Full text of DOI:10.1359/jbmr.2001.16.3.550

JOURNAL OF BONE AND MINERAL RESEARCH
Volume 16, Number 3, 2001
© 2001 American Society for Bone and Mineral Research
The Prospects of Estimating Trabecular Bone Tissue
Properties from the Combination of Ultrasound, Dual-
Energy X-Ray Absorptiometry, Microcomputed
Tomography, and Microfinite Element Analysis*
G.H. VAN LENTHE,1 J.P.W. VAN DEN BERGH,2 A.R.M.M. HERMUS,2 and R. HUISKES1
ABSTRACT
Osteoporosis commonly is assessed by bone quantity, using bone mineral density (BMD) measurements from
dual-energy X-ray absorptiometry (DXA). However, such a measure gives neither information about the
integrity of the trabecular architecture nor about the mechanical properties of the constituting trabeculae. We
investigated the feasibility of deriving the elastic modulus of the trabeculae (the tissue modulus) from
computer simulation of mechanical testing by microfinite element analysis (␮FEA) in combination with
measurements of ultrasound speed of sound (SOS) and BMD measurements. This approach was tested on 15
postmortem bovine bone cubes. The apparent elastic modulus of the specimens was estimated from SOS
measurements in combination with BMD. Then the trabecular morphology was reconstructed using micro-
computed tomography (␮CT). From the reconstruction a mesh for ␮FEA was derived, used to simulate
mechanical testing. The tissue modulus was found by correlating the apparent moduli of the specimens as
assessed by ultrasound with the ones as determined with ␮FEA. A mean tissue modulus of 4.5 GPa (SD, 0.69)
was found. When adjusting the ␮FEA-determined elastic moduli of the entire specimens with their calculated
tissue modulus, an overall correlation of R2 ؍ 96% with ultrasound-predicted values was obtained. We
conclude that the apparent elastic stiffness characteristics as determined from ultrasound correlate linearly
with those from ␮FEA. From both methods in combination, the elastic stiffness of the mineralized tissue can
be determined as an estimator for mechanical tissue quality. This method can already be used for biopsy
specimens, and potentially could be applicable in vivo as well, when clinical CT or magnetic resonance imaging
(MRI) tools with adequate resolution reach the market. In this way, mechanical bone quality could be
estimated more accurately in clinical practice. (J Bone Miner Res 2001;16:550–555)
Key words: ultrasound, trabecular bone, mechanical properties, finite element analysis, microcomputed
tomography, trabecular architecture
diagnosis of osteoporosis, evaluation of fracture risk, pre-
vention of fractures, and management of fracture fixation.
Most osteoporotic fractures occur in cancellous bone. It is
known that cancellous bone strength is highly correlated
with its elastic stiffness.(1–9) Hence, much research is de-
voted to estimating the stiffness properties of trabecular
bone structures, which are easier to determine than strength.
At any particular moment in time, bone strength and stiff-
ness only depend on the mechanical properties of the bone
tissue and on its spatial distribution, the “architecture”
INTRODUCTION
MAIN area in which biomechanical research and tech-
nology are of particular importance to osteoporosis is
the assessment of bone strength. This is important for the
A
*Presented at the 45th annual meeting of the Orthop. Res. Soc.,
Anaheim, California, USA, 1999 (Trans Orthop Res Soc 1999;24:
570), and at the 26th European Symposium on Calcified Tissue
Maastricht, The Netherlands, 1999 (Calcif Tissue Int 1999;
64(Suppl 1):S100).
1Orthopedic Research Laboratory, Institute of Orthopedics, University of Nijmegen, Nijmegen, The Netherlands.
2Department of Endocrinology, University Hospital Nijmegen, Nijmegen, The Netherlands.
550

ESTIMATING TISSUE PROPERTIES FROM ULTRASOUND
551
FIG. 1. The elastic properties of a bone specimen (the “apparent
elastic properties”) depend on the mechanical properties of the bone
tissue and on its spatial distribution, the “architecture.” The elastic
properties of the bone tissue depend, among others, on degree of
mineralization, lamellar arrangement, microcracks, resorption cavities,
osteocyte lacunae, and collagen matrix.
FIG. 2. Overview of the methods used to determine the tissue elastic
modulus. Using SOS and BMD measurements the apparent stiffness of
the trabecular bone specimens can be determined. Using an arbitrary
tissue modulus, the apparent stiffness of the specimens can be deter-
mined also with ␮FEA, based on the ␮CT-determined architecture.
From the combination of both methods, the stiffness of the trabeculae
(the tissue modulus) can be determined.
(Fig. 1). Architecture is defined here as a quality to capture
the distribution of bone tissue in space; hence, as a quality
combining both the spatial arrangement of the trabeculae
and the amount of bone mass. However, only bone density
is commonly used clinically as an estimator for the mechan-
ical properties of bone. Yet, although highly significant, the
correlation between strength or stiffness and bone density
is poor, leaving about 30–50% of unexplained vari-
ance.(1,10,11) At least part of the variation can be explained
by taking the anisotropy of the specimens into account.
Strong evidence for this are the much higher correlations
between apparent density and stiffness when examined in
only one loading direction.(1,5,6,12,13) The combination of
density and a measure of the trabecular anisotropy increased
moduli of the ␮FEA mesh can be determined as the con-
stants determining stiffness.(3,22–25)
Where SOS estimates the apparent stiffness of the entire
specimens, ␮FEA captures the effects of trabecular archi-
tecture only. Hence, in theory, the elastic modulus of the
the predictive value, but still unexplained variance remained mineralized tissue (the tissue modulus) could be assessed by
up to 10–28%.(14–17) One possible reason for the remaining “subtracting” one from the other. We hypothesize that, in
variance is that although bone density represents the amount principle, the combination of ␮FEA and ultrasound could
allow us to determine the contribution of both architecture
and mineralized tissue to the apparent elastic modulus sep-
arately. The purpose of this study was to investigate this
hypothesis in postmortem bovine specimens.
of mineralized tissue in a trabecular architecture, it does not
give an indication of its mechanical properties. Particularly,
the presence of microcracks or other deficiencies (Fig. 1),
which are not detected by dual-energy X-ray absorptiometry
(DXA) or other radiological measurements, may reduce the
strength of cancellous bone much more than bone density
suggests.
MATERIALS AND METHODS
In recent years, new methods have emerged with the
potential to estimate cancellous bone stiffness in a more
A brief overview of the methods used to determine the
direct way. One of these is the quantitative ultrasound tissue elastic modulus is given in Fig. 2. It will be explained
parameter speed of sound (SOS), which depends on both in more detail in this section.
stiffness and density. By determining the SOS through a
bone, using experimental ultrasound scanners, the elastic
Specimens
We used 15 trabecular bone cubes (25 ϫ 25 ϫ 25 mm3),
cut from 8 bovine femora. These femora were freshly ob-
modulus of bone specimens can be assessed, at least by
approximation.(18,19) Using clinical ultrasound scanners,
good correlations were found between SOS and the combi-
nation of stiffness and apparent density,(12,13) stiffness and
tained from a local butcher and kept frozen at Ϫ35°C until
testing. Seven cubes were cut from the femoral neck and
the combination of SOS and bone mineral density eight from the distal condyles.(26) Care was taken to produce
(BMD),(20) or SOS and the combination of stiffness and parallel surfaces. The cubes were aligned according to the
BMD.(21)
anatomical axes (anteroposterior [AP], mediolateral [ML],
and craniocaudal [CC]). Bone marrow was not removed
because it has no measurable effect on SOS.(27)
Another new method involves computer simulation of
mechanical testing with microfinite element analysis
(␮FEA). For this purpose, a graphics reconstruction of the
trabecular architecture is made, using magnetic resonance
imaging (MRI) or microcomputed tomography (␮CT),
which is transformed into a ␮FEA mesh. In a computer
Ultrasound measurement
Before the ultrasound measurements, the specimens were
simulation of mechanical testing, the elastic (Young’s) degassed thoroughly under water. SOS measurements were

552
VAN LENTHE ET AL.
performed under water using the Ultrasound Bone Imaging
Scanner 3000 (DMS, Montpellier, France). This system
uses a pair of focused broadband 0.5-MHz transducers. The
resolution at the focal zone is approximately 4–5 mm. The
specimens were placed in a Perspex holder for easy and
accurate positioning. The configuration was such that lon-
gitudinal sound waves were propagated.(13,28)
The apparent elastic properties of the entire trabecular
bone specimens were determined from SOS. From the mea-
sured longitudinal velocity (vlong), the bar velocity (vbar) was
estimated based on the work of Njeh et al.(13) as
␮FEA
The ␮CT scans were converted to voxel meshes and
coarsened by grouping 4 ϫ 4 ϫ 4 voxels; a new voxel was
assumed to be bone if more than half of its original voxels
represent bone. The finite element representation of the
specimen was detailed enough to obtain accurate values for
the stiffness characteristics.(25,31)
Each element was assigned the same mechanical proper-
ties, with an arbitrarily chosen tissue modulus (Etissue,FEA) of
1 GPa and a Poisson’s ratio of 0.3. It has been found that the
tissue anisotropy has a negligible effect on the apparent
Young’s moduli,(22,23,32) and because the analyses are linear
elastic, the results can be scaled to any isotropic tissue
modulus with the same Poisson’s ratio.
The finite element models were used to calculate the
apparent stiffness of the entire architecture (Eapp,FEA), using
a direct mechanics approach. Six mechanical tests (three
uniaxial strain deformations and three shear deformations)
were simulated and the strains within the trabeculae were
determined as a function of the apparent strains. From the
calculated strains, the complete stiffness matrix, built from
21 independent constants, can be determined.(24,33,34) The
Young’s moduli in each of the three measurement directions
were calculated and used in further analyses. Because all
elements were assigned the same tissue modulus, the finite
element models used evaluate the effect of the architecture
only.
v
bar ϭ 1.055 ⅐ vlong Ϫ 1090 ͑m/s͒.
(1)
The apparent Young’s modulus (Eapp,SOS) was then calcu-
lated for each direction, using a well-known relationship for
waves in elastic materials,(28,29) as
E
app,SOS ϭ ␳ ⅐ v2 ͑Pa͒
(2)
app
bar
where ␳app (kg/m3) is the apparent density of the specimen.
The apparent density was calculated from the BMD as
assessed by DXA.
BMD measurement
BMD measurements were performed in a water tank
along the three orthogonal axes using the high-resolution
scan mode of the QDR 1000 densitometer (Hologic, Bed-
ford, MA, USA). Two areas were scanned: the total area of
625 mm2 and a subregion of 49 mm2 for comparison with
the volume of interest for which the architecture was deter-
mined using ␮CT. No significant difference was found
between the BMD in the two scanned regions; so only the
total area BMD is reported.
The ␮FEA-based moduli of the specimen’s architecture
were then compared with the ultrasound-based moduli. The
scaling factor between the two is the “effective tissue mod-
ulus” Etissue. It was calculated for each specimen separately
(22)
as
3
1
3
Ei, ͑app,SOS͒
E
tissue ϭ Etissue,FEA
⅐
⅐
(4)
͸
ͩ ͪ
Ei, ͑app,FEA͒
The apparent density (␳app) of the specimens was esti-
mated from the strong relationship(6) (R2 ϭ 0.98) between
apparent density and ash density as
iϭ1
where i ϭ 1, 2, and 3 represents the three measurement
directions; Etissue,FEA is the tissue Young’s modulus used in
the FEA; Eapp,SOS is the apparent Young’s modulus as
estimated from SOS; and Eapp,FEA is the apparent Young’s
modulus as estimated from the finite element model. The
tissue modulus calculated using Eq. (4) is uniform and
isotropic throughout the specimen. This concept has been
shown to be valid.(3,22,23,25,32)
BMD
␳
app ϭ 1.79
ϩ 0.0119 ͑g/cm3͒,
(3)
d
in which d is the thickness of the specimens and BMD/day
is the ash density.
␮CT measurement
RESULTS
A cylindrical core, with a diameter of 15.5 mm and a
length of 25 mm, was removed from each specimen in the
CC direction. ␮CT scans were made of the central part of
The descriptive statistics of measured SOS and BMD,
this core, using the ␮CT 20 (Scanco Medical, Bassersdorf, calculated apparent densities, and apparent and tissue
Switzerland), with a resolution of 17 ␮m.(30) A subregion of Young’s moduli are summarized in Table 1. The measured
6.8 ϫ 6.8 ϫ 6.8 mm3, representing the central part of the SOS (vlong) was significantly different (p Ͻ 0.001) for the
cube, was used for subsequent analysis to avoid the influ- three directions. It was highest in the CC direction, indicat-
ence of preparation artifacts. Individual global thresholds ing that this is the stiffest direction.
were applied to discriminate between bone and nonbone and
As expected, no differences in BMD were found in the
to determine the volume fraction. The threshold of each three orthogonal directions (0.73 Ϯ 0.14 g/cm2, 0.74 Ϯ 0.15
specimen was determined using an adaptive method (B. g/cm2 and 0.74 Ϯ 0.15 g/cm2 in the AP, ML, and CC
Koller, personal communication, 1998).
directions, respectively). Therefore, the mean of the three

ESTIMATING TISSUE PROPERTIES FROM ULTRASOUND
553
TABLE 1. MEAN VALUES, SDS, AND RANGES FOR
ULTRASOUND VELOCITY, BMD, APPARENT DENSITY,
THE APPARENT YOUNG’S MODULI AS DETERMINED FROM
ULTRASOUND, AND THE EFFECTIVE TISSUE MODULUS
Mean
1857
1740
1976
0.736
539
439
SD
163
115
182
Range
Vlong,AP (m/s)
Vlong,ML (m/s)
Vlong,CC (m/s)
BMD (g/cm2)
1532–2112
1575–1916
1621–2249
0.540–0.987
399–718
110–801
130–623
153–1147
3307–5744
0.148
␳
(kg/m3)
106
206
161
308
693
app
Eapp,SOS,AP (MPa)
Eapp,SOS,ML (MPa)
Eapp,SOS,CC (MPa)
Etissue (MPa)
324
585
4482
BMD measurements of the whole area was used in the
calculation of the apparent density [Eq. (3)]. We found a
mean apparent density of 539 kg/m3, with an SD of 106
kg/m3. The apparent stiffnesses, as determined from SOS
and apparent density [Eq. (2)], were 439, 324, and 585 MPa
in the AP, ML, and CC directions, respectively. These
values were significantly different (p Ͻ 0.001) for the three
directions.
Based on the ␮CT reconstructions the finite element
models were created. The resulting models consisted of
150,000–350,000 elements. The volume fractions for the
specimens ranged from 0.16 to 0.36.
In all specimens the stiffest direction as determined from
␮FEA equaled the direction of highest SOS. And in all but
one specimen, the other directions also matched. When the
same isotropic tissue modulus (1 GPa) was assumed for all
specimens, high correlations were found between SOS and
␮FEA-determined Young’s moduli: R2 ϭ 0.84 in the AP
direction, 0.88 in the CC direction, and 0.92 in the ML
direction. When SOS was combined with BMD, the corre-
lation with ␮FEA-determined Young’s moduli was 0.92 in
each direction.
Mean values of 4.5 GPa (SD, 0.69 GPa) were found for
the tissue moduli [Eq. (4)]. When the ␮FEA-determined
Young’s moduli were adjusted to the calculated tissue mod-
uli and correlated with the SOS-predicted values an overall
correlation of R2 ϭ 0.96 was obtained (Fig. 3).
FIG. 3. The Young’s modulus as determined from ultrasound
(Eapp,SOS) on the horizontal axis versus those as determined from the
␮FEA (Eapp,FEA) on the vertical axis. A strong correlation was found
between the two.
GPa found when comparing ␮FEA evaluation with labora-
tory testing of trabecular bone.(3,22,23) This implies that the
method we propose for the assessment of tissue modulus is
feasible in principle.
There are several reasons to assume that the relationship
we used to derive the apparent stiffness of the specimens
from SOS [Eq. (1)] can be seen only as a first estimate. First,
no theory exists that fully explains the influence of bone
tissue properties and architecture on ultrasound transmis-
sion through trabecular bone,(35–37) although strong corre-
lations between SOS and stiffness have been found in vitro
for both bovine(12,13) and human trabecular bone(20,21,38,39)
and even stronger correlations for the combined measures of
SOS and BMD(20) or SOS and apparent density(12,13); sec-
ond, because this relationship was derived from a range of
reference materials not including bone; and third, because
the SOS measured by Njeh et al.,(13) also measuring bovine
specimens from identical locations, were significantly
higher than the SOS we measured, indicating that different
ultrasound scanners measure different SOS. This could also
mean that Eq. (1) is not valid in general, but dependent on
the type of scanner. Therefore, we tested different relation-
ships for Eq. (1) of the form vbar ϭ vlong Ϫ C, with C a
constant. We found that the calculated tissue modulus was
DISCUSSION
We found a good correlation (R2 ϭ 0.88 for the combined influenced strongly by the value of C. However, the overall
directions) between apparent Young’s moduli determined correlation between Young’s moduli as determined from
with ultrasound and those determined with ␮FEA simula- ultrasound versus those determined from ␮FEA hardly
tion of mechanical testing, when using an arbitrary, uniform changed.
tissue modulus of 1 GPa in the ␮FEA simulations. The
We used a ␮CT routine to determine individual global
correlation improved to 96% after adjusting the ␮FEA thresholds for each specimen. Recently, it has been
tissue moduli to the ultrasound results. This indicates that shown(40) that this routine underestimates volume fraction
the tissue modulus is not the same for all specimens, but that (vv) by 12.3% when vv is low (vv Ͻ 0.20) and that it
the individual differences are not very large in this data set. overestimates vv by 7.2% when vv is high (vv Ͼ 0.30). We
We found an average value of 4.5 GPa for the tissue checked this with our specimens and found a negative
modulus which is close to the average values of 5.3–7.6 correlation (R2 ϭ 0.69) between the tissue density (deter-

554
VAN LENTHE ET AL.
regions with materials testing and computed tomography. J Or-
thop Res 9:674–682.
11. Lotz JC, Gerhart TN, Hayes WC 1991 Mechanical properties
of metaphyseal bone in the proximal femur. J Biomech 24:
317–329.
mined as ␳tissue ϭ ␳app/vv) and vv. When we corrected vv for
our specimens, there was no association anymore between
␳
and vv.
tissue
The method proposed was tested on postmortem bovine
specimens in this study, which is only a first step. Ulti-
mately, we want to determine the tissue modulus for esti-
mating tissue quality in the clinical setting. Before that can
be realized, a number of problems will have to be solved.
First, a method is required to provide for reconstructions of
trabecular architecture in vivo. Developments in whole-
body CT or peripheral quantitative computed tomography
(pQCT) resolution may provide that or, alternatively, MRI
scanning methods. Second, more work will have to be done
on ultrasound precision, as used clinically. Particularly,
disturbances by soft tissues must be corrected for.
We conclude that the elastic stiffness characteristics of
bovine trabecular bone, as determined from ultrasound,
agreed closely with those from ␮FEA. From both methods
in combination, the elastic stiffness of the mineralized tissue
can be determined as an estimator of mechanical tissue
quality. This method can already be used for biopsy spec-
imens and may eventually be applicable in vivo. In this way,
bone tissue quality could be estimated clinically.
12. Hodgkinson R, Njeh CF, Currey JD, Langton CM 1997 The
ability of ultrasound velocity to predict the stiffness of can-
cellous bone in vitro. Bone 21:183–190.
13. Njeh CF, Hodgskinson R, Currey JD, Langton CM 1996
Orthogonal relationships between ultrasonic velocity and ma-
terial properties of bovine cancellous bone. Med Eng Phys
18:373–381.
14. Hodgkinson R, Currey JD 1990 The effect of variation in
structure on the Young’s modulus of cancellous bone: A
comparison of human and non-human material. J Eng Med
204:115–121.
15. Kabel J, Van Rietbergen B, Odgaard A, Huiskes R 1997 Fabric
and volume fraction can accurately predict mechanical prop-
erties for a wide range of trabecular architectures. Trans Or-
thop Res Soc 22:800.
16. Turner CH, Cowin SC, Rho JY, Ashman RB, Rice JC 1990
The fabric dependence of the orthotropic elastic constants of
cancellous bone. J Biomech 23:549–561.
17. Van Rietbergen B, Ulrich D, Ru¨egsegger P 1998 Elastic pa-
rameters of osteoporotic bone predicted from volume fraction
and MIL. Trans Eur Orthop Res Soc 8:31.
18. Ashman RB, Corin JD, Turner CH 1987 Elastic properties of
cancellous bone: Measurement by an ultrasonic technique.
J Biomech 20:979–986.
19. Rho JY, Ashman RB, Turner CH 1993 Young’s modulus of
trabecular and cortical bone material: Ultrasonic and micro-
tensile measurements. J Biomech 26:111–119.
20. Njeh CF, Kuo CW, Langton CM, Atrah HI, Boivin CM 1997
Prediction of human femoral bone strength using ultrasound
velocity and BMD: An in vitro study. Osteoporos Int 7:471–
477.
21. Hans D, Wu C, Njeh CF, Zhao S, Augat P, Newitt D, Link T,
Lu Y, Majumdar S, Genant HK 1999 Ultrasound velocity of
trabecular cubes reflects mainly bone density and elasticity.
Calcif Tissue Int 64:18–23.
22. Kabel J, Van Rietbergen B, Dalstra M, Odgaard A, Huiskes R
1999 The role of an effective isotropic tissue modulus in the
elastic properties of cancellous bone. J Biomech 32:673–680.
23. Ladd AJC, Kinney JH, Haupt DL, Goldstein SA 1998 Finite-
element modeling of trabecular bone: Comparison with me-
chanical testing and determination of tissue modulus. J Orthop
Res 16:622–628.
ACKNOWLEDGMENTS
This work was sponsored by the Dutch Alternatives to
Animal Experiments Platform.
REFERENCES
1. Goulet RW, Goldstein SA, Ciarelli MJ, Kuhn JL, Brown MB,
Feldkamp LA 1994 The relationship between the structural
and orthogonal compressive properties of trabecular bone.
J Biomech 27:375–389.
2. Hodgkinson R, Currey JD 1993 Separate effects of osteopo-
rosis and density on the strength and stiffness of human
cancellous bone. Clin Biomech 8:262–268.
3. Hou FJ, Lang SM, Hoshaw SJ, Reimann DA, Fyhrie DP 1998
Human vertebral body apparent and hard tissue stiffness.
J Biomech 31:1009–1015.
24. Van Rietbergen B, Odgaard A, Kabel J, Huiskes R 1996 Direct
mechanics assessment of elastic symmetries and properties of
trabecular bone architecture. J Biomech 29:1653–1657.
25. Van Rietbergen B, Weinans H, Huiskes R, Odgaard A 1995 A
new method to determine trabecular bone elastic properties
and loading using micromechanical finite-element models.
J Biomech 28:69–81.
26. Van den Bergh JPW, Van Lenthe GH, Hermus ARMM, Cor-
stens FHM, Smals AGH, Huiskes R 2000 Speed of sound
reflects Young’s modulus as assessed by microstructural finite
element analysis. Bone 26:519–524.
27. Njeh CF, Langton CM 1997 The effect of cortical endplates on
ultrasound velocity through the calcaneus: An in vitro study.
Br J Radiol 70:504–510.
28. Ashman RB, Rho JY 1988 Elastic modulus of trabecular bone
material. J Biomech 21:177–181.
4. Hvid I, Bentzen SM, Linde F, Mosekilde L, Pongsiopetch B
1989 X-ray quantitative computed tomography: The relations
to physical properties of proximal tibial trabecular bone spec-
imens. J Biomech 22:837–844.
5. Keller TS 1994 Predicting the compressive mechanical behav-
ior of bone. J Biomech 27:1159–1168.
6. Keyak JH, Lee IY, Skinner HB 1994 Correlations between
orthogonal mechanical properties and density of trabecular
bone: Use of different densitometric measures. J Biomed Ma-
ter Res 28:1329–1336.
7. Linde F, Hvid I 1989 The effect of constraint on the mechan-
ical behaviour of trabecular bone specimens. J Biomech 22:
485–490.
8. Linde F, Hvid I, Madsen F 1992 The effect of specimen
geometry on the mechanical behaviour of trabecular bone
specimens. J Biomech 25:359–368.
29. Pain HJ 1985 Longitudinal waves. In: Pain HJ (ed.) The
Physics of Vibrations and Waves. Wiley, Chichester, UK, pp.
159–178.
9. Odgaard A, Hvid I, Linde F 1989 Compressive axial strain
distributions in cancellous bone specimens. J Biomech 22:
829–835.
10. Ciarelli MJ, Goldstein SA, Kuhn JL, Cody DD, Brown MB 30. Ru¨egsegger P, Koller B, Mu¨ller R 1996 A microtomographic
1991 Evaluation of orthogonal mechanical properties and den-
sity of human trabecular bone from the major metaphyseal
system for the nondestructive evaluation of bone architecture.
Calcif Tissue Int 58:24–29.

ESTIMATING TISSUE PROPERTIES FROM ULTRASOUND
555
31. Ulrich D, Van Rietbergen B, Weinans H, Ru¨egsegger P 1998 38. Bouxsein ML, Radloff SE 1997 Quantitative ultrasound of the
Finite element analysis of trabecular bone structure: A com-
parison of image-based meshing techniques. J Biomech 31:
1187–1192.
calcaneus reflects the mechanical properties of calcaneal tra-
becular bone. J Bone Miner Res 12:839–846.
39. Han S, Medige J, Davis J, Fishkin Z, Mihalko W, Ziv I 1997
Ultrasound velocity and broadband attenuation as predictors of
load-bearing capacities of human calcanei. Calcif Tissue Int
60:21–25.
32. Van Rietbergen B, Kabel J, Odgaard A, Huiskes R 1997
Determination of trabecular bone tissue elastic properties by
comparison of experimental and finite element results. In: Sol
H, Oomens CWJ (eds.) Material Identification Using Mixed 40. Ding M, Odgaard A, Hvid I 1999 Accuracy of cancellous bone
Numerical Experimental Methods. Kluwer, The Netherlands,
pp. 183–192.
volume fraction measured by micro-CT scanning. J Biomech
32:323–326.
33. Hollister SJ, Kikuchi N 1992 A comparison of homogenization
and standard mechanics analyses for periodic porous compos-
ites. Computational Mech 10:73–95.
34. Suquet PM 1987 Elements of homogenization theory for in-
elastic solid mechanics. In: Sanchez-Palencia E, Zaoui A (eds.)
Homogenization Techniques for Composite Media. Springer,
Berlin, Germany.
35. Haire TJ, Langton CM 1999 Biot theory: A review of its
application to ultrasound propagation through cancellous bone.
Bone 24:291–295.
Address reprint requests to:
Rik Huiskes, Ph.D.
Orthopedic Research Laboratory
Institute of Orthopedics
University of Nijmegen
P.O. Box 9101
6500 HB Nijmegen, The Netherlands
36. Hosokawa A, Otani T 1998 Acoustic anisotropy in bovine
cancellous bone. J Acoust Soc Am 103:2718–2722.
37. Hosokawa A, Otani T 1997 Ultrasonic wave propagation in Received in original form December 22, 1999; in revised form
bovine cancellous bone. J Acoust Soc Am 101:558–562. September 1, 2000; accepted September 18, 2000.