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Keywords:

  • calcaneus;
  • bone density;
  • trabecular architecture;
  • quantitative ultrasound

Abstract

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

Relationships between quantitative ultrasound (QUS), density (bone volume density [BV/TV]), and trabecular architecture were investigated in 69 calcaneal cancellous bone cubes. Ultrasound signal velocity, phase velocity, attenuation, and broadband ultrasonic attenuation (BUA) measurements were made along the mediolateral axis. Density and architectural parameters were measured using microcomputed tomography (μCT). Density yielded the best correlations with QUS (r2 = 73–77%). Of the individual architectural parameters, correlations with QUS were highest for the Structure Model Index (SMI), a parameter quantifying the relative proportion of rods and plates (r2 = 57–63%). After adjustment for density, significant associations with QUS remained for SMI, trabecular spacing (Tb.Sp), and trabecular number (Tb.N), although the variance in QUS attributable uniquely to individual architectural parameters was at best 4%. In multivariate regression models, combinations of density and architectural parameters explained 76–82% of the variance in QUS, representing an r2 increase of, at most, 8% compared with using density alone. However, multivariate models using combinations of architectural parameters alone (i.e., density excluded) also had a good predictive ability for QUS (r2 = 73–81%). Thus, although these data show modest but significant density-independent relationships between QUS and trabecular architecture in the human calcaneus for the first time, the causal relationships behind the variation in acoustic properties remain obscure. Given the relative weakness and complexity of the emerging associations between QUS and architecture, it is prudent to regard QUS measurements in calcaneal bone primarily as an indicator of bone density.


INTRODUCTION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

QUANTITATIVE ULTRASOUND (QUS) of the heel is being used increasingly to assess skeletal status and risk of fracture.(1) Evidence from a number of in vitro studies suggests that QUS is sensitive, in certain circumstances, to cancellous bone architecture in addition to density.2-10) This has led to an implicit assumption that clinical QUS measurements at the heel provide useful information about trabecular architecture in addition to density. There are several reasons for caution before drawing such a conclusion. Many in vitro studies have used high-density animal cancellous bone,2-4, 10) which can display very different acoustic behavior from human bone. Other studies have drawn conclusions about the role of trabecular architecture from QUS measurements in three orthogonal axes,(3, 5, 9) whereas clinical measurements are made in a single direction, thereby limiting the possible influence of architecture. Furthermore, some of these studies have used experimental conditions far removed from the clinical situation, such as crushing(2) or demineralization(10) of real bone or the use of artificial bone-mimicking materials.(7, 8)

Only a handful of previous studies have investigated relationships between QUS, density, and architecture directly in the human calcaneus, and none have reported evidence for significant associations between architecture and QUS independently of density.(6, 11, 12) However, in these studies sample sizes were small (n = 15-20), architecture was assessed using two-dimensional (2D) histomorphometry, and in two of the studies(6, 11) QUS measurements were made on whole feet rather than excised cancellous bone samples. In our earlier study using a large number (n = 70) of vertebral cancellous bone samples and microcomputed tomography (μCT) architecture measurements, significant density-independent relationships between QUS and architecture were observed, albeit as part of a complex orientation-dependent pattern of associations.(9) However, these results cannot be extrapolated necessarily to the heel where clinical measurements are most commonly made. Thus, this study aimed to investigate, for the first time, the relationship of QUS to μCT-derived density and trabecular architecture measurements in a large number of human calcaneal samples.

MATERIALS AND METHODS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

The right calcaneus was harvested from 69 adult cadavers at postmortem as part of the European BIOMED1 concerted action “Assessment of Quality of Bone in Osteoporosis”(13) and stored frozen. A standardized measurement site was defined and marked on the calcaneus as described elsewhere.(14) Then, a cube of cancellous bone approximately 20 × 20 × 20 mm was cut using a band saw from this site. Bone marrow was not removed from the cube.

Ultrasonic measurements were made along the mediolateral axis of the bone cube in a water bath at room temperature. Before measurement, the bone samples were degassed under vacuum in water. A bench-top pulse transmission ultrasound system was used as previously described.(9) Ultrasonic signal velocity was determined using transit time measurements with the first zero crossing point of the waveform used to define arrival. Phase velocity at 600 kHz was determined using a phase spectral analysis approach. The water bath temperature was measured and the temperature dependence of the speed of sound in water was accounted for in the velocity calculations. Thickness-normalized broadband ultrasonic attenuation (BUA) was determined as the slope of attenuation versus frequency over the 200- to 600-kHz frequency range. The attenuation at a single frequency (600 kHz) was recorded also.

After ultrasonic testing, a central 8-mm-diameter trabecular core was cut from the bone cube along the mediolateral axis. This core was measured using a high-resolution μCT providing a spatial resolution of 28 μm.(15) The resulting 3D gray level image with an isotropic voxel size of 14 μm was segmented using a global thresholding technique(16) and a volume of interest (VOI) 4 × 4 × 4 mm3 centrally within the bone core was defined for analysis. Bone volume density (BV/TV) and bone surface-to-volume ratio (BS/BV) were measured directly from the binarized VOI. Trabecular number (Tb.N) was calculated from BV/TV and BS/BV using the parallel plate model.(17) Trabecular thickness (Tb.Th) and trabecular spacing (Tb.Sp) were calculated using a model-independent approach based on fitting maximal spheres within the structure.(18) The Structure Model Index (SMI) was derived using published methods.(19) SMI quantifies the relative proportion of plate and rods, ranging from 0 for a purely platelike structure and 3 for a purely rodlike structure. Finally, the degree of anisotropy (DA), a ratio reflecting the geometrical anisotropy of a structure, was derived using mean intercept length (MIL) measurements.(20) MIL denotes the average distance between bone/marrow interfaces and is measured by tracing test lines in different directions in the examined VOI. From this measurement, an MIL tensor can be calculated by fitting the MIL values to an ellipsoid. Then, the eigenvalues of this tensor can be used to define the DA, which denotes the maximum-to-minimum MIL ratio.

In the absence of differences in composition at the bone material level, BV/TV is effectively an apparent density measurement and contains no information about the trabecular architecture. All of the other μCT parameters reflect architecture to a greater or lesser extent. Therefore, to enhance the clarity of the study, BV/TV henceforth is referred to as density, while all other μCT measurements are termed architecture measurements.

Linear univariate and multivariate regression analyses were used to assess relationships between QUS, density, and trabecular architecture. Associations between QUS and architecture, both without and with adjustment for density, were expressed as correlation coefficients (r) and partial correlation coefficients (rp), respectively. Corresponding levels of significance were determined using the F statistic. Where significant associations between QUS and architecture parameters were found after adjustment for density, squared semipartial correlation coefficients (rSP2) were calculated. These represent the variance in QUS attributable uniquely to a given architectural parameter independently of density and are given by the r2 difference between a model using density and the architecture parameter and a univariate model using density alone. Finally, a backward stepwise multivariate approach was used to develop optimal models (with respect to overall model r2) for predicting QUS properties using combinations of density and architectural variables and using combinations of architectural variables alone.

RESULTS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

All density and architectural measurements were distributed normally, but the four QUS parameters displayed a moderate positive skewness (Table 1). No correction was applied for this because regression analysis is relatively robust with respect to small deviations of variables from the normal distribution.

Table Table 1.. Descriptive Statistics for Ultrasound, Density, and Architecture Measurements
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Density correlated with all of the architectural measures with the exception of DA (Table 2). The strongest correlation was that between SMI and density (Fig. 1A). A number of significant correlations also existed among the architectural parameters themselves, with the highest correlation seen between Tb.Th and BS/BV (r = −0.94; r2 = 88%; Table 2).

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Figure FIG. 1. Correlations between SMI, BV/TV, and BUA. (A) SMI versus BV/TV. All of the architectural parameters, with the exception of DA, correlated significantly with BV/TV (Table 2). The correlation shown here between SMI and BV/TV was the strongest. In many cases, there also were significant correlations among the architectural parameters themselves (Table 2). (B) BUA versus BV/TV. All four QUS parameters correlated with BV/TV, and the relationship between BUA and BV/TV is shown here as an example. (C) BUA and SMI. The QUS parameters correlated significantly with all of the architectural parameters, with the exception of DA. For SMI, Tb.N, and Tb.Th, significant relationships with QUS remained after adjustment for density (Table 3).

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Table Table 2.. Correlations Among Density and Architectural Parameters
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Correlations between QUS parameters and density ranged from r = 0.85 (r2 = 73%) for attenuation to r = 0.88 (r2 = 77%) for signal velocity (Table 3). QUS parameters also correlated significantly with all of the architectural measurements, with the exception of DA (Table 3). To illustrate these findings, the relationships between BUA and density and between BUA and SMI are shown in Figs. 1B and 1C, respectively. After adjustment for density, three architectural parameters (SMI, trabecular separation, and Tb.N) remained significantly associated with QUS (Table 3). Signal velocity, attenuation, and BUA were positively associated with trabecular separation (rSP2 = 2, 4, and 3%, respectively) and negatively associated with SMI (rSP2 = 2, 3, and 2%, respectively) and Tb.N (rSP2 = 1, 2, and 1%, respectively). However, phase velocity did not correlate with any architectural parameter after adjustment for density.

Table Table 3.. Correlations Between QUS and Density or Architectural Parameters
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Multivariate regression models for QUS using density and architectural variables explained 76-82% of the variation in QUS, representing r2 increases of 2-8% over the use of density alone (Table 4). None of the architectural parameters appeared consistently in all of these models. On the other hand, multiple regression models using architectural information alone yielded r2 values that were only slightly lower (73-80%), but a different and more consistent pattern of relationships was observed in that all QUS parameters were associated positively with Tb.Th and TB.N and negatively with SMI and DA (Table 4).

Table Table 4.. Multivariate Regression Models Predicting QUS
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DISCUSSION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

This study used an approach common to earlier studies(4, 6, 9) whereby the correlations between the architectural and ultrasonic properties of cancellous bone have been investigated before and after adjustment for bone density. The results suggested that QUS does reflect some aspects of trabecular architecture in addition to bone density, but only to a limited extent. Most of the variability (73-77%) in QUS in calcaneal bone could be explained by density alone, with, at most, an additional 8% of the variance attributable uniquely to architecture.

The fact that density can explain most of the variation in QUS does not imply that density is the cause of the variation in QUS. Indeed, this study has shown for the first time that a combination of architectural variables generally predicts more of the variation in QUS properties than does density alone. This highlights a fundamental difficulty in attempting to identify the causal determinants of acoustic properties using statistical regression approaches alone. Density and architecture are themselves intercorrelated in cancellous bone, as is seen in our data (Table 2; Fig. 2) and other studies.(4, 6, 9, 21) Much of the explained variance in QUS is shared by both density and architectural factors, with the consequence that it cannot be attributed uniquely to either. One way beyond this ambiguity could be to use regression analysis more intelligently in a theory-testing role. For example, certain acoustic scattering theories(22, 23) predict relationships between attenuation and the number, size, and shape of the scatterers, which could be tested for trabecular bone using suitably formulated regression models. Another approach could be to devise experiments in which causal effects can be assessed directly,(24) for example, using stereolithographic bone mimics in which density and architecture can to some extent be varied independently.(25)

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Figure FIG. 2. Cancellous bone structure in two specimens, as visualized using μCT. (A and B) Two specimens had very similar bone volume densities [(A) 13.0% versus (B) 13.7%, respectively] but very different architectural and acoustic properties. (A) A more rodlike architecture that was reflected in a higher SMI (2.00 vs. 1.16). This specimen exhibited lower signal velocity (1546 vs. 1603 m/s), phase velocity (1518 vs. 1551 m/s), attenuation (6.5 vs. 10.2 dB/cm), and BUA (14.1 vs. 21.2 dB/MHz per cm) than the specimen in panel B. In the data for all 69 cubes, the inverse relationship between SMI and QUS was observed consistently, even after adjustment for density or other architectural parameters (Tables 3 and 4). This suggests that the association between a more rodlike trabecular architecture and decreased ultrasound velocity and attenuation represents a genuine causal relationship. A 4 × 4 × 4 mm VOI is shown, and the mediolateral anatomical axis faces out of the page toward the bottom right.

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Generally, the pattern of relationships seen between QUS and trabecular architecture was not consistent across the different correlation approaches used. For example, Tb.Sp correlated negatively with QUS in the univariate analysis, positively after adjustment for density, and failed to correlate at all in the multivariate models in which density was excluded. This indicates that some variables are acting to suppress or modify the effect of other variables in the regression, making interpretation of the results difficult. One exception to this inconsistency was the observation of a negative association between SMI and QUS throughout the analysis, implying that increased velocity and attenuation was associated with a more platelike trabecular structure. The consistency of this relationship suggests that this may indeed be a genuine causal association. This finding is illustrated by comparing trabecular architecture visually in two specimens with similar densities but very different structure types; ultrasound velocity and attenuation were lower in the specimen with the more rodlike structure (Fig. 2).

Also of note is the consistency in the multivariate analysis using architectural variables alone (Table 4) in which identical patterns of relationships were seen for all four QUS variables. Increasing velocity and attenuation was associated with (a) increasing Tb.N, (b) increasing Tb.Th, (c) more platelike trabecular structure, and (d) decreasing anisotropy. Again, the consistency suggests that this pattern may represent the true underlying pattern of causal relationships, but this conclusion must await further supporting evidence.

Although the relationships between QUS and architecture revealed in this study may offer insights into the underlying interactions between ultrasound and cancellous bone, the complexity and, in many cases, relative weakness of these associations makes them unsuitable for direct clinical use, at least given our present state of knowledge. Rather, we suggest that heel QUS should be considered primarily as reflecting bone density alone, a conclusion that fits with the available clinical evidence. Prospective studies have confirmed the value of ultrasound for predicting hip fracture risk26-28) and provided evidence that calcaneal BUA or hip or calcaneal bone mineral density (BMD) have similar predictive accuracy.(27, 28) In these studies, BUA remained predictive of hip fracture after control for hip BMD,(27, 28) but there was little benefit from a combination of BUA and BMD, and the relationship between calcaneal BUA and hip fracture risk was no longer statistically significant after adjustment for calcaneal BMD.(28) Taken together, these clinical findings suggest that current ultrasound measurements at the heel do not provide clinically relevant information on fracture risk that is independent of calcaneal bone density.

The population CV for bone volume density (CV = 30%) was greater than that of any of the architectural parameters (CV = 8-23%). This indicates less inherent variation in trabecular architecture than in density between individuals and adds further weight to the view that QUS should be considered primarily as reflecting bone density.

A limitation of this study was the relatively small VOI (4 × 4 × 4 mm3) used for the μCT measurements. Consequently, the density and architecture measurements may not have been representative of the larger bone volume measured using ultrasound, reducing the ability to detect relationships between QUS and the other variables. However, the correlations reported here between QUS and density were comparable in strength with those of previous studies,(5, 6, 12, 21) suggesting that the restricted μCT VOI was not a major problem. A further limitation in the architectural measurements was the use of the parallel plate model in deriving Tb.N; future studies should seek to use model-independent parameters wherever possible. The QUS measurements were made at room temperature and, because acoustic measurements generally are temperature dependent, variations in ambient temperature may have contributed to the variance in QUS parameters. In vivo, additional factors may influence acoustic measurements including calcaneal width and shape, overlying soft tissue composition and thickness, foot temperature, and acoustic coupling conditions. These factors would be expected to contribute additional variance to clinical QUS measurements, decreasing the strength of the correlations with density and architecture.

An additional limitation of this study may lie in the assumption of linear relationships among the variables. Studies on cancellous bone specimens spanning a wide density range have reported evidence for nonlinear relationships between QUS and density.(25) However, this work used bone from a single anatomical site with a relatively narrow density range; therefore, any nonlinearity would be expected to be modest. Log transforming the data before regression analysis to account for nonlinearity did not significantly change the overall correlation coefficients for the predictive models but did produce subtle changes in the pattern of relationships seen in the multivariate analysis (data not shown). This further reinforces earlier comments on the need for caution in interpreting the regression results and for approaches that are more robust for identifying the determinants of the acoustic properties of cancellous bone.

In conclusion, this study shows that although bone density can explain most of the variation in the ultrasonic properties of the human calcaneus, significant density-independent relationships with trabecular architecture exist. Furthermore, a combination of architectural measurements can predict QUS as well or better, as can density alone. These results highlight inherent difficulties in seeking to identify the determinants of the acoustic properties of cancellous bone using statistical regression approaches alone. Consequently, further work is needed to establish the underlying causal associations. In the meantime, it is prudent to continue to regard QUS measurements at the heel as primarily an indicator of heel bone density rather than of trabecular architecture.

Acknowledgements

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

The experimental work described in this study was performed at Leuven and Zürich within the framework of the European BIOMED1 concerted action “Assessment of Quality of Bone in Osteoporosis” (contract number BMH1-CT92-0296). S. Boonen is Senior Clinical Investigator of the Fund for Scientific Research-Flanders, Belgium (F.W.O.-Vlaanderen), and holder of the Leuven University Chair for Metabolic Bone Diseases, founded and supported by Merck Sharp & Dohme.

REFERENCES

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES
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