength = -7.168 + 0.04 density	0.92
Power model: log strength = -4.123 + 1.934 log density	0.91

View Larger

TABLE II CORRELATION MATRIX FOR ALL VARIABLES FOR CANCELLOUS BONE*

*The numbers represent the correlation coefficients (r values) from linear regression analysis between the variables. R >0.24 represents a significance of p <0.05, and r >0.38, a significance of p <0.01.

	Age	Gender	Ultimate Stress	Apparent Density	Volume Fraction	Bone-Surface Density	Bone Surface-to-Volume Ratio	Mean Thickness of Trabecular Plate	Mean Density of Trabecular Plate	Mean Separation of Trabecular Plate	No. of Objects per Field
Age	1
Gender	0.253	1
Ultimate stress	-0.651	-0.303	1
Apparent density	-0.663	-0.239	0.96	1
Volume fraction	-0.612	-0.197	0.961	0.974	1
Bone-surface density	-0.205	-0.046	0.533	0.622	0.604	1
Bone surface-to-volume ratio	0.63	0.242	-0.855	-0.855	-0.865	-0.248	1
Mean thickness of trabecular plate	-0.635	-0.201	0.866	0.839	0.875	0.168	-0.956	1
Mean density of trabecular plate	-0.236	-0.084	0.579	0.659	0.642	0.98	-0.289	0.205	1
Mean separation of trabecular plate	0.398	0.12	-0.759	-0.83	-0.825	-0.899	0.557	-0.497	-0.922	1
No. of objects per field	0.417	0.289	-0.318	-0.293	-0.265	0.131	0.597	-0.465	0.118	0.072	1

Add to My JBJS

TABLE II CORRELATION MATRIX FOR ALL VARIABLES FOR CANCELLOUS BONE*

	Age	Gender	Ultimate Stress	Apparent Density	Volume Fraction	Bone-Surface Density	Bone Surface-to-Volume Ratio	Mean Thickness of Trabecular Plate	Mean Density of Trabecular Plate	Mean Separation of Trabecular Plate	No. of Objects per Field
Age	1
Gender	0.253	1
Ultimate stress	-0.651	-0.303	1
Apparent density	-0.663	-0.239	0.96	1
Volume fraction	-0.612	-0.197	0.961	0.974	1
Bone-surface density	-0.205	-0.046	0.533	0.622	0.604	1
Bone surface-to-volume ratio	0.63	0.242	-0.855	-0.855	-0.865	-0.248	1
Mean thickness of trabecular plate	-0.635	-0.201	0.866	0.839	0.875	0.168	-0.956	1
Mean density of trabecular plate	-0.236	-0.084	0.579	0.659	0.642	0.98	-0.289	0.205	1
Mean separation of trabecular plate	0.398	0.12	-0.759	-0.83	-0.825	-0.899	0.557	-0.497	-0.922	1
No. of objects per field	0.417	0.289	-0.318	-0.293	-0.265	0.131	0.597	-0.465	0.118	0.072	1

View Larger

TABLE III BIVARIATE REGRESSION ANALYSIS WITH STRENGTH OF CANCELLOUS BONE AS THE DEPENDENT VARIABLE

*The r² value represents the amount of variation in strength explained by changes in each material variable.

Independent Variable	Regression Coefficient	R² Value*
Density	0.40	0.92 (p < 0.0001)

Volume fraction	0.749	0.92 (p < 0.0001)

Bone-surface density	4.242	0.29 (p < 0.0005)

Bone surface-to-volume ratio	-1.057	0.73 (p < 0.0001)

Mean thickness of trabecular plate	0.183	0.75 (p < 0.0001)

Mean density of trabecular plate	0.183	0.75 (p < 0.0001)

Mean density of trabecular plate	9.324	0.34 (p < 0.0001)

Mean separation of trabecular plate	-0.044	0.58 (p < 0.0001)

No. of objects per field	-0.187	0.10 (p < 0.05)

Add to My JBJS

TABLE III BIVARIATE REGRESSION ANALYSIS WITH STRENGTH OF CANCELLOUS BONE AS THE DEPENDENT VARIABLE

*The r² value represents the amount of variation in strength explained by changes in each material variable.

Independent Variable	Regression Coefficient	R² Value*
Density	0.40	0.92 (p < 0.0001)

Volume fraction	0.749	0.92 (p < 0.0001)

Bone-surface density	4.242	0.29 (p < 0.0005)

Bone surface-to-volume ratio	-1.057	0.73 (p < 0.0001)

Mean thickness of trabecular plate	0.183	0.75 (p < 0.0001)

Mean density of trabecular plate	0.183	0.75 (p < 0.0001)

Mean density of trabecular plate	9.324	0.34 (p < 0.0001)

Mean separation of trabecular plate	-0.044	0.58 (p < 0.0001)

No. of objects per field	-0.187	0.10 (p < 0.05)

View Larger

TABLE IV MULTIVARIATE REGRESSION ANALYSIS WITH STRENGTH OF CANCELLOUS BONE AS THE DEPENDENT VARIABLE

*The t values represent the relative contribution of each variable to the over-all model.†The r² values represent the total variation in strength described by the over-all model.‡P < 0.05.§P < 0.01.¶P < 0.001.

Independent Variable	Partial Regression Coefficient*	R² Value†
All variables (except volume fraction)
Age	0.003 (t = 0.188)	0.96 (p < 0.0001)
Gender	-0.839 (t = 1.861)‡
Density	0.023 (t = 2.553)‡
Bone-surface density	-1.832 (t = 1.095)
Bone surface-to-volume ratio	0.581 (t = 2.156) ‡
Mean thickness of trabecular plate	0.176 (t = 3.668)§
Mean density of trabecular plate	10.193 (t = 2.346) ‡
Mean separation of trabecular plate	0.0131 (t = 1.267)
No. of objects per field	-0.056 (t = 1.299)

Best variables
Age	0.002 (t = 0.122)	0.94 (p < 0.0001)
Gender	-0.98 (t = 2.13) ‡
Density	0.030 (t = 3.989) ¶
Mean thickness of trabecular plate	0.97 (t = 2.747) §
Bone surface-to-volume ratio	0.304 (t = 1.605)
Mean separation of trabecular plate	-0.0042 (t = 0.692)

Stepwise analysis
Density	0.033 (t = 9.942) ¶	0.93 (p < 0.0001)
Mean thickness of trabecular plate	0.044 (t = 2.609) §

Add to My JBJS

TABLE IV MULTIVARIATE REGRESSION ANALYSIS WITH STRENGTH OF CANCELLOUS BONE AS THE DEPENDENT VARIABLE

Independent Variable	Partial Regression Coefficient*	R² Value†
All variables (except volume fraction)
Age	0.003 (t = 0.188)	0.96 (p < 0.0001)
Gender	-0.839 (t = 1.861)‡
Density	0.023 (t = 2.553)‡
Bone-surface density	-1.832 (t = 1.095)
Bone surface-to-volume ratio	0.581 (t = 2.156) ‡
Mean thickness of trabecular plate	0.176 (t = 3.668)§
Mean density of trabecular plate	10.193 (t = 2.346) ‡
Mean separation of trabecular plate	0.0131 (t = 1.267)
No. of objects per field	-0.056 (t = 1.299)

Best variables
Age	0.002 (t = 0.122)	0.94 (p < 0.0001)
Gender	-0.98 (t = 2.13) ‡
Density	0.030 (t = 3.989) ¶
Mean thickness of trabecular plate	0.97 (t = 2.747) §
Bone surface-to-volume ratio	0.304 (t = 1.605)
Mean separation of trabecular plate	-0.0042 (t = 0.692)

Stepwise analysis
Density	0.033 (t = 9.942) ¶	0.93 (p < 0.0001)
Mean thickness of trabecular plate	0.044 (t = 2.609) §

View Large | Download Slide(.ppt)
Add to My JBJS

Fig. 1 Scattergram demonstrating the relationship between ultimate stress (strength) and age. The straight line represents the best-line fit with the use of linear regression analysis. The r² value denotes the amount of variation explained by the line fit to the data. Each point represents the mean value for the bone tested.

View Large | Download Slide(.ppt)
Add to My JBJS

Fig. 2 Scattergram demonstrating the relationship between apparent density and age. The straight line represents the best-line fit with the use of linear regression analysis. Each point represents the mean value for the bone tested.

View Large | Download Slide(.ppt)
Add to My JBJS

Fig. 3 Scattergram demonstrating the relationship between strength and apparent density. The bones of men and women are identified, and separate linear regression is shown for each. The regression equation for the combined data for the bones of men and women is also shown. Each point represents the mean value for the bone tested.

View Large | Download Slide(.ppt)
Add to My JBJS

Fig. 4 Bar graph comparing the mean strengths for the specimens of cancellous bone on the basis of position. Position 1 is posteromedial, 2 is centromedial, 3 is anteromedial, 4 is posterolateral, 5 is centrolateral, and 6 is anterolateral. Analysis of variance demonstrated a significant difference between position 1 and positions 2, 3, and 5; between position 2 and positions 3 and 6; between position 3 and positions 4 and 6; between position 4 and position 5; and between position 5 and position 6 (p < 0.05, Fisher protected least-significant-difference test). The error bars represent the standard deviation.

Materials and Methods

Introduction | Materials and Methods | Results | Discussion | References

The right femora from forty-four individuals, twenty-five men and nineteen women ranging in age from twenty to 102 years, were obtained at the time of autopsy. Femora from patients who had conditions associated with osseous lesions other than osteoporosis were excluded.

Mechanical Testing

The bone was kept frozen at -20 degrees Celsius until machining. The bone tissue was not fixed and was bathed in a physiological saline solution at all stages of machining. Six cylindrical cancellous-bone specimens, 10.0 ± 0.2 millimeters (mean and standard deviation) in both length and diameter, oriented along the superoinferior axis, were manufactured from the distal part of each femur. A special jig allowed specimens to be cut from nearly identical locations, approximately two centimeters from the joint line. The specimens were produced from either the medial or the lateral side and from the anterior, central, or posterior quadrant of the metaphysis.

The specimens were thawed in normal saline solution for two hours and were tested at 19 to 21 degrees Celsius, in a hydrated state; no attempt was made to remove any bone marrow before testing. After the specimens that appeared to have been damaged in the machining process had been discarded, a total of 255 specimens underwent uniaxial compressive testing to failure in the weight-bearing axis (the superoinferior direction) in a compressive testing machine (model M30K; J. J. Lloyd, London, United Kingdom) with a 1000-newton-grade 0.5 per cent load-cell at a strain rate of approximately 0.0017 second^-1 (head speed, one millimeter per minute). This strain rate is similar to that used by authors who previously examined human bone^17,28, thereby allowing comparison with their work. Specimens were placed between two parallel platens and were preloaded to 1.5 megapascals; they then were returned to zero and were loaded to failure, with use of a technique similar to that described by Goldstein et al.¹⁵. Ultimate stress (strength) was calculated by dividing the load at failure by the cross-sectional area (determined from pre-test diametral measurement with a micrometer).

Calculations of Apparent Density

Apparent density was determined after all fat and marrow had been removed from the pores of the bone in a manner similar to that described by Brear et al.⁸. The apparent density was determined on the basis of the dry weight and the volume of the specimen as calculated with use of measurements made with a micrometer. The justification for determining apparent density after defatting and drying was based on the negligible effect that marrow has on mechanical properties, except with exceedingly high strain rates⁹, and on the strong correlation between dry apparent density and mechanical properties found in previous investigations^8,17.

Determination of the Architecture

In order to minimize the effect of position on the trabecular structure, only the forty-three specimens from position number 1 (the posteromedial quadrant) were embedded and fixed in clear methylmethacrylate. The flat surface (that is, the plane perpendicular to the loading axis) was then polished with use of standard metallographic techniques, allowing a clear separation between the trabecular bone and the marrow space to be visualized by reflected-light microscopy at a magnification of sixteen times. An image-analysis system (Magiscan, London, United Kingdom) was used to calculate the total bone-volume percentage; bone-surface density; bone surface-to-volume ratio; and mean thickness, density, and separation of the trabecular plate, according to the techniques of Parfitt et al.³¹. The volume fraction is identical to the total bone-volume percentage. With use of a technique similar to that reported by Hodgskinson and Currey¹⁷, the number of objects per field was measured to provide an indication of the connectivity of the bone. The specimens were polished three times at different levels to allow a mean architectural value to be determined and thus to decrease the effect of variation within the specimen.

Analysis of the Data

Correlation and linear regression analysis was used to explore the relationships between the variables. This was done a priori because it demonstrates trends within the data and is statistically rigorous enough to accept any deviation from linear relationships between the variables, particularly when multiple regression analysis is used. The mean value for a given variable from each bone was used in order to eliminate any problem associated with the age value being common, and therefore not independent, for specimens from the same bone. Multivariate linear regression analysis was used to explore the interrelationships between strength, age, density, and trabecular architecture for bone taken from position 1. Power-law models were also used to examine the relationship between strength and apparent density.

Results

Introduction | Materials and Methods | Results | Discussion | References

Age and Ultimate Stress

There was a significant decrease in compressive strength (Fig. 1) and an almost identical decrease in bone density (Fig. 2) associated with aging (p < 0.001 for both). Ultimate stress and apparent density were highly associated (p < 0.001; Table I); the relationship was almost identical for the bones from men and women (Fig. 3).

Analysis of variance demonstrated a significant difference in strength on the basis of position (p < 0.0001); strength was greatest in the posteromedial position (position 1; Fig. 4). Density alone accounted for more than 87 per cent of the variance in strength in all positions. Analysis of the core data, consisting of all 255 specimens, confirmed the very strong relationship between strength and density (p < 0.001; Table I). Power analysis, with use of the logged values for strength and density, demonstrated r² values that were virtually identical to those in the linear models (Table I).

Age and All Variables

The data from the specimens in position 1, in which architectural analysis was performed, were used to explore the relationship between aging and the other variables (Table II). Similar to the mean bone data, there was a clear decrease in ultimate stress and density associated with aging (r = -0.651, r = -0.663, p < 0.001). Volume fraction, which was highly correlated with density (r = 0.974, p < 0.001), showed a similar decrease with age (r = -0.612, p < 0.001).

The trabecular morphology changed significantly with age (Table II). The surface-to-volume ratio and the mean separation of the trabecular plate both increased with age (r = 0.63, r = 0.398, p < 0.01), whereas the mean thickness of the trabecular plate decreased (r = -0.635, p < 0.001). The number of objects per field also increased with age, suggesting a decrease in bone connectivity (r = 0.417, p < 0.005).

Ultimate Stress and All Variables

The relationship between ultimate stress and the explanatory variables at position 1 was investigated in detail with use of bivariate and multivariate regression techniques (Tables III and IV). Simple bivariate analysis showed that ultimate stress was highly proportional to apparent density (r² = 0.92, p < 0.0001; Table III). The relationship between ultimate stress and volume fraction, which was highly correlated with density, was virtually identical (r² 0.92, p < 0.0001; Table III). Thus, apparent density and volume fraction are virtually interchangeable and provided almost identical results in all of the models. As suggested by the correlation matrix, the trabecular morphology, particularly the mean thickness of the trabecular plate, provided highly significant and predictive models when they were considered as independent variables (Table III).

Given the high correlation between so many of the explanatory variables, particularly density and trabecular morphology, multivariate regression analysis was used to define their interrelationship and to quantify their relative importance. Several models were used in order to explain the data. Models of regression with use of all of the independent variables (except volume fraction, to remove the obvious concordance between density and volume fraction) yielded a highly predictive model. This model demonstrated the significance of density and also suggested that gender and several morphological variables (surface-to-volume ratio, mean thickness of the trabecular plate, and mean density of the trabecular plate) had some independent explanatory power (r² = 0.96; Table IV). In order to remove some of the concordance between the microstructural variables, a second model was created with use of the best independent variables on the basis of the bivariate analysis. This model confirmed the significance of density and included gender as well as the mean thickness of the trabecular plate (Table IV).

Stepwise regression analysis with use of all variables yielded a model in which only density (t = 9.942, p < 0.0001) and the mean thickness of the trabecular plate (t = 2.609, p < 0.01) were significant (r² = 0.93, Table IV). All of the multivariate models demonstrated that the addition of the microstructural variables failed to significantly increase the explanatory power of density alone.

Discussion

Introduction | Materials and Methods | Results | Discussion | References

The compressive strength of cancellous bone decreased by 8.5 per cent each decade, on the basis of the slope of the regression line. Previous work suggesting the strong linear relationship between strength and stiffness in all directions^8,15,21 allows reliable inferences to be made with regard to the effect of aging on the stiffness properties of cancellous bone. Although comparison of the quantitative results of this study with data from previous work is difficult because of differences in the testing conditions, the geometry of the specimens, and other parameters, the deterioration in mechanical strength and the associated change in bone density with age were similar to those found in previous studies^{4,20,28,36,39}. Although none of these earlier studies included an examination of the trabecular architecture, the authors of those investigations proposed that the mechanical changes associated with aging depended not only on changes in bone density but also on changes in the continuity of the trabecular lattice. The current study suggests that changes in the trabecular architecture play only a small independent role.

The changes in the trabecular architecture that were seen with aging in this population were similar to trends that have been suggested by other authors^{1,10,28,31,35}. Loss of trabecular bone was associated with a decrease in the mean thickness and an increase in the mean separation of the trabecular plate without a significant decrease in the mean density of the trabecular plate. Several authors have suggested that age-related bone loss consists of a reduction in the mean width of the trabecular plate in association with fragmentation and complete loss of some trabeculae, leading to a more discontinuous lattice^6,30. The limitations of all bone morphology techniques, which depend on several assumptions^29,37, make it difficult to characterize with certainty the exact mechanism of loss of trabecular bone with aging.

The overwhelming influence of changes in apparent density on the age-related changes in the compressive strength in our study was even higher than predicted on the basis of the literature^{9,14,17,33,34}. In both the bivariate and the multivariate models, density accounted for more than 90 per cent of the variations in strength. As has been seen with cortical bone²⁵, microstructural changes of cancellous bone associated with aging, which are closely linked to changes in density, had very little independent effect on the mechanical properties. The only variable that consistently contributed to the multivariate models was the mean thickness of the trabecular plate, suggesting that the age-related decrease in the mean thickness was disproportionate to the concurrent loss of bone tissue and therefore further decreased the compressive strength. It is clear that other factors seen with aging, such as any changes in trabecular mineralization or the presence of microcalluses⁷, are unlikely to be important independent variables for predicting the mechanical properties of aging cancellous bone.

Other methods of describing the trabecular architecture, based on the connectivity, orientation, and degree of anisotropy of the trabeculae, have been used to investigate the effect of the microstructure on the mechanical properties of cancellous bone^12,16,32 and to examine the relative roles of density and architecture with respect to the direction of mechanical loading^3,17,38. Hodgskinson and Currey¹⁷, using human samples with a similar range of densities as found in our study, showed that the addition of the fabric variable (a numerical description of the architectural orientation) increased the over-all explanatory power of their model as compared with that resulting from the use of density alone. However, the relative differences in the roles of density and fabric in the various testing directions are not clear. Ashman et al.³ found similar r² values between apparent density and stiffness in all directions. Lotz et al.²⁴ demonstrated that the relationship of both modulus and strength to density is significantly different between the transverse and longitudinal directions.

In the current study, the role of density and microstructure with regard to the mechanical properties was explored in one direction. As cancellous bone is clearly anisotropic, particularly in the distal part of the femur, the relative effect of density and architecture might be different in other directions of testing. In particular, it is possible that the age-related changes in mechanical strength in the mediolateral direction (that is, not in the preferred orientation of the trabeculae) may depend more on changes in architecture. Nevertheless, the findings of our study, in which the mechanical changes in the weight-bearing axis were examined, are the most clinically relevant.

Power-law modeling did not improve the statistical relationship between strength and apparent density in our study. Similarly, other investigators have shown that variations in strength and stiffness were explained equally well by linear, power function, and quadratic relationships to apparent density^3,21. However, there are several valid arguments for the use of power-law modeling to describe the mechanical behavior of cancellous bone^9,13,14, and several authors have demonstrated improvements in fit with use of these models^13,17,38.

The establishment of a strong relationship between the strength and apparent density of cancellous bone in an aging population of bone supports the use of non-invasive methods of estimation of bone density to predict changes in bone strength in the elderly. Several authors have shown the close association between determinations of density with non-invasive modalities, particularly quantitative computed tomography, and the mechanical properties of cancellous bone^18,23,26,33. In addition, the findings of our study appear to validate investigations that have suggested a correlation between determinations of density with non-invasive modalities (such as single-photon absorptiometry and quantitative computed tomography) and the risk of hip or Colles fractures^11,19,22.

The findings of the current study, combined with the results of our previous study of cortical bone²⁵, allow comparisons between cortical and cancellous bone, as the concurrent mechanical and tissue changes in the same population of human femora were examined. The relative change in strength with age was significantly greater for the cancellous bone, which decreased by 8.5 per cent each decade as compared with 5 per cent for the cortical bone. This corresponds with the clinical finding that age-related fractures occur more commonly in areas of cancellous bone. In both cortical and cancellous bone, volume fraction (virtually identical to apparent density) was the most important explanatory variable, accounting for 76 and 92 per cent of the age-related variations in strength, respectively. Similarly, changes in the microstructure had very little independent influence on the strength of the cortical and cancellous bone after the role of density (volume fraction) had been taken into consideration. The role of gender was different for the cortical and cancellous bone, suggesting an inherent problem with the use of regression analysis in which gender is the only binary variable. If these findings are valid, it is difficult to explain how gender (or the variable that is highly correlated with it but was not examined in these studies) might influence cortical and cancellous bone in different ways.

NOTE: The authors thank Mr. A. Hart for his technical expertise in the preparation of the specimens, Mr. B. Fleming for his assistance in the imaging analysis, Mr. S. Robertson for his technical expertise in the embedding of the specimens, and Dr. G. Raab for her assistance in the analysis of the data.

References

Introduction | Materials and Methods | Results | Discussion | References

Aaron, J. E.; Makins, N. B.; and |and |Sagreiya, K.: The microanatomy of trabecular bone loss in normal aging men and women. Clin. Orthop.,215: 260-271, 1987.215260 1987 [PubMed]

Ashman, R. B., and |and |Rho, J. Y.: Elastic modulus of trabecular bone material. J. Biomech.,21: 177-181, 1988.21177 1988 [PubMed]

Ashman, R. B.; Rho, J. Y.; and |and |Turner, C. H.: Anatomical variation of orthotropic elastic moduli of the proximal human tibia. J. Biomech.,22: 895-900, 1989.22895 1989 [PubMed]

Bell, G. H.; Dunbar, O.; Beck, J. S.; and |and |Gibb, A.: Variations in strength of vertebrae with age and their relation to osteoporosis. Calcif. Tissue Res.,1: 75-86, 1967.175 1967 [PubMed]

Bengner, U.: Age-related fractures. Epidemiological changes over 30 years in an urban population. Ph.D. thesis, Department of Orthopaedics, Malmö General Hospital, Lund University, Malmö, Sweden, 1987.

Bergot, C.; Laval-Jeantet, A. M.; Preteux, F.; and |and |Meunier, A.: Measurement of anisotropic vertebral trabecular bone loss during aging by quantitative image analysis. Calcif. Tissue Internat.,43: 143-149, 1988.43143 1988

Blackburn, J.; Hodgskinson, R.; Currey, J. D.; and |and |Mason, J. E.: Mechanical properties of microcallus in human cancellous bone. J. Orthop. Res.,10: 237-246, 1992.10237 1992 [PubMed]

Brear, K.; Currey, J. D.; Raines, S.; and |and |Smith, K. J.: Density and temperature effects on some mechanical properties of cancellous bone. Engin. Med.,17: 163-167, 1988.17163 1988

Carter, D. R., and |and |Hayes, W. C.: Bone compressive strength: the influence of density and strain rate. Science,194: 1174-1176, 1976.1941174 1976 [PubMed]

Compston, J. E.; Mellish, R. W.; and |and |Garrahan, N. J.: Age-related changes in iliac crest trabecular microanatomic bone structure in man. Bone,8: 289-292, 1987.8289 1987 [PubMed]

Courtney, A. C.; Wachtel, E. F.; Myers, E. R.; and |and |Hayes, W. C.: Age-related reductions in the strength of the femur tested in a fall loading configuration. Trans. Orthop. Res. Soc.,19: 188, 1994.19188 1994

Cowin, C. C.: The relationship between the elasticity tensor and the fabric tensor. Mech. Mater.,4: 137-147, 1985.4137 1985

Currey, J. D.: Power law models for the mechanical properties of cancellous bone. Engin. Med.,15: 153-154, 1986.15153 1986

Gibson, L. J.: The mechanical behaviour of cancellous bone. J. Biomech.,18: 317-328, 1985.18317 1985 [PubMed]

Goldstein, S. A.; Wilson, D. L.; Sonstegard, D. A.; and |and |Matthews, L. S.: The mechanical properties of human tibial trabecular bone as a function of metaphyseal location. J. Biomech.,16: 965-969, 1983.16965 1983 [PubMed]

Harrigan, T. P., and |and |Mann, R. W.: Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor. J. Mater. Sci.,19: 761-767, 1984.19761 1984

Hodgskinson, R., and |and |Currey, J. D.: The effect of variation in structure on the Young's modulus of cancellous bone: a comparison of human and non-human material. Proc. Inst. Mech. Engin. Part H, J. Engin. Med.,204: 115-121, 1990.204115 1990

Hvid, I.; Bentzen, S. M.; Linde, F.; Mosekilde, L.; and |and |Pongsoipetch, B.: X-ray quantitative computed tomography: the relations to physical properties of proximal tibial trabecular bone specimens. J. Biomech.,22: 837-844, 1989.22837 1989 [PubMed]

Lester, G. E.; Anderson, J. J. B.; Tylavsky, F. A.; Sutton, W. R.; Stinnett, S. S.; DeMasi, R. A.; and |and |Talmage, R. V.: Update on the use of distal radial bone density measurements in prediction of hip and Colles' fracture risk. J. Orthop. Res.,8: 220-226, 1990.8220 1990 [PubMed]

Lindahl, O.: Mechanical properties of dried defatted spongy bone. Acta Orthop. Scandinavica,47: 11-19, 1976.4711 1976

Linde, F.; Norgaard, P.; Hvid, I.; Odgaard, A.; and |and |Soballe, K.: Mechanical properties of trabecular bone. Dependency on strain rate. J. Biomech.,24: 803-809, 1991.24803 1991 [PubMed]

Lotz, J. C., and |and |Hayes, W. C.: The use of quantitative computed tomography to estimate risk of fracture of the hip from falls. J. Bone and Joint Surg.,72-A: 689-700, June 1990.72-A689 1990

Lotz, J. C.; Gerhart, T. N.; and |and |Hayes, W. C.: Mechanical properties of trabecular bone from the proximal femur: a quantitative CT study. J. Comput. Assist. Tomog.,14: 107-114, 1990.14107 1990

Lotz, J. C.; Gerhart, T. N.; and |and |Hayes, W. C.: Mechanical properties of metaphyseal bone in the proximal femur. J. Biomech.,24: 317-329, 1991.24317 1991 [PubMed]

McCalden, R. W.; McGeough, J. A.; Barker, M. B.; and |and |Court-Brown, C. M.: Age-related changes in the tensile properties of cortical bone. The relative importance of changes in porosity, mineralization, and microstructure. J. Bone and Joint Surg.,75-A: 1193-1205, Aug. 1993.75-A1193 1993

Matthews, S.; Pearcy, M. J.; Fazzalari, N. L.; Parkinson, I. H.; Manthey, B. A.; Schultz, C. G.; and |and |Howie, D. W.: Correlations between the mechanical properties, radiology and histomorphometry of human femoral bone. Clin. Biomech.,7: 153-160, 1992.7153 1992

Melton, L. J., III, and Riggs, B. L.: Epidemiology of age-related fractures. In The Osteoporotic Syndrome: Detection, Prevention, and Treatment, pp. 45-72. Edited by L. V. Avioli. New York, Grune and Stratton, 1983.

Mosekilde, L.; Mosekilde, L.; and |and |Danielsen, C. C.: Biomechanical competence of vertebral trabecular bone in relation to ash density and age in normal individuals. Bone,8: 79-85, 1987.879 1987 [PubMed]

Parfitt, A. M.: Stereologic basis of bone histomorphometry; theory of quantitative microscopy and reconstruction of the third dimension. In Bone Histomorphometry. Techniques and Interpretations, pp. 53-87. Edited by R. R. Recker. Boca Raton, Florida, CRC Press, 1983.

Parfitt, A. M.: Age-related structural changes in trabecular and cortical bone: cellular mechanisms and biochemical consequences. Calcif. Tissue Internat.,36 (Supplement 1): 123-S128, 1984.36 (Supplement 1)123 1984

Parfitt, A. M.; Mathews, C. H.; Villanueva, A. R.; Kleerekoper, M.; Frame, B.; and |and |Rao, D. S.: Relationships between surface, volume, and thickness of iliac trabecular bone in aging and in osteoporosis. Implications for the microanatomic and cellular mechanisms of bone loss. J. Clin. Invest.,72: 1396-1409, 1983.721396 1983 [PubMed]

Pugh, J. W.; Rose, R. M.; and |and |Radin, E. L.: Elastic and viscoelastic properties of trabecular bone: dependence on structure. J. Biomech.,6: 475-485, 1973.6475 1973 [PubMed]

Rho, J. Y.; Zerwekh, J. E.; and |and |Ashman, R. B.: Examination of several techniques for predicting trabecular elastic modulus and ultimate strength in the human lumbar spine. Clin. Biomech.,9: 67-71, 1994.967 1994

Rice, J. C.; Cowin, S. C.; and |and |Bowman, J. A.: On the dependence of the elasticity and strength of cancellous bone on apparent density. J. Biomech.,21: 155-168, 1988.21155 1988 [PubMed]

Riemer, B. A.; Eadie, J. S.; Weissman, D. E.; Haut, K. M.; Hollister, S. J.; and |and |Goldstein, S. A.: Characterization of the architecture, tissue properties, and continuum behavior of aging trabecular bone. Trans. Orthop. Res. Soc.,19: 189, 1994.19189 1994

Riggs, B. L.; Wahner, H. W.; Seeman, E.; Offord, K. P.; Dunn, W. L.; Mazess, R. B.; Johnson, K. A.; and |and |Melton, L. J., III: Changes in bone mineral density of the proximal femur and spine with aging. Differences between the postmenopausal and senile osteoporosis syndromes. J. Clin. Invest.,70: 716-723, 1982.70716 1982 [PubMed]

Schwartz, M. P., and |and |Recker, R. R.: Comparison of surface density and volume of human iliac trabecular bone measured directly and by applied stereology. Calcif. Tissue Internat.,33: 561-565, 1981.33561 1981

Turner, C. H.; Cowin, S. C.; Rho, J. Y.; Ashman, R. B.; and |and |Rice, J. C.: The fabric dependence of the orthotropic elastic constants of cancellous bone. J. Biomech.,23: 549-561, 1990.23549 1990 [PubMed]

Weaver, J. K., and |and |Chalmers, J.: Cancellous bone: its strengths and changes with aging and an evaluation of some methods for measuring its mineral content. I. Age changes in cancellous bone. J. Bone and Joint Surg.,48-A: 289-299, March 1966.48-A289 1966

Weinstein, R. S., and |and |Huston, M. S.: Decreased trabecular width and increased trabecular spacing contribute to bone loss with aging. Bone,8: 137-142, 1987.8137 1987 [PubMed]

Topics

View Large | Download Slide(.ppt)
Add to My JBJS

View Larger

TABLE I BIVARIATE REGRESSION ANALYSIS FOR STRENGTH AND APPARENT DENSITY OF CANCELLOUS BONE

*The r² value represents the amount of variation in strength explained by changes in apparent density.

Data	R²Value^*
Mean bone data
Linear model: strength = -5.649 + 0.0356 density	0.94
Power model: log strength = -3.723 + 1.784 log density	0.94
Individual-specimen data
Linear model: strength = -5.555 + 0.0353 density	0.87
Power model: log strength = -3.64 + 1.748 log density	0.87
Position-1 data
Linear model: strength = -7.168 + 0.04 density	0.92
Power model: log strength = -4.123 + 1.934 log density	0.91

Add to My JBJS

TABLE I BIVARIATE REGRESSION ANALYSIS FOR STRENGTH AND APPARENT DENSITY OF CANCELLOUS BONE

*The r² value represents the amount of variation in strength explained by changes in apparent density.

Data	R²Value^*
Mean bone data
Linear model: strength = -5.649 + 0.0356 density	0.94
Power model: log strength = -3.723 + 1.784 log density	0.94
Individual-specimen data
Linear model: strength = -5.555 + 0.0353 density	0.87
Power model: log strength = -3.64 + 1.748 log density	0.87
Position-1 data
Linear model: strength = -7.168 + 0.04 density	0.92
Power model: log strength = -4.123 + 1.934 log density	0.91

View Larger

TABLE II CORRELATION MATRIX FOR ALL VARIABLES FOR CANCELLOUS BONE*

	Age	Gender	Ultimate Stress	Apparent Density	Volume Fraction	Bone-Surface Density	Bone Surface-to-Volume Ratio	Mean Thickness of Trabecular Plate	Mean Density of Trabecular Plate	Mean Separation of Trabecular Plate	No. of Objects per Field
Age	1
Gender	0.253	1
Ultimate stress	-0.651	-0.303	1
Apparent density	-0.663	-0.239	0.96	1
Volume fraction	-0.612	-0.197	0.961	0.974	1
Bone-surface density	-0.205	-0.046	0.533	0.622	0.604	1
Bone surface-to-volume ratio	0.63	0.242	-0.855	-0.855	-0.865	-0.248	1
Mean thickness of trabecular plate	-0.635	-0.201	0.866	0.839	0.875	0.168	-0.956	1
Mean density of trabecular plate	-0.236	-0.084	0.579	0.659	0.642	0.98	-0.289	0.205	1
Mean separation of trabecular plate	0.398	0.12	-0.759	-0.83	-0.825	-0.899	0.557	-0.497	-0.922	1
No. of objects per field	0.417	0.289	-0.318	-0.293	-0.265	0.131	0.597	-0.465	0.118	0.072	1

Add to My JBJS

TABLE II CORRELATION MATRIX FOR ALL VARIABLES FOR CANCELLOUS BONE*

	Age	Gender	Ultimate Stress	Apparent Density	Volume Fraction	Bone-Surface Density	Bone Surface-to-Volume Ratio	Mean Thickness of Trabecular Plate	Mean Density of Trabecular Plate	Mean Separation of Trabecular Plate	No. of Objects per Field
Age	1
Gender	0.253	1
Ultimate stress	-0.651	-0.303	1
Apparent density	-0.663	-0.239	0.96	1
Volume fraction	-0.612	-0.197	0.961	0.974	1
Bone-surface density	-0.205	-0.046	0.533	0.622	0.604	1
Bone surface-to-volume ratio	0.63	0.242	-0.855	-0.855	-0.865	-0.248	1
Mean thickness of trabecular plate	-0.635	-0.201	0.866	0.839	0.875	0.168	-0.956	1
Mean density of trabecular plate	-0.236	-0.084	0.579	0.659	0.642	0.98	-0.289	0.205	1
Mean separation of trabecular plate	0.398	0.12	-0.759	-0.83	-0.825	-0.899	0.557	-0.497	-0.922	1
No. of objects per field	0.417	0.289	-0.318	-0.293	-0.265	0.131	0.597	-0.465	0.118	0.072	1

View Larger

TABLE III BIVARIATE REGRESSION ANALYSIS WITH STRENGTH OF CANCELLOUS BONE AS THE DEPENDENT VARIABLE

*The r² value represents the amount of variation in strength explained by changes in each material variable.

Independent Variable	Regression Coefficient	R² Value*
Density	0.40	0.92 (p < 0.0001)

Volume fraction	0.749	0.92 (p < 0.0001)

Bone-surface density	4.242	0.29 (p < 0.0005)

Bone surface-to-volume ratio	-1.057	0.73 (p < 0.0001)

Mean thickness of trabecular plate	0.183	0.75 (p < 0.0001)

Mean density of trabecular plate	0.183	0.75 (p < 0.0001)

Mean density of trabecular plate	9.324	0.34 (p < 0.0001)

Mean separation of trabecular plate	-0.044	0.58 (p < 0.0001)

No. of objects per field	-0.187	0.10 (p < 0.05)

Add to My JBJS

TABLE III BIVARIATE REGRESSION ANALYSIS WITH STRENGTH OF CANCELLOUS BONE AS THE DEPENDENT VARIABLE

*The r² value represents the amount of variation in strength explained by changes in each material variable.

Independent Variable	Regression Coefficient	R² Value*
Density	0.40	0.92 (p < 0.0001)

Volume fraction	0.749	0.92 (p < 0.0001)

Bone-surface density	4.242	0.29 (p < 0.0005)

Bone surface-to-volume ratio	-1.057	0.73 (p < 0.0001)

Mean thickness of trabecular plate	0.183	0.75 (p < 0.0001)

Mean density of trabecular plate	0.183	0.75 (p < 0.0001)

Mean density of trabecular plate	9.324	0.34 (p < 0.0001)

Mean separation of trabecular plate	-0.044	0.58 (p < 0.0001)

No. of objects per field	-0.187	0.10 (p < 0.05)

View Larger

TABLE IV MULTIVARIATE REGRESSION ANALYSIS WITH STRENGTH OF CANCELLOUS BONE AS THE DEPENDENT VARIABLE

Independent Variable	Partial Regression Coefficient*	R² Value†
All variables (except volume fraction)
Age	0.003 (t = 0.188)	0.96 (p < 0.0001)
Gender	-0.839 (t = 1.861)‡
Density	0.023 (t = 2.553)‡
Bone-surface density	-1.832 (t = 1.095)
Bone surface-to-volume ratio	0.581 (t = 2.156) ‡
Mean thickness of trabecular plate	0.176 (t = 3.668)§
Mean density of trabecular plate	10.193 (t = 2.346) ‡
Mean separation of trabecular plate	0.0131 (t = 1.267)
No. of objects per field	-0.056 (t = 1.299)

Best variables
Age	0.002 (t = 0.122)	0.94 (p < 0.0001)
Gender	-0.98 (t = 2.13) ‡
Density	0.030 (t = 3.989) ¶
Mean thickness of trabecular plate	0.97 (t = 2.747) §
Bone surface-to-volume ratio	0.304 (t = 1.605)
Mean separation of trabecular plate	-0.0042 (t = 0.692)

Stepwise analysis
Density	0.033 (t = 9.942) ¶	0.93 (p < 0.0001)
Mean thickness of trabecular plate	0.044 (t = 2.609) §

Add to My JBJS

TABLE IV MULTIVARIATE REGRESSION ANALYSIS WITH STRENGTH OF CANCELLOUS BONE AS THE DEPENDENT VARIABLE

Independent Variable	Partial Regression Coefficient*	R² Value†
All variables (except volume fraction)
Age	0.003 (t = 0.188)	0.96 (p < 0.0001)
Gender	-0.839 (t = 1.861)‡
Density	0.023 (t = 2.553)‡
Bone-surface density	-1.832 (t = 1.095)
Bone surface-to-volume ratio	0.581 (t = 2.156) ‡
Mean thickness of trabecular plate	0.176 (t = 3.668)§
Mean density of trabecular plate	10.193 (t = 2.346) ‡
Mean separation of trabecular plate	0.0131 (t = 1.267)
No. of objects per field	-0.056 (t = 1.299)

Best variables
Age	0.002 (t = 0.122)	0.94 (p < 0.0001)
Gender	-0.98 (t = 2.13) ‡
Density	0.030 (t = 3.989) ¶
Mean thickness of trabecular plate	0.97 (t = 2.747) §
Bone surface-to-volume ratio	0.304 (t = 1.605)
Mean separation of trabecular plate	-0.0042 (t = 0.692)

Stepwise analysis
Density	0.033 (t = 9.942) ¶	0.93 (p < 0.0001)
Mean thickness of trabecular plate	0.044 (t = 2.609) §