Relationships among ultrasonic and mechanical properties of cancellous bone in human calcaneus in vitro.

Abstract

Clinical bone sonometers applied at the calcaneus measure broadband ultrasound attenuation and speed of sound. However, the relation of ultrasound measurements to bone strength is not well-characterized. Addressing this issue, we assessed the extent to which ultrasonic measurements convey in vitro mechanical properties in 25 human calcaneal cancellous bone specimens (approximately 2 × 4 × 2 cm). Normalized broadband ultrasound attenuation, speed of sound, and broadband ultrasound backscatter were measured with 500 kHz transducers. To assess mechanical properties, non-linear finite element analysis, based on micro-computed tomography images (34-micron cubic voxel), was used to estimate apparent elastic modulus, overall specimen stiffness, and apparent yield stress, with models typically having approximately 25–30 million elements. We found that ultrasound parameters were correlated with mechanical properties with R=0.70–0.82 (p < 0.001). Multiple regression analysis indicated that ultrasound measurements provide additional information regarding mechanical properties beyond that provided by bone quantity alone (p ≤ 0.05). Adding ultrasound variables to linear regression models based on bone quantity improved adjusted squared correlation coefficients from 0.65 to 0.77 (stiffness), 0.76 to 0.81 (apparent modulus), and 0.67 to 0.73 (yield stress). These results indicate that ultrasound can provide complementary (to bone quantity) information regarding mechanical behavior of cancellous bone.

1. Introduction

Quantitative ultrasound (QUS) is a low-cost, portable, non-ionizing alternative to dual energy x-ray absorptiometry (DXA) [1–4]. An official position paper by the International Society for Clinical Densitometry (ISCD) states that QUS at the calcaneus can “predict fragility fracture in postmenopausal women (hip, vertebral and global fracture risk) and men over the age of 65 (hip and all non-vertebral fractures), independently of central DXA bone mineral density (BMD)” [5] A recommendation statement from the U.S. Preventive Services Task Force states that QUS at the calcaneus “predicts fractures of the femoral neck, hip, and spine as effectively as DXA” [6].

Despite the comparable effectiveness of the two modalities, the ISCD position paper also states that “Discordant results between heel QUS and central DXA are not infrequent and are not necessarily an indication of methodological error” [5]. (In this reference, “central DXA” refers to measurements at the spine and femur). One source of discordance is that QUS and DXA are performed at different skeletal sites. Another source of discordance is differences in the physics of ultrasound and x-rays. Although both modalities are highly sensitive to the quantity of bone intercepted by the beam, they may exhibit some disparity because of differences in the mechanisms underlying their interactions with bone.

In order to enhance diagnostic interpretation of calcaneal QUS measurements, there is motivation for investigating fundamental determinants of QUS measurements besides the most obvious one—bone quantity. At the richly trabecular calcaneus region, the mechanical properties associated with the ultrasound measurement depend primarily on bone quantity, trabecular microarchitecture, and trabecular-tissue material properties.

Most current clinical calcaneal bone sonometers measure two parameters in through-transmission through the heel: broadband ultrasonic attenuation (BUA) and speed of sound (SOS). Many studies have confirmed that these two parameters are good indicators of both bone mineral density (BMD) and fracture risk [5, 6]. One investigation found high correlations (R = 0.84 – 0.88) between normalized BUA (nBUA) and mechanical properties of human calcaneus [7]. To the best of the authors’ knowledge, no other studies have been performed to relate QUS parameters to mechanical properties of human calcaneus. Such studies are important in order to corroborate the earlier finding by Langton et al. and also to assess the correlations of mechanical properties with other QUS parameters, including SOS, broadband ultrasound backscatter (BUB), and dispersion (i.e., the rate of change of phase velocity with frequency). BUB is not currently used clinically, but many studies suggest its feasibility and utility [8–11]. In addition, investigation into the relationships between QUS parameters and mechanical properties can provide insight into mechanisms underlying the interaction between ultrasound and cancellous bone, which could help inform future system design as bone sonometry technology evolves.

The first goal of this work was to measure how well ultrasound measurements predict mechanical properties of human calcaneus samples. The second goal was to evaluate how well ultrasound measurements in combination with bone quantity predict mechanical properties of human calcaneus samples, compared with predictability performance based on bone quantity alone.

2. Materials and methods

Ultrasound and mechanical properties were measured on 25 defatted human calcaneus samples (age and gender unknown) so that relationships between the two types of physical properties could be elucidated. Ultrasound properties were measured in water tank experiments involving through-transmission and pulse-echo methods. Mechanical properties were estimated using finite element analysis (FEA). Micro computed tomography (micro-CT) was performed to generate three-dimensional reconstructions of trabecular bone structure to be used as inputs to FEA. Micro-CT also provided estimates of bone volume fraction (BV/TV), which is a measure of bone quantity, to be used in multiple regression analysis to investigate whether ultrasound measurements provide additional information for the prediction of mechanical properties beyond that provided by bone quantity alone.

2.1. Bone samples

The sample preparation procedure has been described previously [12]. Defatting, which has been reported to have a small effect on ultrasound measurements [7, 13–16], was accomplished with a trichloro-ethylene solution. The lateral cortical layers were removed, leaving two parallel surfaces with direct access to trabecular bone. Calcaneal cortical layers are thin (a few mm thick) and have been reported to have a small effect (15%) on measurements of broadband ultrasound attenuation [17]. 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 the ultrasound measurements and all micro-CT analyses. The mean sample thickness was 1.8 cm (standard deviation = 0.2 cm).

Figure 1.

Calcaneus sample. The circles represent ultrasound beam cross-sections for repeated measurements as the ultrasound transducer was sequentially repositioned. The ultrasound measurements from a series of 4–8 locations were averaged in order to approximate the rectangular volume used for micro-CT. After ultrasound measurements, the rectangular volume was cut out for micro-CT analysis.

2.2. Ultrasound Measurements

The ultrasound measurement methods have been reported previously [12]. Bone samples were interrogated in a water tank by ultrasound propagating in the mediolateral (or lateromedial) direction, as is the case with commercial bone sonometers. A Panametrics (Waltham, MA) 5800 pulser/receiver and Panametrics V301 broadband circular transducers (diameter = 2.54 cm, focal length = 3.81 cm, and center frequency = 500 kHz) were used. 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.

Normalized broadband ultrasonic attenuation (nBUA), speed of sound (SOS), and dispersion were measured using a through-transmission method [12]. Normalized BUA was computed as the slope of a least-squares linear regression of attenuation coefficient (dB/cm) vs. frequency [7] from 300 to 700 kHz. This frequency range is typical for clinical bone sonometers. As is common in clinical and investigational bone sonometry, the parameter chosen for SOS was signal velocity rather than phase or group velocity. Relationships among various velocity measures have been described previously [12, 18]. Signal velocity was measured using the third zero crossing in advance of the pulse envelope maximum to mark time-of-arrival, which was near the leading edge of the pulse.

Four to eight ultrasound measurements were performed on each calcaneus sample by sequentially repositioning the ultrasound transducer between consecutive measurements, as shown in Figure 1. Results from all 4–8 measurements on a sample were averaged in order to fully represent a volume that would approximate the rectangular-shaped analysis volume used for micro-CT analysis.

Dispersion was measured by taking the slope of a linear regression to phase velocity vs. frequency from 300 to 700 kHz. Although dispersion is generally positive in soft tissues [19], it is usually negative in cancellous bone [20–24]. Negative dispersion may be due to multiple scattering [25–27] or interference between fast and slow waves that propagate in porous media [28–36].

Backscatter coefficients were measured using a reference phantom method [37, 38]. Backscatter coefficient vs. frequency data were least-squares fit to a power law over the range from 300 kHz to 700 kHz. The midband (500 kHz) value of the power law fit was used to describe broadband ultrasound backscatter (BUB). One important feature of the backscatter coefficient is that it is a fundamental material property of the scattering target (in this case, bone) and is independent of the measurement system, which is why it is a preferred index of scattering in biomedical applications [39]. Other indexes of scattering, such as apparent integrated backscatter (AIB), are useful but depend not only on the scattering properties of the target but also transducer geometry, diffraction effects, and attenuation effects.

Feasibility and utility of backscatter has been demonstrated in clinical trials at the calcaneus, in which the backscatter parameters were relative (i.e., not compensated for attenuation) backscatter coefficient [8], BUB [9], average backscatter coefficient [40], and AIB [10]. Clinical measures of backscatter are usually not compensated for unknown transmission losses at the soft tissue / bone interface [8–10, 40]. Backscatter is sensitive to trabecular thickness [41–46], collagen and mineral content [47], mechanical properties [48, 49], bone mineral density [46, 50], and apparent density [51–54] in human cancellous bone. It is possible to compensate backscatter measurements for the presence of the cortical shell [55].

2.3. Micro-CT

Micro Computed Tomography (Scanco μCT 100, Scanco Medical, Basserdorf, Switzerland) was used to obtain three-dimensional (3D) trabecular microstructure of the calcaneus specimens. Figure 2 shows a reconstructed micro-CT image of a rectangular volume from a calcaneus sample. After the ultrasound measurements had been performed, cancellous bone samples were cut to approximately 2.0 cm × 4.0 cm × 1.8 cm and imaged at an isotropic voxel size of 17.2 μm (nominal resolution). (Specimens were not cut along the thickness dimension, which was maintained at approximately 1.8 cm.) An interior volume, approximately 1.8 cm × 3.6 cm × 1.6 cm was used 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 [56]. Trabecular microstructure such as bone volume fraction (BV/TV), trabecular thickness (Tb.Th), trabecular spacing (Tb.Sp), trabecular number (Tb.N), connectivity density (Conn.D.), structure model index (SMI), and degree of anisotropy (DA) were quantified using previously published methods [57–58].

Figure 2.

Micro-CT reconstructions from calcaneus specimens. The BV/TV values are 0.074 (left) and 0.060 (right).

2.4. Finite element analysis

Finite element analysis (FEA) based on micro computed tomography (micro-CT) reconstructions is now established as an effective way to assess mechanical properties of trabecular bone samples [59–60]. FEA can be linear or nonlinear. Linear FEA can provide estimates of stiffness and apparent elastic modulus, while nonlinear FEA can also provide estimates of yield stress. Elastic modulus has been reported to be well correlated with strength over a range of bone densities [61–63]. However, yield stress may be a superior indicator of strength since failure behavior generally involves nonlinear phenomena such as local material yielding and geometrically large deformations [59].

The FEA simulations [64] employed a finite plasticity material model for trabecular bone [65, 66]. This involved a rate independent elasto-plasticity model [67, 68], previously proposed for modeling solids with elastic-plastic type stress-strain behavior at the macroscopic scale, but applied here at the level of individual trabeculae. The model included linear, isotropic hardening. A rate-type constitutive law was used to define kinematic hardening. Tension-compression asymmetry in trabecular tissue yield strength was incorporated using pseudo-kinematic hardening.

Using previously described methods, [59], the FEA simulations used eight-noded brick “voxel” (cube-shaped) elements and were performed at a down-sampled resolution of 34 μm. (A comparison on a subset of 11 calcaneus samples for 34 vs. 17 μm resolution confirmed a high level of agreement (always within 3%) between the two estimates of mechanical parameters, justifying use of the lower resolution.) In brief, all bone elements were assigned the same homogeneous and isotropic tissue material properties: elastic modulus 18GPa and Poisson’s ratio of 0.3 tensile yield strain of 0.33% and compressive yield strain of 0.81% [59, 64]. Both material and geometric (large deformation) non-linearities were allowed. Displacement-type boundary conditions were used to apply 1% apparent-level compressive strain. Models contained 7 to 44 million elements and were solved using a highly scalable, implicit parallel finite-element framework-Olympus [69] running on a Dell Linux Cluster supercomputer (Stampede, Texas Advanced Computing Center).

The FEA-loading direction was the long axis of the samples. However, it is understood that loading patterns for calcaneus in vivo are complex and not as unidirectional as, say, vertebrae. Outcomes included overall stiffness, defined as the ratio of the reaction force to the applied displacement from the linear response; apparent modulus, as the corresponding modulus for the whole specimen; apparent yield stress, defined using the 0.2% offset method; and the corresponding apparent yield strain.

2.5. Statistical Analysis

A variety of statistical tests were used. We performed univariate least squares regressions with BV/TV and each of the four ultrasound properties (nBUA, SOS, BUB, and dispersion) as independent variables and each of the three mechanical properties (stiffness, apparent modulus, and yield stress) as dependent variables (for a total of 3 × 5 = 15 regressions).

We also compared how well bone quantity in combination with ultrasound measurements predicted mechanical properties. For those comparisons, multiple regressions were performed in which the dependent variable was a mechanical property and the independent variables were BV/TV and each one of the 2⁴ = 16 possible combinations of the four ultrasound measurements (nBUA, SOS, BUB, dispersion). This process was performed for each of the three mechanical properties as dependent variables (for a total of 3 × 16 = 48 regressions).

The additive value of each ultrasound parameter (nBUA, SOS, BUB, dispersion) for assessing mechanical properties of calcaneus samples (beyond that provided by BV/TV) was assessed by the p-value for that parameter in the mulitple regression (which included BV/TV as another independent variable). Goodness of fit of multiple regressions was measured by the adjusted coefficient of determination, R_a, which is related to the correlation coefficient, R, by R_a² = 1 – (1 – R²)(n – 1) / (n – m – 1) where n = total number of data points and m = number of independent variables in regression model [70]. This approach is similar to that taken by Chaffai et al. in multiple regression models to predict ultrasound parameters (nBUA, SOS, and BUB) from BMD and histomorphometric parameters [41]. Another statistical parameter that has been used to assess goodness of fit for multiple regressions is the Mallows C_p statistic [70, 71], which is closely related to R_a [72]. In all analyses, p<0.05 was taken as the level of statistical significance, and no account was made in the assumed level of statistical significance for performing multiple comparisons. Ninety-five percent confidence intervals for correlation coefficients were computed by assuming that the transformed variable z = log_e[(1+R) / (1-R)]/2 was approximately normally distributed [73].

3. Results

Table 1 shows means and standard deviations of morphometric properties of the 25 calcaneus samples. These values are similar to those reported by Ulrich et al. for human calcaneus [74].

Table 1.

Morphometric properties of 25 human calcaneus specimens.

Parameter	Symbol	Mean ± Standard Deviation
Bone Volume Fraction	BV/TV	0.092 ± 0.022
Bone Surface Fraction (1/mm)	BS/BV	21.7 ± 2.7
Trabecular Thickness (μm)	Tb.Th	127 ± 16
Trabecular Number (1/mm)	Tb.N	0.98 ± 0.15
Trabecular Spacing (mm)	Tb.Sp	1.01 ± 0.17
Structural Model Index	SMI	1.60 ± 0.32
Connectivity Density	Conn.D	3.74 ± 1.24
Degree of Anisotropy	DA	1.64 ± 0.11

Figure 3 shows FEA predictions of failed bone tissue in compression (blue) and tension (red) for the cancellous bone samples, with bone volume fractions (BV/TV) shown below each sample. The images show the considerable heterogeneity of human calcaneus and a variety of failure locations. Figure 4 shows scatter plots and least-squares regression linear fits for ultrasound measurements versus mechanical properties in human cancellous bone samples. Table 2 shows correlation coefficients (R) and 95% confidence intervals. The ultrasound parameters—particularly nBUA, SOS, and BUB—are moderately correlated with mechanical properties of cancellous bone. nBUA, SOS, and BUB were all positively correlated with mechanical properties and BV/TV. However, dispersion was negatively correlated with mechanical properties and BV/TV.

Figure 3.

FEA of bone samples. The images show predictions of failed tissue in compression (light blue) and tension (red) for all 25 cancellous bone samples. The bone volume fraction BV/TV is shown below each sample.

Figure 4.

Scatter plots of the measured ultrasound parameters vs. the FEA-derived mechanical properties in 25 human cancellous calcaneus samples.

Table 2.

Correlation coefficients between ultrasonic and mechanical properties of human cancellous bone.

Ultrasound Parameter	Correlation Coefficient (R)
	BV/TV	Stiffness	Apparent Modulus	Yield Stress
nBUA	0.85a (0.68–0.93)	0.77a (0.54–0.90)	0.78a (0.55–0.90)	0.77a (0.52–0.89)
SOS	0.80a (0.59–0.91)	0.78a (0.55–0.90)	0.82a (0.62–0.92)	0.77a (0.54–0.90)
BUB	0.64b (0.32–0.83)	0.76a (0.52–0.89)	0.70b (0.41–0.86)	0.70a (0.42–0.86)
Dispersion	−0.53c (−0.77–−0.16)	−0.52c (−0.77–−0.15)	−0.60c (−0.81–−0.26)	−0.56c (−0.77–−0.15)

Values in parentheses indicate 95% confidence intervals.

^a:p ≤ 0.0001.

^b:p ≤ 0.001.

^c:p ≤ 0.01.

Table 3 shows results for multivariate regression models to predict mechanical properties from linear combinations of bone quantity (BV/TV) and ultrasound measurements. As expected, most (65 – 76%) of the variations in mechanical properties could be explained by variations in bone quantity (BV/TV) (p < 0.0001). The p values for added ultrasound variables suggest that BUB and SOS provided more additional information to BV/TV than nBUA and dispersion. The fact that nBUA provided less additional information to BV/TV than either BUB or SOS could partially result from nBUA exhibiting a higher correlation (than either BUB or SOS) to BV/TV (which is supported by Table 2) and therefore was more redundant in a statistical sense. Adjusted R² values suggest that the additional variance in mechanical properties explained by the combination of bone volume fraction plus ultrasound parameters beyond that explained by only bone volume fraction was ΔR_adj² = 12% (stiffness), 5% (apparent modulus), and 6% (yield stress).

Table 3.

Values of adjusted R² for multivariate regression models to predict mechanical properties from linear combinations of bone quantity (BV/TV) and ultrasound measurements.

Input Multiple Regression Variable(s)	Output Regression Variable
	Stiffness		Apparent Modulus		Yield Stress
	Radj2	p value for ultrasound variable	Radj2	p value for ultrasound variable	Radj2	p value for ultrasound variable
BV/TV	0.65a		0.76a		0.67a
BV/TV, nBUA	0.66a	0.23	0.75a	0.53	0.67a	0.34
BV/TV, SOS	0.68a	0.07e	0.79a	0.05d	0.70a	0.12
BV/TV, BUB	0.76a	0.01c	0.78a	0.08e	0.71a	0.05d
BV/TV, dispersion	0.65a	0.37	0.78a	0.11	0.68a	0.22
BV/TV, SOS, BUB	0.77a		0.81a		0.73a

The p values for the added ultrasound variables in multiple regressions are shown.

^a:p ≤ 0.0001.

^b:p ≤ 0.001.

^c:p ≤ 0.01.

^d:p ≤ 0.05.

^e:p ≤ 0.10.

4. Discussion

Quantitative ultrasound can be approximately as effective as DXA-measured BMD for assessing risk of fracture [6, 75]. Specifically, in a landmark prospective hip-fracture study involving 5662 elderly women [75], BUA and SOS in calcaneus predicted the risk of hip fracture as well as did DXA, and after controlling for the femoral neck BMD, the ultrasonographic variables remained predictive of hip fracture. Other clinical studies have reported similar findings [76, 77]. Moayyeri et al. reported a meta-analysis involving 21 studies and follow-up of 279,124 person-years that indicated that heel ultrasound adjusted for hip BMD showed a significant and independent association with fracture risk [78]. Our finding that nBUA and SOS correlated well (0.64 < R² < 0.72) with bone quantity (BV/TV) partly explains ultrasound’s success in assessing fracture risk since bone strength and fracture risk are clearly related to bone mass and BMD. In addition, our finding that combining ultrasound parameters with bone quantity had greater associations with mechanical properties than did univariate models based on bone quantity alone suggests that these ultrasound measurements can indeed detect some aspect of mechanically-relevant bone quality, presumably some aspect of the microarchitecture since the finite element models did not reflect any variations in material quality. Similarly, Hans et al. [70] and Moayyeri et al., [77] reported that adding heel ultrasound measurements to hip BMD improved hip [70] and total [77] fracture risk assessment in a clinical trials. However, unlike these studies, our study featured site-matched measurements. Also consistent with our findings, Chaffai et al. showed that ultrasound measurements at calcaneus carry some information regarding microarchitecture beyond that contained in BMD [41]. Taken together, these findings provide insight into why ultrasonographic variables have been associated with risk of hip fracture independent of hip BMD. The present study helps to elucidate mechanisms underlying clinical findings.

Comparing our results with the literature, Table 4 shows correlation coefficients between ultrasound and mechanical properties for three studies in human cancellous bone at frequencies near 500 kHz. The correlation coefficients in the present study for nBUA were much closer to values reported by Langton et al. in calcaneus (n=20) [17] than those reported by Hakulinen et al. in medial condyle of femur (n=10) and medial plateau of tibia (n=10) [49]. However, at four higher frequencies, ranging from 1 – 5 MHz, Hakulinen et al. found higher correlations between nBUA and Young’s modulus (0.29 – 0.56) and ultimate strength (0.31 – 0.71) but still not as high as the correlations between nBUA and mechanical properties reported by Langton et al. or in the present investigation. The correlations reported in the present study for SOS and BUB near 500 kHz with mechanical properties in calcaneus tended to be higher than those reported by Hakulinen et al. in tibia and femur. However, as with nBUA, the correlations reported by Hakulinen et al. at the four higher frequency ranges tended to be higher for SOS (0.58 – 0.82) and BUB (0.55 – 0.74) and were sometimes comparable to correlations reported in the present study. Karjalainen et al., found similar correlations between BUB and ultimate strength in the higher frequency ranges (0.46 – 0.76) for human proximal tibia (n = 10) and distal femur (n = 10) [48]. (Karjalainen et al. did not report measurements near 500 kHz and did not report measurements of nBUA, SOS, or dispersion.)

Table 4.

Correlation coefficients between ultrasound and mechanical properties for three studies in human cancellous bone.

	Elasticity				Strength
Study	[7]	[49]	This paper		[7]	[49]	This paper
Site	Calcaneus	Femur & Tibia	Calcaneus		Calcaneus	Femur & Tibia	Calcaneus
n	20	20	25		20	20	25
Frequency Range (kHz)	200–600	300–600	300–700		200–600	300–600	300–700
Mechanical Parameter	Young’s Modulus	Young’s Modulus	Apparent Modulus	Stiffness	Strength	Ultimate Strength	Yield Stress
nBUA (95% CI)	0.88	0.05	0.78 (0.55–0.90)	0.77 (0.54–0.90)	0.84	0.03	0.77 (0.52–0.89)
SOS (95% CI)		0.57	0.82 (0.62–0.92)	0.78 (0.55–0.90)		0.60	0.77 (0.54–0.90)
BUB (95% CI)		0.54	0.70 (0.41–0.86)	0.76 (0.52–0.89)		0.71	0.70 (0.54–0.90
Dispersion (95% CI)			−0.60 (−0.81–−0.26)	−0.52 (−0.77–−0.15)			−0.56 (−0.77–−0.15)

The table shows results obtained in a range of frequencies relevant for clinical bone sonometers. Note that, at four higher frequency ranges, within 1 – 5 MHz, Hakulinen et al. found higher correlations between nBUA and Young’s modulus (0.29 – 0.56) and ultimate strength (0.31 – 0.71).

Differences in experimental methods may partially explain disparities in correlation coefficients between ultrasound and mechanical properties. The present study and the study by Langton et al. measured calcaneus in the mediolateral orientation, with ultrasound propagation perpendicular to the predominant trabecular orientation. In contrast, the studies by Hakulinen et al. and Karjalanen et al. measured tibia and femur, and the angle between the ultrasound propagation and the predominant trabecular orientation was unclear. Another potential source of disparity among the studies is the degree of co-registration of tissue volumes for ultrasound and mechanical measurements, which remains a challenging aspect for these kinds of investigations (as discussed below). Correlations would be expected to decline as co-registration of ultrasound and mechanical measurement volumes diminishes.

The micro-CT-based FEA methodology used in this study has been well validated for predicting strength of trabecular bone cores taken from multiple anatomic sites [79] but nonetheless has some limitations [59]. First, since the models assumed homogeneity of the bone tissue within and across specimens they did not consider variance in apparent-level mechanical properties due to any variance in tissue-level material properties, either within or among bone samples [79]. Therefore, the present results do not reflect any such real variations. Second, our specimens were quite heterogeneous microstructurally, which tended to focus failure locally in those regions of lowest bone volume fraction. Such effects likely diminish the role of BV/TV of the entire specimen on its overall mechanical behavior, but this may actually be representative of real in vivo behavior as such regions of low bone volume fraction do exist in highly osteoporotic individuals. And as noted above, we did not assess femoral or vertebral bone in this study. However, ultrasound is used only at the calcaneus and thus our measurements reflect assessment of the bone that is most relevant for this technology.

One limitation of this study specific to the use of ultrasound is that the ultrasound beam did not interrogate bone samples uniformly throughout the volume of interest. The ultrasound beam intensity at the focal plane for a focused circular transducer is not uniform but rather is distributed according to an Airy pattern, which is maximum near the axis of the transmitter and decreases with distance from the axis. A further complication is that the beam width was frequency dependent. At the low end of the transducer band, 300 kHz, the diameter of the central lobe, 2.44λz/d [80], was 18 mm, which was commensurate with the width of the micro-CT reconstruction volume. At the high end of the transducer band, 700 kHz, the diameter of the central lobe was 8 mm. Therefore, the ultrasound measurements were always weighted toward the center region of the sample, with this effect becoming more pronounced as frequency increased from 300 to 700 kHz. The effect of this spatial weighting of ultrasound measurements could have been to decrease correlations with mechanical properties that had different spatial weighting throughout the volume of interest. In addition, 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 nBUA, SOS, BV/TV, and FEA volumes of interest.

This study involved purely cancellous samples and therefore did not consider the role of cortical bone. It is common practice to remove or avoid cortical layers in bone samples in order to elucidate properties of cancellous bone, including ultrasonic [3, 7, 11–17, 22–24, 27–29, 38, 42] and mechanical [59, 60, 62–64, 79] properties.

The sample size for this study (n = 25) was sufficient to establish that ultrasound parameters provide important additive information to bone quantity. Further study involving larger sample sizes is warranted in order to better quantify the magnitude of this additive information.

5. Conclusion

Correlations between ultrasound parameters and mechanical properties of human cancellous calcaneus were investigated, with nBUA, SOS, and BUB showing high correlations and dispersion showing a moderate correlation. Ultrasound parameters provided information beyond that provided by bone quantity alone for the prediction of mechanical properties of cancellous bone.