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The ability of ultrasound velocity to predict the stiffness of cancellous bone in vitro
Bone Vol. 21, No. 2 August 1997:183-190
ELSEVIER
The Ability of Ultrasound Velocity to Predict the Stiffness of Cancellous Bone In Vitro R. H O D G S K I N S O N , ~ C. F. N J E H , 2 J. D. C U R R E Y , 3 and C. M. L A N G T O N l Centre for Metabolic Bone Disease, University of Hull and Royal Hull Hospitals Trust, Hull, UK 2 Medical Physics Department, Queen Elizabeth Medical Centre, Birmingham, UK 3 Department of Biology, University of York, York, UK
Key Words: Cancellous bone; Ultrasound velocity; Young's modulus; Trabecular structure.
The mechanical status of bones is an important consideration in skeletal pathological conditions such as osteoporosis, which result in fracture at predominantly cancellous bone sites. Density is a ge~d predictor of the stiffness and strength of cancellous bone. However, these mechanical properties are also dependent on the cancellous bone's architecture. The objective of this work was to investigate the ability of ultrasound velocity to predict the Young's modulus of elasticity of cancellous bone. The cancellous bone specimens were 20 mm cubes from bovine femur and 21 mm diameter mediolateral cylinders cored from human calcaneus. Ultrasound velocity (11) and Young's modulus (E) were determined in three orthogonal directions for the bovine cubes [anteroposterior (AP), mediolateral (ML), and proximodistal (PD)], and mediolaterally in the caicaneus. Apparent density (p) was determined after the other tests. Density alone explains 87.6% of the variance of Young's modulus in human calcaneal and bovine femoral bone tested in the PD direction only. Velocity, however, explains 95% and a combination of density and velocity 97%. Velocity and stiffness are not random with respect to the three directions in the bovine specimens. Further, for each cube we obtained the mean of the three values of E and of V, and characterized each value of E and V by their deviation from their mean. There is an extremely strong positive correlation (r = 0.80) showing that the degree of deviation is consistent for E and V, and of the same sign. These results demonstrate that the velocity of ultrasound in cubes of cancellous bone can give structure-specific information. In particular, knowledge of both density and velocity allows better predictions of stiffness than do density or ultrasound velocity on their own. Because there are noninvasive methods of measuring density that do not depend on ultrasonic measurement the combination of these two measurements promises, eventually, to give improved assessment of a bone's weakness and liability to fracture. (Bone 21: 183-190; 1997) © 1997 by Elsevier Science Inc. All rights reserved.
Introduction The mechanical status of bones is an important consideration in skeletal pathological conditions such as osteoporosis, where a period of asymptomatic bone loss reduces bone strength and increases fracture risk, predominantly at cancellous bone sites. Hence, although osteoporosis results from a complex, incompletely understood, set of physiological and biochemical processes, the clinical manifestation (fracture) can be understood in purely mechanical terms. At present, the clinical assessment of osteoporosis relies mainly on bone mineral density (BMD) measurements using dual-energy X-ray absorptiometry (DXA). 24 Although DXA is a convenient and precise method of measurement, it is available in a rather small number of centers, being relatively expensive. Also, the equipment is bulky and uses ionizing radiation, although the average skin entrance dose (24 ~Sv) is considerably less than the typical radiation dose for an anteroposterior chest film (300 ~Sv). To date, conventional DXA systems do not allow textural analysis of the scan images. Density (a scalar quantity) is a good predictor of the stiffness of cancellous bone and, because there is a strong relationship between stiffness and strength of cancellous bone, it is also a good predictor of the strength. 9'12 Density is a particularly good predictor of bone strength if the bone is reasonably uniform in structure. 15'2° However, bone strength and stiffness are also dependent on bone microstructure and architecture (the arrangement of the bony material in space). 1°'13'1s Strength, stiffness, and architecture are all vector quantities. Ultrasound has been developed recently as a tool for the investigation of skeletal status. 16 Ultrasound is a traveling mechanical vibration and the mechanical properties of the medium progressively alter the shape, intensity, and speed of the propagating wave. Broadband ultrasonic attenuation (BUA) and velocity (V) are the two most commonly quoted ultrasound parameters. There has been growing interest in the use of ultrasound measurements for the detection and management of osteoporosis. 7 It has been used in both clinical zl and research environments for the prediction of the mechanical properties of cancellous bone, but there is little evidence that ultrasound gives any more information than would be obtained from a knowledge of the density of the cancellous material, as demonstrated in a previous report from our laboratory. 15 However, in that study, we investigated the relationships between BUA and the mechanical
Address for correspondence and reprints: Dr. R. A. Hodgskinson, Academic Department of Medical Physics, Centre for Metabolic Bone Disease, HS Brocklehurst Building, Hull Royal Infirmary, 230-236 Anlaby Road, Hull HU3 2RW, UK. E-mail: r.a.hodgskinson@pgec. hull.ac.uk © 1997 by ElsevierScienceInc. All rights reserved.
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R. Hodgskinson et al. Ultrasound and stiffness of cancellous bone
properties and density in human calcaneal bone only. The conclusion from that work, in which structural variation in the specimens was low (due to a combination of uniformity of structure between specimens and the fact that we tested in the mediolateral direction only), was that BUA acted merely as a surrogate for apparent density. However, the possibility remains that ultrasound, being propagated in a particular direction, could give directional information. A recent editorial in this journal s reviewed the current understanding of what factors influence the two main ultrasonic parameters, attenuation and velocity. Referring to Langton et al. 15 the authors pointed to evidence that BUA is merely a surrogate measure for density. It was suggested that more work needs to be done on BUA to confirm this and also the question needs to be addressed as to "whether velocity does not measure something different from attenuation. ''s The objective of this work was to investigate the ability of ultrasound velocity to predict the mechanical properties of cancellous bone. To clarify the matter we increased the range of densities and the amount of structural variation compared with that used in 1996 by Langton et al.ls by adding to the human calcaneal specimens, used in the previous study, cubes of bovine cancellous bone which were tested in three directions. Materials and Methods Cancellous bone from two sources was used in this study: bovine femur and human calcaneus. In each bovine specimen ultrasound velocity (V) and Young's modulus (E) were determined in three orthogonal directions. In the human calcaneus they were measured in the mediolateral direction only. The mediolateral direction is the direction measured clinically, and is also the least stiff direction in the calcaneus (see subsequent text). Apparent density (p) was determined after the other tests. Therefore, for each calcaneal specimen we had one value of p, and one value each of Young's modulus (E) and of ultrasound velocity (V). For each bovine specimen we had one value of p and three values of E and of V.
Sample Preparation 18 cubes, each with sides of 20 mm, were prepared from the proximal and distal ends of fresh bovine femora using a high precision fine diamond cutting saw (Exakt), with final smoothing on fine carborundum grit. Care was taken to produce parallel surfaces. The edges of the cubes were approximately in line with the longitudinal (proximodistal, PD), anteroposterior (AP), and mediolateral (ML) axes of the bones from which they were obtained. There is necessarily some uncertainty in defining the anatomical axes of the disarticulated femur and, therefore, in this study, the three axes were our best estimate of the actual anatomical axes. The cubes were, however, all oriented in the same direction in relation to the bone, so any deviation of the cube axes from the actual anatomical axes of the femurs used was consistent for all the bovine specimens. During preparation, the cubes were kept moist. The samples were then frozen at - 2 0 ° C until tested. Prior to the ultrasonic and mechanical measurements, the specimens were thawed, and thoroughly degassed under water in a vacuum desiccator. The degassing process removed any air bubbles trapped within the samples, the presence of which would make the ultrasonic measurements unreliable. The human calcaneal samples were obtained from 20 cadavers (10 male and 10 female) with an age range of 59-90 years. No pathology information was available. After removal of external soft tissue, a coring drill of 21 mm internal diameter was used to remove a sample whose long axis coincided with the
Bone Vol. 21, No. 2 August 1997:183-190 mediolateral direction of the calcaneus. The region of bone removed was the same as that through which ultrasound would pass in a clinical measurement. The cortical endplates were removed using the Exakt, producing cylinders of cancellous bone with parallel end faces. Following preparation the calcaneal samples were handled as described for the bovine material.
Ultrasonic Velocity The contact ultrasonic bone analyzer (CUBA) system 14 was used. It consists of a combined spike generator (transmitter) and digital receiver interfaced to a portable PC with dedicated software. Two 1 MHz (nominal frequency), 13 mm diameter broadband ultrasonic transducers, the transmitter, and the receiver, were mounted in a digital Vernier gauge sliding caliper. The caliper was used to measure sample thickness. Ultrasonic measurements were performed under water. Detergent was added to improve sample wetting. The transducers were placed in direct contact with the sample. Velocity (V) was calculated as the sample thickness divided by the transit time, transit time being defined as the time delay between the leading edge of the excitation pulse and the leading edge of the received ultrasonic pulse. The "leading edge" refers to the "trigger point" time in the case of the excitation pulse, and the time at which the receiving transducer first detects a departure of amplitude from the zero base line for the received pulse. All the measurements were carried out at room temperature (~20°C).
Young's Modulus Young's modulus (E) was obtained by unconfined compressive testing using an Instron 1122 universal testing machine. The specimens were immersed in a water bath at room temperature. Temperature has only a slight effect on the mechanical properties 2 and on the ultrasonic velocity5 of cancellous bone; therefore, room temperature was used rather than physiological temperature for convenience and to allow comparison with most data reported in the literature. The specimens were compressed between the flat end of a smooth but unpolished stainless-steel loading column and the base of the water bath, which sat directly on a 5 kN load cell. The compliance of the loading system was determined at appropriate loads, and corrected for in subsequent elasticity calculations. Linde and Hvid ~7 demonstrated that different constraints on the loaded specimen (placed either directly on wet platens, cemented to the platens, or constrained in a jacket) can produce differences in the measured strain. Because loading was required in three orthogonal directions in our bovine specimens, we did not use cement or otherwise constrain the specimens. Because we used the same loading conditions in all three directions, inconsistencies produced by the end effects will almost certainly be small. In all the bovine cubes, the proximal-distal direction was the last to be tested. The mediolateral and anteroposterior directions were tested first or second randomly. The elasticity of the bovine cubes was measured in the three orthogonal directions in turn; therefore, it was important that the specimen should remain undamaged by the process of measurement in each of the first two directions. To obviate the possibility of loading the cube into the yield region, the compression load was gradually increased over several cycles until the load deformation curve was linear. The specimens in this study were not specifically preconditioned, 17 although the cyclic loading described above will approximate a limited preconditioning regime. The maximum strain on the specimens during these cycles was on average 0.7% for the human calcaneal specimens and 0.4% for the bovine femoral specimens. Odgaard and Linde 19 have
Bone Vol. 21, No. 2 August 1997:183-190
R. Hodgskinson et al. Ultrasound and stiffness of cancellous bone
185
Table 1. A summary of the regression data using elasticity as the response and density (p) and velocity as predictors in each case
Intercept Human calcaneal samples only (n = 20) Predictor: p Predictor: V Predictors: p and V Human calcaneal and bovine femoral AP (n = 18) Predictor: p Predictor: V Predictors: p and V Human calcaneal and bovine femoral ML (n = 18) Predictor: p Predictor: V Predictors: p and V Human calcaneal and bovine femoral PD (n = 18) Predictor: p Predictor: V Predictors: p and V
Coefficient p (t-ratio, p value)
-6.09 -46.9 -19.4
3.13
-8.43 -37.7 -26.8
4.15
-8.81 -35.8 -27.9
4.32
-9.37 -34.0 -27.2
4.56
shown that Young's modulus does not significantly decrease during cyclic compression to 0.8% strain. In our study only 5 of the 38 specimens (all human) exhibited strains marginally above 0.8%, the maximum being 0.92%. We are confident that this process did not damage the material significantly, which would lead to measurement artifacts in subsequent directions. The load and deformation were plotted by a pen recorder. For all specimens the crosshead speed was 1 mm m i n - 1 producing a nominal strain rate of about 0.0017 sec-1. Young's modulus was calculated from the maximum slope of the stress-strain curve in the preyield region. The mechanical measurements were performed on defatted samples. Carter and ttayes 3 have shown that the marrow in the intertrabecular spaces has no effect on the mechanical behavior of trabecular bone at the strain rate used in our investigation. In general, we believe that any artifacts such as those due to a lack of preconditioning, specimen constraint, or removal of marrow will be consistent between the specimens. Any lack of accuracy in determining Young's modulus can only have degraded the relationships we report.
Apparent Density Apparent density, 9, !is defined as the ratio of dehydrated tissue mass to total specimen volume. The density measurements were performed after the ultrasonic and mechanical testing. To obtain the dehydrated tissue mass, fat was removed from the specimen, as described by Brear et al.2 This involved subjecting the specimen to a high-speed jet of water, and then compressed air. This process was repeated until no fat was visible. The specimens were then tumbled overnight in ~a excess of 2:1 chloroform:methanol mixture. The defatted cubes were then dried at 70°C to constant weight. Volume was obtained from the external dimensions of the cube. The dry weight divided by the volume gave the apparent density (kg m-3). In the regression equations presented here the values are logged (base 10), because we wished to obtain power law relationships .4 Results
2.42 (6.13, <0.001)
1.75 (4.85, <0.001)
1.50 (4.39, <0.001)
1.56 (5.02, <0.001)
Coefficient V (t-ratio, p value)
R2 (%)
15.1 4.66 (2.22, 0.040)
88.5 71.6 90.6
12.2 7.50 (7.22, <0.001)
91.3 94.2 96.4
11.6 8.03 (9.04, <0.001)
89.1 94.9 96.6
11.0 7.76 (10.66, <0.001)
87.6 95.0 97.0
1). However, the equation using both V and p produces a somewhat higher value of R 2 (90.6%) than either explanatory variable used on its own. Table 1 shows that both density and velocity make a statistically significant contribution to the amount of variance explained in Young's modulus, independently of each other. The contribution is highly significant in the case of density (p < 0.001), less so for velocity (p = 0.04). Because the density range of the calcaneus was rather small (143-375 kg m 3), and the different specimens were of rather uniform architecture, we increased both the density and the architecture range by including data from the bovine samples. It has been shown in previous studies that cancellous bone taken from different species, and from different bones in different species, usually has roughly the same distribution of relationships between the different variables. 11 However, we show here that the distributions of Young's modulus as a function of both density and velocity differ between the human and bovine material. Nevertheless, we regard the use of material from two different species as a useful procedure because the differences in distribution, particularly that of Young's modulus vs. density, can be explained in terms of architectural differences between the human and bovine bone, and we were particularly interested in determining the ability of ultrasound velocity to measure architecture. We first analyzed our data using the general linear model. This model can test for differences in both the slope of the regression lines fitted to separate data sets and also the heights of the distributions. The distributions of Young's modulus vs. density, and Young's modulus vs. velocity, were tested for each combination of the bovine and human data. In all cases, there was a significant statistical difference (p < 0.01) in slope between the human and the bovine data, except in the case of Young's modulus considered as a function of density for the human data and anteroposterior (AP) bovine data. Once it is established that a difference in slope exists between two distributions it is extremely problematic to assess any difference in heights of the distributions. We do, however, summarize the observed differences of the bovine compared with the human data in the final two rows of Table 2. The importance of these differences is discussed later.
Human Calcaneal Specimens Only
Human Calcaneal and Bovine Femoral Specimens Taken Together
The predictive value of V for Young's modulus is less than that of p, the R 2 values being 71.6% and 88.5%, respectively (Table
We first consider the effect of adding to the human calcaneal data the bovine femoral cancellous cubes measured in what was
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Bone Vol. 21, No. 2 August 1997:183-190
Table 2. A summary table showing the range of data for E, p, and V, and the regression slopes and intercepts for various relationships in each of the specimen groups Femur Calcaneus
AP
Range E (MPa) p (kg m -3) V (m sec 1)
6.0-81.3 143-375 1479-1778
186-1585 309-692 1820-2344
282-1905 309-692 1950-2399
426-2399 309-692 2042-2570
Slope Evs. p
3.13
Evs. V
15.1
pvs. V
4.29
2.42 [0.77, 3.65, n.s.] 8.34 [0.55, 9.64, <0.01] 2.84
2.03 [0.65, 11.57, <0.01] 7.40 [0.49, 12.61, <0.01] 3.02
1.98 [0.63, 10.64, <0.01] 6.68 [0.44, 15.9, <0.01] 2.35
229 [4.3] 3.26, 2.29
347 [6.4] 3.29, 2.57
458 [8.5] 3.31, 2.74
Intercept Evs. p [at log p = 2.5 (316 kg m-3)] E vs. V
54 3.25, 2.01
ML
PD
Values in brackets corresponding to "Slope" summarize the statistical significance of the difference in slope between bovine femur and human calcaneal data [ratio, F value, p value]. Values corresponding to "Intercept," E vs. p, refer to the value of E (unlogged) corresponding to the intercepts of the human and bovine regressions with a line drawn from log p = 2.5. The ratio of each bovine intercept to the human intercept is given in brackets. In the row "E vs. V" represents the coordinates (logged) for the lower bounds of each bovine regression line and the upper bound of the human line (V, E). always their least stiff direction (AP). We did this because the calcaneus was also measured in its least stiff direction. With the increased range of both density and velocity values, we find (Table 1) that V is now a slightly better predictor of E than is p; R 2 = 94.2% and 91.3%, respectively. If both V and p are used as explanatory variables R 2 is 96.4%, leaving only 3.6% of the variance unexplained. This is perhaps as high as one can expect it to be in a biological system. A similar effect is seen when the bovine data is of mediolateral (ML) and proximodistal (PD) origin. The relationships are summarized in Table 1 and Figures 1-4. In all three combined data sets, density and velocity acted as highly significant predictors (p < 0.001), independently of each other (Table 1). The plots of log softness as a function of log density, in the three different directions, suggest that the human calcaneal and bovine femoral specimens have two distinct stiffness distributions, with roughly equal slopes, but different heights, depending on the bovine cube direction included. When log stiffness is plotted as a function of log velocity, then the distribution appears more continuous, although somewhat curvilinear because the distributions for the two tissues have different slopes. There is considerable statistical difficulty in dealing with regressions that use sets of data points generated from the same specimen, if some of the data points are correlated, as is stiffness in the three directions presented here. That is, specimens with low values for density are likely also to have generally low values for stiffness and velocity, even though these latter two will vary somewhat in the three directions. Density is scalar, and cannot vary with direction. For this investigation we wished to test how reliable velocity was at distinguishing variation in architecture within the bovine cubes only, where the structural variation was greater, by virtue of the use of all three directions. We did this by a nonparametric and a parametric method.
Orthogonal Data for Bovine Femoral Specimens Only Nonparametric test. There is only one value of density for each cube. Therefore, it would be surprising if variations in density
between cubes gave much information about variation in E in three directions. (It is possible, of course, that denser and therefore stifler specimens might be more, or less, anisotropic than less dense and less stiff specimens, or vice versa. There is no evidence that this was so in our specimens and it has not been the case in previous experiments, l° ) Taking, as the null hypothesis that, in each cube, the variation in V as a function of direction is unrelated to the variation in E, then the rank of the values of E in each cube should bear no relation to the ranks of the values of V. This is not the case. Ranking the values for E as 1 (lowest), 2, and 3, the means for the ranks in each direction were 1.00, 2.03, 2.97, for AP, ML, and PD, respectively. In all specimens the PD direction was stiffest or equal to stiffest, A P least stiff, and ML intermediate. In only one sample were the PD and M L moduli equal. The values for V were somewhat less regularly distributed. Nevertheless, the mean values of V for the ranks in the corresponding directions were 1.56, 1.86, and 2.58 for AP, ML, and PD, respectively. Friedman's A N O V A for ranks 22 were: E: X22 = 35.0, p < 0.0001; V; X22 = 8.7, p = 0.013. These tests show that the results for velocity and stiffness are certainly not random with respect to direction. Page's L test can be used to determine whether the mean ranks for the values for Young's modulus in the three directions accord with the mean ranks of velocity 22 (L3A 8 = 234.5, p < 0.01). This finding strongly suggests that differences in stiffness values accord with differences in velocity.
Parametric test. For each cube we obtained the mean value of log E and of log V, and characterized each individual value of these properties in the three directions by its deviation from its respective mean. The plot of the deviations from the mean are shown in F i g u r e 5. There is an extremely strong positive correlation (r = 0.84, p < 0.0001). This shows that, in any cube, if the value of E is far from its mean, then the value of V tends also to be far from its mean, and in the same direction.
Bone Vol. 21, No. 2 August 1997:183-190
R. Hodgskinson et al. Ultrasound and stiffness of cancellous bone
187
Bovine femur ML
Bovine femur AP
0
0
0
E
E
~ffi 2
~r,n 2 >-
o _.1
0 ,_1
Human calcaneus
Human calcaneus 0
2.1
I
I
I
I
I
I
I
2.2
2.3
2.4
2.5
2.6
2.7
2.8
(a)
0
2.1
2.9
I
I
I
I
I
I
I
2.2
2.3
2.4
2.5
2.6
2.7
2.8
(a)
Log density
2.9
Log density
Bovine femur AP
Bovine femur ML
o
"0 0
'10 O
E
~e--2
E "~2
o >-
0 >-
r~
y
,-t
O'l O ,-I
0 ,-I
Human calcaneus
0
3.15
(b)
Human calcaneus
f
I
I
I
I
3.20
3.25
3.30
3.35
3.40
0
3.45
Log velocity
3.15
(b)
I
I
~
I
I
3.20
3.25
3.30
3.35
3.40
3.45
Log velocity
Figure 1. The relationship between Young's modulus plotted as (a) a function of density and Ib) a function of velocity for the human calcaneus and the bovine femur in the anteroposterior (AP) direction.
Figure 2. Young's modulus plotted as (a) a function of density and (b) a function of velocity for the human calcaneus and the bovine femur in the mediolateral (ML) direction.
Discussion
feature being measured is an architectural variable, such as fabric, which is direction-dependent. On the other hand, it could well be a variable, such as the quality of the bone material, which is likely to be scalar or at least to have a considerably lower anisotropy than fabric. W e have shown that the architectural (fabric) variance between the specimens of calcaneal bone used was quite small. 15 This explains why density accounts for a very substantial portion of the variance in the mechanical property of the tissue by itself. The message from analysis of femoral and calcaneal data together is again that we obtain more information by using both p and V as opposed to either one alone, even after allowing for the reduction in the number of degrees of freedom resulting from
The findings from the; analysis of the human calcaneal specimens show that V can act as a surrogate measure of p, but is not as effective as p on its own in accounting for the variance in the mechanical property to be predicted: stiffness. However, when p and V are used together, the explanatory power is greater, implying that V is measuring some feature of the cancellous bone (other than its incomplete measure of p) that adds to the explanatory power of the regression equation. Because, in the human calcaneus, we are measuring V in one direction only, we cannot tell whether it is giving information about a scalar or a vector property of the bone. On one hand, it is possible that the extra
188
R. Hodgskinson et al. Ultrasound and stiffness of cancellous bone
Bone Vol. 21, No. 2 August 1997:183-190
Bovine femur
¢0 '10 O
0
E -=~2
E r~
-o) 2
:=
t-
>..
0 >..
O~ O ._1
0 ...I
Human calcaneus
Human calcaneus 0 2.1
I
I
I
I
I
I
r
2.2
2.3
2.4
2.5
2.6
2.7
2.8
(a)
0 2.9
2.1
2.2
I
I
I
I
I
I
2.3
2.4
2.5
2.6
2.7
2.8
(a)
Log density
2.9
LogDens~
4 Bovine femur PD Bovine femur
0
O
E
/
O >O ,-I
ML
E
~2 0 _d
Human calcaneus Human calcaneus
0
3.15 (b)
I
I
I
I
I
3.20
3.25
3.30
3.35
3.40
0
3.45
Log velocity
Figure 3. Young's modulus plotted as (a) a function of density and (b) a function of velocity for the human calcaneus and the bovine femur in the proximodistal (PD) direction. introducing another explanatory variable. As with the human calcaneal specimens by themselves, V is varying to some extent as a function of density, but also as function of something else. We now consider the form of the relationships between the E and p and E and V i n the three directions (Figures 1 - 4 and Table 2). There is a different pattern of the scatter in stiffness depending on whether density or velocity is the explanatory variable. The slopes of E as a function of p and E as a function of V are different for the human and the various bovine data (Figures 1 - 4 and Table 2). In both the density and velocity distribution the AP bovine direction shows the greatest similarity with the human data in terms of slope; however, we have shown that all bovine slopes differ significantly from the human slope.
3.15 (b)
I
I
I
I
I
3.20
3.25
3.30
3.35
3.40
3.45
Log velocity
Figure 4. (a) Four regression lines for Young's modulus as a function of density. The regression lines do not extend beyond the values of the x variables. (b) Four regression lines for Young's modulus as a function of velocity. The regression lines do not extend beyond the values of the x variables. The labels of the bovine directions indicate the lower bounds of the regression lines referred to in Table 2.
Once it is established that there is a difference in the slope of two distributions it is problematic to quantify differences in height. However, the heights of the distribution are such that stiffness as a function of p seems to show two separate distributions in the bovine and human data sets, whereas stiffness as a function of velocity appears to approach a single, albeit curvilinear distribution (Figure 4a, b). We summarize the differences in height by the ratio given in Table 2. This is the ratio of (unlogged) values of the intercepts of the human and bovine data with a line drawn from log p = 2.5 for density. The ratio for each
Bone Vol. 21, No. 2 August 1997:183-190
0.06
-
R. Hodgskinson et al. Ultrasound and stiffness of cancellous bone
-
0.04
OoulP o >
0.02
E
•
•
•
•o
°
•
•
0
=_~j___e e _ . . . . o.oo
. . . . . . . . . . . . . . . . .
~= -0.02 n" -0.04
-0.06 -0.4
I
I
I
-0.3
-0.2
-0.1
0.0
I
I
0.t
0.2
0.3
Residuals from log mean stiffness
Figure 5. The residuals about the mean for velocity plotted as a function of the residuals about the mean for Young's modulus in the three bovine cube directions. If velocity were acting as a scalar property, there would be no correlation (circles: PD; squares: ML; triangles: AP). of the bovine sets in the density distribution ranges from 4.3 (AP) to 8.5 (PD). The velocity data approximate more closely to a single distribution. The pattern of distributions is just what one would expect if velocity were giving directional information, and density were not. Figure 4b shows three regressions summarizing distributions for log modulus as a function of log velocity in bovine bone. They are almost coincident except that they are spread out along their common axis. We summarize this shift by the coordinates of the lower bound of the regression line in the three bovine sets and the upper bound of the human set (Table 2). As can be seen there is a progressive shift (AP to ML to PD) in the bovine distributions away from the human distribution. In the region where they coincide velocity gives virtually the same prediction for Young's modulus regardless of loading direction. This is not the case when density is used as a predictor. In that case knowledge of the direction of loading is also needed (Figure 4a). Another possible explanation for the difference in heights of the distributions of E as a function of density between the human bone and any bovine cube direction should be considered. It may relate to bone quality. The human bone, coming from relatively aged people (aged 5cL90 years), probably was of poorer quality
189
than that of the bovine specimens, thus having a lower value of E for any particular value of density. It is possible partially to distinguish directly between the effects of architecture and bone quality by making use of the fact that, in each bovine cube, we measured E and V in three orthogonal directions. The nonparametric test we employed showed that the ranks of V for each cube correlate quite closely with the ranks for E. We performed this test to step around the statistical complexity of dealing with separate sets of data from one specimen. Even more compelling is Figure 5, which demonstrates that the deviations of the velocity values from their mean are positively correlated with deviations of E values from their mean. Because density and bone quality have no effect on these departures, being invariant with direction in each cube, these results demonstrate incontrovertibly that V is affected by the architecture of the cubes. Heaney and Kanis 8 describe some evidence 15 which shows that BUA acts as a surrogate for density in cancellous bone and they question whether velocity is measuring something different from attenuation (e.g., structure). Our present work has demonstrated that, in the particular specimens considered, velocity is affected by architectural variation. When used in combination with a measure of density it is possible to explain virtually all the variance in the measured stiffness of the samples. These findings warrant further investigation particularly with a view to replacing the invasive measure of apparent density used here with a noninvasive determination by quantitative computed tomography (QCT) or DXA. In a previous study n5 we demonstrated that BUA does not add any explanatory power over and above that provided by density for cancellous bone stiffness. However, our velocity data here were treated in a slightly different way as compared with the BUA data in our other study; that is, the BUA data were based solely on human calcaneal samples and did not include bovine femoral data. Table 3 summarizes the BUA data treated in such a way as to be directly comparable with the velocity data. As can be seen, BUA is considerably worse than density at predicting the measured stiffness of the specimens in the new data set, and a combination of density and BUA is only marginally better than density alone. In contrast, as we have seen, velocity provides far better explanatory power than density alone, a combination of the two providing the best fit. This strongly suggests that BUA and velocity are, to some extent, measuring different properties of the cancellous bone. It is of interest that adding BUA to velocity leads to a small, but significant, increase in R 2 (Table 3), compared with the value for velocity alone, similar to the effect of adding density to velocity. A combination of velocity and BUA and density provides the best fit of all. The predictive power of velocity for cancellous bone stiffness
Table 3. A summary table showing the amount of variance (R2) in Young's modulus (response) explained by various combinations of predictors Calcaneus and femur Predictor Density BUA Density and BUA Velocity Velocity and density Velocity and BUA Density, velocity, and BUA
AP (%)
ML (%)
PD (%)
91 59 92 [4.7, p < 0.05] 94 96 [25.6, p << 0.01] 96 [17.8, p << 0.01] 97
89 62 92 [12.6, p << 0.01] 95 97 [19.3, p << 0.01] 96 [17.7, p << 0.01] 98
88 58 90 [9.9, p < 0.01] 95 97 [25.3, p << 0.01] 97 [17.6, p << 0.01] 98
The figures in brackets [F value, p value] indicates the significance of the increase in R 2 when the second named predictor is added to the first named predictor.
190
R. H o d g s k i n s o n et al. Ultrasound a n d stiffness o f cancellous bone
as measured in this study is greater than that reported by others. 2'23 This probably reflects our use of both human and bovine material, providing an increase in the range of architectural variability and, more importantly, of density. Bouxsein et al. t report a correlation of only 0.76 between speed of sound (SOS) through intact human calcanei and the compressive (elastic) modulus of cancellous bone cubes taken from their interiors. The modulus and velocity data obtained from bovine cubes by Turner and Eich 23 (which we have reanalyzed) show a relatively weak association using either apparent velocity of ultrasound (AVU) or ultrasonic transmission velocity (UTV) (R 2 = 48% and 33%, respectively). As in our study, but unlike in that of Bouxsein et al., Turner and Eich's ultrasonic measurements were made on isolated cubes. The results from our study suggest that ultrasound velocity has the potential to provide a more accurate means of assessing fracture risk in vivo than techniques such as DXA which provide only density information. Of course, care must be taken in extrapolating from in vitro studies to the clinical situation. For instance, in a recent in vivo study, SOS and BUA at the calcaneus were assessed as predictors for hip fracture. 6 Although both SOS and BUA had predictive capacity for hip fracture, BUA was the better predictor. This was not the case in our study, where stepwise regression always picked velocity as the best predictor of the mechanical property in all three directions, ahead of density, with BUA last. We have demonstrated that velocity gives a measure of architecture beyond that given by density alone. The theoretical and clinical implications of this finding should be pursued in future work.
B o n e Vol. 21, No. 2 August 1997:183-190
7. 8. 9.
10. 11.
12.
13.
14.
15.
16. 17. 18. 19.
Acknowledgments: The provision o f an S E R C studentship for C.F.N. is gratefully a c k n o w l e d g e d . W e thank Dr. Philip Q u i n l a n (Department o f P s y c h o l o g y , University of York) for statistical advice.
20.
21.
References 1. Bouxsein, M. L., Radloff, S. E., and Hayes, W. C. Quantitative ultrasound of the calcaneus reflects trabecular bone strength, modulus and morphology. J Bone Miner Res 10(Suppl. 1):S175; 1995. 2. Brear, K., Currey, J. D., Raines, S., and Smith, K. J. Density and temperature effects on some mechanical properties of cancellous bone. Eng Med 17:163167; 1988. 3. Carter, D. R. and Hayes, W. C. Bone compressive strength: The influence of density and strain rate. Science 194:1174-1175; 1976. 4. Currey, J. D. Power law models for the mechanical properties of cancellous bone. Eng Med 15:153-154; 1986. 5. Evans, J. A. and Tavakoli, M. B. Ultrasonic attenuation and velocity in bone. Phys Med Biol 35:1387-1396; 1990. 6. Hans, D., Dargent-Molina, P., Schott, A. M/~Sebert, J. L., Cormier, C., Kotzki, P. O., Delmas, P. D., Pouilles, J. M., Breart, G., and Meunier, P. J. Ultrasono-
22. 23. 24.
graphic heel measurements to predict hip fracture in elderly women: The EPIDOS prospective study. Lancet 346:511-514; 1996. Hans, D., Schott, A. M., and Meunier, P. J. Ultrasonic assessment of bone: A review. Eur J Med 2:157-163; 1993. Heaney, R. P. and Kanis, J. A. Editorial: The interpretation and utility of ultrasound measurements of bone. Bone 18:491-492; 1996. 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 204:115-121; 1990. Hodgskinson, R. and Currey, J. D. Effect of structural variation on Young's modulus of non-human cancellous bone. Proc lnst Mech Eng 20:43-52; 1990. 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. Hodgskinson, R. and Currey, J. D. The separate effects of osteoporosis and density on the strength and stiffness of human cancellous bone. Clin Biomech 8:262-268; 1993. Kleerekoper, M., Villaneuva, A. R., Stanciu, J., Rao, D. S., and Parfitt, A. M. The role of three dimensional trabecular microstructure in the pathogenesis of vertebral compression fractures Calcif Tissue Int 37:594-597; 1985. 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 Meas I 1:243249; 1990. Langton, C. M., Njeh, C. F., Hodgskinson, R., and Currey, J. D. Prediction of mechanical properties of the human calcaneus by broadband ultrasonic attenuation. Bone 18:495-503; 1996. Langton, C. M., Palmer, S. B., and Porter, R. W. The measurement of broadband ultrasonic attenuation in cancellous bone. Eng Med 13:89-91; 1984. Linde, F. and Hvid, I. Stiffness behaviour of trabecular bone specimens. J Biomech 20:83-89; 1987. Mosekilde, Li. Sex differences in age-related loss of vertebral trabecular bone mass and structure-biomechanical consequences. Bone 10:425-432; 1989. Odgaard, A. and Linde, F. The underestimation of Young's modulus in compressive testing of cancellous bone specimens. J Biomecb 24:691-698; 1991. Rice, J. C., Cowin, C. S., and Bowman, A. J. On the dependence of the elasticity and strength of cancellous bone on apparent density. J Biomech 21:155-168; 1988. Ross, P., Huang, C., Davis, J., Imose, K., Vogel, J., and Wasnich, R. Predicting vertebral deformity using bone densitometry at various sites and calcaneal ultrasound. Bone 16:325-332; 1995. Siegel, S. and Castellan, N. J. Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill; 1988. Turner, C. H. and Eich, M. Ultrasonic velocity as a predictor of strength in bovine cancellous bone. Calcif Tissue Int 49:116-119; 1991. Wahner, H. W. and Fogelman, I. The Evaluation of Osteoporosis: Dual Energy X-Ray Absorptiometry in Clinical Practice. Cambridge: Cambridge University Press; 1994.
Date Received: September 18, 1996 Date Revised." April 9, 1997 Date Accepted: April 9, 1997
ELSEVIER
The Ability of Ultrasound Velocity to Predict the Stiffness of Cancellous Bone In Vitro R. H O D G S K I N S O N , ~ C. F. N J E H , 2 J. D. C U R R E Y , 3 and C. M. L A N G T O N l Centre for Metabolic Bone Disease, University of Hull and Royal Hull Hospitals Trust, Hull, UK 2 Medical Physics Department, Queen Elizabeth Medical Centre, Birmingham, UK 3 Department of Biology, University of York, York, UK
Key Words: Cancellous bone; Ultrasound velocity; Young's modulus; Trabecular structure.
The mechanical status of bones is an important consideration in skeletal pathological conditions such as osteoporosis, which result in fracture at predominantly cancellous bone sites. Density is a ge~d predictor of the stiffness and strength of cancellous bone. However, these mechanical properties are also dependent on the cancellous bone's architecture. The objective of this work was to investigate the ability of ultrasound velocity to predict the Young's modulus of elasticity of cancellous bone. The cancellous bone specimens were 20 mm cubes from bovine femur and 21 mm diameter mediolateral cylinders cored from human calcaneus. Ultrasound velocity (11) and Young's modulus (E) were determined in three orthogonal directions for the bovine cubes [anteroposterior (AP), mediolateral (ML), and proximodistal (PD)], and mediolaterally in the caicaneus. Apparent density (p) was determined after the other tests. Density alone explains 87.6% of the variance of Young's modulus in human calcaneal and bovine femoral bone tested in the PD direction only. Velocity, however, explains 95% and a combination of density and velocity 97%. Velocity and stiffness are not random with respect to the three directions in the bovine specimens. Further, for each cube we obtained the mean of the three values of E and of V, and characterized each value of E and V by their deviation from their mean. There is an extremely strong positive correlation (r = 0.80) showing that the degree of deviation is consistent for E and V, and of the same sign. These results demonstrate that the velocity of ultrasound in cubes of cancellous bone can give structure-specific information. In particular, knowledge of both density and velocity allows better predictions of stiffness than do density or ultrasound velocity on their own. Because there are noninvasive methods of measuring density that do not depend on ultrasonic measurement the combination of these two measurements promises, eventually, to give improved assessment of a bone's weakness and liability to fracture. (Bone 21: 183-190; 1997) © 1997 by Elsevier Science Inc. All rights reserved.
Introduction The mechanical status of bones is an important consideration in skeletal pathological conditions such as osteoporosis, where a period of asymptomatic bone loss reduces bone strength and increases fracture risk, predominantly at cancellous bone sites. Hence, although osteoporosis results from a complex, incompletely understood, set of physiological and biochemical processes, the clinical manifestation (fracture) can be understood in purely mechanical terms. At present, the clinical assessment of osteoporosis relies mainly on bone mineral density (BMD) measurements using dual-energy X-ray absorptiometry (DXA). 24 Although DXA is a convenient and precise method of measurement, it is available in a rather small number of centers, being relatively expensive. Also, the equipment is bulky and uses ionizing radiation, although the average skin entrance dose (24 ~Sv) is considerably less than the typical radiation dose for an anteroposterior chest film (300 ~Sv). To date, conventional DXA systems do not allow textural analysis of the scan images. Density (a scalar quantity) is a good predictor of the stiffness of cancellous bone and, because there is a strong relationship between stiffness and strength of cancellous bone, it is also a good predictor of the strength. 9'12 Density is a particularly good predictor of bone strength if the bone is reasonably uniform in structure. 15'2° However, bone strength and stiffness are also dependent on bone microstructure and architecture (the arrangement of the bony material in space). 1°'13'1s Strength, stiffness, and architecture are all vector quantities. Ultrasound has been developed recently as a tool for the investigation of skeletal status. 16 Ultrasound is a traveling mechanical vibration and the mechanical properties of the medium progressively alter the shape, intensity, and speed of the propagating wave. Broadband ultrasonic attenuation (BUA) and velocity (V) are the two most commonly quoted ultrasound parameters. There has been growing interest in the use of ultrasound measurements for the detection and management of osteoporosis. 7 It has been used in both clinical zl and research environments for the prediction of the mechanical properties of cancellous bone, but there is little evidence that ultrasound gives any more information than would be obtained from a knowledge of the density of the cancellous material, as demonstrated in a previous report from our laboratory. 15 However, in that study, we investigated the relationships between BUA and the mechanical
Address for correspondence and reprints: Dr. R. A. Hodgskinson, Academic Department of Medical Physics, Centre for Metabolic Bone Disease, HS Brocklehurst Building, Hull Royal Infirmary, 230-236 Anlaby Road, Hull HU3 2RW, UK. E-mail: r.a.hodgskinson@pgec. hull.ac.uk © 1997 by ElsevierScienceInc. All rights reserved.
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8756-3282/97/$17.00 PII $8756-3282(97)00098-7
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properties and density in human calcaneal bone only. The conclusion from that work, in which structural variation in the specimens was low (due to a combination of uniformity of structure between specimens and the fact that we tested in the mediolateral direction only), was that BUA acted merely as a surrogate for apparent density. However, the possibility remains that ultrasound, being propagated in a particular direction, could give directional information. A recent editorial in this journal s reviewed the current understanding of what factors influence the two main ultrasonic parameters, attenuation and velocity. Referring to Langton et al. 15 the authors pointed to evidence that BUA is merely a surrogate measure for density. It was suggested that more work needs to be done on BUA to confirm this and also the question needs to be addressed as to "whether velocity does not measure something different from attenuation. ''s The objective of this work was to investigate the ability of ultrasound velocity to predict the mechanical properties of cancellous bone. To clarify the matter we increased the range of densities and the amount of structural variation compared with that used in 1996 by Langton et al.ls by adding to the human calcaneal specimens, used in the previous study, cubes of bovine cancellous bone which were tested in three directions. Materials and Methods Cancellous bone from two sources was used in this study: bovine femur and human calcaneus. In each bovine specimen ultrasound velocity (V) and Young's modulus (E) were determined in three orthogonal directions. In the human calcaneus they were measured in the mediolateral direction only. The mediolateral direction is the direction measured clinically, and is also the least stiff direction in the calcaneus (see subsequent text). Apparent density (p) was determined after the other tests. Therefore, for each calcaneal specimen we had one value of p, and one value each of Young's modulus (E) and of ultrasound velocity (V). For each bovine specimen we had one value of p and three values of E and of V.
Sample Preparation 18 cubes, each with sides of 20 mm, were prepared from the proximal and distal ends of fresh bovine femora using a high precision fine diamond cutting saw (Exakt), with final smoothing on fine carborundum grit. Care was taken to produce parallel surfaces. The edges of the cubes were approximately in line with the longitudinal (proximodistal, PD), anteroposterior (AP), and mediolateral (ML) axes of the bones from which they were obtained. There is necessarily some uncertainty in defining the anatomical axes of the disarticulated femur and, therefore, in this study, the three axes were our best estimate of the actual anatomical axes. The cubes were, however, all oriented in the same direction in relation to the bone, so any deviation of the cube axes from the actual anatomical axes of the femurs used was consistent for all the bovine specimens. During preparation, the cubes were kept moist. The samples were then frozen at - 2 0 ° C until tested. Prior to the ultrasonic and mechanical measurements, the specimens were thawed, and thoroughly degassed under water in a vacuum desiccator. The degassing process removed any air bubbles trapped within the samples, the presence of which would make the ultrasonic measurements unreliable. The human calcaneal samples were obtained from 20 cadavers (10 male and 10 female) with an age range of 59-90 years. No pathology information was available. After removal of external soft tissue, a coring drill of 21 mm internal diameter was used to remove a sample whose long axis coincided with the
Bone Vol. 21, No. 2 August 1997:183-190 mediolateral direction of the calcaneus. The region of bone removed was the same as that through which ultrasound would pass in a clinical measurement. The cortical endplates were removed using the Exakt, producing cylinders of cancellous bone with parallel end faces. Following preparation the calcaneal samples were handled as described for the bovine material.
Ultrasonic Velocity The contact ultrasonic bone analyzer (CUBA) system 14 was used. It consists of a combined spike generator (transmitter) and digital receiver interfaced to a portable PC with dedicated software. Two 1 MHz (nominal frequency), 13 mm diameter broadband ultrasonic transducers, the transmitter, and the receiver, were mounted in a digital Vernier gauge sliding caliper. The caliper was used to measure sample thickness. Ultrasonic measurements were performed under water. Detergent was added to improve sample wetting. The transducers were placed in direct contact with the sample. Velocity (V) was calculated as the sample thickness divided by the transit time, transit time being defined as the time delay between the leading edge of the excitation pulse and the leading edge of the received ultrasonic pulse. The "leading edge" refers to the "trigger point" time in the case of the excitation pulse, and the time at which the receiving transducer first detects a departure of amplitude from the zero base line for the received pulse. All the measurements were carried out at room temperature (~20°C).
Young's Modulus Young's modulus (E) was obtained by unconfined compressive testing using an Instron 1122 universal testing machine. The specimens were immersed in a water bath at room temperature. Temperature has only a slight effect on the mechanical properties 2 and on the ultrasonic velocity5 of cancellous bone; therefore, room temperature was used rather than physiological temperature for convenience and to allow comparison with most data reported in the literature. The specimens were compressed between the flat end of a smooth but unpolished stainless-steel loading column and the base of the water bath, which sat directly on a 5 kN load cell. The compliance of the loading system was determined at appropriate loads, and corrected for in subsequent elasticity calculations. Linde and Hvid ~7 demonstrated that different constraints on the loaded specimen (placed either directly on wet platens, cemented to the platens, or constrained in a jacket) can produce differences in the measured strain. Because loading was required in three orthogonal directions in our bovine specimens, we did not use cement or otherwise constrain the specimens. Because we used the same loading conditions in all three directions, inconsistencies produced by the end effects will almost certainly be small. In all the bovine cubes, the proximal-distal direction was the last to be tested. The mediolateral and anteroposterior directions were tested first or second randomly. The elasticity of the bovine cubes was measured in the three orthogonal directions in turn; therefore, it was important that the specimen should remain undamaged by the process of measurement in each of the first two directions. To obviate the possibility of loading the cube into the yield region, the compression load was gradually increased over several cycles until the load deformation curve was linear. The specimens in this study were not specifically preconditioned, 17 although the cyclic loading described above will approximate a limited preconditioning regime. The maximum strain on the specimens during these cycles was on average 0.7% for the human calcaneal specimens and 0.4% for the bovine femoral specimens. Odgaard and Linde 19 have
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R. Hodgskinson et al. Ultrasound and stiffness of cancellous bone
185
Table 1. A summary of the regression data using elasticity as the response and density (p) and velocity as predictors in each case
Intercept Human calcaneal samples only (n = 20) Predictor: p Predictor: V Predictors: p and V Human calcaneal and bovine femoral AP (n = 18) Predictor: p Predictor: V Predictors: p and V Human calcaneal and bovine femoral ML (n = 18) Predictor: p Predictor: V Predictors: p and V Human calcaneal and bovine femoral PD (n = 18) Predictor: p Predictor: V Predictors: p and V
Coefficient p (t-ratio, p value)
-6.09 -46.9 -19.4
3.13
-8.43 -37.7 -26.8
4.15
-8.81 -35.8 -27.9
4.32
-9.37 -34.0 -27.2
4.56
shown that Young's modulus does not significantly decrease during cyclic compression to 0.8% strain. In our study only 5 of the 38 specimens (all human) exhibited strains marginally above 0.8%, the maximum being 0.92%. We are confident that this process did not damage the material significantly, which would lead to measurement artifacts in subsequent directions. The load and deformation were plotted by a pen recorder. For all specimens the crosshead speed was 1 mm m i n - 1 producing a nominal strain rate of about 0.0017 sec-1. Young's modulus was calculated from the maximum slope of the stress-strain curve in the preyield region. The mechanical measurements were performed on defatted samples. Carter and ttayes 3 have shown that the marrow in the intertrabecular spaces has no effect on the mechanical behavior of trabecular bone at the strain rate used in our investigation. In general, we believe that any artifacts such as those due to a lack of preconditioning, specimen constraint, or removal of marrow will be consistent between the specimens. Any lack of accuracy in determining Young's modulus can only have degraded the relationships we report.
Apparent Density Apparent density, 9, !is defined as the ratio of dehydrated tissue mass to total specimen volume. The density measurements were performed after the ultrasonic and mechanical testing. To obtain the dehydrated tissue mass, fat was removed from the specimen, as described by Brear et al.2 This involved subjecting the specimen to a high-speed jet of water, and then compressed air. This process was repeated until no fat was visible. The specimens were then tumbled overnight in ~a excess of 2:1 chloroform:methanol mixture. The defatted cubes were then dried at 70°C to constant weight. Volume was obtained from the external dimensions of the cube. The dry weight divided by the volume gave the apparent density (kg m-3). In the regression equations presented here the values are logged (base 10), because we wished to obtain power law relationships .4 Results
2.42 (6.13, <0.001)
1.75 (4.85, <0.001)
1.50 (4.39, <0.001)
1.56 (5.02, <0.001)
Coefficient V (t-ratio, p value)
R2 (%)
15.1 4.66 (2.22, 0.040)
88.5 71.6 90.6
12.2 7.50 (7.22, <0.001)
91.3 94.2 96.4
11.6 8.03 (9.04, <0.001)
89.1 94.9 96.6
11.0 7.76 (10.66, <0.001)
87.6 95.0 97.0
1). However, the equation using both V and p produces a somewhat higher value of R 2 (90.6%) than either explanatory variable used on its own. Table 1 shows that both density and velocity make a statistically significant contribution to the amount of variance explained in Young's modulus, independently of each other. The contribution is highly significant in the case of density (p < 0.001), less so for velocity (p = 0.04). Because the density range of the calcaneus was rather small (143-375 kg m 3), and the different specimens were of rather uniform architecture, we increased both the density and the architecture range by including data from the bovine samples. It has been shown in previous studies that cancellous bone taken from different species, and from different bones in different species, usually has roughly the same distribution of relationships between the different variables. 11 However, we show here that the distributions of Young's modulus as a function of both density and velocity differ between the human and bovine material. Nevertheless, we regard the use of material from two different species as a useful procedure because the differences in distribution, particularly that of Young's modulus vs. density, can be explained in terms of architectural differences between the human and bovine bone, and we were particularly interested in determining the ability of ultrasound velocity to measure architecture. We first analyzed our data using the general linear model. This model can test for differences in both the slope of the regression lines fitted to separate data sets and also the heights of the distributions. The distributions of Young's modulus vs. density, and Young's modulus vs. velocity, were tested for each combination of the bovine and human data. In all cases, there was a significant statistical difference (p < 0.01) in slope between the human and the bovine data, except in the case of Young's modulus considered as a function of density for the human data and anteroposterior (AP) bovine data. Once it is established that a difference in slope exists between two distributions it is extremely problematic to assess any difference in heights of the distributions. We do, however, summarize the observed differences of the bovine compared with the human data in the final two rows of Table 2. The importance of these differences is discussed later.
Human Calcaneal Specimens Only
Human Calcaneal and Bovine Femoral Specimens Taken Together
The predictive value of V for Young's modulus is less than that of p, the R 2 values being 71.6% and 88.5%, respectively (Table
We first consider the effect of adding to the human calcaneal data the bovine femoral cancellous cubes measured in what was
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Bone Vol. 21, No. 2 August 1997:183-190
Table 2. A summary table showing the range of data for E, p, and V, and the regression slopes and intercepts for various relationships in each of the specimen groups Femur Calcaneus
AP
Range E (MPa) p (kg m -3) V (m sec 1)
6.0-81.3 143-375 1479-1778
186-1585 309-692 1820-2344
282-1905 309-692 1950-2399
426-2399 309-692 2042-2570
Slope Evs. p
3.13
Evs. V
15.1
pvs. V
4.29
2.42 [0.77, 3.65, n.s.] 8.34 [0.55, 9.64, <0.01] 2.84
2.03 [0.65, 11.57, <0.01] 7.40 [0.49, 12.61, <0.01] 3.02
1.98 [0.63, 10.64, <0.01] 6.68 [0.44, 15.9, <0.01] 2.35
229 [4.3] 3.26, 2.29
347 [6.4] 3.29, 2.57
458 [8.5] 3.31, 2.74
Intercept Evs. p [at log p = 2.5 (316 kg m-3)] E vs. V
54 3.25, 2.01
ML
PD
Values in brackets corresponding to "Slope" summarize the statistical significance of the difference in slope between bovine femur and human calcaneal data [ratio, F value, p value]. Values corresponding to "Intercept," E vs. p, refer to the value of E (unlogged) corresponding to the intercepts of the human and bovine regressions with a line drawn from log p = 2.5. The ratio of each bovine intercept to the human intercept is given in brackets. In the row "E vs. V" represents the coordinates (logged) for the lower bounds of each bovine regression line and the upper bound of the human line (V, E). always their least stiff direction (AP). We did this because the calcaneus was also measured in its least stiff direction. With the increased range of both density and velocity values, we find (Table 1) that V is now a slightly better predictor of E than is p; R 2 = 94.2% and 91.3%, respectively. If both V and p are used as explanatory variables R 2 is 96.4%, leaving only 3.6% of the variance unexplained. This is perhaps as high as one can expect it to be in a biological system. A similar effect is seen when the bovine data is of mediolateral (ML) and proximodistal (PD) origin. The relationships are summarized in Table 1 and Figures 1-4. In all three combined data sets, density and velocity acted as highly significant predictors (p < 0.001), independently of each other (Table 1). The plots of log softness as a function of log density, in the three different directions, suggest that the human calcaneal and bovine femoral specimens have two distinct stiffness distributions, with roughly equal slopes, but different heights, depending on the bovine cube direction included. When log stiffness is plotted as a function of log velocity, then the distribution appears more continuous, although somewhat curvilinear because the distributions for the two tissues have different slopes. There is considerable statistical difficulty in dealing with regressions that use sets of data points generated from the same specimen, if some of the data points are correlated, as is stiffness in the three directions presented here. That is, specimens with low values for density are likely also to have generally low values for stiffness and velocity, even though these latter two will vary somewhat in the three directions. Density is scalar, and cannot vary with direction. For this investigation we wished to test how reliable velocity was at distinguishing variation in architecture within the bovine cubes only, where the structural variation was greater, by virtue of the use of all three directions. We did this by a nonparametric and a parametric method.
Orthogonal Data for Bovine Femoral Specimens Only Nonparametric test. There is only one value of density for each cube. Therefore, it would be surprising if variations in density
between cubes gave much information about variation in E in three directions. (It is possible, of course, that denser and therefore stifler specimens might be more, or less, anisotropic than less dense and less stiff specimens, or vice versa. There is no evidence that this was so in our specimens and it has not been the case in previous experiments, l° ) Taking, as the null hypothesis that, in each cube, the variation in V as a function of direction is unrelated to the variation in E, then the rank of the values of E in each cube should bear no relation to the ranks of the values of V. This is not the case. Ranking the values for E as 1 (lowest), 2, and 3, the means for the ranks in each direction were 1.00, 2.03, 2.97, for AP, ML, and PD, respectively. In all specimens the PD direction was stiffest or equal to stiffest, A P least stiff, and ML intermediate. In only one sample were the PD and M L moduli equal. The values for V were somewhat less regularly distributed. Nevertheless, the mean values of V for the ranks in the corresponding directions were 1.56, 1.86, and 2.58 for AP, ML, and PD, respectively. Friedman's A N O V A for ranks 22 were: E: X22 = 35.0, p < 0.0001; V; X22 = 8.7, p = 0.013. These tests show that the results for velocity and stiffness are certainly not random with respect to direction. Page's L test can be used to determine whether the mean ranks for the values for Young's modulus in the three directions accord with the mean ranks of velocity 22 (L3A 8 = 234.5, p < 0.01). This finding strongly suggests that differences in stiffness values accord with differences in velocity.
Parametric test. For each cube we obtained the mean value of log E and of log V, and characterized each individual value of these properties in the three directions by its deviation from its respective mean. The plot of the deviations from the mean are shown in F i g u r e 5. There is an extremely strong positive correlation (r = 0.84, p < 0.0001). This shows that, in any cube, if the value of E is far from its mean, then the value of V tends also to be far from its mean, and in the same direction.
Bone Vol. 21, No. 2 August 1997:183-190
R. Hodgskinson et al. Ultrasound and stiffness of cancellous bone
187
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Bovine femur AP
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Figure 1. The relationship between Young's modulus plotted as (a) a function of density and Ib) a function of velocity for the human calcaneus and the bovine femur in the anteroposterior (AP) direction.
Figure 2. Young's modulus plotted as (a) a function of density and (b) a function of velocity for the human calcaneus and the bovine femur in the mediolateral (ML) direction.
Discussion
feature being measured is an architectural variable, such as fabric, which is direction-dependent. On the other hand, it could well be a variable, such as the quality of the bone material, which is likely to be scalar or at least to have a considerably lower anisotropy than fabric. W e have shown that the architectural (fabric) variance between the specimens of calcaneal bone used was quite small. 15 This explains why density accounts for a very substantial portion of the variance in the mechanical property of the tissue by itself. The message from analysis of femoral and calcaneal data together is again that we obtain more information by using both p and V as opposed to either one alone, even after allowing for the reduction in the number of degrees of freedom resulting from
The findings from the; analysis of the human calcaneal specimens show that V can act as a surrogate measure of p, but is not as effective as p on its own in accounting for the variance in the mechanical property to be predicted: stiffness. However, when p and V are used together, the explanatory power is greater, implying that V is measuring some feature of the cancellous bone (other than its incomplete measure of p) that adds to the explanatory power of the regression equation. Because, in the human calcaneus, we are measuring V in one direction only, we cannot tell whether it is giving information about a scalar or a vector property of the bone. On one hand, it is possible that the extra
188
R. Hodgskinson et al. Ultrasound and stiffness of cancellous bone
Bone Vol. 21, No. 2 August 1997:183-190
Bovine femur
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Figure 3. Young's modulus plotted as (a) a function of density and (b) a function of velocity for the human calcaneus and the bovine femur in the proximodistal (PD) direction. introducing another explanatory variable. As with the human calcaneal specimens by themselves, V is varying to some extent as a function of density, but also as function of something else. We now consider the form of the relationships between the E and p and E and V i n the three directions (Figures 1 - 4 and Table 2). There is a different pattern of the scatter in stiffness depending on whether density or velocity is the explanatory variable. The slopes of E as a function of p and E as a function of V are different for the human and the various bovine data (Figures 1 - 4 and Table 2). In both the density and velocity distribution the AP bovine direction shows the greatest similarity with the human data in terms of slope; however, we have shown that all bovine slopes differ significantly from the human slope.
3.15 (b)
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Figure 4. (a) Four regression lines for Young's modulus as a function of density. The regression lines do not extend beyond the values of the x variables. (b) Four regression lines for Young's modulus as a function of velocity. The regression lines do not extend beyond the values of the x variables. The labels of the bovine directions indicate the lower bounds of the regression lines referred to in Table 2.
Once it is established that there is a difference in the slope of two distributions it is problematic to quantify differences in height. However, the heights of the distribution are such that stiffness as a function of p seems to show two separate distributions in the bovine and human data sets, whereas stiffness as a function of velocity appears to approach a single, albeit curvilinear distribution (Figure 4a, b). We summarize the differences in height by the ratio given in Table 2. This is the ratio of (unlogged) values of the intercepts of the human and bovine data with a line drawn from log p = 2.5 for density. The ratio for each
Bone Vol. 21, No. 2 August 1997:183-190
0.06
-
R. Hodgskinson et al. Ultrasound and stiffness of cancellous bone
-
0.04
OoulP o >
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~= -0.02 n" -0.04
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Figure 5. The residuals about the mean for velocity plotted as a function of the residuals about the mean for Young's modulus in the three bovine cube directions. If velocity were acting as a scalar property, there would be no correlation (circles: PD; squares: ML; triangles: AP). of the bovine sets in the density distribution ranges from 4.3 (AP) to 8.5 (PD). The velocity data approximate more closely to a single distribution. The pattern of distributions is just what one would expect if velocity were giving directional information, and density were not. Figure 4b shows three regressions summarizing distributions for log modulus as a function of log velocity in bovine bone. They are almost coincident except that they are spread out along their common axis. We summarize this shift by the coordinates of the lower bound of the regression line in the three bovine sets and the upper bound of the human set (Table 2). As can be seen there is a progressive shift (AP to ML to PD) in the bovine distributions away from the human distribution. In the region where they coincide velocity gives virtually the same prediction for Young's modulus regardless of loading direction. This is not the case when density is used as a predictor. In that case knowledge of the direction of loading is also needed (Figure 4a). Another possible explanation for the difference in heights of the distributions of E as a function of density between the human bone and any bovine cube direction should be considered. It may relate to bone quality. The human bone, coming from relatively aged people (aged 5cL90 years), probably was of poorer quality
189
than that of the bovine specimens, thus having a lower value of E for any particular value of density. It is possible partially to distinguish directly between the effects of architecture and bone quality by making use of the fact that, in each bovine cube, we measured E and V in three orthogonal directions. The nonparametric test we employed showed that the ranks of V for each cube correlate quite closely with the ranks for E. We performed this test to step around the statistical complexity of dealing with separate sets of data from one specimen. Even more compelling is Figure 5, which demonstrates that the deviations of the velocity values from their mean are positively correlated with deviations of E values from their mean. Because density and bone quality have no effect on these departures, being invariant with direction in each cube, these results demonstrate incontrovertibly that V is affected by the architecture of the cubes. Heaney and Kanis 8 describe some evidence 15 which shows that BUA acts as a surrogate for density in cancellous bone and they question whether velocity is measuring something different from attenuation (e.g., structure). Our present work has demonstrated that, in the particular specimens considered, velocity is affected by architectural variation. When used in combination with a measure of density it is possible to explain virtually all the variance in the measured stiffness of the samples. These findings warrant further investigation particularly with a view to replacing the invasive measure of apparent density used here with a noninvasive determination by quantitative computed tomography (QCT) or DXA. In a previous study n5 we demonstrated that BUA does not add any explanatory power over and above that provided by density for cancellous bone stiffness. However, our velocity data here were treated in a slightly different way as compared with the BUA data in our other study; that is, the BUA data were based solely on human calcaneal samples and did not include bovine femoral data. Table 3 summarizes the BUA data treated in such a way as to be directly comparable with the velocity data. As can be seen, BUA is considerably worse than density at predicting the measured stiffness of the specimens in the new data set, and a combination of density and BUA is only marginally better than density alone. In contrast, as we have seen, velocity provides far better explanatory power than density alone, a combination of the two providing the best fit. This strongly suggests that BUA and velocity are, to some extent, measuring different properties of the cancellous bone. It is of interest that adding BUA to velocity leads to a small, but significant, increase in R 2 (Table 3), compared with the value for velocity alone, similar to the effect of adding density to velocity. A combination of velocity and BUA and density provides the best fit of all. The predictive power of velocity for cancellous bone stiffness
Table 3. A summary table showing the amount of variance (R2) in Young's modulus (response) explained by various combinations of predictors Calcaneus and femur Predictor Density BUA Density and BUA Velocity Velocity and density Velocity and BUA Density, velocity, and BUA
AP (%)
ML (%)
PD (%)
91 59 92 [4.7, p < 0.05] 94 96 [25.6, p << 0.01] 96 [17.8, p << 0.01] 97
89 62 92 [12.6, p << 0.01] 95 97 [19.3, p << 0.01] 96 [17.7, p << 0.01] 98
88 58 90 [9.9, p < 0.01] 95 97 [25.3, p << 0.01] 97 [17.6, p << 0.01] 98
The figures in brackets [F value, p value] indicates the significance of the increase in R 2 when the second named predictor is added to the first named predictor.
190
R. H o d g s k i n s o n et al. Ultrasound a n d stiffness o f cancellous bone
as measured in this study is greater than that reported by others. 2'23 This probably reflects our use of both human and bovine material, providing an increase in the range of architectural variability and, more importantly, of density. Bouxsein et al. t report a correlation of only 0.76 between speed of sound (SOS) through intact human calcanei and the compressive (elastic) modulus of cancellous bone cubes taken from their interiors. The modulus and velocity data obtained from bovine cubes by Turner and Eich 23 (which we have reanalyzed) show a relatively weak association using either apparent velocity of ultrasound (AVU) or ultrasonic transmission velocity (UTV) (R 2 = 48% and 33%, respectively). As in our study, but unlike in that of Bouxsein et al., Turner and Eich's ultrasonic measurements were made on isolated cubes. The results from our study suggest that ultrasound velocity has the potential to provide a more accurate means of assessing fracture risk in vivo than techniques such as DXA which provide only density information. Of course, care must be taken in extrapolating from in vitro studies to the clinical situation. For instance, in a recent in vivo study, SOS and BUA at the calcaneus were assessed as predictors for hip fracture. 6 Although both SOS and BUA had predictive capacity for hip fracture, BUA was the better predictor. This was not the case in our study, where stepwise regression always picked velocity as the best predictor of the mechanical property in all three directions, ahead of density, with BUA last. We have demonstrated that velocity gives a measure of architecture beyond that given by density alone. The theoretical and clinical implications of this finding should be pursued in future work.
B o n e Vol. 21, No. 2 August 1997:183-190
7. 8. 9.
10. 11.
12.
13.
14.
15.
16. 17. 18. 19.
Acknowledgments: The provision o f an S E R C studentship for C.F.N. is gratefully a c k n o w l e d g e d . W e thank Dr. Philip Q u i n l a n (Department o f P s y c h o l o g y , University of York) for statistical advice.
20.
21.
References 1. Bouxsein, M. L., Radloff, S. E., and Hayes, W. C. Quantitative ultrasound of the calcaneus reflects trabecular bone strength, modulus and morphology. J Bone Miner Res 10(Suppl. 1):S175; 1995. 2. Brear, K., Currey, J. D., Raines, S., and Smith, K. J. Density and temperature effects on some mechanical properties of cancellous bone. Eng Med 17:163167; 1988. 3. Carter, D. R. and Hayes, W. C. Bone compressive strength: The influence of density and strain rate. Science 194:1174-1175; 1976. 4. Currey, J. D. Power law models for the mechanical properties of cancellous bone. Eng Med 15:153-154; 1986. 5. Evans, J. A. and Tavakoli, M. B. Ultrasonic attenuation and velocity in bone. Phys Med Biol 35:1387-1396; 1990. 6. Hans, D., Dargent-Molina, P., Schott, A. M/~Sebert, J. L., Cormier, C., Kotzki, P. O., Delmas, P. D., Pouilles, J. M., Breart, G., and Meunier, P. J. Ultrasono-
22. 23. 24.
graphic heel measurements to predict hip fracture in elderly women: The EPIDOS prospective study. Lancet 346:511-514; 1996. Hans, D., Schott, A. M., and Meunier, P. J. Ultrasonic assessment of bone: A review. Eur J Med 2:157-163; 1993. Heaney, R. P. and Kanis, J. A. Editorial: The interpretation and utility of ultrasound measurements of bone. Bone 18:491-492; 1996. 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 204:115-121; 1990. Hodgskinson, R. and Currey, J. D. Effect of structural variation on Young's modulus of non-human cancellous bone. Proc lnst Mech Eng 20:43-52; 1990. 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. Hodgskinson, R. and Currey, J. D. The separate effects of osteoporosis and density on the strength and stiffness of human cancellous bone. Clin Biomech 8:262-268; 1993. Kleerekoper, M., Villaneuva, A. R., Stanciu, J., Rao, D. S., and Parfitt, A. M. The role of three dimensional trabecular microstructure in the pathogenesis of vertebral compression fractures Calcif Tissue Int 37:594-597; 1985. 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 Meas I 1:243249; 1990. Langton, C. M., Njeh, C. F., Hodgskinson, R., and Currey, J. D. Prediction of mechanical properties of the human calcaneus by broadband ultrasonic attenuation. Bone 18:495-503; 1996. Langton, C. M., Palmer, S. B., and Porter, R. W. The measurement of broadband ultrasonic attenuation in cancellous bone. Eng Med 13:89-91; 1984. Linde, F. and Hvid, I. Stiffness behaviour of trabecular bone specimens. J Biomech 20:83-89; 1987. Mosekilde, Li. Sex differences in age-related loss of vertebral trabecular bone mass and structure-biomechanical consequences. Bone 10:425-432; 1989. Odgaard, A. and Linde, F. The underestimation of Young's modulus in compressive testing of cancellous bone specimens. J Biomecb 24:691-698; 1991. Rice, J. C., Cowin, C. S., and Bowman, A. J. On the dependence of the elasticity and strength of cancellous bone on apparent density. J Biomech 21:155-168; 1988. Ross, P., Huang, C., Davis, J., Imose, K., Vogel, J., and Wasnich, R. Predicting vertebral deformity using bone densitometry at various sites and calcaneal ultrasound. Bone 16:325-332; 1995. Siegel, S. and Castellan, N. J. Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill; 1988. Turner, C. H. and Eich, M. Ultrasonic velocity as a predictor of strength in bovine cancellous bone. Calcif Tissue Int 49:116-119; 1991. Wahner, H. W. and Fogelman, I. The Evaluation of Osteoporosis: Dual Energy X-Ray Absorptiometry in Clinical Practice. Cambridge: Cambridge University Press; 1994.
Date Received: September 18, 1996 Date Revised." April 9, 1997 Date Accepted: April 9, 1997