Bone microstructure and elastic tissue properties are reflected in QUS axial transmission measurements.

Abstract

Accurate clinical interpretation of the sound velocity derived from axial transmission devices requires a detailed understanding of the propagation phenomena involved and of the bone factors that have an impact on measurements. In the low megahertz range, ultrasonic propagation in cortical bone depends on anisotropic elastic tissue properties, porosity and the cortical geometry (e.g., thickness). We investigated 10 human radius samples from a previous biaxial transmission study using a 50-MHz scanning acoustic microscope (SAM) and synchrotron radiation microcomputed tomography. The relationships between low-frequency axial transmission sound speed at 1 and 2 MHz, structural properties (cortical width Ct.Wi, porosity, Haversian canal density and material properties (acoustic impedance, mineral density) on site-matched cross-sections were investigated. Significant linear multivariate regression models (1 MHz: R(2) = 0.84, p < 10(-4), root-mean-square error (RMSE) = 38 m/s, 2 MHz: R(2) = 0.65, p < 10(-4), RMSE = 48 m/s) were found for the combination of Ct.Wi with porosity and impedance. A new model was derived that accounts for the nonlinear dispersion relation with Ct.Wi and predicts axial transmission velocities measured at different ultrasonic frequencies (R(2) = 0.69, p < 10(-4), RMSE = 52 m/s).

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doi:10.1016/j.ultrasmedbio.2005.05.002
● Original Contribution
BONE MICROSTRUCTURE AND ELASTIC TISSUE PROPERTIES ARE
REFLECTED IN QUS AXIAL TRANSMISSION MEASUREMENTS
KAY RAUM,*†INGRID LEGUERNEY,* FLORENT CHANDELIER,* EMMANUEL BOSSY,*
MARYLINE TALMANT,* AMENA SAÏED,* FRANÇOISE PEYRIN,‡§and PASCAL LAUGIER*
*Laboratoire d’Imagerie Paramétrique, CNRS/Université Paris 6, Paris, France;†Q-BAM Group, Department of
Orthopedics, Martin Luther University of Halle-Wittenberg, Halle, Germany;‡CREATIS, Villeurbanne, France; and
§ESRF, Grenoble, France
(Received 17 December 2004, revised 25 April 2005, in final form 11 May 2005)
Abstract—Accurate clinical interpretation of the sound velocity derived from axial transmission devices requires
a detailed understanding of the propagation phenomena involved and of the bone factors that have an impact on
measurements. In the low megahertz range, ultrasonic propagation in cortical bone depends on anisotropic
elastic tissue properties, porosity and the cortical geometry (e.g., thickness). We investigated 10 human radius
samples from a previous biaxial transmission study using a 50-MHz scanning acoustic microscope (SAM) and
synchrotron radiation microcomputed tomography. The relationships between low-frequency axial transmission
sound speed at 1 and 2 MHz, structural properties (cortical width Ct.Wi, porosity, Haversian canal density and
material properties (acoustic impedance, mineral density) on site-matched cross-sections were investigated.
Significant linear multivariate regression models (1 MHz: R2? 0.84, p < 10?4, root-mean-square error (RMSE)
? 38 m/s, 2 MHz: R2? 0.65, p < 10?4, RMSE ? 48 m/s) were found for the combination of Ct.Wi with porosity
and impedance. A new model was derived that accounts for the nonlinear dispersion relation with Ct.Wi and
predicts axial transmission velocities measured at different ultrasonic frequencies (R2? 0.69, p < 10?4, RMSE
? 52 m/s). (E-mail: kay.raum@medizin.uni-halle.de)© 2005 World Federation for Ultrasound in Medicine &
Biology.
Key Words: Acoustic microscopy, Bone, Elastic properties, Microstructure, Synchrotron-CT, Ultrasound.
INTRODUCTION
Although various nonskeletal factors, such as the liability to
fall, contribute to fracture risk, the diagnosis of osteoporosis
relies on assessment of skeletal status. This requires wide-
spread development of facilities for the assessment of sev-
eral alterations in bone intrinsic properties, such as reduc-
tion in bone mass and changes in its spatial distribution,
increase in porosity and modification of the bone matrix
material, itself. The latter refers to the deterioration of
biomechanical competence of the bone material per se and
is reflected in changes in stiffness, strength and toughness
(Zioupos and Currey 1998). Clinical bone assessment using
conventional x-ray densitometry is centered on the mea-
surement of bone mineral density (BMD), but it does not
address other skeleton abnormalities. To encompass the
multiple aspects of bone fragility, several other noninvasive
modalities have been developed. Among them, quantitative
ultrasound (QUS) technologies offer several advantages,
such as cheapness, portability and absence of ionizing ra-
diation. Like x-ray densitometry techniques, QUS has been
adapted to assess different skeletal sites. Clinical devices
based on transmission measurements of the speed of sound
(SOS) and broadband bone ultrasound attenuation (BUA)
through the calcaneus are now widely used (Njeh et al.
1997) and evidence lends support to their use for the as-
sessment of fracture risk (Gluer et al. 2004; Hans et al.
1996). More recently, axial transmission techniques have
been developed to assess cortical bone properties at the
peripheral skeleton (e.g., tibia, radius or finger phalanges)
(Foldes et al. 1995; Lowet and van der Perre 1996; Bossy et
al. 2004a; Moilanen et al. 2003). The question of the impact
of bone properties contributing to bone strength in varia-
tions of axial transmission SOS is central to the debate (Lee
et al. 1997; Sievanen et al. 2001).
The wave equation that governs the propagation of
ultrasonic (elastic) waves in solids relates the propaga-
Address correspondence to: Dr. Kay Raum, Dept. of Orthope-
dics, Q-BAM Group, Martin Luther University of Halle, Halle 06097
Germany. E-mail: kay.raum@medizin.uni-halle.de
Ultrasound in Med. & Biol., Vol. 31, No. 9, pp. 1225–1235, 2005
Copyright © 2005 World Federation for Ultrasound in Medicine & Biology
Printed in the USA. All rights reserved
0301-5629/05/$–see front matter
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tion characteristics, such as sound velocity to the density,
elasticity and structure of the propagating material. Many
examples exist in material science where ultrasound
(US) has been used to characterize material properties
(i.e., stiffness and density) and microstructure (Kundu
2003). In the bone densitometry field, many studies have
investigated the relationships between axial transmission
SOS and bone mass (Bossy et al. 2004c; Lee et al. 1997;
Sievanen et al. 2001), microstructure (Bossy et al. 2004b,
2004c) and biomechanical competence. The data indicate
that SOS correlates moderately with BMD and can pre-
dict ultimate strength (Lee et al. 1997). In addition, the
separate contributions to sound velocity of cortical thick-
ness, intracortical porosity and degree of mineralization
have been clarified experimentally in human radius spec-
imens (Bossy et al. 2004c) and by means of finite dif-
ference simulations (Bossy et al. 2002, 2004b). How-
ever, none of these studies has looked specifically at the
influence of intrinsic elastic properties on axial transmis-
sion SOS.
Elasticity (or stiffness) is one important character-
istic of bone material biomechanical competence. Age-
ing has been shown adversely to affect the elastic prop-
erties of human cortical bone and the reduction in stiff-
ness is accompanied by a reduction also in strength and
toughness (Zioupos and Currey 1998; Zioupos, 2001).
All this suggests that SOS measurements in cortical bone,
which are deterministically related to the elastic modulus
of the material, should provide useful information on any
deterioration in bone mechanical properties. However,
the rather low ultrasonic frequencies (in the megahertz
range) that are used for in vivo examination of cortical
skeletal sites convey information on both material stiff-
ness and structure and their contributions cannot be eas-
ily separated. We need to understand better the contri-
bution of intrinsic stiffness (i.e., tissue level stiffness) to
SOS measurement. This may provide a better insight into
the value of clinical QUS technologies to assess age- or
disease-related bone quality deterioration.
Toward this goal, the tissue-level elastic properties
must be measured. High-resolution synchrotron radiation
(SR) or X ray-based microcomputed tomography (? CT)
techniques provide excellent volumetric information on
the distribution of mineral within the tissue (Lang et al.
1998; Laugier et al. 1997), but the problem of relating
tissue mineralization to tissue elasticity has not yet been
solved. Furthermore, this technique is inherently not
sensitive to elastic anisotropy. Nanoindentation provides
local measurements of the elastic properties of bone, but
without imaging capability (Fan et al. 2002; Hoffler et al.
2000; Jamsa et al. 2002; Rho et al. 1999, 2001a, 2001b;
Roy et al. 1999, 2001; Swadener et al. 2001). A high-
resolution scanning acoustic microscope (SAM) has
been used both for qualitative imaging of the cortical
microstructure (Katz and Meunier 1993, 1997; Meunier
et al. 1988) as well as for quantitative evaluation of
sound velocity (Hasegawa et al. 1994, 1995; Pidaparti et
al. 1996; Takano et al. 1996, 1999; Turner et al. 1995) or
acoustical impedance (Meunier et al. 1991; Raum et al.
2003, 2004; Weiss et al. 1998). These acoustical param-
eters directly reflect elastic properties such as stiffness
(Meunier et al. 1991; Raum and Brandt 2003) and bulk
modulus (Raum and Brandt 2003). In addition, the
acoustic impedance has been shown to be sensitive to
elastic anisotropy (Raum et al. 2004). The spatial reso-
lution is fixed by the operating frequency and the numer-
ical aperture of the transducer. Raum et al. (2004) inves-
tigated the influence of these parameters on the estima-
tion of acoustic impedance, porosity and Haversian canal
density (N.Ca/Ar). They concluded that a spatial resolu-
tion of approximately 20 ?m (obtained at 50 MHz) is
required for a reliable separation of tissue from the
Haversian canals in human cortical bone. Thus, this
result suggests that this spatial resolution is appropriate
for assessing elastic properties at the tissue level.
In this in vitro study, we have used SR-?CT and
50-MHz SAM to examine the relative contributions of
cortical structure, degree of mineralization and acoustic
impedance (representing tissue stiffness) on the SOS
measured with a clinical device on human radius speci-
mens. The ability of acoustic microscopy quantitatively
to characterize bone samples is well-established. Never-
theless, its ability quantitatively to assess bone elastic
properties at the tissue level assumes an accurate extrac-
tion of microstructure. The accuracy of extracting struc-
tural parameters using SAM was evaluated by compari-
son with site-matched SR-?CT images.
MATERIALS AND METHODS
Samples
A subset of 10 excised human radius samples from
a previous QUS investigation (Bossy et al. 2004c) was
prepared for SAM inspection. The sample population
included two women and eight men donors of ages
between 68 and 90 y (mean ? SD: 75.9 ? 6.8 y).
Cross-sections were cut adjacent to the region, where
QUS measurements have been performed. The sections
were then fixed with Technovit®3040 resin (Heraeus
Kulzer, Hanau, Germany) on special sample holders.
After shock freezing the sample and holder in liquid
nitrogen, flat tissue surfaces were prepared using an ultra
milling machine (Reichert Jung Ultrafräse, Leica GmbH,
Bensheim, Germany).
Before synchrotron data acquisition, the anterior
and posterolateral regions were extracted and defatted
for 12 h in dichloromethane (C2H2Cl2) solution. The
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specimens were finally dried by exposure to air at room
temperature for 48 h.
Ethics approval for collection of samples was
granted by the Human Ethics Committee of the Institute
of Anatomy at the University René Descartes (Paris,
France). The tissue donors or their legal guardians pro-
vided informed written consent to provide their tissues
for investigation, in accord with legal clauses stated in
the French Code of Public Health (Code de la Santé
Publique Français).
Experimental set-up
Bidirectional axial transmission. (a) Background.
The SOS data were obtained from a previous in vitro
study using the bidirectional axial transmission tech-
nique (Bossy et al. 2004c). This technique was devel-
oped at the LIP (Paris, France) and involves 1-MHz or
2-MHz US propagation along the cortex of long bone in
two opposite directions, with automatic correction for
soft tissue and probe inclination (Bossy et al. 2004a).
SOS is derived from the measured arrival time of the
fastest signal propagating along the bone axis.
The nature of this propagation along the cortex has
been studied in detail, both experimentally (Bossy et al.
2004c) and by means of finite difference simulations
(Bossy et al. 2002, 2004b). The sensitivity of SOS to
cortical thickness has been clearly related to a change in
the nature of the propagating wave (Bossy et al. 2002,
2004b; Nicholson et al. 2002) from a compressional
mode (the lateral wave) to a guided mode (equivalent to
the S0Lamb mode in a plate model). Briefly, the lateral
wave is observed for a cortical thickness-to-wavelength
ratio larger than 0.5 (i.e., thick cortical bone), whereas
the guided mode is observed for a cortical thickness-to-
wavelength ratio less than 0.25 (i.e., thin cortical bone).
Typical bone thickness varies from 1 to 3.5 mm in the
human radius (Bossy et al. 2004c; Sievanen et al. 2001).
At 1 MHz, the wavelength is approximately 4 mm and,
therefore, for cortical thickness greater than 2 mm, SOS
does not depend on the cortical thickness. Below this
limit, finite difference simulations (Bossy et al. 2004b)
predicted a smooth but nonlinear transition from the
compression velocity (? 4000 m/s) to the guided mode
velocity (? 3650 m/s for a 1-mm thick cortical layer). At
2 MHz, the wavelength is approximately 2 mm and,
therefore, SOS should not be much affected by the cor-
tical thickness.
In the lower and upper limits of the thickness-
related behavior, SOS is an explicit function of the elastic
mechanical properties. In the upper limit (large cortical
thickness-to-wavelength ratio), the lateral wave velocity
is close to the longitudinal bulk compression wave ve-
locity given by (C33eff/?eff)1/2, where ?effis the bone
mass density and C33effis the elastic modulus in the
direction of the bone axis. These two quantities, ?effand
C33eff, refer to effective bone properties spatially aver-
aged over a resolution cell with dimension on the order
of the US wavelength. These effective properties ?effand
C33efftake into account the bone structure and, thus, are
different from the mineral density and stiffness at the
tissue level. According to the model, SOS is then ex-
pected for thick bones to have a causal link with the axial
elastic modulus. For thinner bone, the velocity of the S0
equivalent guided mode may be expressed as a combi-
nation of different effective elastic coefficients as:
vS0??
?eff
C33eff
??1?
C13eff2
C11eff?C33eff?,(1)
where C11effand C33effare the effective stiffness coeffi-
cients for a transverse isotropic medium (Bossy et al.
2004b). Mechanical anisotropy influences the velocity of
the guided mode and SOS depends also on elastic mod-
ulus in the transverse direction.
(b) Experimental procedure. For each sample (intact
radius), SOS measurements were performed using probes
with 1-MHz (SOS1MHz) and 2-MHz (SOS2MHz) center
frequencies, respectively, on standardized regions-of-in-
terest (ROIs). The longitudinal position of this region
(approximately 1 cm long) was defined by a fixed frac-
tion (3/10) of the radius length from the distal extremity.
SOS was measured in the anterior and posterolateral
positions, as indicated in Fig. 1. These regions of mea-
surement correspond approximately to those usually
measured in vivo at the distal radius using the axial
transmission technique. The measurements were per-
formed at room temperature, using a standard US cou-
pling gel between probe and the specimen. To be able to
compare the values obtained at 1 MHz and 2 MHz, the
Fig. 1. Acoustic impedance image of a cross-section obtained at
50 MHz. The analyzed anterior, posterolateral and endosteal/
periosteal subregions are highlighted. M ? medial, P ? pos-
terior, L ? lateral, A ? anterior.
Axial transmission and tissue elasticity ● K. RAUM et al.
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probes need to be cross-calibrated. Plexiglas and alumi-
num were chosen as calibration materials, because of
their compressional bulk wave velocities being both
lower and higher than the velocity of approximately
3500 to 4200 m/s commonly found in human cortical
bone. The probes were cross-calibrated on a Plexiglas
plate to give the same value of SOS (2770 m/s). Then,
measurements at 1 MHz and 2 MHz performed on a thick
aluminum block (SOS ? 6200 m/s) produced a differ-
ence of 1.6%, the SOS at 1 MHz being slightly lower
than at 2 MHz. The difference results from a near-field
effect that has been described in a previous paper (Bossy
et al. 2004b). Based on the 1.6% difference found on
aluminum and numerical simulations of this near-field
effect, a difference of approximately 0.8% between
SOS1MHzand SOS2MHzon bone (SOS ? 4000 m/s) could
be extrapolated (Bossy et al. 2004b). This factor was
used to compensate for the near-field effect and to cor-
rect SOS2MHzvalues.
Acoustic microscopy. (a) Experimental procedure.
A custom SAM developed in the Q-BAM laboratory
(Halle, Germany) was used. It consists of a three-axis
high-precision scanning stage, a 200-MHz pulser/re-
ceiver (Panametrics 5900PR, Waltham, MA, USA) and a
500-MS/s A/D card (Gage CS8500, Gage Applied Tech-
nologies, Inc., Lachine, QUE, Canada). All components
are controlled by custom software (SAMEx, Q-BAM,
Halle, Germany). A spherically focused transducer
(V605, Valpey Fisher, Hopkinton, MA, USA) with a
center frequency of 49 MHz and a relative bandwidth of
84% provided a spatial resolution of approximately 23
?m. The samples prepared for SAM measurements were
completely immersed in a temperature-controlled tank
filled with distilled degassed water at 25°C. Sample
surfaces were placed in the focal plane of the transducer
and C-scans were acquired, where for each scanned
point, the entire pulse echo signal was stored (Fig. 1).
The spatial increment between two adjacent scan points
was set to 20 ?m.
(b) Impedance calibration and evaluation. The max-
imum spatial resolution is achieved if the sample surface
coincides with the focal plane of the transducer. For this
confocal measurement set-up, all parts of the incoming
spherical wave front are in phase and plane-wave prop-
agation in the direction of the sound field axis can be
assumed. For an infinite homogeneous half space, the
reflected amplitude is directly proportional to the reflec-
tion coefficient (Hirsekorn et al. 1995, 1996) and can
be converted into a value of the acoustic impedance
Z ? ?cp, where ? is the mass density and cpis the
compressional wave velocity (1 rayl ? kg m?2s?1)
(Meunier et al. 1991; Raum 2003; Raum et al. 2003;
Shieh et al. 1995; Zimmerman et al. 1994). Homoge-
neous reference materials were used for the impedance
calibration and defocus correction, as described else-
where (Raum et al. 2004). Briefly, for the C-scan data,
the amplitudes of the Hilbert-transformed envelope sig-
nal were defocus-corrected using a time-of-flight (TOF)-
dependent correction function, converted into reflection
coefficients R and, finally, into values of the acoustic
impedance Z using the relation:
R?Z2?Z1
Z2?Z1,(2)
where Z1and Z2are the acoustic impedances in the
coupling fluid and in the sample, respectively.
Synchrotron acquisition. After SAM inspection, the
samples were imaged using synchrotron radiation mic-
rotomography (SR-?CT) at the ESRF (European Syn-
chrotron Radiation Facility, Grenoble, France). The ex-
periment was performed on beamline ID19, where a 3-D
parallel beam ?CT set-up has been developed (Salome et
al. 1999). The system is operational for acquiring 3-D
images of bone samples at various spatial resolutions
(voxel sizes between 15 ?m to 0.3 ?m). Because the aim
of the experiment was to compare the SAM and SR-?CT
images with a comparable spatial resolution, we selected
a pixel size on the detector of 4.9 ?m (spatial resolution
of approximately 10 ?m). Using the 2048 ? 2048
charge-coupled-device (CCD)-based 2-D detector, this
choice enables getting a FOV of 10 ? 10 mm2and, thus,
encompass the entire cortical sample. Different insertion
devices (one wiggler and two undulators) conditioning
the spectrum and spreading of the beam may be used on
the beamline. Undulators produce higher intensity and
more focused ray-like spectra. Due to the sample size
(? 7 ? 5 ? 4 mm3), it was possible to use the U32
undulator. The energy was set 23.3 keV (obtained as the
third harmonic of the U32 undulator with a gap of 19
mm). As compared with the wiggler, the intensity of the
beam was increased by a factor of 10 and the acquisition
time limited to 2 s by view. For each sample, 900
radiographic images under different angles of view were
recorded.
The 3-D images were then obtained by applying an
exact tomographic reconstruction algorithm, based on
filtered backprojection (Fig. 2). The size of the cubic
voxel in the reconstructed images was 4.9 ?m. A 3-D
volume-of-interest (VOI) made of 1300 ? 900 ? 600
voxels was reconstructed in each sample. The mean
degree of mineralization of bone (DMB, g/cm3) was
derived from the measurement of the local grey levels of
the voxels of the segmented 3-D volume. Grey levels
were converted to volumetric tissue mineralization ex-
pressed as g/cm3of hydroxyapatite, as detailed by Nuzzo
et al. (2002).
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Page 5

Image reconstruction and parameter extraction.
Several steps were necessary to ensure site-matched
analysis of the SAM and SR-?CT images. Each 3-D
reconstructed SR-?CT volume was sequentially rotated
around the x and y axes to ensure that the cross-section
surface scanned with the acoustic microscope was par-
allel to the x-y plane (Fig. 2). Then, mean DMB and
porosity were calculated for subsequent z slices selected
at increasing depths below the bone boundary. It can be
seen, in Fig. 3, that, because of the partial volume effect,
both parameters gradually increase or decrease at the
boundary. The first slice below the surface for which a
steady-state was reached, was used for further analysis.
Then, tissue was separated from the Haversian canals by
using threshold masks (Raum et al. 2004). Thresholds
were set to the mean of tissue and noise level (DMB:
0.6 g/cm3; Z: 5 Mrayl). From these binary images, the
structural parameter Haversian canal density N.Ca/Ar
(number of detected canals N.Ca within the selected
cortical bone area Ar, 1/mm2), porosity Po (ratio between
the area covered by the Haversian canals to the total
selected bone area, %) and median canal diameter
Ca.Dm (the equivalent diameter was determined from
the area of the individual canals, ?m) were extracted.
For mineral density and impedance estimation, the
binary masks were eroded using a disk with a radius of two
pixels (40 ?m) for the SAM and one pixel (4.9 ?m) for the
SR-?CT images. This procedure ensured exclusion of
boundary pixels for which DMB or Z values are artificially
reduced by the partial volume effect. For the remaining
pixels, the mean, median, SD and standard error were
determined. All structural and tissue parameters were eval-
uated in the anterior (A) and posterolateral (PL) regions, for
which axial transmission SOS measurements have been
performed previously. These regions were further divided
into a fraction close to the periosteum Ps (approximately
one quarter of the total cortical thickness, ranging between
0.2 mm and 0.5 mm), and a remaining fraction bounded by
the endosteum Es (Fig. 1). In addition, the analysis was also
performed on the outer 1-mm thick cortical layer, because
axial transmission SOS (1 MHz) reflects preferentially the
bone properties in the periosteal region of approximately 1
mm in depth, as shown by the finite difference simulation
results (Bossy et al. 2004b). All ROIs were selected man-
ually. Cortical width (Ct.Wi, mm) was measured separately
for the A and PL regions in the SAM images at 10 locations
and averaged for each section.
Data analysis
The normality of the distributions was tested with
the Lilliefors test. The Bland and Altman method (Bland
and Altman 1986), linear regression and Pearson corre-
lation coefficients were used to compare structural pa-
rameters from the SR-?CT and SAM. Linear regression
and Pearson correlation coefficients were used to study
the association between different bone structural or ma-
terial properties. Differences of parameter estimations
between anterior and posterolateral regions were as-
sessed using paired two-sided t-tests. For the parameter
comparison between the Es, Ps and 1-mm subregions,
two-way ANOVA (with the sample number as the sec-
ond predictor variable) or nonparametric Kruskal–Wallis
tests (in cases of nonnormal distributions), followed by
post hoc multiple comparison Tukey tests were applied.
Optimal combination of bone properties for predicting
the low frequency SOS (SOS1MHzand SOS2MHz) were
evaluated using multifactorial linear and nonlinear re-
gression. All statistical computations were made using
the Matlab statistics toolbox (The Mathworks Inc.,
Natick, MA, USA).
Fig. 2. 3-D volume reconstruction of a posterolateral section
imaged by SR-?CT. Each volume data set was sequentially
rotated around the x and y axis until the upper cross-section
surface, which was scanned by SAM before, was parallel to the
x-y plane.
Fig. 3. Slice selection for the SR-?CT surface cross-section
reconstruction. Because of partial volume effect, slice at the
surface boundary (air/bone) exhibits decreased mean DMB and
increased Po values. The first slice for which parameters
reached steady-state (—-) was used for further analysis. In the
example, selected slice corresponds to a layer approximately 9
?m below the surface.
Axial transmission and tissue elasticity ● K. RAUM et al.
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RESULTS
Structural parameter estimation
N.Ca/Ar,Ca.DmandPoestimationsobtainedfromthe
SR-?CT and SAM images were compared by linear regres-
sion. For all parameters, the correlation was highly signif-
icant (p ? 0.0001), with a slope of one. Canal density was
slightly underestimated in the SAM images (N.Ca/ARSAM
? N.Ca/ArSR-?CT?2.05 mm?2, R2? 0.62, RMSE ? 2.31
mm?2),butcanaldiameterandporositywereoverestimated
(Ca.DmSAM? Ca.DmSR-?CT? 16 ?m, R2? 0.68, RMSE
? 6.83 ?m; PoSAM? PoSR-?CT? 1.94%, R2? 0.73,
RMSE?1.82%).TheoffsetsarewithinorclosetotheSDs
of the regressions and remain independent of the estimated
mean values. However, for further structural analysis, the
SR-?CT estimates were used. N.Ca/Ar was not correlated
with porosity, but appeared to determine the lower bound
(Fig. 4). Porosity was correlated with the square of the
Haversian canal diameter (R2? 0.66, p ? 0.0001).
Anatomic variations
The comparison between the parameter estimates
for the Es, Ps and outer 1-mm region is summarized in
Table 1. The acoustic impedance was significantly higher
in the Es region compared with the Ps region. The
highest Haversian canal density was observed in the
1-mm layer. The porosity varied significantly between all
different regions, with the highest values in the Es re-
gion, the lowest values in the Ps region and intermediate
values in the 1-mm layer. The canal diameter decreased
from the Es to the Ps region. No differences of the degree
of mineralization were observed between Es and 1-mm
regions. The minor increase in the Ps part was not
statistically supported.
Between the anterior and posterolateral regions,
there were no significant structural differences, but there
was a modest difference in Z for the Ps and outer 1-mm
regions (Table 2).
Univariate regression
Cortical width was significantly correlated with the
SOS1MHz(r ? 0.56, p ? 0.01), but not with SOS2MHz.
Further correlations were found between SOS and
Fig. 4. Relation between Haversian canal density N.Ca/Ar and
porosity Po. N.Ca/Ar was not correlated with Po, but deter-
mined the lower bound for the tissue porosity.
Table 1. Estimated structural and tissue properties in the
endosteal, periosteal and in the 1-mm outer cortical regions
(mean and SD)
EndostealPeriosteal1 mm
DMB (g/cm3)
Z (Mrayl)
1.13 ? 0.03
8.2 ? 0.5
1.14 ? 0.02
8.0 ? 0.6
1.13 ? 0.02
8.1 ? 0.5
N.Ca/ArSR-?CT(1/mm2)
10.7 ? 3.411.2 ? 4.6 12.4 ? 3.7
N.Ca/ArSAM(1/mm2)
9.9 ? 3.18.0 ? 4.111.7 ? 3.2
PoSR-?CT(%)
6.2 ? 2.6 2.3 ? 0.9 3.6 ? 1.5
PoSAM(%)
8.5 ? 3.3 3.0 ? 1.7 6.3 ? 2.1
Ca.DmSR-?CT(?m)
59 ? 1044 ? 10* 48 ? 6
Ca.DmSAM(?m)
74 ? 1056 ? 16* 65 ? 11
Significant differences (two-way ANOVA followed by post hoc
multiple comparison Tukey test, p ? 0.05) are indicated with connec-
tive bars.
* Not normally distributed (Lilliefors test, p ? 0.05), Kruskal–
Wallis test was used.
Table 2. Estimated structural and tissue properties in the
anterior and posterolateral regions (mean and SD)
Anterior Posterolateral
SOS1MHz(m/s)
SOS2MHz(m/s)
DMBEs(g/cm3)
DMBPs(g/cm3)
DMB1mm(g/cm3)
ZEs(Mrayl)
ZPs(Mrayl)
Z1mm(Mrayl)
N.Ca/ArEs(1/mm2)
N.Ca/ArPs(1/mm2)
N.Ca/Ar1mm(1/mm2)
PoEs(%)
PoPs(%)
Po1mm(%)
Ca.DmEs(?m)
Ca.DmPs(?m)
Ca.Dm1mm(?m)
Ct.Wi (mm)
3933 ? 102
3995 ? 86
1.13 ? 0.02
1.14 ? 0.03
1.13 ? 0.03
8.3 ? 0.5
8.2 ? 0.6
8.2 ? 0.5
10.2 ? 3.3
11.7 ? 4.6
12.1 ? 3.9
6.4 ? 2.7
2.5 ? 0.7
3.8 ? 1.6
62 ? 8
46 ? 13†
50 ? 7
1.9 ? 0.5
3905 ? 88
3984 ? 78
1.14 ? 0.02
1.15 ? 0.01
1.14 ? 0.02
8.2 ? 0.5
7.8 ? 0.5*
8.0 ? 0.6*
11.2 ? 3.7
10.6 ? 4.8
12.7 ? 3.7
6.0 ? 2.6
2.0 ? 1.0
3.3 ? 1.3
56 ? 11
41 ? 5
46 ? 5
1.9 ? 0.6
The subscripts Es, Ps and 1mm indicate that the corresponding
parameters have been derived in the endosteal, periosteal and 1-mm
thick outer cortical layer, respectively.†Not normally distributed (Lil-
liefors test, p ? 0.05). * Significant differences (paired t-test, p ?
0.05).
1230 Ultrasound in Medicine and BiologyVolume 31, Number 9, 2005

Page 7

N.Ca/Ar in the Es part at both frequencies (1 MHz: r ?
?0.62, p ? 0.004; 2 MHz: r ? ?0.47, p ? 0.04) and
with N.Ca/Ar in the 1-mm region at 1 MHz (r ? ?0.53,
p ? 0.02), respectively. Moreover, weak but significant
correlations were observed between DMB and Po for the
Es (r ? ?0.46, p ? 0.04) and Ps (r ? ?0.59, p ? 0.006)
regions, but not for the 1-mm sections. The acoustic
impedance Z was neither correlated with the degree of
mineralization of bone (p ? 0.13) nor with porosity (p ?
0.22).
Multivariate regression
Because the number of cases was low (n ? 19 after
pooling A and PL sections), the number of input vari-
ables had to be restricted for the multivariate linear
regression analysis. All parameter combinations with
two or three input variables were tested for significance
of the standardized individual regression coefficients ?.
Significant models were only obtained for combinations
of cortical width, either with impedance (R2: 0.40 to
0.52, p ? 0.005), or with N.Ca/Ar or porosity as a third
variable (adjusted R2: 0.54 to 0.84, p ? 0.0001). The
different R2correspond to the evaluated regions and
frequencies, respectively (see Tables 3 and 4). The high-
est R2and lowest RMSE values were obtained with
parameters determined in the Ps region, followed by the
1-mm region. The parameter sets from the Es region
produced either the lowest R2or insignificant models.
The R2for the 2-MHz models were generally lower
compared with the 1-MHz models.
Although both tissue elasticity (represented by Z)
and porosity can be assumed to alter the low-frequency
propagation velocity in a linear or close to linear way
(Bossy et al. 2004b; Sakata et al. 2004), the width-
dependence is caused by a change of the nature of the
first arriving signal from a compression mode (velocity
cp? 4000 m/s) to the first symmetric Lamb mode S0
(velocity cS0? 3650 m/s). A plot of SOS as a function of
Ct.Wi/? (where ? is the wavelength of the compressional
mode) is shown in Fig. 5.
As predicted by finite difference simulations
(Bossy et al. 2004b), this dependency is nonlinear. It is
intuitive that any linear model for Ct.Wi would predict
infinite SOS estimates, if Ct.Wi is increased far beyond
the evaluated range. The model was, therefore, mod-
ified assuming a linear-dependence of the compres-
sional wave velocity cpon Z and porosity and a
nonlinear-dependence on the cortical width. The latter
should decrease the estimated velocity SOS continu-
ously from cpfor Ct.Wi ? ? to cS0for Ct.Wi ?? ?,
e.g.,
SOS?B1G?B2
Ct.Wi
??·cP(Z,PO)?B0, (3)
where G() is a function that describes the width-depen-
dence of SOS. Among other evaluated functions, the best
approximation of this nonlinear behavior was obtained
using a hyperbolic tangent function:
Table 3. Multivariate linear prediction models for the 1-MHz SOS estimation
SOS1MHz
Region
Intercept
(ms?1)
?1
?2
?3
R2
RMSE
(ms?1)
Ct.Wi, Z
Ct.Wi, Z
Ct.Wi, Z
Ct.Wi, Z, N.Ca/Ar
Ct.Wi, Z, Po
Es
Ps
2957
2987
2848
3049
2858
0.78†
0.78†
0.83†
0.71†
1.10‡
0.48*
0.54*
0.57†
0.53*
0.67‡
–
–
–
0.44†
0.50†
0.52†
0.61†
0.84‡
69.8
65.6
64.5
58.1
37.8
1 mm
1 mm
Ps
?0.34*
?0.62‡
The table shows the model constant, standardized regression coefficients ?i(in the order as the parameters appear in the first column), the adjusted
R2and RMSE of the model (significance level p: * ? 0.05;†? 0.005;‡? 0.0001).
Table 4. Multivariate linear prediction models for the 2-MHz SOS estimation
SOS2MHz
Region
Intercept
(ms?1)
?1
?2
?3
R2
RMSE
(m/s)
Ct.Wi, Z
Ct.Wi, Z
Ct.Wi, Z
Ct.Wi, Z, N.Ca/Ar
Ct.Wi, Z, Po
Es
Ps
3006
3090
2932
3111
2997
0.66†
0.67†
0.73†
0.71†
0.93‡
0.62*
0.66†
0.71†
0.67†
0.77‡
–
–
–
0.40†
0.45†
0.48†
0.54†
0.65‡
62.5
60.0
57.9
54.5
47.5
1 mm
Ps
Ps
?0.33*
?0.51†
The table shows the model constant, standardized correlation coefficients ?i(in the order as the parameters appear in the first column), the adjusted
R2and RMSE of the model (significance level p: * ? 0.05;†? 0.005;‡? 0.0001).
Axial transmission and tissue elasticity ● K. RAUM et al.
1231

Page 8

SOS?tanh?BCt.Wi
Ct.Wi
??(BZ·Z?BPo·PO?B1)?B0,
(4a)
where BCt.Wi, Bz, BPoand B0are the regression coeffi-
cients. The term:
tanh?BCt.Wi
Ct.Wi
??B1
(4b)
did not have a significant impact in the regression and
was, therefore, withdrawn. The final model:
SOS?BZtanh?BCt.Wi
?BPotanh?BCt.Wi
Ct.Wi
??Z
Ct.Wi
??PO?B0(5)
is not restricted to a single frequency and allowed the
pooling of the 1- and 2-MHz data. Two-parameter re-
gressions were performed with a fixed coefficient BCt.Wi
and the best predictive variables APsand PoPs. BCt.Wiwas
then varied until the residuals of the model became
independent of the ratio Ct.Wi/?. The final model was
highly significant (R2? 0.69, p ? 1e-5, RMSE ? 51.8
m/s). All observations were within the 95% prediction
bounds and the residuals were normally distributed. The
regression coefficients are summarized in Table 5. Anal-
ysis of the semipartial correlation coefficients indicates
that, after controlling for the effects of porosity, 70% of
the remaining variance is still explained by variations of
Z. For a width larger than the wavelength and mean
values for impedance and porosity (Zperi? 8 Mrayl,
Poperi? 2.26%), the predicted compressional velocity
(Ct.Wi ?? ?) is 4044 ? 49 m/s. In this case, the model
predicts an increase of 79 m/s/Mrayl and a decrease of 52
m/s % of porosity. The variation of SOS as a function of
Ct.Wi is shown in Fig. 6. At a width-to-wavelength ratio
Ct.Wi/? ? 0.35, the estimated sound velocity decreased
by 5%. Moreover, the slopes of Z and porosity depen-
dencies become dependent on Ct.Wi/?.
DISCUSSION
In the present study, we investigated, for the first
time, the relationship between SOS measured by low-
Fig. 5. SOS1MHzand SOS2MHzas a function of cortical width-
to-wavelength ratio (?1MHz? 4 mm, ?2MHz? 2 mm). The
dependency obtained by finite difference simulations is super-
imposed (from Bossy et al. 2004b).
Fig. 6. Cortical width dependence, ( · · · · ) prediction bounds,
of estimated velocities at 1 and 2 MHz for mean impedance (Z
? 8 Mrayl) and porosity (2.26%).
Table 5. Nonlinear prediction model, eqn (4), with absolute (Bi), standardized (?), partial and semipartial correlation
coefficients (n ? 38, R2? 0.69, p ? 1e-5, RMSE ? 51.8 m/s, p for the individual parameters in the last row). All
parameter were obtained from the periosteal region.
B0
(m · s?1)
BZ
(m · s?1· Mrayl?1)
BPo
(m · s%?1)
BCt.Wi
Bi
?
Partial corr.
Semipartial corr.
p
3530 ? 49
–
–
–
–
79 ? 9
1.01
0.842
0.839
?10?5
?52 ? 12
?0.48
?0.596
?0.399
?10?4
2.0
–
–
–
–
1232 Ultrasound in Medicine and Biology Volume 31, Number 9, 2005

Page 9

frequency bidirectional axial transmission and micro-
structural and elastic cortical bone properties determined
using high-resolution SR-?CT and SAM, respectively.
Impedance images indicate that the resolution of the
acoustic imaging system was suitable to resolve the
majority of the Haversian canals. Only very small canals
(Ca.Dm ? 25 ?m) and osteocyte lacunae could not be
separated from the bone tissue. The comparison of struc-
tural parameter estimates from SAM images with those
from regional matched SR-?CT images reveals small but
systematic offsets for all evaluated parameters. Although
the failure to detect the smallest canals can be attributed
to the physical resolution limit of the 50-MHz trans-
ducer, the spatial sampling rate (pixel size: 20 ? 20
?m2) prohibits a higher accuracy of area measurements.
This presumably led to the overestimation of canal di-
ameter and porosity. Data acquisition with a smaller
spatial increment or improved image processing (e.g.,
interpolation before parameter extraction) might help to
improve the accuracy without the necessity of increasing
the ultrasonic frequency. Nevertheless, most of the tissue
could be reliably separated from the Haversian canals,
which allowed study of the individual contributions of
structural and intrinsic elastic tissue properties to the
sound velocity measured in bidirectional axial transmis-
sion.
The use of bone samples from previous studies
required prolonged storage at ?20 °C, as well as several
cycles of freezing and thawing. This procedure does not
alter the elastic properties of the tissue (Linde and So-
rensen 1993; Pelker et al. 1984). The samples were
intentionally defatted after SAM inspection because it
causes a stiffening of the tissue (Linde and Sorensen
1993). However, the degree of mineralization of tissue is
presumably not altered by this procedure.
Porosity, degree of mineralization and BMD have
been determined to be predictive parameters for the SOS
(Bossy et al. 2004a, 2004b, 2004c; Lee et al. 1997;
Sievanen et al. 2001). For example, significant correla-
tions between SOS measured in vivo at 1.25 MHz and
volumetric BMD were reported by Sievanen et al.
(2001), both at the tibia (R2? 0.29, p ? 10?3) and at the
radius (R2? 0.34, p ? 10?3). In an in vitro study, Bossy
et al. (2004c) found that approximately 60% of the
variance of SOS (at 1 MHz) in human radius was ex-
plained by BMD or, equivalently, by a combination of
degree of mineralization of bone and porosity. Moreover,
Bossy et al. (2004b, 2004c) have shown that the proper-
ties of a thin cortical layer close to the periosteum
contribute more strongly to the axial wave propagation
velocity compared with properties averaged over the
cortex. However, the correlation coefficients R2between
SOS and BMD obtained for the studies conducted in the
MHz range are between 0.3 and 0.57, suggesting addi-
tional influences not being assessed with the applied
methods.
The predominant contribution of the subperiosteal
layer on SOS was confirmed in this study. For almost all
models, R2was highest when structural and impedance
values were chosen from this region. In contradiction to
the previous report (Bossy et al. 2004b), however, degree
of mineralization of bone was not a significant predictor
of SOS. The discrepancy between both studies could be
caused by several factors. First, the 10-sample subset
might have been insufficient to reach the significance
level obtained in the 39-sample population of the previ-
ous study (R2? 0.38, p ? 10?4). Second, Bossy et al.
(2004b) used a simple threshold to segment SR-?CT
images obtained with a lower spatial resolution (approx-
imately 20 ?m). It is likely that differences in the spatial
resolution and segmentation procedure might have re-
sulted in differences in degree of mineralization of bone
estimation in both studies. This hypothesis is supported
by the finding (Bossy et al. 2004c) that the correlation of
SOS with volumetric BMD (including pores) is consid-
erably higher (R2? 0.57, p ? 10?5) than the correlation
with tissue mineralization degree alone (R2? 0.38, p ?
10?4).
Interestingly, the acoustic impedance was found to
be a predominant determinant of SOS. After compensa-
tion for the nonlinear dependence of SOS on Ct.Wi and
controlling for the effects of porosity (semipartial corre-
lation), Z explained 70% of the remaining variability of
SOS. Considering that the acoustic impedance is a strong
predictor of bone elasticity (Bumrerraj and Katz 2001;
Katz and Meunier 1997; Meunier et al. 1991; Raum
2003), it can be inferred from our study that elasticity is
also a strong predictor of low-frequency SOS. Because
tissue elasticity is not only determined by the degree of
mineralization, but also by many other factors (e.g.,
collagen cross-links, size and composition of mineral
crystals and anisotropy), Z appears to be a better indica-
tor for it than the degree of mineralization of bone.
Further studies may wish to gauge changes in tissue
elasticity (using acoustic microscopy) and their effect on
axial transmission SOS against well-characterized de-
fects in bone material, as can be seen in various bone
diseases or in small animal models.
The dependence of SOS on intracortical porosity in
the model (?52 ? 12 m · s?1· %?1; Ct.Wi ?? ?) is
greater than the value predicted by Bossy et al. (2004c)
(?24 ? 11 m · s?1· %?1; Ct.Wi ? 2.1 ? 0.5 mm). For
the 1-MHz data and the mean value of Ct.Wi ? 1.94 mm
reported here, the predicted slope is ?39 ? 9
m · s?1· %?1. Moreover, it should be noted that the
slope obtained from finite difference simulations (Bossy
et al. 2004b) was slightly nonlinear, having a steeper
slope for low porosity values (e.g., ?28 m · s?1· %?1
Axial transmission and tissue elasticity ● K. RAUM et al.
1233

Page 10

for Po ? 0 to 7% vs. ?20 m · s?1· %?1for Po ? 0 to
15%). These findings are consistent within the 95%
confidence intervals.
The proposed model describes axial transmission
SOS (the velocity of the first arriving signal) in the whole
cortical thickness range as a function of its microstruc-
tural and elastic tissue properties. Because it is not re-
stricted to a single frequency, it can be applied to all
currently available axial transmission devices. Moreover,
the Ct.Wi/? ratio in the model could be used with mul-
tifrequency approaches, to assess cortical thickness and
effective elastic tissue properties (combination of tissue
elasticity and porosity) separately. We hypothesize that
these properties are strongly associated with bone
strength.
The small number of specimens, as well as the
narrow age range of the donors, is a limitation of this
study. We tried partly to compensate for this limitation
by the use of both male and female samples, by the
selection of several ROIs for each sample and by pooling
the measurements performed at 1 and 2 MHz. However,
the results need to be confirmed on a larger sample
population with a wide range of values for each of the
estimated parameters.
Although SOS is accurately predicted for the pure
compressional propagation mode (Ct.Wi ?? ?), as well
as for the nonlinear transition zone (Ct.Wi ? ?/2), the
model becomes independent of elastic and structural
properties, if the cortical width approaches zero (e.g.,
pure guided propagation mode). Incorporating precise
prediction of the guided propagation modes, including
tissue anisotropy, will be subject of future work.
The internationally agreed upon definition of os-
teoporosis (ConsensusDevelopment
1993) acknowledges the notion that, in diseased pa-
tients, there is less bone and an alteration in its mi-
croarchitecture, but implicitly assumes that the intrin-
sic material “quality” of the remaining bone tissue is
normal. This is a simplified view of a more complex
situation, in which different physicochemical or com-
positional factors influencing bone quality are also
subject to modifications during ageing (Zioupos 2001)
or during bone metabolic diseases. These factors con-
tribute to tissue elasticity and to bone strength, but
none of them can be easily assessed macroscopically
or in vivo. In contrast, elasticity can be assessed using
US-based techniques. Low-frequency US is perfectly
appropriate to probe structural elasticity, whereas
high-frequency US has the capability directly to probe
material elasticity at the tissue level. The novelty of
the experimental results presented here is precisely to
identify the impact of tissue elasticity on macroscop-
ically determined speed of sound.
Conference
Acknowledgements—The authors are grateful for the financial support
by the DAAD PPP program (#D/0122910), the Deutsche Forschungs-
gemeinschaft (grant RA1380/1-1) and the MAE program PAI PRO-
COPE (04544UM). One of the authors (K. Raum) acknowledges sup-
port from CNRS (Poste Chercheur Associé).
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