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The Journal of Bone and Joint Surgery 79:421-7 (1997)
© 1997 The Journal of Bone and Joint Surgery, Inc.

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){dagger}, JOSEPH A. McGEOUGH, PH.D., D.SC.{ddagger} and CHARLES M. COURT-BROWN, M.B., CH.B., M.D.§, EDINBURGH, SCOTLAND

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


   Abstract
Top
 Abstract
Introduction
 Materials and Methods
 Results
 Discussion
 References
 
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.


   Introduction
Top
 Abstract
 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 elderly5,27. 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 effect2,17, apparent density and trabecular architecture strongly influence the mechanical properties of cancellous-bone tissue9,14,17,21,33. 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 issues6,28,31,35,40. 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.


   Materials and Methods
Top
 Abstract
 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 bone17,28, 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 investigations8,17.

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
Top
 Abstract
 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).



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  		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.

 


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  		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.

 

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

 


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  		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.

 
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).



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  		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.

 

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).


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  		TABLE II CORRELATION MATRIX FOR ALL VARIABLES FOR CANCELLOUS BONE*

 
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).


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

 

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

 
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
Top
 Abstract
 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 directions8,15,21 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 studies4,20,28,36,39. 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 authors1,10,28,31,35. 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 lattice6,30. The limitations of all bone morphology techniques, which depend on several assumptions29,37, 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 literature9,14,17,33,34. 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 bone12,16,32 and to examine the relative roles of density and architecture with respect to the direction of mechanical loading3,17,38. 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 density3,21. However, there are several valid arguments for the use of power-law modeling to describe the mechanical behavior of cancellous bone9,13,14, and several authors have demonstrated improvements in fit with use of these models13,17,38.

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 bone18,23,26,33. 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 fractures11,19,22.

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.


   Footnotes
 
*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.

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

{ddagger}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.


   References
Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 References
 

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