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Prediction of mechanical properties of the human calcaneus by broadband ultrasonic attenuation
Bone Vol. 18, No. 6 June 1996:495-503 ELSEVIER
ORIGINAL ARTICLES
Prediction of Mechanical Properties of the Human Calcaneus by Broadband Ultrasonic Attenuation C. M. L A N G T O N , 1 C. F. N J E H , 2 R. H O D G S K I N S O N , 3 a n d J. D. C U R R E Y 3 I Centre for Metabolic Bone Disease, Hull, UK 2 Health Research Institute, Sheffield Hallam University, Sheffield, UK 3 Department of Biology, University of York, York, UK
in the human calcaneus for the identification and monitoring of osteoporosis was first described by Langton et al. 13 It is widely agreed that B U A is related to both the density and structure of cancellous bone. 6't4 Evidence for this consists of both theoretical analysis of the propagation of ultrasound through an open-celled porous structure such as cancellous bone 3 and in vitro studies of cancellous bone samples. Langton et al. 14 studied cancellous cubes from equine third metacarpals exhibiting either predominantly rod-like structure or predominantly plate-like structure. A high degree of orientational anisotropy for BUA was observed for each cube. Since the density of the cube is invariant with direction, Langton et al. t4 suggested that the variation in BUA was due to orientational variations in cancellous bone structure. This was confirmed by measurement of "fabric". 8"9 Gluer et al. 7 studied cubic samples of bovine cancellous bone and defined a semiquantitative index (alignment) for the predominant trabecular orientation with respect to the direction of ultrasound propagation, varying from - 2 (perpendicular) to +2 (parallel). The difference in B U A from parallel to perpendicular propagation was commensurate with the difference in BUA reported between osteoporotic and healthy individuals, and the authors concluded that B U A depends upon bone structure. For the clinical measurement of B U A in the calcaneus, however, we are restricted to a single anatomical orientation, namely, the mediolateral direction. The purpose of this article is first to demonstrate the value of using B U A of the human calcaneus to predict compressive strength, and second to determine the dependence of B U A upon its material properties.
Broadband ultrasonic attenuation (dB MHz cm -~, nBUA) was determined for specimens from 20 human caicanei, along with apparent density, elasticity (Young's modulus), and compressive strength. The calcanei were modified to provide "whole" (only soft tissue removed), "core" (mediolateral cores corresponding to in vivo measurement region), "can" (cortical end plates removed from core), and "def" (core defatted) samples. The nBUA values for the various modifications were highly correlated. The presence of the cortical endplates creates a significant nBUA, probably due to complex phase interactions, nBUAca . was a good predictor of elasticity (R z = 75.7%) and strength (R 2 = 73.6%). Apparent density was a better predictor of the mechanical variables than nBUA, with R z values of 88.5% for elasticity and 87.6% for strength. The morphological anisotropy defined by "fabric" for the specimens was extremely uniform. The coefficient of variation in nBUA (40.5%) and compressive strength (64.4%) was significantly greater than for apparent density (23.5%) and fabric (6.7%). It is well known that a power law relationship exists between apparent density and elasticity or strength in cancellous bone. An interesting finding in this work is that there also appears to be a power law relationship between nBUA and apparent density, with an exponent of approximately 2, which, in the light of clinical implications, warrants further investigation. (Bone 18:495-503; 1996) Key Words: Architecture; BUA; Calcaneus; Cancellous bone; Density; Mechanical properties.
Methods
Introduction
Sample Preparation
Osteoporosis may be defined as the loss of bone resulting in an increased risk of fracture. The bone loss may take the form of generalized trabecular thinning or removal of entire trabeculae. We may assume therefore that the "gold standard" for bone health is the mechanical integrity of the bone. Several noninvasive measurement techniques have been developed to measure the degree of mineralisation of bone. 1,12,~8 These are assumed to be reliable surrogates for bone density and hence reliable indicators of fracture risk. The measurement of broadband ultrasonic attenuation (BUA)
The specimens were obtained post mortem from 20 cadavers (ten males and ten females) with an age range of 59 to 90 years. No pathological information on the specimens was available. The specimens were kept frozen at -20°C, until being thawed before testing. Once thawed, the specimens were thoroughly degassed under water in a vacuum desiccator prior to ultrasonic testing. The specimens were wet during all mechanical and ultrasonic measurements. The ultrasonic measurements were carried out under water at room temperature, to ensure good acoustic coupling. Detergent was added to the water to improve sample wetting. Broadband ultrasonic attenuation measurements were carried out in turn on calcaneal specimens that had four different degrees
Address for correspondence and reprints: Dr. C. M. Langton, Centre for Metabolic Bone Disease, Hull Royal Infirmary, HS Brocklehurst Building, Anlaby Rd., Hull HU3 2RW, UK. © 1996 by Elsevier Science Inc. All rights reserved.
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C.M. Langton et al. Mechanical properties of human calcaneus by BUA
of modification: only soft tissue removed (whole); cylindrical specimen produced with the cortical end plates still intact (core); end plates removed with marrow intact (can); defatted (def). Before ultrasonic testing, external soft tissue was removed. After the first ultrasonic measurements, a coring drill with an internal diameter of 21 mm was used to remove samples whose long axis was in the mediolateral direction. The central axis of the core corresponded to the central axes used by the McCue CUBAclinical and L U N A R Achilles commercial systems. The Walker Sonix UBA575 measures a lower and more posterior region of the calcaneus. After a second set of ultrasound measurements, the cortical end surfaces were removed using a diamond impregnated band saw to leave a cylinder consisting only of cancellous bone and fat that was remeasured. The final ultrasound measurements were performed after fat had been removed from the specimen, in the manner described by Brear et alfl At each stage of modification, ultrasound measurements were repeated five times and the precision calculated.
Broadband Ultrasonic Attenuation The Contact Ultrasonic Bone Analyser (CUBA) system j5 was used. A short rf pulse (nominal frequency 1 MHz) is emitted by a 13-mm-diam broadband transducer and, after passing through the sample, is received by a similar transducer at the far side. The two transducers are mounted in a calliper attached to a vernier gauge used to measure specimen thickness, and immersed in degassed water. The received ultrasonic signal is fed into a computerinterfaced digitizer unit. A fast Fourier transform (FFF) calculates the frequency spectrum of the ultrasound signal. To determine BUA, the frequency spectrum is compared with and without the sample in position, providing an attenuation vs. frequency trace. The slope of the linear regression between 0.2 and 0.6 MHz is then calculated. This provides an area density value of BUA in units o f d B MHz ~ from a defined cross-sectional area but unknown thickness. Dividing this by the sample thickness provides a volumetric density BUA parameter of units dB MHz -j cm -~, referred to as nBUA. The CUBAclinical system incorporates 19-mm-diam ultrasound transducers coupled to a subjects heel via compressible silicone pads. The CUBA system used for the current study incorporates 13-mm-diam transducers with the faces placed in direct contact with the in vitro samples. The electronics and software for the two CUBA systems are similar; the differences relate to transducer separation measurement and correction for incorporation of silicone pads.
Mechanical Testing Mechanical testing was carried out on the defatted cylinders. Young's modulus (E) and compressive strength (or) were obtained by unconfined compressive testing in an Instron 1122 testing machine. The loading direction (mediolateral) was the same as that in which the acoustic measurements were determined. The specimens were immersed in a water bath at room temperature. Differences in temperature over the range from room temperature to 38°C have only a slight effect on mechanical properties 2 and ultrasonic behavior. 4 The defatted cancellous cylinders were compressed between the end of a smooth stainless-steel loading column and the base of the water bath, which itself lay directly on a 5 kN load cell. The compliance of the loading system was measured and allowed for in the calculations. The compressive load was increased pro-
Bone Vol. 18, No. 6 June 1996:495-503 gressively over several cycles until the load-deformation curve was approximately linear. 8 The head speed was 1 mm min -~, producing a nominal strain rate of 0.0017 s-~. The strain rate incorporated, although lower than that observed in physiological practice, provides a controllable test condition and reliable data. ~ Young's modulus was defined as the maximum slope of the stress-strain curve in the most linear portion of the preyield region. Compressive strength was calculated from the first maximum load that each cube attained. (If compression testing of cancellous specimens is continued, the specimen eventually compacts, and can bear very high loads, even though it is completely destroyed.) Care was taken to load the bone to only just after the first maximum, so that the macroscopic structure was insignificantly affected.
Apparent Density We define "apparent density" as the ratio of the dehydrated, defatted tissue mass to the total specimen volume. The defatted cylinders were dried to constant weight at 60-70°C.
Fabric The morphological anisotropy of the bone was determined using a modification of the method described by Hodgskinson and Currey. 8 Briefly, after all other tests had been carried out, each cylinder was cut in half parallel to its long axis. The exposed surface was filled with black resin, polished, and subjected to computer-aided stereological analysis. The computer superimposes a 40 line array onto each image, and calculates the total number of trabecular encounters for the 40 lines and the total length of these encounters. Mean intercept length (MIL) is then calculated by dividing these two values. This procedure is repeated at 5 ° intervals over a range of 175 °. MIL is plotted as a function of angle, and an ellipse is fitted to this raw data. A single value of fabric is calculated as a function of the ratio of the lengths of the major and minor axes of the ellipse and the angular deviation of the major axis from a particular mechanical loading direction. This has a high value, about 1.5, when the trabeculae are predominantly oriented in the direction of loading, and a low one, about 0.5, when predominantly oriented normal to the direction of loading, and about 1 when it is roughly isotropic. As described later, the cylinders in this study had extremely low and invariant values of fabric. The experimental protocol is summarized in the following flow chart: Whole heel --4 Soft tissue removal from calcaneus ---) n B U A (whole) measurement ~ Core taken ~ n B U A (core) measurement --~ Cortices removed --~ n B U A (can) measurement --~ Defatted ---> n B U A (def) measurement ---> Mechanical measurements (elasticity and strength) --~ Dried --+ Apparent density measurement --* Morphometric measurement. Results A summary of the data (mean, standard deviation, and coefficient of variation) is provided in T a b l e 1, correlation coefficients between relevant properties in T a b l e 2, and regression equations on the log-transformed values of density, elasticity, and strength in Table 3. The precision (coefficient of variation, CV%) for the nBUA data for the various stages of modification is shown in Table 1. It was not possible to determine the precision of the mechanical and fabric data since only one measurement was obtained for
Bone Vol. 18, No. 6 June 1996:495-503
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Table 1. Data summary, p: apparent density (kg rn-3); E: Young's modulus (MPa); cr: compressive strength (MPa); nBUA: broadband ultrasonic attenuation (dB MHz -t cm-I) for each modification. N = 20 in all cases except fabric, where N = 19
Mean SD CV% Precision
Age
p
E
~r
76.3 9.89 13.0
262.1 61.4 23.4
35.63 23.18 65.1
0.48 0.31 64.5
each sample. Our analysis used the relationships between logtransformed values because the untransformed relationships are curvilinear and the log-transformed relationships are effectively linear. The gradient o f the regression line for each logtransformed relationship is therefore the exponent value for the particular relationship. Table 4 provides regression equations between linear nBUA values for the various stages of calcaneal specimen modification. Discussion
Mechanical Properties of Cancellous Bone Cores The values for mechanical properties and density refer to the properties of the isolated core without end plates. As usually found, 9 Young's modulus and strength are very closely related to each other with an R 2 of 92.4% (illustrated in Figure 1). Young's modulus and strength are well predicted by density. The log-transformed regression equations (Table 3) give an R 2 value of 88.5% with Young's modulus and 87.6% with strength. This is in accordance with what has frequently been found. 9'1° We were initially surprised to find the exponents for the relationships to be 3.13 for Young's modulus and 2.92 for strength. It is usual to find values not exceeding 2.4 for the exponent. 9'1° This apparently anomalous relationship is probably caused by the characteristic structure of the cancellous bone within the calcaneus: sheets connected by cross struts (Figure 2). The structure was loaded in the direction of the cross struts, and normal to the sheets. A cubic relationship is predicted by Gibson 5 for a "parallel plate structure," which may be considered to be an idealized version of the cancellous structure in the calcaneus. The fabric values have a very low variance and are consistent (p = 0.56) between male (0.685 -+ 0.045) and female subjects (0.671 - 0.045). The coefficient of variation (standard deviation × 100/mean) is 6.7%, whereas that of density is 23.4%. The fabric values have no significant correlation with the other variables. Furthermore, unlike the usual situation in cancellous bone, because the fabric values are almost invariant, adding fabric as an extra explanatory variable to the equation relating the mechanical Table 2. Correlation coefficients between mechanical and ultrasonic properties of the calcaneal samples. Note: all variables are linear, not log transformed
Density (kg m-3)
Fabric
Elasticity (MPa)
Strength (MPa)
nBUA whole
nBUA core
nBUA can
nBUA def
23.06 8.15 35.3 4.8
20.59 7.28 35.4 5,3
18.28 7.40 40.5 3.2
18.79 7.37 39.2 4.3
Fabric 0.678 0.045 6.7
properties to density hardly improves the explanatory power of the equation at all: Young' s modulus: log E = -6.10 + log E = -6.00 + Strength: log ~r = -7.46 + log cr = -7.42 +
3.13 log p, R 2 = 88.5%, 3.13 log p + 0.62 log fabric, R2 = 88.4%; 2.92 log p, R 2 = 87.6%, 2.92 log p + 0.23 log fabric, R 2 = 86.8%.
The fabric was derived from the flat surfaces exposed when the cylinders were cut in half, parallel to the long axis. Note was not taken, however, of the orientation of the cylinder, so that the plane of the cut could vary around this axis. Due to the structural symmetry of the cancellous bone within this region of the calcaneus, the lack of knowledge of the angle of cut with respect to the long axis is not considered significant, indicated by the consistency of the fabric data.
Broadband Ultrasonic Attenuation The precision for the nBUA data for the various stages of modification (Table 1) was similar in magnitude to that obtained for Table 3. Mechanical property and density regression equations. All use log-transformed values, s is the standard error of y estimate. R2 is the adjusted value accounting for the numbers of degrees of freedom. In each case, the title of the table is the y variable x variable
R2
Exponent
Intercept
s
78.3 75.6 86.0 81.7
Apparent density (y variable) 0.46 0.47 0.44 0.44
1.80 1.81 1.88 1.86
0.05 0.05 0.04 0.05
88.5 72.2 64.8 75.7 76.5
b Young's modulus (y variable) 3.13 1.47 1.44 1.36 1.42
-6.10 -0.51 -0.40 -0.22 -0.31
0.12 0.19 0.21 0.17 0.17
87.6 69.3 62.1 73.6 72.7
Strength (y variable) 2.92 1.35 1.32 1.26 1.30
-7.46 -2.22 -2.12 - 1.96 -2.02
0.12 0.18 0.20 0.17 0.17
a
nBUAwhole nBUAcore nBUAcan nBUAdef
Density nBUAwhole nBUAcore nBUAcan nBUAdef
c
Fabric Elasticity Strength nBUAwhole nBUAcore nBUAcan nBUAdef
0.005 0.96 0.92 0.89 0.87 0.94 0.92
0.008 -0.03 0.18 0.19 0.04 0.05
0.95 0.85 0.83 0.89 0.88
0.83 0.80 0.87 0.84
Density nBUAwhole nBUAcore nBUAcan nBUAdef
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C.M. Langton et al. Mechanical properties of human calcaneus by BUA
Bone Vol. 18, No. 6 June 1996:495-503
Table 4. Correlation and statistical significance between BUA values for the calcaneal specimens treated in different ways nBUAcore
nBUAcan
nBUAdef
X coefficient 1.09 -+0.07 1.02 + 0.09 0.93 _+0.08
nBUAwhole nBUAcore
neus were unity _+10%. The intercept between whole calcaneus and core was insignificant, confirming that the core effectively represents the region of calcaneus measured in vivo. The intercept between core and defatted samples was also minimal, indicating that the replacement of a viscoelastic material (fat) with a purely viscous material (water) does not significantly affect the nBUA. The whole calcaneus and the core sample had nBUA values approximately 3.5 dB MHz cm -1 above the cancellous (p = 0.03) and defatted (p = 0.07) samples, indicating that the presence of the cortical end plates creates a significant nBUA, probably due to the curved shape resulting in complex phase interactions within the propagating ultrasonic pulse.
1.03 +_0.09 0.91 _+0.09
nBUAcan
0.96 -+0.07 Intercept 0.72-+ 1.47 4.31 -+ 2.01
nBUAwhole p value nBUAcore
ns
p value nBUAcan p value
nBUAwhole nBUAcore nBUAcan
0.97
3.66 + 1.90
p - 0.03 3,57 _ 1.49
p = 0.07 3.48 - 1.83
p = 0.03
p - 0.07 0.31 _+ 1.47 ns
0.93 0.95
Mechanical and Ultrasound Correlation
The correlation coefficients relating the mechanical variables to density are only slightly higher than those relating them to the various measures of nBUA (Table 2). The correlation between log nBUA for the cancellous cores (can) and log apparent density showed the best correlation (Figure 4) with a n R 2 of 86.0%. nBUA has R 2 values of =65% to 77% for Young's modulus and of 62% to 74% for strength (nBUAcan shown in Figure 5), while density has R 2 values of 88.5% for Young's modulus and 87.6% for strength (Figure 6). However, the most relevant value to take is that for nBUAwhole because that is the nearest to the measurements that can be made in the clinical situation. The correlation R 2 values are 72.2% for Young's modulus and 69.3% for strength (Figure 7). That is to say, =70% of the variation in the mechanical properties of the cancellous cylinder can be "explained" statistically by variation in the values for nBUA determined from transducers placed against the outer cortices of the calcaneus. The relationship between nBUAcan, density, and elasticity was further investigated using multiple regression analysis. The relationship between density and elasticity has already been described in Table 3:
0.93 0.92 0.95
BUA in vivo, the improvement in positioning accuracy probably being compromised by the additional incorporation of sample length variability. The precision (CV%) for the "can" samples was significantly lower than for the "whole" and "core" samples (p = 0.0004 and p = 0.0001, respectively), indicative of the consistent sample length measurement across the fiat and parallel end faces of the "can" samples. Table 4 and Figure 3 show that the nBUA values for the specimens treated in different ways are highly correlated with each other, the lowest correlation having an r value of 0.92. The important factors are the regression x coefficients, indicating the degree of linearity and the intercept values, indicating any nBUA offset with sample modification. The regression x coefficients for all correlations between the various modifications of the calca0.2-
ill
O•
•
•
-0.2 -
Log strength (MPa)
-0.4n n
-0.6-
-0.8 -
-1
-1.2 0,6
I 0.8
I 1
I 1.2
I 1.4
I 1.6
Log elasticity (MPa)
Figure l. Relationship between compressive strength and Young's modulus.
I
I
1.8
2
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C.M. Langton et al. Mechanical properties of human calcaneus by BUA
499
does not improve the amount of variance explained for elasticity. The same is true for strength: log tr = -7.46 + 2.92 log p,
Re
= 87.6%.
log tr = -7.38 + 3.13 log p - 0.104 log nBUAcan, R 2 = 87.0%.
Figure 2. Photograph showing characteristic structure of the cancellous bone within the calcaneus.
log E = - 6 . 1 0 + 3.13 log p, R 2 = 88.5%. We can also see from Table 3 that there is a strong relationship between log elasticity and nBUAcan (R = 75.7%) and between density and nBUAcan (R = 86.0%). The regression equation using both density and nBUAcan as explanatory variables is log E = -6.19 + 3.18 log p - 0.024 log n B U A can, R e = 87.9%. As can be seen, the addition of BUA to the regression equation
The high correlation coefficient of 0.94 between nBUAcan and apparent density is in support of previous in vitro studies of the calcaneus, shown in T a b l e 5. McKelvie et al. ]7 and McCloskey et al. 16 correlated n B U A with both QCT and physical density. McKelvie et al. obtained correlation coefficients of 0.86 and 0.83 with QCT and physical density, respectively, while McCloskey et al. obtained correlation coefficients of 0.80 and 0.85 with QCT and physical density, respectively. These findings are, however, not in agreement with comparative studies of the calcaneus in vivo. BUA and density (measured by established clinical techniques) at the calcaneus showed only moderate significance. For instance, Waud et a1.19 obtained a correlation coefficient of 0.73 with area density measured by DXA, and Gluer et al. 6 obtained a correlation coefficient of 0.72 with area density measured by SXA in a population of 25 females and a correlation coefficient of only 0.58 when 8 males were added. The effect of overlying soft tissue in the in vivo situation has been shown to have minimal effect on the B U A value ~t and cannot therefore explain the disparity with in vitro studies. As a further means of analysis, the relative standard error of estimates (standard error of estimate (SEE) x 100/mean) have been compared, and are shown in Table V. The relative SEE value of 14.7% obtained is comparable to the in vivo study by Gluer et al., who considered a broad age range (20-75 years), but lower than the in vitro study by McCloskey et al., who used a similar age range (47-87) to the current study. One would expect that the relative SEE would, however, increase with age range due to the higher variability. However, in comparing previous studies, we have to note that they are not comparable in design. Gluer et al. 6 compared BUA
40
whole
iio
35
~
e
•
30
•
25
. j.--
•
o
yo oo
nBUA 20 (dB MHz cm "t) 15 10
j j
o
r e,.Qre ,o n Core regression
0 0
I 5
I 10
I 15
I 20
I 25
I 30
I 35
nBUAcan (dB MHz cm "1)
Figure 3. Relationship between nBUA of whole calcanei, and of cored samples, with that of cancellous samples with endplates removed.
500
C.M. Langton et al. Mechanical properties of human calcaneus by BUA
Bone Vol. 18, No. 6 June 1996:495-503
2.6
2.5
• •
Log density (kg m 4)
•
2.4 •
mm
2.3
2.2
2.1 0.4
I
I
I
I
I
I
0.6
0.8
1
1.2
1.4
1.6
Log nBUAcan (dB MHz cm "~) Figure 4. Relationship between apparent density and nBUA of cancellous bone samples. with SXA, both measurements considering a volume of cancellous bone of known cross-sectional area but unknown thickness, providing an area-density, whereas McCloskey et al. ]6 compared BUA (area density) with true volume-density parameters derived from physical density measurements and QCT. In the current study, we have compared nBUA with apparent density, both true volumetric parameters. 0.2
It is well known that power law relationships exist between apparent density and elasticity and between apparent density and strength. Regression of logarithmic parameters suggests that a power law relationship also exists between apparent density and nBUA. This suggests that regression of linear parameters, although providing significant R 2, is in fact describing a tangent to a nonlinear relationship that would exhibit a finite rather than
°
0"
mm
•
-0.2 "
-0.4 "
Log strength (MPa)
-0.6 "
-0.8 "
-1
-1.2 0.4
I
I
l
I
I
I
0.6
ON8
1
1.2
1.4
1.6
Log nBUAcan (dB MHz cm "1)
Figure 5. Relationship between compressive strength and nBUA of cancellous bone samples.
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C.M. Langton et al. Mechanical properties of human calcaneus by BUA
501
0.2
•
•
-0.2
-0.4 Log
strength (MPa)
-0.6
-0.8
-1.2 2.1
I
I
I
2.2
2.3
2.4
I 2.5
I 2.6
Log density (kg rn4)
Figure 6. Relationship between compressive strength and apparent density. zero intercept between, for example, nBUAcan and apparent density, illustrated in Figure 8. The existence of a power law relationship between nBUA and apparent density has important implications, first for clinical investigations, particularly when
correlating BUA with established bone densitometric techniques, and second in defining the dependence of nBUA upon material and structural parameters of cancellous bone. For example, based upon a quadratic relationship, a 2% reduction in density will
0.2
mm
-0.2
-0.4 Log
strength (MPa)
-0.6
-0.8
-1.2 0.6
I
I
I
I
0.8
1
1.2
1.4
Log nBUAwhole (dB MHz cm "1)
Figure 7. Relationship between compressive strength and nBUA of whole calcaneus.
I 1.6
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C.M. Langton et al. Mechanical properties of human calcaneus by BUA
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Table 5. Correlation coefficients and subject ages for in vivo and in vitro comparative studies between BUA and density in the calcaneus
Density Author
No./sex
Method
Age
SEE%
r
Mean
SD
Range
0.72 0.73
45.6 51
10
20-75 35-85
0.86 0.83 0.80 0.85
64.4
15.7
20-84
69.3
3.4
47-87
0.94
76.3
In vivo (BUA)
Gluer et al. ~ Waud et al, 19
25 F 64 F
SXA DXA
17.1 In vitro
McKelvie et al. n7 (nBUA) McCloskey et al. ~6 (BUA)
28 13 F/12 M
10 F/10 M
QCT Physical QCT Physical Apparent
25.9 21.6 Current (nBUA) 14.7
correspond to a 4% reduction in nBUA, this should be considered when comparing the sensitivity and precision of BUA with conventional bone densitometry techniques. Conclusions The nBUA values for the specimens treated in different ways were highly correlated with each other, having regression coefficients near unity. The intercept values confirmed both that the core represents the region of calcaneus measured in vivo and that the presence of the cortical end plates creates a significant nBUA, probably due to the curved shape resulting in complex phase interactions within the propagating ultrasonic pulse. n B U A of the whole calcaneus is a good predictor of both the elasticity and compressive strength of its cancellous bone. The prediction of elasticity by n B U A is predominantly due to the
10
59-90
strong correlation between the latter and density. Due to the significant relationship between nBUA and density, a combination of these two parameters does not significantly improve the prediction of elasticity or compressive strength. We have shown previously that BUA is influenced by structure in cancellous bone. In this study n B U A does not have any explanatory power for the mechanical properties measured apart from that due to its correlation with density. However, the morphological anisotropy was extremely uniform, suggesting that the trabecular pattern was consistent between calcaneal samples. We would therefore not expect any direct measure (fabric) or indirect measure (nBUA) of trabecular anisotropy to increase the amount of mechanical variance explained after density is taken into account. Comparison with previous in vivo and in vitro studies is complicated by variations in the age range of subjects and design of the studies; for example, the use of both area-density (BUA,
400
m
300 •
J
u m
Density (kg m "1) 200
100
y intercept = 120 kg m a
I 5
I 10
I 15
I 20
I 25
I 30
nBUAcan (dB MHz cm "1)
Figure 8. Relationship between apparent density and nBUA of cancellous bone samples. Linear data.
I 35
Bone Vol. 18, No. 6 June 1996:495-503 SXA, DXA) or volume-density (nBUA, QCT, apparent density) parameters. An interesting finding is that there appears to be a power law relationship between nBUA and apparent density, with an exponent of approximately 2. Previous studies have simply reported only linear regression and the existence of a power law has important clinical implications, particularly when correlating nBUA with established bone densitometric techniques. We should consider the limitations of this study. Analysis of cylindrical samples taken from the calcaneus in a mediolateral direction, although representing the region analyzed in vivo, had a smaller cross-sectional area. Also, mechanical testing could not be performed in the principal superior-inferior in vivo loading direction. Future studies could consider rectangular sections with dimensions commensurate with in vivo measurement. The calcaneal specimens were obtained from a limited and elderly age range of subjects who did not correspond to previous in vivo studies, future studies should consider a broader age range with a potentially higher structural variation.
Acknowledgments: The cadaveric calcaneal samples were kindly provided b y Dr. E. V. M c C l o s k e y . C.F.N. a c k n o w l e d g e s the support o f the S E R C ; R.H. a n d J.D.C. a c k n o w l e d g e the support o f A c t i o n Research.
References 1. Alhara, M. E. Bone density measurements. Calcif Tissue Int (suppl.) 49:2123; 1991. 2. Brear, K., Currey, J. D., Raines, S., and Smith, K. J. Density and temperature effects on some mechanical properties of cancellous bone. Engin Med 17:163167; 1988. 3. Boutinaud, R. X. Propagation of ultrasound through cancellous bone. M.Phil./ Ph.D. transfer report. Sheffield, UK: Sheffield Hallam University; 1992. 4. Evans, J. A. and Tavakoli, M. B. Temperature and direction dependence of the attenuation and velocity of ultrasound in cancellous and cortical bone. Current Research in Osteoporosis and Bone Mineral Measurement II. Bath: British Institute of Radiology; 1992; 42. 5. Gibson, L. J. The mechanical behavior of cancellous bone. J Biomech 18:317328; 1985. 6. Gluer, C. C., Vahlensieck, M., Faulkner, K. G., Engelke, K., Black, D., and Genant, H. K. Site-matched calcaneal measurements of broadband ultrasonic attenuation and single x-ray absorptiometry: Do they measure different skeletal properties? J Bone Miner Res 7:1071-1079; 1992.
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7. Gluer, C. C., Wu, C Y., and Genant, H. K. Broadband ultrasonic attenuation signals depend on trabecular orientation: An in vitro study. Osteopor Int 3:185191; 1993. 8. Hodgskinson, R. and Currey, J. D. Effects of structural variation on Young's modulus of non-human cancellous bone. Proc Inst Mech Eng 204(H1):43-52; 1990. 9. Hodgskinson, R. and Currey, J.D. The effect of variation in structure on Young's modulus of cancellous bone: a comparison of human and non-human material. Proc Inst Mech Eng 204(H 1): 115-21; 1990. 10. Hodgskinson, R. and Currey, J.D. Young's modulus, density and material properties in cancellous bone over a large density range. J Mater Sci. Mater. Med. 3:377-381; 1992. 11. Kotzki, P. O., Buyck, D., Hans, D., Thomas, E., Bonnel, F., Meunier, P. J., and Rossi, M. Influence of fat on ultrasound measurements of the os calcis. Calcif Tissue Int 54:91-95; 1994. 12. Lang, P., Steiger, P., Faulkner, K., Gluer, C., and Genant, H. K. Current techniques and recent development in quantitative bone densitometry. Radiol Clin N Am 29:49-76; 1991. 13. Langton, C. M., Palmer, S. B., and Porter, R. W. The measurement of broadband ultrasonic attenuation in cancellous bone. Engin Med 13:89-91; 1984. 14. Langton, C. M., Evans, G. P., Hodgskinson, R., and Riggs, C. M. Ultrasonic, elastic and structural properties of cancellous bone. Current research in osteoporosis and bone mineral measurements. Bath: British Institute of Radiology; 1990; 10-11. 15. Langton, C.M., Ali, A. V., Riggs, C. M., Evans, G. P., and Bonfield, W. A contact method for the assessment of ultrasonic velocity and broadband attenuation in cortical and cancellous bone. Clin Phys Physiol. Meast 11:243-249; 1990. 16. McCloskey, E. V., Murray, S. A., Charlesworth, D., Miller, C., Fordham, J., Clifford, K., Atkins, R., and Kanis, J. A. Assessment of broadband attenuation in the os calcis in vitro. Clin Sci 78:221-225; 1992. 17. McKelvie, M. L., Fordham, J., Clifford, C., and Palmer, S. B. In vitro comparison of quantitative computed tomography and broadband ultrasonic attenuation of trabecular bone. Bone 10:101-104; 1989. 18. Ostlere, S.J. and Gold, R.H. Osteoporosis and bone density measurement methods. Clin Orthop Relat Res 271:149-163; 1991. 19. Wand, C. E., Lew, R., and Baran, D. T. The relationship between ultrasound and densitometric measurements of bone mass at the calcaneus in women. Calcif Tissue Int 51:415-418; 1992.
Date Received: February 28, 1995 Date Revised: November 1, 1995 Date Accepted: November 1, 1995
ORIGINAL ARTICLES
Prediction of Mechanical Properties of the Human Calcaneus by Broadband Ultrasonic Attenuation C. M. L A N G T O N , 1 C. F. N J E H , 2 R. H O D G S K I N S O N , 3 a n d J. D. C U R R E Y 3 I Centre for Metabolic Bone Disease, Hull, UK 2 Health Research Institute, Sheffield Hallam University, Sheffield, UK 3 Department of Biology, University of York, York, UK
in the human calcaneus for the identification and monitoring of osteoporosis was first described by Langton et al. 13 It is widely agreed that B U A is related to both the density and structure of cancellous bone. 6't4 Evidence for this consists of both theoretical analysis of the propagation of ultrasound through an open-celled porous structure such as cancellous bone 3 and in vitro studies of cancellous bone samples. Langton et al. 14 studied cancellous cubes from equine third metacarpals exhibiting either predominantly rod-like structure or predominantly plate-like structure. A high degree of orientational anisotropy for BUA was observed for each cube. Since the density of the cube is invariant with direction, Langton et al. t4 suggested that the variation in BUA was due to orientational variations in cancellous bone structure. This was confirmed by measurement of "fabric". 8"9 Gluer et al. 7 studied cubic samples of bovine cancellous bone and defined a semiquantitative index (alignment) for the predominant trabecular orientation with respect to the direction of ultrasound propagation, varying from - 2 (perpendicular) to +2 (parallel). The difference in B U A from parallel to perpendicular propagation was commensurate with the difference in BUA reported between osteoporotic and healthy individuals, and the authors concluded that B U A depends upon bone structure. For the clinical measurement of B U A in the calcaneus, however, we are restricted to a single anatomical orientation, namely, the mediolateral direction. The purpose of this article is first to demonstrate the value of using B U A of the human calcaneus to predict compressive strength, and second to determine the dependence of B U A upon its material properties.
Broadband ultrasonic attenuation (dB MHz cm -~, nBUA) was determined for specimens from 20 human caicanei, along with apparent density, elasticity (Young's modulus), and compressive strength. The calcanei were modified to provide "whole" (only soft tissue removed), "core" (mediolateral cores corresponding to in vivo measurement region), "can" (cortical end plates removed from core), and "def" (core defatted) samples. The nBUA values for the various modifications were highly correlated. The presence of the cortical endplates creates a significant nBUA, probably due to complex phase interactions, nBUAca . was a good predictor of elasticity (R z = 75.7%) and strength (R 2 = 73.6%). Apparent density was a better predictor of the mechanical variables than nBUA, with R z values of 88.5% for elasticity and 87.6% for strength. The morphological anisotropy defined by "fabric" for the specimens was extremely uniform. The coefficient of variation in nBUA (40.5%) and compressive strength (64.4%) was significantly greater than for apparent density (23.5%) and fabric (6.7%). It is well known that a power law relationship exists between apparent density and elasticity or strength in cancellous bone. An interesting finding in this work is that there also appears to be a power law relationship between nBUA and apparent density, with an exponent of approximately 2, which, in the light of clinical implications, warrants further investigation. (Bone 18:495-503; 1996) Key Words: Architecture; BUA; Calcaneus; Cancellous bone; Density; Mechanical properties.
Methods
Introduction
Sample Preparation
Osteoporosis may be defined as the loss of bone resulting in an increased risk of fracture. The bone loss may take the form of generalized trabecular thinning or removal of entire trabeculae. We may assume therefore that the "gold standard" for bone health is the mechanical integrity of the bone. Several noninvasive measurement techniques have been developed to measure the degree of mineralisation of bone. 1,12,~8 These are assumed to be reliable surrogates for bone density and hence reliable indicators of fracture risk. The measurement of broadband ultrasonic attenuation (BUA)
The specimens were obtained post mortem from 20 cadavers (ten males and ten females) with an age range of 59 to 90 years. No pathological information on the specimens was available. The specimens were kept frozen at -20°C, until being thawed before testing. Once thawed, the specimens were thoroughly degassed under water in a vacuum desiccator prior to ultrasonic testing. The specimens were wet during all mechanical and ultrasonic measurements. The ultrasonic measurements were carried out under water at room temperature, to ensure good acoustic coupling. Detergent was added to the water to improve sample wetting. Broadband ultrasonic attenuation measurements were carried out in turn on calcaneal specimens that had four different degrees
Address for correspondence and reprints: Dr. C. M. Langton, Centre for Metabolic Bone Disease, Hull Royal Infirmary, HS Brocklehurst Building, Anlaby Rd., Hull HU3 2RW, UK. © 1996 by Elsevier Science Inc. All rights reserved.
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8756-3282/96/$15.00 PII $8756-3282(96)00086-5
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of modification: only soft tissue removed (whole); cylindrical specimen produced with the cortical end plates still intact (core); end plates removed with marrow intact (can); defatted (def). Before ultrasonic testing, external soft tissue was removed. After the first ultrasonic measurements, a coring drill with an internal diameter of 21 mm was used to remove samples whose long axis was in the mediolateral direction. The central axis of the core corresponded to the central axes used by the McCue CUBAclinical and L U N A R Achilles commercial systems. The Walker Sonix UBA575 measures a lower and more posterior region of the calcaneus. After a second set of ultrasound measurements, the cortical end surfaces were removed using a diamond impregnated band saw to leave a cylinder consisting only of cancellous bone and fat that was remeasured. The final ultrasound measurements were performed after fat had been removed from the specimen, in the manner described by Brear et alfl At each stage of modification, ultrasound measurements were repeated five times and the precision calculated.
Broadband Ultrasonic Attenuation The Contact Ultrasonic Bone Analyser (CUBA) system j5 was used. A short rf pulse (nominal frequency 1 MHz) is emitted by a 13-mm-diam broadband transducer and, after passing through the sample, is received by a similar transducer at the far side. The two transducers are mounted in a calliper attached to a vernier gauge used to measure specimen thickness, and immersed in degassed water. The received ultrasonic signal is fed into a computerinterfaced digitizer unit. A fast Fourier transform (FFF) calculates the frequency spectrum of the ultrasound signal. To determine BUA, the frequency spectrum is compared with and without the sample in position, providing an attenuation vs. frequency trace. The slope of the linear regression between 0.2 and 0.6 MHz is then calculated. This provides an area density value of BUA in units o f d B MHz ~ from a defined cross-sectional area but unknown thickness. Dividing this by the sample thickness provides a volumetric density BUA parameter of units dB MHz -j cm -~, referred to as nBUA. The CUBAclinical system incorporates 19-mm-diam ultrasound transducers coupled to a subjects heel via compressible silicone pads. The CUBA system used for the current study incorporates 13-mm-diam transducers with the faces placed in direct contact with the in vitro samples. The electronics and software for the two CUBA systems are similar; the differences relate to transducer separation measurement and correction for incorporation of silicone pads.
Mechanical Testing Mechanical testing was carried out on the defatted cylinders. Young's modulus (E) and compressive strength (or) were obtained by unconfined compressive testing in an Instron 1122 testing machine. The loading direction (mediolateral) was the same as that in which the acoustic measurements were determined. The specimens were immersed in a water bath at room temperature. Differences in temperature over the range from room temperature to 38°C have only a slight effect on mechanical properties 2 and ultrasonic behavior. 4 The defatted cancellous cylinders were compressed between the end of a smooth stainless-steel loading column and the base of the water bath, which itself lay directly on a 5 kN load cell. The compliance of the loading system was measured and allowed for in the calculations. The compressive load was increased pro-
Bone Vol. 18, No. 6 June 1996:495-503 gressively over several cycles until the load-deformation curve was approximately linear. 8 The head speed was 1 mm min -~, producing a nominal strain rate of 0.0017 s-~. The strain rate incorporated, although lower than that observed in physiological practice, provides a controllable test condition and reliable data. ~ Young's modulus was defined as the maximum slope of the stress-strain curve in the most linear portion of the preyield region. Compressive strength was calculated from the first maximum load that each cube attained. (If compression testing of cancellous specimens is continued, the specimen eventually compacts, and can bear very high loads, even though it is completely destroyed.) Care was taken to load the bone to only just after the first maximum, so that the macroscopic structure was insignificantly affected.
Apparent Density We define "apparent density" as the ratio of the dehydrated, defatted tissue mass to the total specimen volume. The defatted cylinders were dried to constant weight at 60-70°C.
Fabric The morphological anisotropy of the bone was determined using a modification of the method described by Hodgskinson and Currey. 8 Briefly, after all other tests had been carried out, each cylinder was cut in half parallel to its long axis. The exposed surface was filled with black resin, polished, and subjected to computer-aided stereological analysis. The computer superimposes a 40 line array onto each image, and calculates the total number of trabecular encounters for the 40 lines and the total length of these encounters. Mean intercept length (MIL) is then calculated by dividing these two values. This procedure is repeated at 5 ° intervals over a range of 175 °. MIL is plotted as a function of angle, and an ellipse is fitted to this raw data. A single value of fabric is calculated as a function of the ratio of the lengths of the major and minor axes of the ellipse and the angular deviation of the major axis from a particular mechanical loading direction. This has a high value, about 1.5, when the trabeculae are predominantly oriented in the direction of loading, and a low one, about 0.5, when predominantly oriented normal to the direction of loading, and about 1 when it is roughly isotropic. As described later, the cylinders in this study had extremely low and invariant values of fabric. The experimental protocol is summarized in the following flow chart: Whole heel --4 Soft tissue removal from calcaneus ---) n B U A (whole) measurement ~ Core taken ~ n B U A (core) measurement --~ Cortices removed --~ n B U A (can) measurement --~ Defatted ---> n B U A (def) measurement ---> Mechanical measurements (elasticity and strength) --~ Dried --+ Apparent density measurement --* Morphometric measurement. Results A summary of the data (mean, standard deviation, and coefficient of variation) is provided in T a b l e 1, correlation coefficients between relevant properties in T a b l e 2, and regression equations on the log-transformed values of density, elasticity, and strength in Table 3. The precision (coefficient of variation, CV%) for the nBUA data for the various stages of modification is shown in Table 1. It was not possible to determine the precision of the mechanical and fabric data since only one measurement was obtained for
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Table 1. Data summary, p: apparent density (kg rn-3); E: Young's modulus (MPa); cr: compressive strength (MPa); nBUA: broadband ultrasonic attenuation (dB MHz -t cm-I) for each modification. N = 20 in all cases except fabric, where N = 19
Mean SD CV% Precision
Age
p
E
~r
76.3 9.89 13.0
262.1 61.4 23.4
35.63 23.18 65.1
0.48 0.31 64.5
each sample. Our analysis used the relationships between logtransformed values because the untransformed relationships are curvilinear and the log-transformed relationships are effectively linear. The gradient o f the regression line for each logtransformed relationship is therefore the exponent value for the particular relationship. Table 4 provides regression equations between linear nBUA values for the various stages of calcaneal specimen modification. Discussion
Mechanical Properties of Cancellous Bone Cores The values for mechanical properties and density refer to the properties of the isolated core without end plates. As usually found, 9 Young's modulus and strength are very closely related to each other with an R 2 of 92.4% (illustrated in Figure 1). Young's modulus and strength are well predicted by density. The log-transformed regression equations (Table 3) give an R 2 value of 88.5% with Young's modulus and 87.6% with strength. This is in accordance with what has frequently been found. 9'1° We were initially surprised to find the exponents for the relationships to be 3.13 for Young's modulus and 2.92 for strength. It is usual to find values not exceeding 2.4 for the exponent. 9'1° This apparently anomalous relationship is probably caused by the characteristic structure of the cancellous bone within the calcaneus: sheets connected by cross struts (Figure 2). The structure was loaded in the direction of the cross struts, and normal to the sheets. A cubic relationship is predicted by Gibson 5 for a "parallel plate structure," which may be considered to be an idealized version of the cancellous structure in the calcaneus. The fabric values have a very low variance and are consistent (p = 0.56) between male (0.685 -+ 0.045) and female subjects (0.671 - 0.045). The coefficient of variation (standard deviation × 100/mean) is 6.7%, whereas that of density is 23.4%. The fabric values have no significant correlation with the other variables. Furthermore, unlike the usual situation in cancellous bone, because the fabric values are almost invariant, adding fabric as an extra explanatory variable to the equation relating the mechanical Table 2. Correlation coefficients between mechanical and ultrasonic properties of the calcaneal samples. Note: all variables are linear, not log transformed
Density (kg m-3)
Fabric
Elasticity (MPa)
Strength (MPa)
nBUA whole
nBUA core
nBUA can
nBUA def
23.06 8.15 35.3 4.8
20.59 7.28 35.4 5,3
18.28 7.40 40.5 3.2
18.79 7.37 39.2 4.3
Fabric 0.678 0.045 6.7
properties to density hardly improves the explanatory power of the equation at all: Young' s modulus: log E = -6.10 + log E = -6.00 + Strength: log ~r = -7.46 + log cr = -7.42 +
3.13 log p, R 2 = 88.5%, 3.13 log p + 0.62 log fabric, R2 = 88.4%; 2.92 log p, R 2 = 87.6%, 2.92 log p + 0.23 log fabric, R 2 = 86.8%.
The fabric was derived from the flat surfaces exposed when the cylinders were cut in half, parallel to the long axis. Note was not taken, however, of the orientation of the cylinder, so that the plane of the cut could vary around this axis. Due to the structural symmetry of the cancellous bone within this region of the calcaneus, the lack of knowledge of the angle of cut with respect to the long axis is not considered significant, indicated by the consistency of the fabric data.
Broadband Ultrasonic Attenuation The precision for the nBUA data for the various stages of modification (Table 1) was similar in magnitude to that obtained for Table 3. Mechanical property and density regression equations. All use log-transformed values, s is the standard error of y estimate. R2 is the adjusted value accounting for the numbers of degrees of freedom. In each case, the title of the table is the y variable x variable
R2
Exponent
Intercept
s
78.3 75.6 86.0 81.7
Apparent density (y variable) 0.46 0.47 0.44 0.44
1.80 1.81 1.88 1.86
0.05 0.05 0.04 0.05
88.5 72.2 64.8 75.7 76.5
b Young's modulus (y variable) 3.13 1.47 1.44 1.36 1.42
-6.10 -0.51 -0.40 -0.22 -0.31
0.12 0.19 0.21 0.17 0.17
87.6 69.3 62.1 73.6 72.7
Strength (y variable) 2.92 1.35 1.32 1.26 1.30
-7.46 -2.22 -2.12 - 1.96 -2.02
0.12 0.18 0.20 0.17 0.17
a
nBUAwhole nBUAcore nBUAcan nBUAdef
Density nBUAwhole nBUAcore nBUAcan nBUAdef
c
Fabric Elasticity Strength nBUAwhole nBUAcore nBUAcan nBUAdef
0.005 0.96 0.92 0.89 0.87 0.94 0.92
0.008 -0.03 0.18 0.19 0.04 0.05
0.95 0.85 0.83 0.89 0.88
0.83 0.80 0.87 0.84
Density nBUAwhole nBUAcore nBUAcan nBUAdef
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Table 4. Correlation and statistical significance between BUA values for the calcaneal specimens treated in different ways nBUAcore
nBUAcan
nBUAdef
X coefficient 1.09 -+0.07 1.02 + 0.09 0.93 _+0.08
nBUAwhole nBUAcore
neus were unity _+10%. The intercept between whole calcaneus and core was insignificant, confirming that the core effectively represents the region of calcaneus measured in vivo. The intercept between core and defatted samples was also minimal, indicating that the replacement of a viscoelastic material (fat) with a purely viscous material (water) does not significantly affect the nBUA. The whole calcaneus and the core sample had nBUA values approximately 3.5 dB MHz cm -1 above the cancellous (p = 0.03) and defatted (p = 0.07) samples, indicating that the presence of the cortical end plates creates a significant nBUA, probably due to the curved shape resulting in complex phase interactions within the propagating ultrasonic pulse.
1.03 +_0.09 0.91 _+0.09
nBUAcan
0.96 -+0.07 Intercept 0.72-+ 1.47 4.31 -+ 2.01
nBUAwhole p value nBUAcore
ns
p value nBUAcan p value
nBUAwhole nBUAcore nBUAcan
0.97
3.66 + 1.90
p - 0.03 3,57 _ 1.49
p = 0.07 3.48 - 1.83
p = 0.03
p - 0.07 0.31 _+ 1.47 ns
0.93 0.95
Mechanical and Ultrasound Correlation
The correlation coefficients relating the mechanical variables to density are only slightly higher than those relating them to the various measures of nBUA (Table 2). The correlation between log nBUA for the cancellous cores (can) and log apparent density showed the best correlation (Figure 4) with a n R 2 of 86.0%. nBUA has R 2 values of =65% to 77% for Young's modulus and of 62% to 74% for strength (nBUAcan shown in Figure 5), while density has R 2 values of 88.5% for Young's modulus and 87.6% for strength (Figure 6). However, the most relevant value to take is that for nBUAwhole because that is the nearest to the measurements that can be made in the clinical situation. The correlation R 2 values are 72.2% for Young's modulus and 69.3% for strength (Figure 7). That is to say, =70% of the variation in the mechanical properties of the cancellous cylinder can be "explained" statistically by variation in the values for nBUA determined from transducers placed against the outer cortices of the calcaneus. The relationship between nBUAcan, density, and elasticity was further investigated using multiple regression analysis. The relationship between density and elasticity has already been described in Table 3:
0.93 0.92 0.95
BUA in vivo, the improvement in positioning accuracy probably being compromised by the additional incorporation of sample length variability. The precision (CV%) for the "can" samples was significantly lower than for the "whole" and "core" samples (p = 0.0004 and p = 0.0001, respectively), indicative of the consistent sample length measurement across the fiat and parallel end faces of the "can" samples. Table 4 and Figure 3 show that the nBUA values for the specimens treated in different ways are highly correlated with each other, the lowest correlation having an r value of 0.92. The important factors are the regression x coefficients, indicating the degree of linearity and the intercept values, indicating any nBUA offset with sample modification. The regression x coefficients for all correlations between the various modifications of the calca0.2-
ill
O•
•
•
-0.2 -
Log strength (MPa)
-0.4n n
-0.6-
-0.8 -
-1
-1.2 0,6
I 0.8
I 1
I 1.2
I 1.4
I 1.6
Log elasticity (MPa)
Figure l. Relationship between compressive strength and Young's modulus.
I
I
1.8
2
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does not improve the amount of variance explained for elasticity. The same is true for strength: log tr = -7.46 + 2.92 log p,
Re
= 87.6%.
log tr = -7.38 + 3.13 log p - 0.104 log nBUAcan, R 2 = 87.0%.
Figure 2. Photograph showing characteristic structure of the cancellous bone within the calcaneus.
log E = - 6 . 1 0 + 3.13 log p, R 2 = 88.5%. We can also see from Table 3 that there is a strong relationship between log elasticity and nBUAcan (R = 75.7%) and between density and nBUAcan (R = 86.0%). The regression equation using both density and nBUAcan as explanatory variables is log E = -6.19 + 3.18 log p - 0.024 log n B U A can, R e = 87.9%. As can be seen, the addition of BUA to the regression equation
The high correlation coefficient of 0.94 between nBUAcan and apparent density is in support of previous in vitro studies of the calcaneus, shown in T a b l e 5. McKelvie et al. ]7 and McCloskey et al. 16 correlated n B U A with both QCT and physical density. McKelvie et al. obtained correlation coefficients of 0.86 and 0.83 with QCT and physical density, respectively, while McCloskey et al. obtained correlation coefficients of 0.80 and 0.85 with QCT and physical density, respectively. These findings are, however, not in agreement with comparative studies of the calcaneus in vivo. BUA and density (measured by established clinical techniques) at the calcaneus showed only moderate significance. For instance, Waud et a1.19 obtained a correlation coefficient of 0.73 with area density measured by DXA, and Gluer et al. 6 obtained a correlation coefficient of 0.72 with area density measured by SXA in a population of 25 females and a correlation coefficient of only 0.58 when 8 males were added. The effect of overlying soft tissue in the in vivo situation has been shown to have minimal effect on the B U A value ~t and cannot therefore explain the disparity with in vitro studies. As a further means of analysis, the relative standard error of estimates (standard error of estimate (SEE) x 100/mean) have been compared, and are shown in Table V. The relative SEE value of 14.7% obtained is comparable to the in vivo study by Gluer et al., who considered a broad age range (20-75 years), but lower than the in vitro study by McCloskey et al., who used a similar age range (47-87) to the current study. One would expect that the relative SEE would, however, increase with age range due to the higher variability. However, in comparing previous studies, we have to note that they are not comparable in design. Gluer et al. 6 compared BUA
40
whole
iio
35
~
e
•
30
•
25
. j.--
•
o
yo oo
nBUA 20 (dB MHz cm "t) 15 10
j j
o
r e,.Qre ,o n Core regression
0 0
I 5
I 10
I 15
I 20
I 25
I 30
I 35
nBUAcan (dB MHz cm "1)
Figure 3. Relationship between nBUA of whole calcanei, and of cored samples, with that of cancellous samples with endplates removed.
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2.6
2.5
• •
Log density (kg m 4)
•
2.4 •
mm
2.3
2.2
2.1 0.4
I
I
I
I
I
I
0.6
0.8
1
1.2
1.4
1.6
Log nBUAcan (dB MHz cm "~) Figure 4. Relationship between apparent density and nBUA of cancellous bone samples. with SXA, both measurements considering a volume of cancellous bone of known cross-sectional area but unknown thickness, providing an area-density, whereas McCloskey et al. ]6 compared BUA (area density) with true volume-density parameters derived from physical density measurements and QCT. In the current study, we have compared nBUA with apparent density, both true volumetric parameters. 0.2
It is well known that power law relationships exist between apparent density and elasticity and between apparent density and strength. Regression of logarithmic parameters suggests that a power law relationship also exists between apparent density and nBUA. This suggests that regression of linear parameters, although providing significant R 2, is in fact describing a tangent to a nonlinear relationship that would exhibit a finite rather than
°
0"
mm
•
-0.2 "
-0.4 "
Log strength (MPa)
-0.6 "
-0.8 "
-1
-1.2 0.4
I
I
l
I
I
I
0.6
ON8
1
1.2
1.4
1.6
Log nBUAcan (dB MHz cm "1)
Figure 5. Relationship between compressive strength and nBUA of cancellous bone samples.
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0.2
•
•
-0.2
-0.4 Log
strength (MPa)
-0.6
-0.8
-1.2 2.1
I
I
I
2.2
2.3
2.4
I 2.5
I 2.6
Log density (kg rn4)
Figure 6. Relationship between compressive strength and apparent density. zero intercept between, for example, nBUAcan and apparent density, illustrated in Figure 8. The existence of a power law relationship between nBUA and apparent density has important implications, first for clinical investigations, particularly when
correlating BUA with established bone densitometric techniques, and second in defining the dependence of nBUA upon material and structural parameters of cancellous bone. For example, based upon a quadratic relationship, a 2% reduction in density will
0.2
mm
-0.2
-0.4 Log
strength (MPa)
-0.6
-0.8
-1.2 0.6
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1
1.2
1.4
Log nBUAwhole (dB MHz cm "1)
Figure 7. Relationship between compressive strength and nBUA of whole calcaneus.
I 1.6
502
C.M. Langton et al. Mechanical properties of human calcaneus by BUA
Bone Vol. 18, No. 6 June 1996:495-503
Table 5. Correlation coefficients and subject ages for in vivo and in vitro comparative studies between BUA and density in the calcaneus
Density Author
No./sex
Method
Age
SEE%
r
Mean
SD
Range
0.72 0.73
45.6 51
10
20-75 35-85
0.86 0.83 0.80 0.85
64.4
15.7
20-84
69.3
3.4
47-87
0.94
76.3
In vivo (BUA)
Gluer et al. ~ Waud et al, 19
25 F 64 F
SXA DXA
17.1 In vitro
McKelvie et al. n7 (nBUA) McCloskey et al. ~6 (BUA)
28 13 F/12 M
10 F/10 M
QCT Physical QCT Physical Apparent
25.9 21.6 Current (nBUA) 14.7
correspond to a 4% reduction in nBUA, this should be considered when comparing the sensitivity and precision of BUA with conventional bone densitometry techniques. Conclusions The nBUA values for the specimens treated in different ways were highly correlated with each other, having regression coefficients near unity. The intercept values confirmed both that the core represents the region of calcaneus measured in vivo and that the presence of the cortical end plates creates a significant nBUA, probably due to the curved shape resulting in complex phase interactions within the propagating ultrasonic pulse. n B U A of the whole calcaneus is a good predictor of both the elasticity and compressive strength of its cancellous bone. The prediction of elasticity by n B U A is predominantly due to the
10
59-90
strong correlation between the latter and density. Due to the significant relationship between nBUA and density, a combination of these two parameters does not significantly improve the prediction of elasticity or compressive strength. We have shown previously that BUA is influenced by structure in cancellous bone. In this study n B U A does not have any explanatory power for the mechanical properties measured apart from that due to its correlation with density. However, the morphological anisotropy was extremely uniform, suggesting that the trabecular pattern was consistent between calcaneal samples. We would therefore not expect any direct measure (fabric) or indirect measure (nBUA) of trabecular anisotropy to increase the amount of mechanical variance explained after density is taken into account. Comparison with previous in vivo and in vitro studies is complicated by variations in the age range of subjects and design of the studies; for example, the use of both area-density (BUA,
400
m
300 •
J
u m
Density (kg m "1) 200
100
y intercept = 120 kg m a
I 5
I 10
I 15
I 20
I 25
I 30
nBUAcan (dB MHz cm "1)
Figure 8. Relationship between apparent density and nBUA of cancellous bone samples. Linear data.
I 35
Bone Vol. 18, No. 6 June 1996:495-503 SXA, DXA) or volume-density (nBUA, QCT, apparent density) parameters. An interesting finding is that there appears to be a power law relationship between nBUA and apparent density, with an exponent of approximately 2. Previous studies have simply reported only linear regression and the existence of a power law has important clinical implications, particularly when correlating nBUA with established bone densitometric techniques. We should consider the limitations of this study. Analysis of cylindrical samples taken from the calcaneus in a mediolateral direction, although representing the region analyzed in vivo, had a smaller cross-sectional area. Also, mechanical testing could not be performed in the principal superior-inferior in vivo loading direction. Future studies could consider rectangular sections with dimensions commensurate with in vivo measurement. The calcaneal specimens were obtained from a limited and elderly age range of subjects who did not correspond to previous in vivo studies, future studies should consider a broader age range with a potentially higher structural variation.
Acknowledgments: The cadaveric calcaneal samples were kindly provided b y Dr. E. V. M c C l o s k e y . C.F.N. a c k n o w l e d g e s the support o f the S E R C ; R.H. a n d J.D.C. a c k n o w l e d g e the support o f A c t i o n Research.
References 1. Alhara, M. E. Bone density measurements. Calcif Tissue Int (suppl.) 49:2123; 1991. 2. Brear, K., Currey, J. D., Raines, S., and Smith, K. J. Density and temperature effects on some mechanical properties of cancellous bone. Engin Med 17:163167; 1988. 3. Boutinaud, R. X. Propagation of ultrasound through cancellous bone. M.Phil./ Ph.D. transfer report. Sheffield, UK: Sheffield Hallam University; 1992. 4. Evans, J. A. and Tavakoli, M. B. Temperature and direction dependence of the attenuation and velocity of ultrasound in cancellous and cortical bone. Current Research in Osteoporosis and Bone Mineral Measurement II. Bath: British Institute of Radiology; 1992; 42. 5. Gibson, L. J. The mechanical behavior of cancellous bone. J Biomech 18:317328; 1985. 6. Gluer, C. C., Vahlensieck, M., Faulkner, K. G., Engelke, K., Black, D., and Genant, H. K. Site-matched calcaneal measurements of broadband ultrasonic attenuation and single x-ray absorptiometry: Do they measure different skeletal properties? J Bone Miner Res 7:1071-1079; 1992.
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7. Gluer, C. C., Wu, C Y., and Genant, H. K. Broadband ultrasonic attenuation signals depend on trabecular orientation: An in vitro study. Osteopor Int 3:185191; 1993. 8. Hodgskinson, R. and Currey, J. D. Effects of structural variation on Young's modulus of non-human cancellous bone. Proc Inst Mech Eng 204(H1):43-52; 1990. 9. Hodgskinson, R. and Currey, J.D. The effect of variation in structure on Young's modulus of cancellous bone: a comparison of human and non-human material. Proc Inst Mech Eng 204(H 1): 115-21; 1990. 10. Hodgskinson, R. and Currey, J.D. Young's modulus, density and material properties in cancellous bone over a large density range. J Mater Sci. Mater. Med. 3:377-381; 1992. 11. Kotzki, P. O., Buyck, D., Hans, D., Thomas, E., Bonnel, F., Meunier, P. J., and Rossi, M. Influence of fat on ultrasound measurements of the os calcis. Calcif Tissue Int 54:91-95; 1994. 12. Lang, P., Steiger, P., Faulkner, K., Gluer, C., and Genant, H. K. Current techniques and recent development in quantitative bone densitometry. Radiol Clin N Am 29:49-76; 1991. 13. Langton, C. M., Palmer, S. B., and Porter, R. W. The measurement of broadband ultrasonic attenuation in cancellous bone. Engin Med 13:89-91; 1984. 14. Langton, C. M., Evans, G. P., Hodgskinson, R., and Riggs, C. M. Ultrasonic, elastic and structural properties of cancellous bone. Current research in osteoporosis and bone mineral measurements. Bath: British Institute of Radiology; 1990; 10-11. 15. Langton, C.M., Ali, A. V., Riggs, C. M., Evans, G. P., and Bonfield, W. A contact method for the assessment of ultrasonic velocity and broadband attenuation in cortical and cancellous bone. Clin Phys Physiol. Meast 11:243-249; 1990. 16. McCloskey, E. V., Murray, S. A., Charlesworth, D., Miller, C., Fordham, J., Clifford, K., Atkins, R., and Kanis, J. A. Assessment of broadband attenuation in the os calcis in vitro. Clin Sci 78:221-225; 1992. 17. McKelvie, M. L., Fordham, J., Clifford, C., and Palmer, S. B. In vitro comparison of quantitative computed tomography and broadband ultrasonic attenuation of trabecular bone. Bone 10:101-104; 1989. 18. Ostlere, S.J. and Gold, R.H. Osteoporosis and bone density measurement methods. Clin Orthop Relat Res 271:149-163; 1991. 19. Wand, C. E., Lew, R., and Baran, D. T. The relationship between ultrasound and densitometric measurements of bone mass at the calcaneus in women. Calcif Tissue Int 51:415-418; 1992.
Date Received: February 28, 1995 Date Revised: November 1, 1995 Date Accepted: November 1, 1995