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In Vivo Characterization of Cortical Bone Using Guided
Waves Measured by Axial Transmission
Quentin Vallet, Nicolas Bochud, Christine Chappard, Pascal Laugier,
Jean-Gabriel Minonzio
To cite this version:
Quentin Vallet, Nicolas Bochud, Christine Chappard, Pascal Laugier, Jean-Gabriel Minonzio. In Vivo
Characterization of Cortical Bone Using Guided Waves Measured by Axial Transmission. IEEE Trans-
actions on Ultrasonics, Ferroelectrics and Frequency Control, Institute of Electrical and Electronics
Engineers, 2016, 63 (9), pp.1361 - 1371. �10.1109/TUFFC.2016.2587079�. �hal-01386612�
For Review Only
JOURNAL OF IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 1
In vivo characterization of cortical bone using
guided waves measured by axial transmission
Quentin Vallet, Nicolas Bochud, Christine Chappard, Pascal Laugier, and Jean-Gabriel Minonzio
Abstract—Cortical bone loss is not fully assessed by current X-
ray methods, and there is an unmet need in identifying women at
risk of osteoporotic fracture who should receive a treatment. The
last decade has seen the emergence of ultrasound axial transmis-
sion techniques to assess cortical bone. Recent axial transmission
techniques exploit the multimode waveguide response of long
bones such as the radius. A recent ex vivo study by our group
evidenced that a multimode axial transmission approach can yield
simultaneous estimates of cortical thickness and stiffness.
The aim
of the present work is to move one step forward to evaluate the
feasibility of measuring multimode guided waves in vivo and to
infer from it cortical thickness. Measurements were taken on the
forearm of 14 healthy subjects with the goal to test the accuracy of
the
estimated thickness using the bidirectional axial transmission
method implemented on a dedicated 1-MHz linear ultrasound
array. This setup allows determining in vivo the dispersion curves
of guided waves transmitted in the cortical layer of the radius. An
inverse procedure based on the comparison between measured
and modeled dispersion curves predicted by a two-dimensional
transverse isotropic free plate waveguide model allowed an
estimation of cortical thickness, despite the presence of soft
tissue. The cortical thickness values were validated by comparison
with site-matched estimates derived from X-ray high-resolution
peripheral quantitative computed tomography. Results showed a
significant correlation between both measurements (r
2
= 0.7,
p < 0.05, RM SE = 0.21 mm) . This
pilot study demonstrates
the potential of bidirectional axial transmission for the in vivo
assessment of
cortical thickness, a bone strength-related factor.
Index Terms—Quantitative ultrasound (QUS), cortical bone,
axial transmission, guided waves, cortical thickness.
I. INTRODUCTION
O
STEOPOROSIS is a medical threat with a consequent
increase in bone fragility and susceptibility to fracture.
There is an increasing awareness about osteoporosis, because
of the consequences of fractures on morbidity, quality of life
and mortality [1]. Fracture risk is currently estimated in vivo
by bone mineral density (BMD), measured by dual energy X-
ray absorptiometry (DXA). However, BMD does not identify
all individuals at risk of fracture [2], [3].
Cortical bone plays an important role on the skeletal
biomechanical stability [4]–[6]. Cortical loss, which results in
cortical thinning and porosity increase, is a key factor in non-
vertebral fracture risk [7]. The determination of the structural
Paper re-submitted April 14th, 2016. This work was supported in part
by the Fondation pour la Recherche M
´
edicale through project number FRM
DBS201311228444.
Q. Vallet, N. Bochud, P. Laugier and J.-G. Minonzio are with the
Sorbonne Universit
´
es, UPMC Univ Paris 06, CNRS, INSERM, Labora-
toire d’Imagerie Biom
´
edicale (LIB), F-75006, Paris, France, e-mail: (see
quentin.vallet@upmc.fr).
C. Chappard is with the B2OA, UMR 7052 CNRS, Universit
´
e Denis
Diderot, Pres University Sorbonne Paris Cit
´
e, France.
and material properties of cortical bone is thus essential to
understand the impact of bone loss on the skeleton [8], [9].
Such observations have triggered studies for alternative
diagnostic modalities showing capacity to reach a quantitative
assessment of cortical bone quality beyond BMD. Among
others, quantitative ultrasound (QUS) techniques have been
proposed as an alternative to DXA. Transverse transmission
techniques, in which ultrasound is transmitted transversally to
the long axis of the bone, have been applied to the forearm to
clinically estimate BMD at the 1/3 radius [10] or the cortical
thickness (Ct.Th) at the distal radius on the basis of the
principle of the Biot fast and slow waves phenomenon [11],
[12]. Altenatively, a pulse echo technique has been reported
enabling the in vivo assessment of Ct.Th of the tibia based on
power spectra of ultrasonic echoes containing reflections from
front and back surfaces [13], [14].
Ultrasound (US) axial transmission (AT) techniques exploit
the propagation of guided waves (GW) in the cortical layer
along the main axis of the bone [15]. Several implementations
of AT have been reported based on the measurement of the
velocity of the first arriving signal (FAS) [16]–[19], of the
fundamental flexural guided mode (equivalent to the Lamb A
0
-
mode for a plate) [20], [21] or of the dispersion spectrum of
multiple GW [22]–[27]. While multimode AT techniques have
been extensively tested in laboratory conditions on phantoms
or ex vivo [22], [23], only the methods based on FAS or on
the fundamental flexural guided mode have been tested in
vivo [28]. FAS was found to be a relevant factor in fracture
discrimination in several clinical studies [29]–[35].
An interesting feature of GW-based AT approaches is their
potential to yield estimates of waveguide properties such
as thickness and stiffness by fitting a physical model of
the waveguide to the measured dispersion curves. Numerous
phantom and ex vivo studies focused on such GW model-
based approaches. Among these, authors reported estimates
of Ct.Th using a fixed elasticity [25], [36], elastic properties
(e.g., Young modulus) assuming a fixed thickness [37] or si-
multaneous estimates of both geometric and elastic properties
of the cortical bone [27].
The latter study [27] was based on a dedicated 1-MHz
linear ultrasound array, consisting of one group of receivers
surrounded by two groups of emitters, allowing the deter-
mination of the frequency-dependent wave numbers (i.e., the
dispersion curves) of multiple guided modes [38], [39]. The
inverse procedure was based on the comparison between the
experimental dispersion curves and a two-dimensional (2-D)
transverse isotropic free plate waveguide model using a least-
square optimization criterion and a gradient-based method (i.e.
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JOURNAL OF IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 3
0.4 0.6 0.8 1 1.2 1.4 1.6
0
1
2
3
4
5
6
=⇒
f variation
Frequency, f [MHz]
Wave number, k [rad/mm]
0
0.2
0.4
0.6
0.8
1
(a) Initial Norm function
0 1 2 3 4 5 6
0
0.2
0.4
0.6
0.8
1
Wave number, k [rad/mm]
Amplitude
f
i
= 1 MHz
(b) Initial Norm function amplitudes at f
i
= 1 MHz,
S(k)
|f
i
0 1 2 3 4 5 6
0
0.2
0.4
0.6
0.8
1
Wave number, k [rad/mm]
Amplitude
f
i
= 1 MHz
(c) Dilated Norm function amplitudes at f
i
= 1 MHz,
S
d
(k)
|f
i
0 1 2 3 4 5 6
0
0.2
0.4
0.6
0.8
1
Wave number, k [rad/mm]
Amplitude
f
i
= 1 MHz
(d) Dilated Norm function amplitudes fixed to 0 at f
i
= 1
MHz, S
d
(k)
|f
i
,k↓
= 0
0.4 0.6 0.8 1 1.2 1.4 1.6
0
1
2
3
4
5
6
Frequency, f [MHz]
Wave number, k [rad/mm]
0
0.2
0.4
0.6
0.8
1
(e) Dilated Norm function
0.4 0.6 0.8 1 1.2 1.4 1.6
0
1
2
3
4
5
6
Frequency, f [MHz]
Wave number, k [rad/mm]
Denoised data
Noise
(f) Statistical denoising over the 10 measurement repeti-
tions
Fig. 2. Signal processing steps (dilation and statistical denoising) for the extraction of the (f,k)-pairs from the Norm function and the two directions of
propagation.
the inclination angle between the probe and the bone, which
could result from the presence of overlying soft tissue.
A wideband pulse with a central frequency of 1 MHz (-
6dB power spectrum spanning the frequency range from 0.2
to 1.8 MHz) is used to excite every emitters. A sampling
frequency of 20 MHz (1024 time samples, 12 bits) is chosen to
record temporal signals after 16 averages by hardware (Altha
¨
ıs
Technologies, Tours, France). For in vivo measurements, a
particular attention has been given to the alignment between
the probe and the main axis of the radius using a custom-made
Human Machine Interface (HMI), which provides a real-time
feedback on the experimental dispersion curves to guide the
alignment.
Note that the measurement protocol consists of 4 acquisi-
tions with intermediate repositioning, whereas each acquisition
results from 10 measurement repetitions without moving the
probe. For each single measurement, the signals are recorded
for both directions, i.e., by firing sequentially each group of
emitters on both side of the group of receivers. In that way,
the resulting number of measurements on each subject was 2
directions × 10 measurements × 4 acquisitions.
C. Signal processing
In order to extract the experimental dispersion curves, repre-
sented by the frequency-dependent wave numbers (i.e., k(f)),
a SVD was applied to the multidimensional 2 × N
E
× N
R
radio-frequency signals corresponding to all possible pairs of
emitter-receiver. The signal processing to obtain the dispersion
curves has been extensively described previously in [38]: (1)
the radio-frequency signals were Fourier transformed with
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