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Keywords:

  • cancellous bone;
  • calcaneus;
  • damage;
  • elastic modulus;
  • quantitative ultrasound

Abstract

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

This study investigated the ability of quantitative ultrasound (QUS) to detect reductions in the elastic modulus of cancellous bone caused by mechanical damage. Ultrasonic velocity and attenuation were measured using an in-house parametric imaging system in 46 cancellous bone cores from the human calcaneus. Each core was subjected to a mechanical testing regime to (a) determine the predamage elastic modulus, (b) induce damage by applying specified strains in excess of the yield strain, and (c) measure the postdamage elastic modulus. The specimens were divided into four groups: a control group subjected to a nominally nondestructive 0.7% maximum strain (ϵm) and three damage groups subjected to increasing strain levels (ϵm = 1.5, 3.0, and 4.5%). QUS measurements before and after the mechanical testing showed no significant differences between the control group and damage groups, despite highly significant (p < 0.001) reductions in the elastic modulus of up to 72%. These results indicate that current QUS techniques do not intrinsically reflect the elastic properties of cancellous bone. This is consistent with ultrasonic properties being determined by other factors (apparent density and/or architecture), which normally are associated strongly with elastic properties, but only when bone is mechanically intact. Clinically, this implies that ultrasound cannot be expected to detect bone fragility in the absence of major changes in bone density and/or trabecular architecture.


INTRODUCTION

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

QUANTITATIVE ULTRASOUND (QUS) is being used increasingly for the evaluation of bone diseases such as osteoporosis.(1) Clinically, heel QUS is comparable with femoral bone mineral density (BMD) measurements in predicting risk of hip fracture.(2) In vitro studies indicate that heel QUS correlates with the mechanical properties of calcaneal bone samples(3) and of the intact proximal femur.(4,5) However, despite the growing body of evidence for strong correlations between QUS and other physical properties, the fundamental interactions between ultrasound and cancellous bone remain poorly understood. In particular, despite ongoing work, (6–8) currently no comprehensive validated theoretical model exists for ultrasonic wave propagation in cancellous bone.

QUS correlates in vitro with cancellous bone density, (9–13) architecture,(10,11) and elasticity.(12,13) However, given that the three types of measurement all intercorrelate among themselves,(12,13) it is unclear which factors are (i.e., causally) related intrinsically to ultrasonic properties and which correlate indirectly with QUS simply because of their association with other physical factors. The particular aim of this study was to determine, by inducing mechanical damage artificially in cancellous bone cores, whether an intrinsic relationship exists between QUS and elastic modulus in the absence of major changes in density or architecture. Clinically, this question is important because it has been suggested that QUS is indeed sensitive to microdamage and elasticity changes,(14,15) whereas X-ray bone densitometry is not. Confirming or refuting this hypothesis has important implications in terms of the clinical interpretation of QUS results, the types of pathology that QUS can be expected to detect, and the underlying physics of acoustic wave propagation in cancellous bone.

MATERIALS AND METHODS

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

Forty eight adult cadaver feet (mean age, 82 years; age range, 50-99 years; 30 females and 18 males), cut at the midtibial level with all soft tissues intact, were obtained through the Harvard Anatomic Gifts Program. Radiographs of the feet were taken to exclude fractures or metastatic disease, of which no cases were seen. A coring site was defined matching that used by the Sahara clinical sonometer (Hologic, Inc., Waltham, MA, U.S.A.) and was marked on the skin. Mediolateral cores were cut under water irrigation from the frozen feet using a 14-mm-diameter diamond-tipped core drill (Starlite Industries, Rosemont, PA, U.S.A.) in a drill press. Soft tissue was dissected away and the bone cortices were removed with two parallel cuts using an Isomet low-speed circular wafer saw (Buehler, Lake Bluff, IL, U.S.A.) again under irrigation. Bone marrow was removed from the cores by water-jetting and immersion in a water-filled ultrasonic cleaning bath at 40°C. The diameter and length of the prepared cores, determined using digital calipers (mean of five measurements), were 14.7 ± 0.1 mm and 17.7 ± 1.1 mm, respectively (mean ± SD).

Bone densitometry was performed on the cores using a dual-energy X-ray densitometer (QDR2000+; Hologic, Inc.) operating in high resolution (small animal) mode. Cores were placed on the manufacturer's specified Plexiglas block in a thin-walled plastic box under 2 cm of water and were scanned along their long axis. Volumetric BMD (vBMD; g/cm3) was calculated by dividing the measured areal BMD (g/cm2) by the core length.

Ultrasonic measurements were made with an in-house parametric imaging system similar to that described elsewhere.(16) The system consisted of a pair of 29-mm-diameter focused (focal length, 52 mm) 1-MHz broadband transducers (model V394; Panametrics, Inc., Waltham, MA, U.S.A.) mounted 100 mm apart within a temperature-controlled water bath at 35°C. A pulser-receiver (Panametrics 5072PR) operating in pulse transmission mode was used to drive the transmitting transducer and amplify signals from the receiving transducer. The latter were captured with a high-speed digitizer (DSA 524; Thurlby Thandar Instruments Ltd., Huntingdon, U.K.) sampling at 20 MHz and transferred to a PC for analysis. Signal velocity (using the first zero-crossing approach) and 600 kHz phase velocity were determined using published methods.(17) Attenuation at 600 kHz and broadband ultrasonic attenuation (slope of attenuation vs. frequency from 200 to 600 kHz) were determined from the power spectra of the received pulses, as in previous studies.(16,18)

Cores were degassed in water under a partial vacuum and then suspended in the measurement tank on an acoustically transparent cradle of four fine cotton threads. Using an X-Y scanning mechanism, the transducers were moved over a 24 mm × 24 mm area centered on the core with a step interval of 1.6 mm, and QUS measurements were made at each location. Linear interpolation was applied to expand the original 16 × 16 data sets into 61 × 61 pixel parametric images for display and analysis using Matlab (The MathWorks, Inc., Natick, MA, U.S.A.). A circular 8.4-mm-diameter central region of interest entirely within the core was used to determine mean QUS values excluding any edge artifacts. QUS measurements were made on the cores before and after the mechanical damage procedure described in the following paragraph.

A mechanical test regime was developed to produce controlled and quantifiable damage in the cores. Under this protocol, cores were compressed axially between two parallel steel platens in a computer-controlled servohydraulic mechanical testing instrument (model 8550; Instron Corp., Canton, MA, U.S.A.). Displacement was measured using a 25-mm gauge length extensometer (model 3542-025M-015-ST; Interlaken Technology Corp., Eden Prairie, MN, U.S.A.) attached to the platens immediately above and below the specimen, eliminating the need to correct for machine compliance.(3,19) The specimen was subjected to a small initial preload (<10N), and then it was preconditioned with eight successive ramps to 0.7% strain, returning to the preload after each ramp (Fig. 1). This was followed by the main “damage” cycle (cycle 9) ramping to a specified maximum strain level (ϵm) of either 0.7 (“nondestructive,” control group), 1.5, 3.0, or 4.5%, and returning to the preload state. Three further cycles (cycles 10-12) to 0.7% strain were then applied. The tests were performed in strain control at a strain rate of 0.001 s−1, and each test took approximately 3 minutes to complete. The original, predamage, elastic modulus was determined as the slope of the linear fit to the stress-strain curve for cycle 9 between 0.4% and 0.6% strain. The postdamage modulus was measured in the same way on cycle 12. Induced mechanical damage was quantified by the percentage reduction in elastic modulus. The height of the core was measured again using digital calipers 24 h after the mechanical test in order to determine the residual strain induced by the testing regime.

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Figure FIG. 1. Mechanical testing regime. Cores were subjected to a small preload (<10N) and preconditioned with eight cycles to 0.7% strain. Cycle 9 was the damage cycle, in which a specified maximum strain (0.7, 1.5, 3.0, and 4.5%) was applied depending on the group to which the specimen had been assigned. Finally, a further three cycles to 0.7% strain were applied. The predamage modulus was determined from a linear fit to the stress-strain curve on cycle 9 between 0.4% and 0.6% strain. The postdamage modulus was determined similarly on cycle 12. The figure shows typical data for a core tested to 3% strain. The reduction in elastic modulus was 55% in this case, as is visually evident in the lower slope postdamage compared with predamage.

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Cores were assigned randomly to one of the four groups (ϵm = 0.7, 1.5, 3.0, or 4.5%), giving nominally 12 cores per group. However, two cores proved to have very low predamage elastic moduli (<1 MPa), suggestive of either preexisting fracture or coring damage, and these were excluded leaving a total of 46 cores in the study. Human error led to one core in the 3.0% strain group being mechanically tested at the 0.7% strain level. These circumstances resulted in the actual numbers of cores per group varying (n = 10-13; Table 1).

Table Table 1.. Baseline Measurements on Cores Before Mechanical Damage (Mean ± SD)
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One-way analysis of variance (ANOVA) was used to test for significant differences in the predamage measurements among the four groups. Linear and power law regression analysis was used to assess correlations among the predamage measurements. To investigate changes in elastic modulus and QUS properties after damage was induced, one-way nonparametric ANOVA (Kruskal-Wallis) was used to compare differences in percentage changes across the four groups. In addition, one-sample nonparametric tests (Wilcoxen signed rank tests) were used to assess whether the percentage changes in a particular group differed significantly from zero. Because 20 one-sample tests were performed (four groups and five measured parameters), we applied a Bonferroni adjustment for multiple comparisons with an overall significance level of p = 0.05, giving a significance level for each test of p = 0.0025. Finally, correlations between the percentage change in elastic modulus and the percentage change in QUS parameters after damage were assessed using linear regression analysis.

RESULTS

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

Before mechanical damage, vBMD, modulus, and QUS values did not differ significantly among the four groups (Table 1). There were strong correlations between all four QUS parameters and vBMD (r2 = 0.86-0.94; p < 0.001) and also between the QUS parameters and E (r2 = 0.85-0.87; p < 0.001; Fig. 2). In addition, there was a strong association between E and vBMD (r2 = 0.86; p < 0.001; Fig. 2). In all cases the relationships were nonlinear and were best fitted by power law regression models (Fig. 2).

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Figure FIG. 2. Correlations between broadband ultrasound attenuation (BUA), elastic modulus, and vBMD in the predamage data. (A) BUA and vBMD, (B) elastic modulus and vBMD, and (C) elastic modulus and BUA. In all cases, power law regression models (shown) gave higher r2 values than linear regression models. All correlations were significant at p < 0.001. Signal velocity, phase velocity, and attenuation (not shown) all showed similar correlation trends to that of BUA shown here.

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After the mechanical testing and the consequent induction of damage, there were highly significant differences in the percentage changes in elastic modulus among the four groups (p < 0.001; Fig. 3). In the ϵm = 1.5, 3.0, and 4.5% groups the mean (±SD) percentage changes in elastic modulus were −20 ± 10%, −52 ± 15%, and −72 ± 12%, respectively (Fig. 3). These changes were all significantly different from zero and from each other (p < 0.001). In contrast, the percentage changes in QUS values did not differ among the four groups and in no group did the change in QUS values after damage achieve statistical significance (Fig. 3). No significant correlations existed between the percentage change in any of the QUS parameters and the percentage change in elastic modulus after damage.

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Figure FIG. 3. Changes in elastic modulus and QUS parameters after mechanical damage. Percentage changes (mean ± SD) after mechanical damage are shown for each of the four strain groups. (A) Elastic modulus showed a significant, progressive reduction with increasing strain (* p < 0.001). (B-E) In contrast, there were no significant postdamage changes in any of the QUS parameters.

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Significant residual strains were observed only in the 3.0% and 4.5% strain groups (residual strain = −0.54 ± 0.38% and −0.87 ± 0.47%; p = 0.002 and p = 0.0001, respectively).

DISCUSSION

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

Progress toward a better understanding of the relationships between QUS and other physical properties of bone is complicated by the intercorrelations among the different measurements. Elasticity, density, and architecture are all strongly interrelated in cancellous bone, making it difficult to ascertain which of these physical properties actually determine acoustic properties, rather than just fortuitously correlate with them. In this study, we sought an experimental approach that addressed this difficulty by producing a reduction in elastic modulus without inducing major changes in either density or architecture and then assessing the ability of QUS measurements to detect this reduction.

Our results indicated that QUS was not sensitive to elasticity changes after mechanical damage, even when large reductions in elastic modulus (up to 72%) occurred. This finding implies that there is no intrinsic relationship between QUS and elastic modulus in cancellous bone. Consequently, the well-established ability of QUS to predict elastic modulus in cancellous bone must arise indirectly because of other factors, most likely density and architecture, which correlate both with QUS and elasticity.

This result has important implications both clinically and in terms of the physics underlying QUS measurements in bone. It implies that current QUS methods cannot be expected to detect cancellous bone fragility in the absence of major accompanying density or architectural changes. This does not contradict the proven clinical ability of QUS to predict fracture risk associated with bone loss in osteoporosis. The reduction in bone elastic modulus and strength in osteoporosis is likely to be caused by, largely, concomitant changes in density and architecture. However, when the mechanical properties of cancellous bone are compromised without appreciable density or architectural changes, the resulting increase in fragility is unlikely to be detected by QUS. Such a situation could arise, for example, when stresses locally exceed the elastic limit but the bone as a whole does not fracture. The absence of an intrinsic association between elastic and acoustic properties therefore represents an important limitation, which should be borne in mind when interpreting clinical QUS measurements.

Ultrasound velocity (c) in a homogeneous isotropic solid bar whose cross-sectional dimensions are much less than the wavelength is determined by the density (ρ) and elastic modulus (E):

  • equation image

Thus, according to this equation, a reduction in elastic modulus of 72%, as seen in our data, should produce a 47% reduction in ultrasound velocity. We observed no significant change in velocity, confirming, not surprisingly, that the bar wave equation cannot be applied to cancellous bone in this context. In addition, our findings question the validity of Biot's theory in cancellous bone, because this theoretical approach predicts the elastic modulus of the cancellous framework to be a major determinant of velocity.(7,20) On the other hand, models consistent with our results include simple “mixture law” theories(21) and Schoenberg's theory.(8,22) According to the former, sound speed in a composite medium is determined only by the bulk sound speeds in the different components and the relative volume fractions of those components. Similarly, in Schoenberg's theory,(8,22) velocity in a stratified medium is not explicitly a function of elastic modulus, and, in addition, is predicted to vary with orientation, as is the case in cancellous bone.

Potential problems with our approach include the possibility of significant density and/or architectural changes associated with the mechanical testing that could have confounded the interpretation of the results. However, we observed no QUS changes, whereas the potential confounding effect of density or architectural change would presumably tend to contribute to QUS changes. Also, to minimize the possibility of density or architectural changes, the applied mechanical strains were kept below 5%, and the induced residual strains were less than 1% (i.e., there was a large degree of elastic recovery). This implies that any apparent density changes associated with our damage protocol would have been small (<1%).

By applying known strains in excess of the yield strain, we were able to produce controlled reductions in the elastic modulus of cancellous bone samples. However, we did not investigate the damage mechanisms. Hence, we do not know whether the damage produced was representative of the in vivo situation. Nevertheless, the approach we adopted was similar to that used in a previous study in which the damage mechanisms were investigated histologically.(23) In that earlier work, strains of 2.5% produced predominantly transverse cracks and shear bands in trabeculae without gross disruption of the trabecular framework.(24) In human vertebral bone, complete fractures of trabeculae are rare even when loaded to strains of 15%.(23) These observations suggest that our damage protocol is unlikely to have significantly altered the trabecular architecture.

It has been shown that compressive mechanical testing of cancellous bone between platens underestimates elastic modulus by typically 20%, primarily because of the end artifacts.(19) This inaccuracy can be overcome by measuring strain directly on the bone sample, but this in turn can be problematic, particularly in fragile, low-density bone specimens such as those used in the current study. We compromised by measuring displacements with an extensometer placed on the platens above and below the specimen. This may have led to systematic inaccuracies in our strain and modulus measurements. However, because our primary purpose was comparison between groups, this was not considered a major drawback.

Our study dealt with the elastic modulus of the cancellous framework as a continuum and its relationship to QUS measurements. We did not study the elastic properties of the trabeculae themselves, and it remains possible that elasticity at the trabecular material level is related intrinsically to ultrasonic properties. The damage induced in our study is unlikely to have produced systematic changes in trabecular material properties, such as might be produced by demineralization, for example. It may be useful in future studies to address the issue of the sensitivity of QUS to trabecular material properties using a similar approach to that of the current work.

To summarize, this study showed that QUS was unable to detect reductions in the elastic modulus of cancellous bone caused by mechanical damage. We conclude from this that there is no causal relationship between elastic modulus and QUS measurements in human cancellous bone from the calcaneus. Clinically, this indicates that heel QUS cannot be expected to detect bone fragility without major accompanying density or architectural changes. Moreover, from a fundamental viewpoint, it provides strong evidence for the validity, or otherwise, of existing theoretical models of the propagation of ultrasound in cancellous bone.

ACKNOWLEDGMENTS

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

We thank Kristy Salisbury for technical assistance with aspects of this work. This work was supported by the National Institutes of Health grant AR44661.

REFERENCES

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