Ultrasound technology has emerged as a new tool in the assessment of osteoporosis. Ultrasound parameters usually are measured in transmission; there is a potential for the analysis of backscattered signals to provide information on bone microarchitecture. The aim of this study was to explore a new technological development of the method, adding backscatter coefficient to transmission parameters, and to examine the appropriate thresholds to identify postmenopausal osteoporotic women. We examined 210 postmenopausal women (including 60 with osteoporotic fractures) and 30 healthy premenopausal controls. They had lumbar spine and hip bone mineral density (BMD) measurement and quantitative ultrasound (QUS) evaluation at the os calcis, measured in transmission (broadband ultrasound attenuation [BUA], speed of sound [SOS], ratio of transit time [dt] to BUA [dt/BUA], and “strength” index [STI]) and reflexion (broadband ultrasound backscattering [BUB]). The standardized CVs (sCVs) were between 2.27% and 3.40% for QUS measured in transmission and 4.41% for BUB. The odds ratio (OR) for fracture discrimination adjusted for age was 2.77 for hip BMD and between 1.6 and 2.9 for QUS. After adjustment for hip BMD, ORs were still highly significant for SOS, STI, and dt/BUA. According to hip BMD T score, prevalence of osteoporosis in our population was 39%. To detect the same prevalence, T scores ranged between −0.95 and −1.42 for QUS. QUS parameters have adequate ability to discriminate osteoporotic patients from controls. The World Health Organization (WHO) threshold for diagnosis of osteoporosis does not apply to this technology. The clinical utility of BUB at the os calcis, in addition to usual ultrasound parameters, is not yet proven. However, BUB evaluation, which does not require two transducers and may be implemented in conventional reflection mode systems, warrants further studies.
ULTRASOUND TECHNOLOGY has emerged as a new tool in the assessment of osteoporosis.(1) The technology is radiation free, portable, and inexpensive, with a potential for widespread use. Several prospective studies have shown that fracture risk can be evaluated by ultrasound in postmenopausal women,(2–10) and the measurements are able to discriminate between patients with osteoporotic fractures and age-matched controls.(11–13) Devices have been designed to measure peripheral bones, in which there is little overlying tissue such as os calcis. The value of os calcis assessment in osteoporosis evaluation is well known.(14)
Most of the devices measure broadband ultrasound attenuation (BUA; dB/MHz) and/or velocity (m/s), which is given as speed of sound (SOS) or bone velocity (Vb) in a transmission mode. Information derived from transmitted signals processing has not been fully studied in a clinical setting, and other parameters can be estimated from this mode. Moreover, the potential of quantitative ultrasound (QUS) parameters for bone characterization still is not exploited fully. Transmission measurements only partially exploit the information related to the interaction between the elastic wave and bone microarchitecture. The assessment of bone strength demands increasing knowledge not only about bone mineral density (BMD), but also about microscopic bone structure. Ultrasonic tissue characterization using the analysis of backscattered signals has shown the potential to provide the information needed for the assessment of tissue microstructure.(15, 16) Cancellous bone can be considered as a heterogeneous scattering medium: a fluidlike medium (marrow) containing small discrete scattering particles (trabeculae). The parameter used for measuring backscatter from biological tissue is the backscatter coefficient, defined as the differential scattering cross-section (i.e., the fraction of scattered ultrasonic power removed by scattering from the intensity of the incident ultrasonic wave) per unit volume in the 180° direction with respect to the incident beam.(15) Because the backscatter coefficient is related to medium characteristics such as the average density number (i.e., number of scatterers per unit volume), size, separation, orientation, and scattering strength of scatterers,(15) a backscattering measurement technique exploiting scattering from the internal microarchitecture of bone should give more information about this microarchitecture. In addition, skeletal sites, which are difficult to reach by transmission, such as the femoral neck could be evaluated by the backscattering technique. A few studies have shown the in vitro and in vivo feasibility of this backscatter approach on the calcaneus.(17–19)
The aim of this study was to assess and compare a number of QUS parameters at the os calcis measured both in transmission and in backscatter modes in postmenopausal osteoporosis. We determined whether a combination of QUS results is able to improve osteoporotic fracture discrimination over a single parameter.
MATERIALS AND METHODS
This study was conducted with a UBIS 5000 device (DMS, Montpellier, France). Ultrasonic measurements were performed by using a pair of broadband focused transducers, immersed in a water bath with a controlled temperature (30 ± 2°C). The device could be activated in two different modes: transmission and reflection.
The measurement procedure consisted of moving the transducers using a two-dimensional (2D) scanning mechanism over a 60 × 60 grid (1-mm pixel size, 60 mm × 60 mm field of view) and recording the transmitted and reflected raw radiofrequency (rf) signals. Radiofrequency signals were digitized at 8 MHz using an 8-bit A/D convertor. The signals transmitted through the heel were processed to calculate the slope of attenuation (BUA, dB/MHz) and the SOS (m/s) and to generate BUA and SOS images. The method has been described previously in details.(13, 20) The circular region of least attenuation (14-mm-diameter region of interest [ROI]) was determined automatically for further investigation.(20) Parameter values used in this clinical study were the average parameters values corresponding to the entire automatic ROI.
Two additional parameters in transmission were obtained by combining measurements derived from the signals transmitted through the heel. The strength index (STI) is a linear combination of both BUA and SOS given by STI = 0.67 BUA + 0.28 SOS − 393. The second parameter is the ratio dt/BUA (dB−1), where dt represents the differential transit time between the reference signal (i.e., signal transmitted through water without the heel in the ultrasound path) and the signal transmitted through the heel. It can be shown that dt and BUA are both proportional to bone width (see Appendix A). The ratio dt/BUA eliminates the bias related to the thickness of the calcaneus.
The backscatter coefficient was measured using a substitution technique, in which the signal scattered from the region under test is compared with the signal from a standard reflecting target.(21) Backscatter data acquisition was performed with the transducers used in pulse-echo mode. The analysis of backscattering signals was restricted to a segment of the echo signal defined by a time gate, as shown in Fig. 1. A time gate of 128 samples was used to select the data from a standardized physical location in the calcaneus. The center of the window was set at the middistance between both transducers. This location approximately corresponded to the center of the calcaneus. The gate position and duration were such that the signals were selected from a scattering volume consistently included in the os calcis. The sampling rate was 8 MHz, resulting in a duration of the data window of 16 μs. Considering a mean SOS of 1525 m/s in the heel,(20) the spatial extent of the gated bone sample volume corresponding to the time window was approximately 12 mm and still was much shorter than the width of the calcaneus. These gated signals were used to compute the frequency-averaged backscatter coefficient (broadband ultrasound backscatter [BUB], dB) for the gated bone tissue in the ROI. The backscatter power was estimated from the mean square of the spectrum averaged over all the spatial locations corresponding to the ROI. To deconvolve the response of the measuring equipment from the backscatter data, a calibration spectrum (reference signal) is obtained by reflecting an ultrasonic pulse off a standard reflecting target positioned in water at a distance corresponding to the center of the gated region as depicted in Fig. 1. A steel plate was used as the standard reflector. The frequency-dependent backscatter coefficient was then computed by performing a log spectral subtraction of the tissue spectra from the calibration spectrum, applying correcting factors compensating for the attenuation that occurs when the pulse travels through bone and accounting for the geometry of the scattering volume (see Appendix B). The frequency-averaged backscatter coefficient was obtained by integrating the result in the frequency bandwidth of the transducer, that is, from 0.2-0.6 MHz. In this formulation, the backscatter coefficient is computed in terms of the energy of the scattered radiation from the tissue relative to the energy of the reference signal from a perfectly reflecting plane reflector. This backscatter coefficient, when expressed in decibels, is negative, which means that the backscattered energy is weaker than the signal reflected from a perfect reflector. When properly compensated for attenuation and geometrical factors, the backscatter coefficient is independent of the measuring instrument and depends only on the microstructure and acoustic properties of the scattering volume under test.(22)
BMD (g/cm2) was measured using dual-energy X-ray absorptiometry (DXA), QDR 2000 and 4500 (Hologic, Inc., Waltham, MA, USA). The two devices have been previously cross-calibrated using a Hologic spine phantom, according to the manufacturer's recommendation. At the lumbar spine, the second, third, and fourth vertebrae were measured (anteroposterior view). Fractured vertebrae were excluded from analysis. At the upper extremity of the left femur, total hip BMD, which is the mean of the different subregions of the femur, was considered.
The reproducibility of the QUS parameters was evaluated in 49 women aged 51.8 ± 16.6 years, who had duplicate scans with repositioning. We calculated the CV (%) and the standardized CV (sCV; %),(23) according to
where d is the difference between duplicate scans, n is the number of patients, m1 and m2 are the mean results of the first and second scans respectively, and SD is the standard deviation of the results of the 49 patients.
A total of 240 women are the basis of the study. Two hundred ten patients were postmenopausal women who were referred to our unit for evaluation of bone density. Data collected during the visit included age, menopause age, body mass index (BMI; kg/m2), and past and current use of antiosteoporotic drugs, including hormonal replacement therapy. This population included 60 patients, mean age 65.8 ± 7.9 years, with either vertebral, wrist, and/or hip fracture. All of these women were selected by the same physician (C.R.), who assessed that the fractures were caused by bone fragility based on the circumstances under which fractures occurred and radiological data. Thirty-two of these patients (53.3%) were receiving an antiosteoporotic drug. The 150 other postmenopausal women were aged 61.3 ± 6.9 years and 80 were receiving a treatment for prevention of osteoporosis. These two subgroups were similar in BMI (24.4 ± 6.3 and 24.4 ± 4.1, respectively). BMD status was different at the spine: 0.784 ± 0.119 g/cm2 and 0.858 ± 0.147 g/cm2 (p = 0.002) in the fractured and nonfractured subgroups, respectively. Total hip BMD was 0.714 ± 0.094 and 0.807 ± 0.120, respectively (p = 0.0001), in these two groups.
Thirty healthy premenopausal women, volunteers drawn from members of staff and medical students, served as controls. They were 36.4 ± 11.1 years old, with a BMI of 22.3 ± 3.0. BMD was 1.004 ± 0.150 g/cm2 and 0.906 ± 0.146 g/cm2 at the spine and hip, respectively.
Correlations between BMDs and QUS parameters were evaluated by Pearson correlation coefficients. For QUS and hip BMD, a T score was calculated, as the ratio of the difference between the mean values of patients and controls, by the SD of controls. The discriminating values were determined based on the areas under the receiver operating characteristic (ROC) curves. With this method, an area under the curve (AUC) of 1 indicates ideal diagnostic performance.
Mean and SD were reported for all studied parameters. When means were compared between groups, a two-tailed Wilcoxon rank test at the 5% significance level was used.
The influence of QUS parameters on the fracture risk was assessed by the odds ratios (ORs) per SD of controls, estimated with a logistic regression model. ORs were adjusted for age and then for age and hip BMD. A stepwise multiple logistic regression was performed to analyze the effect of a combination of QUS parameters and BMD. Several combinations of BMD and QUS parameters were investigated. Among the identified best-performing combinations, nested models (i.e., models obtained when adding parameters to another model) were compared using the likelihood ratio test (LRT) at the 5% significance level.
A diagnostic threshold of QUS for osteoporosis was calculated based on the T score. We calculated the percentage of women who had a total hip T score ≤ −2.5; for each QUS we calculated the T score that detected the same percentage of women.
Finally, we examined the efficiency of QUS to screen patients for further evaluation by DXA according to Baran et al.(24) In this strategy, patients are categorized by QUS according to age and T score. Three categories are determined: appropriate therapeutic intervention (if T < −2), need for further evaluation by DXA (if 0 > T > −2 in women 65 years or older and 1 > T > −2 in women younger than 65 years), and no need for further evaluation.
All analyses were performed using SAS 6.12 (SAS Institute, Cary, NC, USA) and S Plus 4.5 (Mathsoft, Inc., Seattle, WA, USA) software packages.
The reproducibility results are reported in Table 1. CV was high for dt/BUA, which is an expected result because of the low mean value of this parameter. However, it is well known that a CV value in itself is not meaningful but needs to be standardized, by comparison to the variability of the parameter in the population or to its variation over time, according to the clinical question to be answered. When standardized by the variability of the population, the best sCV was obtained for STI and the poorest sCV was obtained for BUB. sCVs were comparable for BUA, SOS, and dt/BUA.
Table Table 1.. Reproducibility of QUS Parameters
Raw values of QUS parameters in the three populations are reported in Table 2. All parameters were distributed normally. QUS parameters were different in postmenopausal women than in controls and in fractured postmenopausal patients as compared with nonfractured patients. Using the T score, to take into account the variance of the controls, dt/BUA showed the largest difference among the populations.
Table Table 2.. Ultrasound Parameters Values in the Three Groups (mean ± SD)
Highly significant correlation coefficients were observed among QUS parameters. There was a moderate but highly significant correlation between BUB and BUA (r = 0.73; p = < 10−4) and a strong correlation between STI, SOS, and dt/BUA (r > 0.95). Weak but significant correlations were found between all QUS parameters and hip BMD (Table 3).
Table Table 3.. Pearson's Correlation Between QUS and the Total Hip BMD in the Whole Populationa
The ORs of hip BMD and QUS parameters for fracture discrimination, adjusted for age, are reported in Table 4. After adjustment for age, all the QUS parameters were discriminant; ORs were between 1.6 and 2.9. However, after adjustment for age and total hip BMD, discriminative value of BUA and BUB was no longer significant. Discrimination of osteoporotic fractures was still highly significant for SOS, STI, and dt/BUA; the ORs were 2.14 (1.21-3.79), 2.0 (1.17-3.42), and 1.9 (1.2-3.0), respectively.
Table Table 4.. Age-Adjusted ORs and AUC for Fracture Discrimination
We tested a number of combinations of QUS parameters with total hip BMD. There was no increase in AUC with any combinations. The ORs were higher than those of single parameters but with a large overlap of CIs (Table 5). The LRT was highly significant for the combination of BMD with SOS, STI, and dt/BUA (p = 0.0066, 0.0087, and 0.0084, respectively) but not for the combination with other parameters. The use of two QUS parameters in combination with BMD did not enhance fracture risk prediction (data not shown).
Table Table 5.. Age-Adjusted ORs and AUC when Combining Several Diagnostic Variables
Among the 210 postmenopausal women, 82 (39%) had a total hip BMD T score ≤ −2.5. All QUS parameters were able to discriminate these patients from nonosteoporotic ones; the range of ORs was 2.06 (1.48-2.85) for BUB to 3.17 (2.01-5.00) for STI. To obtain the same prevalence of osteoporosis, the diagnostic thresholds for QUS expressed in T score were −1.00, −1.33, −1.41, −0.95, and −1.42 for BUA, SOS, STI, BUB, and dt/BUA, respectively.
QUS parameters were categorized according to Baran et al.'s criteria.(24) Considering BUB results in women 65 years or more, 62% of them would have been sent for further evaluation by DXA; all of them were either osteopenic or osteoporotic. Among the 19 women regarded as normal, 5 women were osteopenic and 9 women were osteoporotic. When we examined the DXA results (at either spine or hip), we observed that among the 11 patients with recommended treatment based on QUS, 3 patients were osteopenic and 8 patients were osteoporotic.
In postmenopausal women younger than 65 years, 87% would have been sent for DXA evaluation and 8% were actually normal. One patient was normal using QUS, but osteoporotic according to DXA. Among those with recommended treatment, none was normal at spine and/or hip.
This is the first clinical study conducted in osteoporotic patients using BUB at the os calcis.
In osteoporosis, bone fragility is caused by both a loss of bone mass and a deterioration of trabecular bone microarchitecture. The ability to nondestructively characterize the microarchitecture of the trabecular network would be useful for the evaluation of osteoporosis that affects this component of bone. In spite of recent advances of high-resolution X-ray computed tomography, magnetic resonance microimaging and radiographic images processing showing the potential for in vivo microarchitecture characterization,(25–28) only bone mass reduction can be assessed in current practice using X-ray densitometry techniques. The development of QUS means to detect noninvasively microarchitectural changes associated with osteoporosis was a motivating factor of this study. The attenuation of ultrasound results from scattering and absorption of the ultrasound wave. Biot's theory,(29) a phenomenological theory of acoustic propagation in a porous elastic solid saturated by a viscous fluid, has been adapted to model ultrasound through cancellous bone. Although Biot's theory has successfully predicted SOS, there has been consistent discrepancy between measured and predicted attenuation, possibly owing to important contribution of scattering to signal loss in addition to absorption due to viscous friction at internal interfaces between bone and marrow.(30) Based on the experience with measurements in soft tissue, the microarchitecture (shape, size, spatial distribution, and number of scatterers per unit volume) and elastic properties of the scattering particles contribute to the magnitude and frequency dependence of the backscattered signals assessed by BUB.(15) Ultrasonic backscatter measurements at the calcaneus recently have been introduced for their potential to assess directly the microstructure of trabecular bone by our group(17, 18) and others.(19, 31) In contrast to Wear and Garra(19) who performed apparent backscatter measurements at the calcaneus, without correcting the backscattered signals for attenuation, our data were compensated for the attenuation factor, leading to a more accurate estimate (see Appendix B).
Aging and the osteoporotic process lead to a decrease in trabecular thickness, a loss of bone trabeculae, and a decrease in connectivity, all together contributing to changes of the scattering properties by modifying the size, number density, and spatial distribution of scatterers. In theory, these changes decrease the backscatter intensity. Our data confirm an age-related and osteoporosis-related decrease of BUB.
However, whether backscatter measurement provides additional information independently of BMD and has the potential to lead to further improvement of fracture assessment was not established in this study and remains highly speculative. We observed that, at best, only half of the variance of BUB was explained by BUA (r = 0.73). Therefore, one could argue that different bone properties are measured in transmission and backscatter. On the other hand, after adjustment to hip BMD, the discriminative value of BUB was no longer significant. In addition, the combination of BUB with another QUS parameter measured in transmission did not enhance significantly fracture risk prediction. These results suggest that no additional information is provided by backscatter measurements. Subsequently, moderate to low correlation coefficients between BUB and QUS transmission parameters are likely to be caused by several sources of variability (e.g., soft tissue, temperature, and cortical interfaces), which are not very relevant for fracture risk assessment but affect differently various QUS parameters. In fact, the correlation between BUB and BUA observed in this study is lower than that reported by our group in a previous in vitro study (r = 0.86) on human calcaneus specimens,(17) but it is usual to observe higher correlation coefficients in in vitro studies because of a better control of experimental conditions. The same study reported a strong correlation between BUB and BMD (r = 0.82), meaning that more than two-thirds of the variance of BUB is already explained by BMD. Is the remaining third of the variance explained by microarchitecture? To answer this question, the relationships of transmission and backscatter QUS to microarchitecture of human calcaneus have been investigated recently by our group using synchrotron radiation microtomography.(32) Again, BUB and BMD were found to be correlated strongly (r = 0.89), and furthermore, no significant independent association existed between microstructure and backscatter coefficient after adjustment for density. These findings are similar to those of previous in vitro studies failing to clearly show that independent information (except for anisotropy) related to bone microstructure could be extracted from QUS measurements in transmission.(33, 34) It has been suggested that these results could be attributed to the strong covariance effect between microarchitecture and density at the calcaneus.(34) If that should be confirmed, the aim to develop specific ultrasound measurements that are more specific to either bone mass or bone structure would be marred by the variation in parallel of both bone microarchitecture and density. Whether these results can be extended to measurement sites other than the calcaneus or to bone diseases other than osteoporosis remains to be shown. Clearly, a better understanding of the interaction between ultrasound waves and bone microarchitecture represents one of the areas that warrants further investigations.
The reproducibility of the parameters measured in transmission was very close to those published with other systems(35) or the same device.(13, 20) As expected, precision of STI is high (sCV, 2.27%). Temperature and immersion time-related drifts of BUA and SOS are in opposite direction(36); thus, such a combination has a reduced sensitivity to these experimental factors.(37) On the other hand, the poorer precision was found with BUB (sCV, 4.41%), which can be explained by the more complex sequence of data acquisition and signal processing required to extract BUB.
The Ultrasound Bone Imaging System (UBIS) device does not measure and account for the width of the calcaneus; both BUA and SOS are dependent on the calcaneus width and therefore do not reflect bone material properties alone. Calculating the ratio dt/BUA has the advantage to adjust the measurements for bone width, without requiring measuring it, that is, without loss of precision. This parameter may prove to be useful for pediatric studies, when foot size and heel width are expected to vary dramatically as a function of age.
Our data on BUA and SOS are in agreement with previous cross-sectional studies.(12, 13) QUS parameters are able to discriminate osteoporotic patients from controls. The results of the logistic regression analyses indicate that the risk of fracture, expressed as OR, increases 1.5- to 3.0-fold for each SD decrease in QUS parameters. These data are very similar to the results of prospective studies using QUS.(2–10)
Conflicting results have been reported on combining hip BMD measurement and QUS assessment at the os calcis in the osteoporotic fracture prediction. In two large prospective studies,(3, 5) the relative risk of hip fracture calculated for the decrease in BUA was still statistically significant after adjustment for hip BMD, but using the ROC curves showed that the combination of QUS and BMD is not better than either one alone.(38) Our data are in agreement with these results; the age-adjusted area under the ROC curve was 0.76, 0.76, and 0.78 for hip BMD alone or hip BMD in combination with BUA or SOS, respectively. The use of AUC has a practical limitation; it represents the probability that the test results of a random pair of subjects are ranked correctly; but in practice the test is not given to pairs of diseased and nondiseased subjects.(39) Thus, we considered the assessment of risk given by ORs. They were similar for hip BMD alone or hip BMD in combination with BUA. In contrast, the OR calculated for the combination of hip BMD and SOS was higher: 4.0 (2.0-7.2). Similar results were obtained for the combination with parameters related to ultrasound velocity (STI and dt/BUA). The reason for this difference between attenuation-related QUS and velocity-related QUS remains unclear.
In 1994, the World Health Organization (WHO) recommended thresholds of bone density in postmenopausal women to diagnose osteoporosis.(40) The threshold able to identify osteoporotic patients is a T score ≤ −2.5. However, there is poor concordance of measurements among bone sites.(41) This is related to both anatomical and biological changes among bones as well as errors of accuracy of the different techniques. In our population, the thresholds (T scores) applied to QUS to observe the same prevalence of osteoporosis as calculated at the hip varied from −0.9 to −1.4. These data are in agreement with a previous study.(42) These differences mean that the WHO criteria cannot be used for QUS. Moreover, depending on the parameter studied at the os calcis, different thresholds should be used for the diagnosis of osteoporosis. The diversity is a key point in the advantages of QUS technology; however, the clinical utility of QUS is highly dependent on expression of the results.
According to our study, the majority of patients having a low QUS parameter at the os calcis are actually osteopenic or osteoporotic at the spine and/or the hip. However, following the current recommendations, a large number of patients will be referred for axial measurements by DXA. Thus, in the perspective of using QUS without axial measurements, new thresholds must be designed.
Our study fails to show that combining different QUS parameters at the same site improve the discriminative value after adjustment for hip BMD. In contrast, it has been shown recently that combining the results from multiple bone sites measured by SOS has the potential to improve discrimination of hip fracture.(43)
At the os calcis, new QUS parameters including BUB measured in reflection mode offer an alternative to BUA and SOS measurements, although their clinical utility in addition to current transmission measurements is not yet proven. At this site, additional information that is related to trabecular network microarchitecture does not add to usual transmission parameters. However, BUB evaluation in other bones may be of interest. BUB measurement does not require two transducers. It may be implemented in conventional reflection-mode imaging systems. BUB evaluation of other peripheral or axial skeletal sites needs to be studied further.
APPENDIX A: ULTRASONIC MEASUREMENTS IN TRANSMISSION
Ultrasonic measurements are conducted using a substitution method in a through-transmission normal incidence configuration. A broadband ultrasound pulse is received first without and then with the heel interposed between the transducers. With no intervening tissue, the calibration signal is obtained through water. Its amplitude spectrum is A0(f), where A0(f) is the instrumentation transfer function including the amplitude spectrum of the input electrical signal, the transfer functions of transmitting and receiving transducers and electronics. With the heel placed in the path of the ultrasonic beam, the amplitude spectrum of the received signal can be written as follows:
where T is the combined transmission coefficients associated with the single crossing of a wave at the different interfaces (i.e., water/skin, skin/bone, bone/skin, and skin/water interfaces), α(f) is the frequency-dependent attenuation coefficient, and e−α(f)l characterizes the effect of the attenuation filter on the ultrasound pulse for a propagation path l. Given the fact that the attenuation in soft tissue is much smaller than in cancellous bone, it is reasonable to assume that soft tissues have a minor impact on the attenuation filter and that the attenuation is caused solely by bone. Therefore, α(f) represents the attenuation coefficient of the calcaneus and l represents its width. In addition, the transmission coefficient T generally is assumed to be frequency independent, a reasonable assumption in view of the relatively flat interfaces orientated approximately perpendicularly to the beam axis in the ROI.
One defines the insertion signal loss IL (dB), on a logarithmic scale, as the ratio:
where 8.68 is a numerical factor accounting for the conversion in decibels. The extraction of the BUA from the insertion loss further assumes the frequency variation of the attenuation in bone to be linear. Therefore, the attenuation coefficient is modeled as follows:
where β is the slope of the attenuation coefficient. In practice, BUA (dB/MHz) is given by the slope of the linear regression fit to ILdB in the frequency bandwidth of the transducers, typically 0.2-0.6 MHz. Therefore, using Eqs. A2 and A3, BUA is given by the following formula:
clearly showing that BUA is proportional to the thickness of bone. The average SOS through the heel is determined from the difference dt between the times for the received pulse arrival, without and with the heel in the path of the ultrasound beam, assuming that sound velocity in soft tissue is equal to sound velocity in water. Therefore, dt is simply given by the following equation:
where cwater is the sound velocity in water. SOS is given by
The method of calculating arrival time currently implemented in UBIS 5000 uses the phase spectrum analysis.(44)
As for the estimation of BUA, the method does not account for the width of the calcaneus, and both BUA and SOS are dependent on it as shown by Eqs. A4 and A6. In contrast, the ratio dt/BUA (dB−1) may be defined to provide a measurement independent of bone thickness:
This ratio is independent of bone geometry and reflects only intrinsic bone properties. The ratio dt/BUA eliminates the bias related to the thickness of the calcaneus. The advantage of the method is to adjust the measurements for bone thickness, without requiring measuring it, that is, without loss of precision.
APPENDIX B: ULTRASONIC MEASUREMENTS IN REFLECTION
The measurement method uses a substitution technique in which the signal scattered from the region under test is compared with the signal from a standard reflecting target (e.g., steel plate). A Hamming time window of 128 samples is used to select the data from a standardized physical location in the calcaneus. The center of the window is set at the middistance between both transducers (i.e., at the focal length of the transducers). This location approximately corresponds to the center of the calcaneus. Backscattering power from the selected region in the ROI is quantified by the spatially averaged power spectrum of the gated backscattering signal over the ROI. Averaging is necessary to remove pure statistical variations in the reflected signal because of random phase of the elementary waves scattered by each scattering trabeculae. The ROI was circular, 14 mm in diameter, and contained 176 consecutive lines. The deconvolution of the electromechanical response of the measuring equipment from the backscatter data were computed by performing the log spectral subtraction of the tissue spectra from the calibration spectrum from the standard reflecting target as follows:
where 〈SB(f)〉 is the spatial average backscattered power spectrum and S0(f) is the reference spectrum from the standard reflecting target. This yields an apparent backscatter coefficient μB(f) (dB). This apparent backscatter coefficient must be compensated for several sources of error including the signal loss caused by partial transmission at bone interface and attenuation in bone, the frequency dependence of the volume insonified by the transducer and the effect of the gating function. A particular problem in the quantitative study of scattering is the presence of attenuation in tissues. All echo amplitudes represent the product of a local scattering strength and an appreciable attenuation loss that occurs when the signal traverses the specimen to reach the scattering volume of bone under test and then to return to the transducer. All true measurements of scattering from within tissue thus must be corrected for attenuation. The compensation for the attenuation may be performed by applying an inverse attenuation filter. However, this requires the knowledge of the transmission coefficient at bone interface and attenuation coefficient α(f). In this study, our backscatter coefficient differs from the true one in that it is not compensated for unknown partial transmission at bone interface. However, the attenuation may be derived from the data acquired in the through-transmit mode and, therefore, may be compensated. To obtain the attenuation coefficient, the thickness l of the calcaneus has to be measured. The measurements made here were done using a pulse-echo technique, which did not require the physical measurement of bone thickness. The technique involved measurements of pulse times of flight, from which the calcaneus thickness could be estimated. The reflection of an incident pulse at the bone cortical boundary generates a high-amplitude echo returning back to the transducer as depicted in Fig. B1. An adaptive threshold is used to detect automatically the echo signal. Times-of-flight t1 and t2 of the echoes reflected back toward each transducer by the closest bone cortical boundary were measured. The schematic is shown in Fig. B1. Knowing the fixed distance L separating both transducers, the thickness l of the calcaneus may be calculated (assuming a constant SOS in water and surrounding soft tissues) according to
An estimate of the attenuation coefficient may then be derived using Eqs. A3, A4, and B2:
and then injected in the inverse attenuation filter. The frequency-dependent backscatter coefficient is derived following the method of Roberjot et al.(22):
where C(f) is the attenuation correction term and factors(f) is a frequency-dependent scattering volume correction term (i.e., a term accounting for time gate length and frequency-dependent beam width and shape). The attenuation correction term is given by(45)
and the volume compensation term may be written as
where (1/0.63)2 is the compensation term for the Hamming gate function, d is the gate length, z is the attenuated path within the bone until the gated volume, k = 2π/λ is the wave number, a is the transducer radius, and F is the focal length.
The accuracy of the method has been evaluated previously by comparing results from suspended spheres in gelatin to theoretical predictions.(22)
The frequency-averaged (or integrated) backscatter coefficient is obtained by integrating the result in the frequency bandwidth of the transducer 0.2-0.6 MHz (fmin − fmax):