Over the past few decades, early osteoporosis detection using ultrasonic bone quality evaluation has gained prominence. Specifically, various studies focused on axial transmission using ultrasonic guided waves and have highlighted this technique's sensitivity to intrinsic properties of long cortical bones. This work aims to demonstrate the potential of low-frequency ultrasonic guided waves to infer the properties of the bone inside which they are propagating. A proprietary ultrasonic transducer, tailored to transmit ultrasonic guided waves under 500 kHz, was used for the data collection. The gathered data underwent two-dimensional fast Fourier transform processing to extract experimental dispersion curves. The proposed inversion scheme compares experimental dispersion curves with simulated dispersion curves calculated through the semi-analytical iso-geometric analysis (SAIGA) method. The numerical model integrates a bone phantom plate coupled with a soft tissue layer on its top surface, mimicking the experimental bone phantom plates. Subsequently, the mechanical properties of the bone phantom plates were estimated by reducing the misfit between the experimental and simulated dispersion curves. This inversion leaned heavily on the dispersive trajectories and amplitudes of ultrasonic guided wave modes. Results indicate a marginal discrepancy under 5% between the mechanical properties ascertained using the SAIGA-based inversion and those measured using bulk wave pulse-echo measurements.
REFERENCES
1.
W. H. Organization
, “Assessment of fracture risk and its application to screening for postmenopausal osteoporosis,” in Report of a WHO Study Group
, Rome, Italy (June 22–25, 1992) (
World Health Organization
,
Geneva
, 1994
), https://apps.who.int/iris/handle/10665/39142 (Last viewed June 28, 2022).2.
W. H. Organization
, Guidelines for Preclinical Evaluation and Clinical Trials in Osteoporosis
(
World Health Organization
,
Geneva
, 1998
), https://apps.who.int/iris/handle/10665/42088 (Last viewed June 28, 2022).3.
N.
Bochud
,
Q.
Vallet
,
J.-G.
Minonzio
, and
P.
Laugier
, “
Predicting bone strength with ultrasonic guided waves
,” Sci. Rep.
7
(1
), 43628
(2017
).4.
P.
Laugier
and
G.
Haïat
, Bone Quantitative Ultrasound
(
Springer Netherlands
,
Dordrecht
, 2011
).5.
P.
Laugier
and
Q.
Grimal
, Bone Quantitative Ultrasound: New Horizons
, Advances in Experimental Medicine and Biology Vol. 1364 (
Springer International Publishing
,
Cham
, 2022
).6.
C.
Cooper
,
G.
Campion
, and
L. J.
Melton
, “
Hip fractures in the elderly: A world-wide projection
,” Osteoporosis Int.
2
(6
), 285
–289
(1992
).7.
J. A.
Kanis
,
O.
Johnell
,
A.
Oden
,
B.
Jonsson
,
C.
De Laet
, and
A.
Dawson
, “
Risk of hip fracture according to the World Health Organization criteria for osteopenia and osteoporosis
,” Bone
27
(5
), 585
–590
(2000
).8.
L. J.
Melton
,
E. A.
Chrischilles
,
C.
Cooper
,
A. W.
Lane
, and
B. L.
Riggs
, “
How many women have osteoporosis?
,” J. Bone Miner. Res.
20
(5
), 886
–892
(2005
).9.
A.
Randell
,
P. N.
Sambrook
,
T. V.
Nguyen
,
H.
Lapsley
,
G.
Jones
,
P. J.
Kelly
, and
J. A.
Eisman
, “
Direct clinical and welfare costs of osteoporotic fractures in elderly men and women
,” Osteoporosis Int.
5
(6
), 427
–432
(1995
).10.
S. R.
Cummings
,
D. B.
Karpf
,
F.
Harris
,
H. K.
Genant
,
K.
Ensrud
,
A. Z.
LaCroix
, and
D. M.
Black
, “
Improvement in spine bone density and reduction in risk of vertebral fractures during treatment with antiresorptive drugs
,” Am. J. Med.
112
(4
), 281
–289
(2002
).11.
O.
Johnell
,
J. A.
Kanis
,
A.
Odén
,
I.
Sernbo
,
I.
Redlund-Johnell
,
C.
Petterson
,
C.
De Laet
, and
B.
Jönsson
, “
Mortality after osteoporotic fractures
,” Osteoporos. Int.
15
(1
), 38
–42
(2004
).12.
K.
Engelke
,
C.
Libanati
,
Y.
Liu
,
H.
Wang
,
M.
Austin
,
T.
Fuerst
,
B.
Stampa
,
W.
Timm
, and
H. K.
Genant
, “
Quantitative computed tomography (QCT) of the forearm using general purpose spiral whole-body CT scanners: Accuracy, precision and comparison with dual-energy X-ray absorptiometry (DXA)
,” Bone
45
(1
), 110
–118
(2009
).13.
N.
Li
,
X.-m.
Li
,
L.
Xu
,
W.-j.
Sun
,
X.-g.
Cheng
, and
W.
Tian
, “
Comparison of QCT and DXA: Osteoporosis detection rates in postmenopausal women
,” Int. J. Endocrinol.
2013
, 895474
.14.
W.
Kalender
,
K.
Engelke
,
T. P.
Fuerst
,
C.-C.
Glüer
,
P.
Laugier
, and
J.
Shepherd
, “
Quantitative aspects of bone densitometry: Contents
,” J. ICRU
9
(1
), NP.2
–NP
(2009
).15.
C.-C.
Glüer
, “
Quantitative ultrasound techniques for the assessment of osteoporosis: Expert agreement on current status
,” J. Bone Miner. Res.
12
(8
), 1280
–1288
(1997
).16.
Q.
Grimal
,
J.
Grondin
,
S.
Guérard
,
R.
Barkmann
,
K.
Engelke
,
C.-C.
Glüer
, and
P.
Laugier
, “
Quantitative ultrasound of cortical bone in the femoral neck predicts femur strength: Results of a pilot study
,” J. Bone Miner. Res.
28
(2
), 302
–312
(2013
).17.
J.-G.
Minonzio
,
M.
Talmant
, and
P.
Laugier
, “
Guided wave phase velocity measurement using multi-emitter and multi-receiver arrays in the axial transmission configuration
,” J. Acoust. Soc. Am.
127
(5
), 2913
–2919
(2010
).18.
N.
Bochud
,
Q.
Vallet
,
Y.
Bala
,
H.
Follet
,
J.-G.
Minonzio
, and
P.
Laugier
, “
Genetic algorithms-based inversion of multimode guided waves for cortical bone characterization
,” Phys. Med. Biol.
61
(19
), 6953
–6974
(2016
).19.
D.
Pereira
,
A.
Le Duff
,
G.
Painchaud-April
, and
P.
Belanger
, “
Simulation-based inversion for the characterization of adhesively bonded joints using ultrasonic guided waves
,” IEEE Trans. Ultrason, Ferroelect, Freq. Contr.
69
(7
), 2400
–2407
(2022
).20.
M.
Asif
,
M. A.
Khan
,
S. Z.
Khan
,
R. S.
Choudhry
, and
K. A.
Khan
, “
Identification of an effective nondestructive technique for bond defect determination in laminate composites–A technical review
,” J. Composite Mater.
52
(26
), 3589
–3599
(2018
).21.
K.
Heller
,
L.
Jacobs
, and
J.
Qu
, “
Characterization of adhesive bond properties using Lamb waves
,” NDT&E
33
(8
), 555
–563
(2000
).22.
S. I.
Rokhlin
,
B.
Xie
, and
A.
Baltazar
, “
Quantitative ultrasonic characterization of environmental degradation of adhesive bonds
,” J. Adhes. Sci. Technol.
18
(3
), 327
–359
(2004
).23.
M.
Ponschab
,
D. A.
Kiefer
, and
S. J.
Rupitsch
, “
Simulation-based characterization of mechanical parameters and thickness of homogeneous plates using guided waves
,” IEEE Trans. Ultrason, Ferroelect, Freq. Contr.
66
(12
), 1898
–1905
(2019
).24.
L.
Bai
,
K.
Xu
,
D.
Li
,
D.
Ta
,
L. H.
Le
, and
W.
Wang
, “
Fatigue evaluation of long cortical bone using ultrasonic guided waves
,” J. Biomech.
77
, 83
–90
(2018
).25.
A.
Guha
,
M.
Aynardi
,
P.
Shokouhi
, and
C. J.
Lissenden
, “
Identification of long-range ultrasonic guided wave characteristics in cortical bone by modelling
,” Ultrasonics
114
, 106407
(2021
).26.
R.
Barkmann
,
E.
Kantorovich
,
C.
Singal
,
D.
Hans
,
H. K.
Genant
,
M.
Heller
, and
C.-C.
Glüer
, “
A new method for quantitative ultrasound measurements at multiple skeletal sites: First results of precision and fracture discrimination
,” J. Clin. Densitom.
3
(1
), 1
–7
(2000
).27.
M.
Muller
,
P.
Moilanen
,
E.
Bossy
,
P.
Nicholson
,
V.
Kilappa
,
J.
Timonen
,
M.
Talmant
,
S.
Cheng
, and
P.
Laugier
, “
Comparison of three ultrasonic axial transmission methods for bone assessment
,” Ultrasound Med. Biol.
31
(5
), 633
–642
(2005
).28.
C. F.
Njeh
,
I.
Saeed
,
M.
Grigorian
,
D. L.
Kendler
,
B.
Fan
,
J.
Shepherd
,
M.
McClung
,
W. M.
Drake
, and
H. K.
Genant
, “
Assessment of bone status using speed of sound at multiple anatomical sites
,” Ultrasound Med. Biol.
27
(10
), 1337
–1345
(2001
).29.
M.
Talmant
,
S.
Kolta
,
C.
Roux
,
D.
Haguenauer
,
I.
Vedel
,
B.
Cassou
,
E.
Bossy
, and
P.
Laugier
, “
In vivo performance evaluation of bi-directional ultrasonic axial transmission for cortical bone assessment
,” Ultrasound Med. Biol.
35
(6
), 912
–919
(2009
).30.
M.
Sasso
,
G.
Haiat
,
M.
Talmant
,
P.
Laugier
, and
S.
Naili
, “
Singular value decomposition-based wave extraction in axial transmission: Application to cortical bone ultrasonic characterization [correspondence]
,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr.
55
(6
), 1328
–1332
(2008
).31.
G.
Haïat
,
S.
Naili
,
Q.
Grimal
,
M.
Talmant
,
C.
Desceliers
, and
C.
Soize
, “
Influence of a gradient of material properties on ultrasonic wave propagation in cortical bone: Application to axial transmission
,” J. Acoust. Soc. Am.
125
(6
), 4043
–4052
(2009
).32.
D.
Hans
,
L.
Genton
,
S.
Allaoua
,
C.
Pichard
, and
D. O.
Slosman
, “
Hip fracture discrimination study
,” J. Clin. Densitom.
6
(2
), 163
–172
(2003
).33.
K. M.
Knapp
,
K. M.
Knapp
,
G. M.
Blake
,
T. D.
Spector
, and
I.
Fogelman
, “
Multisite quantitative ultrasound: Precision, age- and menopause-related changes, fracture discrimination, and T-score equivalence with dual-energy X-ray absorptiometry
,” Osteoporosis Int.
12
(6
), 456
–464
(2001
).34.
J.-G.
Minonzio
,
J.
Foiret
,
P.
Moilanen
,
J.
Pirhonen
,
Z.
Zhao
,
M.
Talmant
,
J.
Timonen
, and
P.
Laugier
, “
A free plate model can predict guided modes propagating in tubular bone-mimicking phantoms
,” J. Acoust. Soc. Am.
137
(1
), EL98
–EL104
(2015
).35.
P.
Moilanen
,
P. H.
Nicholson
,
V.
Kilappa
,
S.
Cheng
, and
J.
Timonen
, “
Assessment of the cortical bone thickness using ultrasonic guided waves: Modelling and in vitro study
,” Ultrasound Med. Biol.
33
(2
), 254
–262
(2007
).36.
R. M.
Zebaze
,
A.
Ghasem-Zadeh
,
A.
Bohte
,
S.
Iuliano-Burns
,
M.
Mirams
,
R. I.
Price
,
E. J.
Mackie
, and
E.
Seeman
, “
Intracortical remodelling and porosity in the distal radius and post-mortem femurs of women: A cross-sectional study
,” Lancet
375
(9727
), 1729
–1736
(2010
).37.
P.
Moilanen
,
P.
Nicholson
,
V.
Kilappa
,
S.
Cheng
, and
J.
Timonen
, “
Measuring guided waves in long bones: Modeling and experiments in free and immersed plates
,” Ultrasound Med. Biol.
32
(5
), 709
–719
(2006
).38.
P.
Moilanen
, “
Ultrasonic guided waves in bone
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Contr.
55
(6
), 1277
–1286
(2008
).39.
D.
Ta
,
W.
Wang
,
Y.
Wang
,
L. H.
Le
, and
Y.
Zhou
, “
Measurement of the dispersion and attenuation of cylindrical ultrasonic guided waves in long bone
,” Ultrasound Med. Biol.
35
(4
), 641
–652
(2009
).40.
D.
Pereira
,
G.
Haiat
,
J.
Fernandes
, and
P.
Belanger
, “
Simulation of acoustic guided wave propagation in cortical bone using a semi-analytical finite element method
,” J. Acoust. Soc. Am.
141
(4
), 2538
–2547
(2017
).41.
J.
Foiret
,
J.-G.
Minonzio
,
C.
Chappard
,
M.
Talmant
, and
P.
Laugier
, “
Combined estimation of thickness and velocities using ultrasound guided waves: A pioneering study on in vitro cortical bone samples
,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr.
61
(9
), 1478
–1488
(2014
).42.
J.
Chen
,
J.
Foiret
,
J.-G.
Minonzio
,
M.
Talmant
,
Z.
Su
,
L.
Cheng
, and
P.
Laugier
, “
Measurement of guided mode wavenumbers in soft tissue–bone mimicking phantoms using ultrasonic axial transmission
,” Phys. Med. Biol.
57
(10
), 3025
–3037
(2012
).43.
T. N.
Tran
,
L.
Stieglitz
,
Y. J.
Gu
, and
L. H.
Le
, “
Analysis of ultrasonic waves propagating in a bone plate over a water half-space with and without overlying soft tissue
,” Ultrasound Med. Biol.
39
(12
), 2422
–2430
(2013
).44.
P.
Moilanen
,
M.
Talmant
,
V.
Kilappa
,
P.
Nicholson
,
S.
Cheng
,
J.
Timonen
, and
P.
Laugier
, “
Modeling the impact of soft tissue on axial transmission measurements of ultrasonic guided waves in human radius
,” J. Acoust. Soc. Am.
124
(4
), 2364
–2373
(2008
).45.
Y.
Li
,
K.
Xu
,
Y.
Li
,
F.
Xu
,
D.
Ta
, and
W.
Wang
, “
Deep learning analysis of ultrasonic guided waves for cortical bone characterization
,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr.
68
, 935
–951
(2021
).46.
D.
Pereira
,
J.
Fernandes
, and
P.
Belanger
, “
Ex vivo assessment of cortical bone properties using low-frequency ultrasonic guided waves
,” IEEE Trans. Ultrason., Ferroelectr., Freq. Contr.
67
(5
), 910
–922
(2020
).47.
F.
Seyfaddini
,
H.
Nguyen-Xuan
, and
V.-H.
Nguyen
, “
A semi-analytical isogeometric analysis for wave dispersion in functionally graded plates immersed in fluids
,” Acta Mech.
232
(1
), 15
–32
(2021
).48.
F.
Seyfaddini
,
H.
Nguyen-Xuan
, and
V.-H.
Nguyen
, “
Wave dispersion analysis of three-dimensional vibroacoustic waveguides with semi-analytical isogeometric method
,” Comput. Methods Appl. Mech. Eng.
385
, 114043
(2021
).49.
M.
Muller
,
D.
Mitton
,
P.
Moilanen
,
V.
Bousson
,
M.
Talmant
, and
P.
Laugier
, “
Prediction of bone mechanical properties using QUS and pQCT: Study of the human distal radius
,” Med. Eng. Phys.
30
(6
), 761
–767
(2008
).50.
J.-Y.
Rho
,
L.
Kuhn-Spearing
, and
P.
Zioupos
, “
Mechanical properties and the hierarchical structure of bone
,” Med. Eng. Phys.
20
(2
), 92
–102
(1998
).51.
V.
Sansalone
,
S.
Naili
,
V.
Bousson
,
C.
Bergot
,
F.
Peyrin
,
J.
Zarka
,
J. D.
Laredo
, and
G.
Haïat
, “
Determination of the heterogeneous anisotropic elastic properties of human femoral bone: From nanoscopic to organ scale
,” J. Biomech.
43
(10
), 1857
–1863
(2010
).52.
A.
Sarvazyan
, “
Elastic properties of soft tissues
,” in Handbook of Elastic Properties of Solids, Liquids, and Gases
(
Academic Press
,
New York
, 2001
), Vol.
III
.53.
M.-B.
Vu
and
T.
Nguyen-Sy
, “
On the effective anisotropic elastic properties of porous hydroxyapatite, porous collagen, and cortical bone: A homogenization scheme with percolation threshold concept
,” Math. Mech. Solids
24
(4
), 1091
–1102
(2019
).54.
R. O.
Potts
,
D. A.
Chrisman
, and
M.
Buras
, “
The dynamic mechanical properties of human skin in vivo
,” J. Biomech.
16
(6
), 365
–372
(1983
).55.
J.-G.
Minonzio
,
N.
Bochud
,
Q.
Vallet
,
Y.
Bala
,
D.
Ramiandrisoa
,
H.
Follet
,
D.
Mitton
, and
P.
Laugier
, “
Bone cortical thickness and porosity assessment using ultrasound guided waves: An ex vivo validation study
,” Bone
116
, 111
–119
(2018
).56.
J.
Wu
and
F.
Cubberley
, “
Measurement of velocity and attenuation of shear waves in bovine compact bone using ultrasonic spectroscopy
,” Ultrasound Med. Biol.
23
(1
), 129
–134
(1997
).57.
M.
Sasso
,
G.
Haïat
,
Y.
Yamato
,
S.
Naili
, and
M.
Matsukawa
, “
Dependence of ultrasonic attenuation on bone mass and microstructure in bovine cortical bone
,” J. Biomech.
41
(2
), 347
–355
(2008
).58.
S.
Naili
,
M.-B.
Vu
,
Q.
Grimal
,
M.
Talmant
,
C.
Desceliers
,
C.
Soize
, and
G.
Haïat
, “
Influence of viscoelastic and viscous absorption on ultrasonic wave propagation in cortical bone: Application to axial transmission
,” J. Acoust. Soc. Am.
127
(4
), 2622
–2634
(2010
).59.
D.
Royer
and
E.
Dieulesaint
, Elastic Waves in Solids I: Free and Guided Propagation
(
Springer Science & Business Media
,
New York
, 1999
).60.
Z. A. B.
Ahmad
,
J. M.
Vivar-Perez
, and
U.
Gabbert
, “
Semi-analytical finite element method for modeling of Lamb wave propagation
,” CEAS Aeronaut. J.
4
(1
), 21
–33
(2013
).61.
W.
Karunasena
,
A. H.
Shah
, and
S. K.
Datta
, “
Wave propagation in a multilayered laminated cross-ply composite plate
,” J. Appl. Mech.
58
(4
), 1028
–1032
(1991
).62.
M. V.
Predoi
,
M.
Castaings
,
B.
Hosten
, and
C.
Bacon
, “
Wave propagation along transversely periodic structures
,” J. Acoust. Soc. Am.
121
(4
), 1935
–1944
(2007
).63.
L.
Piegl
and
W.
Tiller
, The NURBS Book
(
Springer Science & Business Media
,
New York
, 1996
).64.
D.
Starkey
, “
NURBS: Non-uniform rational B-splines
” (2009
), https://www.cs.montana.edu/courses/spring2009/525/dslectures/NURBS.pdf (Last viewed October 5, 2023).65.
T. D.
Mast
, “
Empirical relationships between acoustic parameters in human soft tissues
,” Acoust. Res. Lett. Online
1
(2
), 37
–42
(2000
).66.
D.
Alleyne
and
P.
Cawley
, “
A two-dimensional Fourier transform method for the measurement of propagating multimode signals
,” J. Acoust. Soc. Am.
89
(3
), 1159
–1168
(1991
).67.
M. O.
Culjat
,
D.
Goldenberg
,
P.
Tewari
, and
R. S.
Singh
, “
A review of tissue substitutes for ultrasound imaging
,” Ultrasound Med. Biol.
36
(6
), 861
–873
(2010
).68.
S.
Nobakhti
and
S. J.
Shefelbine
, “
On the relation of bone mineral density and the elastic modulus in healthy and pathologic bone
,” Curr. Osteoporos. Rep.
16
(4
), 404
–410
(2018
).69.
T. S.
Keller
,
Z.
Mao
, and
D. M.
Spengler
, “
Young's modulus, bending strength, and tissue physical properties of human compact bone
,” J. Orthop. Res.
8
(4
), 592
–603
(1990
).70.
M.
Granke
,
Q.
Grimal
,
A.
Saïed
,
P.
Nauleau
,
F.
Peyrin
, and
P.
Laugier
, “
Change in porosity is the major determinant of the variation of cortical bone elasticity at the millimeter scale in aged women
,” Bone
49
(5
), 1020
–1026
(2011
).71.
W. J.
Parnell
,
M. B.
Vu
,
Q.
Grimal
, and
S.
Naili
, “
Analytical methods to determine the effective mesoscopic and macroscopic elastic properties of cortical bone
,” Biomech. Model. Mechanobiol.
11
(6
), 883
–901
(2012
).© 2024 Acoustical Society of America.
2024
Acoustical Society of America
You do not currently have access to this content.
