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. Author manuscript; available in PMC: 2019 Dec 26.
Published in final edited form as: J Acoust Soc Am. 2012 Feb;131(2):1605–1612. doi: 10.1121/1.3672701

Relationships of quantitative ultrasound parameters with cancellous bone microstructure in human calcaneus in vitro.

Keith A Wear 1, Srinidhi Nagaraja 1, Maureen L Dreher 1, Sheng L Gibson 2
PMCID: PMC6931152  NIHMSID: NIHMS1064093  PMID: 22352530

Abstract

Ultrasound parameters (attenuation, phase velocity, and backscatter), bone mineral density (BMD), and microarchitectural features were measured on 29 human cancellous calcaneus samples in vitro. Regression analysis was performed to predict ultrasound parameters from BMD and microarchitectural features. The best univariate predictors of the ultrasound parameters were the indexes of bone quantity: BMD and bone volume fraction (BV/TV). The most predictive univariate models for attenuation, phase velocity, and backscatter coefficient yielded adjusted squared correlation coefficients of 0.69 – 0.73. Multiple regression models yielded adjusted correlation coefficients of 0.74 – 0.83. Therefore, attenuation, phase velocity, and backscatter are primarily determined by bone quantity, but multiple regression models based on bone quantity plus microarchitectural features achieve slightly better predictive performance than models based on bone quantity alone.

Keywords: quantitative ultrasound, cancellous bone, microstructure, bone mineral density

I. INTRODUCTION

Because of low cost, portability, and lack of ionizing radiation, quantitative ultrasound is an attractive alternative to x-ray bone densitometry for the assessment of osteoporotic fracture risk (Langton et al., 1984;Laugier, 2008; Laugier, 2011; Barkmann and Glüer, 2011). A recent position paper by the International Society for Clinical Densitometry indicates growing acceptance of quantitative ultrasound (Krieg et al., 2008).

It is well understood that fracture risk depends not only on BMD (the current gold standard diagnostic measurement) but also on structural properties of the bone. Correlative studies involving quantitative ultrasound measurements and micro computed tomography (microCT) measurements on cancellous bone samples provide insight into relationships between macroscopic ultrasound properties and microarchitectural features. Previous regression studies have been conducted in human calcaneus (Nicholson et al., 2001;Chaffai et al., 2002;Wear and Laib, 2003), tibia and femur (Hakulinen et al., 2006;Karjalainen et al., 2009), and femur (Padilla et al., 2008). The literature in this area of investigation was recently reviewed thoroughly by Padilla et al. (2008). These studies were based on linear regression analysis, which is the most straightforward approach when the true functional dependencies of the output variables (e.g., ultrasound properties) on the input variables (e.g., BMD and microarchitectural features) are unknown.

This paper reports multiple regression analysis to predict quantitative ultrasound parameters from BMD and microarchitectural measurements in 29 human cancellous calcaneus samples in vitro. This analysis provides insight into determinants of clinical ultrasound measurements. The calcaneus is important because it is the most common bone measured by clinical bone sonometers.

The contributions of this paper are as follows. 1) This paper reports multiple regression analysis to predict broadband ultrasonic attenuation and phase velocity as functions of BMD and microarchitecture in human calcaneus and provides independent data to compare with similar human calcaneus studies reported previously by Nicholson et al. (2001) and Chaffai et al. (2002). 2) This paper reports measurements of relationships between ultrasound backscatter, BMD, and micro-architecture in human calcaneus and investigates the degree of reproducibility of similar studies reported previously only by Chaffai et al. (2002) and Wear and Laib (2003). (The latter study utilized a different set of bone samples than the set reported in the present paper and only considered mean trabecular thickness but not other microarchitectural features such as bone volume fraction and mean trabecular number). 3) This paper provides an analysis of the range of values of correlation coefficients among ultrasound parameters, BMD, and microarchitectural features reported in this study and previous studies on human cancellous bone (Nicholson et al., 1998;Trebacz and Natali, 1999;Nicholson et al., 2001;Chaffai et al., 2002;Hakulinen et al., 2006;Padilla et al., 2008;Karjalainen et al., 2009).

II. METHODS

A. Bone samples

Twenty-nine excised human calcaneus samples (extracted from 29 human calcanei) were defatted using a trichloro-ethylene solution. According to previous studies, defatting has a small effect on ultrasound parameters (Langton et al., 1996;Alves et al., 1996;Njeh and Langton, 1997;Nicholson and Bouxsein, 2002;Hoffmeister et al., 2002). The lateral cortical layers were sliced off leaving two parallel surfaces with direct access to trabecular bone. Cortical end-plates have been reported to have a small but measureable (15%) effect on measurements of broadband ultrasound attenuation (Xia et al., 2005). A thin layer of cortical bone remained along the other surfaces of the bone. This cortical layer (see periphery of bone sample in Figure 1) was excluded from regions of interest for bone densitometry, microCT, and ultrasound measurements. The mean sample thickness was 1.8 cm (standard deviation = 0.23 cm).

1.

1.

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A slice from a micro-computed tomogram of calcaneus. Some trabeculae appear to terminate as they move into and out of the imaging plane. Image acquired by Andres Laib, Scanco Medical AG, Bruttisellen, Switzerland. A −3 dB beam cross section at 500 kHz is shown.

B. Bone Densitometry

Bone mineral density (BMD) was measured using a Hologic QDR 4500 dual energy x-ray absorptiometry (DXA) system operating in single beam mode. Areal density was determined for central regions of interest (ROIs) so that cortical bone was excluded. The ROIs were approximately 1.8 cm × 3.6 cm × 1.8 cm (where the last dimension corresponds to the bone sample thickness, which is in the direction parallel to the DXA beam and perpendicular to the plane of Figure 1). Duplicate measurements (without repositioning) were performed on each specimen. The average coefficient of variation for the duplicate areal density determinations was 1.6%. The average areal density (g/cm2) was divided by the thickness of each sample to give volumetric density (g/cm3).

C. MicroCT

Three-dimensional (3-D) trabecular bone microstructure was measured using micro computed tomography (μCT 100, Scanco Medical, Basserdorf, Switzerland). The Scanco μCT 100 is a cabinet cone-beam scanner with a microfocus x-ray source and a charge coupled device detector (3072 × 400 elements array). After ultrasound and DXA measurements had been performed, cancellous bone specimens were cut down to dimensions approximately 2.0 cm × 4.0 cm × 1.8 cm and imaged at an isotropic voxel size of 17.2 μm (nominal resolution). This resolution has been reported to be sufficient to reveal significant differences between normal and osteoporotic human trabecular bone for bone volume fraction (BV/TV), trabecular thickness (Tb.Th), degree of anisotropy (DA), trabecular number (Tb.N), trabecular spacing (Tb.Sp), and structural model index (SMI) (Isaksson et al., 2011). Within the 2.0 cm × 4.0 cm × 1.8 cm reconstruction volume, an interior volume, approximately 1.8 cm × 3.6 cm × 1.6 cm (similar to the DXA analysis volume) was delineated for micro-structural analysis. A constant threshold to distinguish trabecular bone from background was chosen through histogram analysis of each specimen. The threshold was designated at a value below the broad peak in the histogram corresponding to trabeculae. From these segmented images, automated distance transformation algorithms were used to calculate BV/TV, Tb.Th, Tb.Sp, Tb.N, SMI, bone surface fraction (BS/BV), and connectivity density (Conn.D.) based on methods of Hildebrand and Ruegsegger (Ruegsegger et al., 1996;Hildebrand and Ruegsegger, 1997;Hildebrand et al., 1999). Principal material orientations (H1, H2, and H3) and degree of anisotropy (DA) were calculated using 3-D mean intercept length techniques.

D. Ultrasound

Prior to ultrasonic interrogation, samples were vacuum degassed underwater in a desiccator. Subsequently, samples were allowed to thermally equilibrate to room temperature. Water temperature was measured with a digital thermometer for each experiment and ranged between 19°C and 21°C. The relative orientation between the ultrasound beam and the calcaneus samples was the same as with in vivo measurements performed with commercial bone sonometers, in which sound propagates in the mediolateral (or lateromedial) direction. Samples were interrogated in a water tank using a Panametrics (Waltham, MA) 5800 pulser/receiver and Panametrics V301 1” diameter, focused (focal length = 1.5”), broadband transducers with center frequencies of 500 kHz. Bone samples were placed in the focal plane. The diameter of the central lobe of the focused beam at the focal plane ranged from 18 mm to 8 mm across the analysis band from 300 kHz to 700 kHz. (The central lobe width is given by 2.44λz/d, where λ = wavelength, z = focal length, and d = transducer aperture diameter (Goodman, 1968)). The central portions of the samples were scanned in order to approximate as closely as possible the ROI used in the DXA measurements. Received signals were digitized (8 bit, 10 MHz) using a LeCroy (Chestnut Ridge, NY) 9310C Dual 400 MHz oscilloscope and stored on computer (via GPIB) for off-line analysis.

A through-transmission method was used to measure normalized broadband ultrasonic attenuation (nBUA) and velocities. Using two opposing coaxially-aligned transducers (one transmitter and one receiver), transmitted signals were recorded both with and without the bone sample in the acoustic path. The bone samples were larger in cross-sectional area than the receiving transducer aperture. Attenuation coefficient was estimated using a log spectral difference technique (Kuc and Schwartz, 1979). Attenuation was characterized by the slope of a least-squares linear fit of attenuation coefficient (dB/cm) vs. frequency, resulting in the nBUA (dB/cmMHz) (Langton 1996). Phase velocity and signal velocity were measured using methods published previously (Wear, 2000a; Wear, 2000b; Wear, 2007. For signal velocity, the third zero crossing in advance of pulse envelope maximum (which corresponded approximately to the leading edge of the pulse used in this investigation) was used as a time-of-arrival marker. Since the speed of sound in calcaneus, approximately 1475–1650 m/s (Droin et al., 1998), is comparable to that in distilled water at room temperature, approximately 1480–1490 m/s, potential diffraction-related errors (Xu and Kaufman 1993) in this substitution technique may be ignored (Droin et al. 1998). All frequency domain analysis was performed over the range from 300 kHz to 700 kHz.

Backscatter coefficients were measured using a reference phantom method (Yao et al., 1990). Good agreement between experimental measurements using this method and theoretical predictions based on Faran’s theory of scattering (Faran, 1951) for ultrasonic backscatter coefficients from phantoms consisting of glass spheres embedded in gelatin has previously been reported by this laboratory (Wear, 1999). The backscatter coefficient vs. frequency data were least-squares fit to a power law relationship over the range from 300 kHz to 700 kHz. The midband (500 kHz) value of the power law fit was used in the regression analysis. Backscatter data were gated to exclude the specular reflection at the front surface of the bone sample. Although backscatter measurements are less commonly used to characterize bone than attenuation and sound speed, many studies suggest that backscatter is a useful index of cancellous bone properties (Roberjot et al., 1996; Wear and Garra, 1998; Wear, 1999; Hoffmeister et al., 2000; Roux et al, 2001; Hoffmeister et al., 2002; Jenson et al., 2003; Wear and Laib, 2003; Hakulinen et al., 2005; Hakulinen et al., 2006; Jenson et al., 2006; Hoffmeister et al., 2006; Padilla et al., 2006; Riekkinen et al., 2007; Riekkinen et al., 2008; Ta et al., 2008; Padilla et al., 2008; Wear, 2008; Karjalainen et al., 2009; Litniewski et al., 2009; Litniewski et al., 2011; Hoffmeister, 2011; Padilla and Wear, 2011).

For both through-transmission and pulse-echo measurements, each bone sample was scanned (in 5 mm steps) along the major axis of the bone sample (see Figure 1) so that measurements were acquired from the purely cancellous portion of the bone (that is, avoiding the cortical layer along the periphery). Thus, a frequency-dependent volume of interest was swept out with dimensions approximately [1.8 cm (at 300 kHz) – 0.8 cm (at 700 kHz)] × 3.6 cm × 1.8 cm (where the last dimension corresponds to the bone sample thickness, which is in the direction perpendicular to the plane of Figure 1). Since backscatter data were gated to exclude specular reflections at the front surfaces of calcaneus samples, backscatter volumes of interest were a few millimeters smaller in the thickness dimension than attenuation and velocity volumes of interest. Since an ultrasound beam has maximum intensity near its axis of symmetry, the ultrasound measurements were influenced more by the properties of the central regions of the bone samples than the noncentral regions. This is in contrast to the DXA and microCT measurements, which measured the bone samples essentially uniformly throughout the volumes of interest. This disparity in measurement spatial uniformity could reduce correlations between ultrasound and x-ray-based measurements, especially for highly inhomogeneous bone samples.

E. Data Analysis

Stepwise multiple regression analysis was performed to build linear models of ultrasound parameters as functions of BMD and microarchitectural features. The MATLAB (Natick, MA) function “stepwise” was used. In the case of backscatter coefficient, the data were log transformed prior to multiple regression analysis.

III. RESULTS

Figure 1 shows a slice of a microCT image of a calcaneus sample.

Table 1 shows the means, standard deviations, minima and maxima of ultrasound parameters, density, and microarchitectural parameters. The SMI, which in general can vary from 0 for plate-like architectures to 3 for rod-like architectures (Hildebrand and Ruegsegger, 1997) had a mean value of 2.34, suggesting that the bone samples tended to be more rod-like than plate-like.

Table 1.

Means, standard deviations, minima and maxima of ultrasound parameters density parameters and architectural parameters.

Mean Std.Dev. Min Max
Ultrasound parameters:
 nBUA (dB/cmMHz) 10.45 4.60 2.47 19.39
 Signal velocity (m/s) 1543 40 1476 1615
 Phase velocity (m/s) 1518 30 1472 1575
 Backscat. Coef. (1/cmSr) 0.0219 0.0166 0.0012 0.0793
Density:
 BMD (g/cc) 0.122 0.056 0.002 0.201
Architectural parameters:
 BV/TV 0.086 0.031 0.019 0.151
 BS/BV (1/mm) 22.0 3.1 16.2 30.2
 Tb.Th (micron) 126 17 99 168
 Tb.N (1/mm) 0.99 0.16 0.69 1.29
 Tb.Sp (mm) 1.00 0.17 0.74 1.41
 SMI 2.34 0.45 1.57 3.64
 Connectivity (1/mm3) 3.74 1.26 1.50 6.99
 DA 1.65 0.11 1.42 1.91
 H1 (mm) 0.90 0.19 0.62 1.34
 H2 (mm) 1.47 0.33 1.04 2.44
 H3 (mm) 1.02 0.23 0.71 1.75
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Table 2 shows Pearson’s correlation coefficients between BMD and microarchitectural parameters. Table 3 shows Pearson’s correlation coefficients between ultrasound parameters and BMD / microarchitectural parameters. The best univariate predictors of the ultrasound parameters were the indexes of bone quantity, BV/TV and BMD.

Table 2.

Pearson’s correlation coefficients between BMD and architectural parameters. n: nonsignificant, a: p < 0.05, b: p < 0.01, c: p < 0.001, d: p < 0.0001.

BMD BV/TV BS/BV Tb.Th Tb.N Tb.Sp SMI Conn DA H1 H2 H3
BMD 1.00d 0.78d −0.56b 0.32n 0.12n −0.19n −0.74d 0.44a 0.29n −0.71d −0.57b −0.64c BMD
BV/TV 1.00d −0.68d 0.49b 0.13n −0.18n −0.75d 0.41a 0.38a −0.67d −0.52b −0.63c BV/TV
BS/BV 1.00d −0.91d 0.41a −0.35n 0.73d 0.18n −0.61c 0.17n −0.04n 0.14n BS/BV
Tb.Th 1.00d −0.35n 0.30n −0.46a −0.32n 0.58c 0.00n 0.19n −0.02n Tb.Th
Tb.N 1.00d −0.98d 0.24n 0.78d −0.25n −0.65c −0.71d −0.64c Tb.N
Tb.Sp 1.00d −0.22n −0.75d 0.20n 0.69d 0.74d 0.65c Tb.Sp
SMI 1.00d −0.18n −0.45a 0.48b 0.30n 0.43a SMI
Conn 1.00d −0.17n −0.84d −0.85d −0.81d Conn
DA 1.00d −0.03n 0.29n 0.04n DA
H1 1.00d 0.94d 0.89d H1
H2 1.00d 0.87d H2
H3 1.00d H3
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Table 3.

Pearson’s correlation coefficients between ultrasound parameters and BMD and architectural parameters. n: nonsignificant, a: p < 0.05, b: p < 0.01, c: p < 0.001, d: p < 0.0001.

BMD BV/TV BS/BV Tb.Th Tb.N Tb.Sp SMI Conn DA H1 H2 H3
nBUA 0.80d 0.85d −0.60c 0.50b 0.16n −0.22n −0.68d 0.37a 0.41a −0.64c −0.48b −0.60c
Sig Velocity 0.90d 0.77d −0.47a 0.30n 0.19n −0.25n −0.61c 0.43a 0.20n −0.65c −0.55b −0.60c
PhaseVelocity 0.86d 0.81d −0.45a 0.27n 0.21n −0.26n −0.63c 0.46a 0.23n −0.65c −0.54b −0.61c
Backscat Coef 0.75d 0.84d −0.75d 0.62c −0.16n 0.14n −0.83d 0.11n 0.60c −0.47b −0.27n −0.38a
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Figure 2 shows measurements of nBUA plotted vs. BV/TV for the 29 bone samples. A linear regression fit to the data, BUA (dB/cmMHz) = −0.31 + 125.5 × BV/TV, is also shown.

2.

2.

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Measurements of nBUA plotted vs. BV/TV for the 29 bone samples. A linear regression fit to the data is also shown. The dotted lines show the linear regression fit plus or minus one standard error.

Figure 3 shows measurements of phase velocity at 500 kHz (PV) plotted vs. BV/TV for the 29 bone samples. The dotted line shows the linear fit to data from parallel-nylon-wire phantoms previously reported (Wear, 2005), suggesting that empirical dependence of phase velocity on BV/TV is similar in cancellous bone samples and parallel-nylon-wire phantoms. (Aluminum-foam phantoms also exhibit ultrasonic properties similar to cancellous bone (Le et al., 2010; Zhang et al., 2011)). Figure 3 also shows theoretical predictions of the dependence of phase velocity on BV/TV predicted using Biot and Biot-related theory for poroelastic solids.

3.

3.

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Measurements of phase velocity (PV) (at 500 kHz) plotted vs. BV/TV for the 29 bone samples. The dotted line shows the linear fit to data from parallel-nylon-wire phantoms previously reported (Wear, 2005). The other lines show theoretical forms based on Biot theory (Biot 1956a, 1956b, 1956c, 1962, 1963), which has been applied to bone by many investigators (McKelvie and Palmer 1991; Williams 1992; Hosokawa and Otani 1997, 1998; Haire and Langton 1999; Pakula and Kubik, 2002; Hughes et al. 2003; Lee et al. 2003; Mohamed et al. 2003; Cardoso et al. 2003; Fellah et al. 2004; Hosokawa, 2005; Wear et al. 2005; Lee and Yoon 2006; Hughes et al. 2007; Pakula et al. 2008; Fellah et al. 2008; Sebaa et al. 2008; Cardoso et al., 2008; Aygun et al., 2009; Cowin and Cardoso, 2010; Buchanan et al., 2011; Cardoso and Cowin, 2011). The parameters for theoretical predictions were fluid (water) density = 1 g/cm3, fluid viscosity = 0.01 g /cm·s, bulk modulus of fluid = 2.2 GPa, density of solid phase = 1.8 g/cm3, Young’s modulus of the solid phase (Es) = 13 GPa or 8.3GPa, Poisson’s ratio of solid phase = 0.32, Poisson’s ratio of trabecular frame = 0.23. The values for the exponent m, where the Young’s modulus of the skeletal frame Eb = Es (BV/TV)m, were m = 2.14 (for Es = 13 GPa) or m = 1.75 (for Es = 8.3 GPa) (Wear et al., 2005; Pakula et al, 2008).

Figure 4 shows measurements of backscatter coefficient plotted vs. BV/TV for the 29 bone samples. A power law fit to the data is also shown.

4.

4.

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Measurements of backscatter coefficient plotted vs. BV/TV for the 29 bone samples. A power law fit to the data is also shown. The dotted lines show the power law fit plus or minus one standard error.

Table 4 shows univariate and multivariate regression models that predict ultrasound parameters from BMD and microarchitectural parameters. Multiple regressions resulted in substantial increases (over univariate regressions based on BMD) in the adjusted squared correlation coefficients for nBUA and backscatter coefficient, and a moderate increase for phase velocity.

Table 4.

Linear regression models for ultrasound parameters. The third column is the square of the adjusted correlation coefficient of the regression. The fourth column is the increase in the square of the adjusted correlation coefficient compared to a univariate regression based on BMD as the independent variable.

Dependent Variable Independent Variables radj2 Δradj2
nBUA BMD 0.63
BV/TV 0.70
BMD, BV/TV 0.75 0.12
BMD, BV/TV, Tb.Th 0.76 0.13
BMD, BV/TV, Tb.Th, BS/BV 0.82 0.19
BMD, BV/TV, Tb.Th, BS/BV, Tb.N 0.83 0.20
Phase Velocity BMD 0.73
BV/TV 0.64
BMD, BV/TV 0.77 0.04
BMD, BV/TV, BS/BV 0.79 0.06
Signal Velocity BMD 0.81
BV/TV 0.59
BMD, BV/TV, BS/BV, Tb.Th 0.84 0.03
Backscatter Coef. BMD 0.54
BV/TV 0.69
BMD, BV/TV, Tb.Th 0.73 0.19
BV/TV, Tb.Th 0.74
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IV. DISCUSSION

Regarding the statistical aspects of the dependencies of nBUA, phase velocity, and backscatter coefficient on BMD and microarchitecture in human calcaneus, the regression analysis presented in this paper is for the most part in agreement with two previous reports (Nicholson et al., 2001; Chaffai et al., 2002). As with previous investigations with nBUA and phase velocity (Nicholson et al., 2001) or nBUA, phase velocity and backscatter coefficient (Chaffai et al., 2002), the best univariate predictors of the ultrasound parameters were the indexes of bone quantity, BMD and BV/TV. The best univariate models for nBUA, phase velocity, and backscatter coefficient yielded squared correlation coefficients of 0.69 – 0.73, a little lower on average than values reported by Nicholson et al. (2001), 0.74, and Chaffai et al. (2002), 0.71 – 0.81. Multiple regression models for attenuation, phase velocity and backscatter raised squared adjusted correlation coefficients to 0.74 – 0.83, consistent with values reported by Nicholson et al. (2001), 0.82, and Chaffai et al. (2002), 0.79 – 0.81.

Table 5 shows univariate correlation coefficients between ultrasound parameters and indexes of bone quantity in human calcaneus in vitro for the present study and previous studies by Nicholson et al. (2001) and Chaffai et al. (2002). The studies show moderate agreement. The correlation coefficients from Chaffai et al. (2002) tended to be higher than those for the present study, especially for phase velocity vs. BV/TV, backscatter coefficient vs. BV/TV, and backscatter coefficient vs. BMD. However, as shown in Table 5, the correlation coefficients from Chaffai et al. (2002) in all cases were within or near (±0.01) the high end of the 95% confidence intervals for the correlation coefficients from the present study. Moreover, it is possible that the widths of the 95% confidence intervals for correlation coefficients for Chaffai et al. were comparable to those for the present study since the numbers of samples for the two studies were similar (25 vs. 29). If so, this would imply overlap in 95% confidence intervals for the two studies. However, if differences in correlation coefficients between the two studies are meaningful, then there are some potential contributing factors that might help explain this. First, there may have been biological differences in the populations studied, as evidenced by the differences in Tb.Th: 72 ± 18 μm (Chaffai et al.) vs. 127 ± 17 μm (present study). Second, Chaffai et al. used sample volumes that were thinner in the ultrasound propagation direction (approximately 1 cm vs. approximately 1.8 cm for attenuation and velocity—slightly smaller in both studies for backscatter since gating was performed to exclude specular echoes) perhaps resulting in greater intra-sample homogeneity. Third, Chaffai et al. performed microCT analysis on 7-mm-diameter-cylindrical cores rather than 1.6 cm × 3.6 cm × 1.6 cm rectangular-shaped volumes the present study. Such small diameter samples may have been required for the European Synchrotron Radiation Facility (ESRF) utilized by Chaffai et al., which had a higher spatial resolution of 10 μm than the spatial resolution of 17.2 μm in the present study). Fourth, Chaffai et al. used a different frequency band of analysis (200 kHz – 600 kHz) than the one used in the present study (300 kHz – 700 kHz).

Table 5.

Univariate correlation coefficients between ultrasound parameters and indexes of bone quantity in human calcaneus in vitro for three studies: 1. Nicholson et al. (2001), 2. Chaffai et al. (2002), and 3. the present study. 95% confidence intervals for the present study are shown in parentheses.

nBUA vs. BV/TV 0.861, 0.882, 0.85 (0.69 – 0.93)3
nBUA vs. BMD - 0.842, 0.80 (0.61 – 0.91)3
phase velocity vs. BV/TV 0.861, 0.902, 0.81 (0.62 – 0.91)3
phase velocity vs. BMD - 0.902, 0.86 (0.71 – 0.93)3
signal velocity vs. BV/TV 0.881, - 0.77 (0.55 – 0.89)3
signal velocity vs. BMD - - 0.90 (0.80 – 0.95)3
backscatter coefficient vs. BV/TV - 0.912, 0.84 (0.68 – 0.92)3
backscatter coefficient vs. BMD - 0.892, 0.75 (0.52 – 0.88)3
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In the present study, the square of the correlation coefficient between signal velocity and BMD (r2 = 0.81) was higher than the correlation between phase velocity and BMD (r2 = 0.74) (see Table 5). Haïat et al., (2005) reported similar results for human femur (r2 = 0.82 for signal velocity and r2 = 0.67 for phase velocity).

The statistical aspects of the dependencies of nBUA, phase velocity, and backscatter coefficient on BMD and microarchitecture in human calcaneus measured in this paper may be compared with results by others not only in human calcaneus but also in tibia and femur as shown in Table 6 and Figure 5 (Nicholson et al., 1998;Trebacz and Natali, 1999;Nicholson et al., 2001;Chaffai et al., 2002;Hakulinen et al., 2006;Padilla et al., 2008;Karjalainen et al., 2009). The average correlation coefficients for all three ultrasound parameters are relatively high, near 0.8, for the indexes of bone quantity (BMD and BV/TV) and lower for the remaining parameters. However, the relatively large ranges of values reported in different studies suggest that considerable uncertainty remains regarding the correlation coefficients between ultrasound parameters and microarchitectural features. Variances among different studies are probably due to a combination of differences in skeletal sites, sample preparation, ultrasound measurement methodology, microCT hardware and microarchitectural feature estimation algorithm. A recent report addresses the effect of microCT image resolution (Isaksson et al., 2011).

Table 6.

Means, standard deviations and numbers of reported values for correlation coefficients between ultrasound parameters, BMD, and microarchitectural features from the present paper and seven other papers (Nicholson et al., 1998;Trebacz and Natali, 1999;Nicholson et al., 2001;Chaffai et al., 2002;Hakulinen et al., 2006;Padilla et al., 2008;Karjalainen et al., 2009).

Means BMD BV/TV BS/BV Tb.Th Tb.N Tb.Sp DA SMI
Attenuation 0.83 0.83 −0.68 0.63 0.59 −0.55 0.30 −0.74
Velocity 0.85 0.80 −0.61 0.53 0.61 −0.57 0.12 −0.69
Backscatter 0.75 0.78 −0.69 0.58 0.41 −0.47 0.38 −0.69
Std. Dev.s
Attenuation 0.04 0.12 0.11 0.16 0.25 0.24 0.13 0.08
Velocity 0.09 0.15 0.18 0.28 0.25 0.23 0.30 0.11
Backscatter 0.14 0.11 0.16 0.18 0.50 0.37 0.26 0.20
n
Attenuation 5 6 4 6 5 5 3 2
Velocity 5 6 4 6 5 5 3 2
Backscatter 3 5 4 5 3 5 3 2
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5.

5.

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Means for absolute values of correlation coefficients for ultrasound parameters versus BMD and microarchitectural features from the present study and seven others (Nicholson et al., 1998;Trebacz and Natali, 1999;Nicholson et al., 2001;Chaffai et al., 2002;Hakulinen et al., 2006;Padilla et al., 2008;Karjalainen et al., 2009). Error bars denote standard deviations.

CONCLUSION

Ultrasound parameters (attenuation, phase velocity, and backscatter), bone mineral density (BMD), and microarchitectural features were measured on 29 human cancellous calcaneus samples in vitro. Regression analysis was performed to predict ultrasound parameters from BMD and microarchitectural features. The best univariate predictors of the ultrasound parameters were the indexes of bone quantity: BMD and bone volume fraction (BV/TV). Therefore, attenuation, phase velocity, and backscatter coefficient are primarily determined by bone quantity, but multiple regression models based on bone quantity plus microarchitectural features achieve slightly better predictive performance than models based on bone quantity alone.

ACKNOWLEDGEMENTS

The authors are grateful to 1) the FDA Office of Women’s Health for funding, 2) Dr. James Reynolds and Angela Stuber, NIH Clinical Center, who helped with DXA measurements, and 3) Dr. Andres Laib, Scanco Medical AG, Bruttisellen, Switzerland for producing a microCT image. The mention of commercial products, their sources, or their use in connection with material reported herein is not to be construed as either an actual or implied endorsement of such products by the Department of Health and Human Services. Certain equipment, instruments or materials are identified in this paper to adequately specify the experimental details. Such identification does not imply recommendation by the National Institute of Standards and Technology, nor does it imply the materials are necessarily the best available for the purpose.

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