IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, . 61, . 2, FEBRUARY 2014 302
0885–3010
©
2014 IEEE
Influence of Porosity, Pore Size, and Cortical
Thickness on the Propagation of Ultrasonic
Waves Guided Through the Femoral Neck
Cortex: A Simulation Study
Kerstin Rohde, Daniel Rohrbach, Claus-C. Glüer, Pascal Laugier, Quentin Grimal,
Kay Raum, and Reinhard Barkmann
Abstract—The femoral neck is a common fracture site in el-
derly people. The cortical shell is thought to be the major con-
tributor to the mechanical competence of the femoral neck, but
its microstructural parameters are not sufficiently accessible
under in vivo conditions with current X-ray-based methods. To
systematically investigate the influences of pore size, porosity,
and thickness of the femoral neck cortex on the propagation of
ultrasound, we developed 96 different bone models (combining
6 different pore sizes with 4 different porosities and 4 different
thicknesses) and simulated the ultrasound propagation using a
finite-difference time-domain algorithm. The simulated single-
element emitter and receiver array consisting of 16 elements (8
inferior and 8 superior) were placed at anterior and posterior
sides of the bone, respectively (transverse transmission). From
each simulation, we analyzed the waveform collected by each
of the inferior receiver elements for the one with the shortest
time of flight. The first arriving signal of this waveform, which
is associated with the wave traveling through the cortical shell,
was then evaluated for its three different waveform character-
istics (TOF: time point of the first point of inflection of the
received signal, Δt: difference between the time point at which
the signal first crosses the zero baseline and TOF, and A: am-
plitude of the first extreme of the first arriving signal). From
the analyses of these waveform characteristics, we were able to
develop multivariate models to predict pore size, porosity, and
cortical thickness, corresponding to the 96 different bone mod-
els, with remaining errors in the range of 50 μm for pore size,
1.5% for porosity, and 0.17 mm for cortical thickness.
I. I
I
elderly people, a fracture at the proximal femur has
a negative impact on the life quality and can even lead
to death, with a mortality rate of up to 36% depending on
age [1], [2]. The most frequent fractures, of equal propor-
tion, are the pertrochanteric and intracapsular fractures.
A prediction of the risk for suffering the latter type is still
a challenging task because the factors which contribute to
intracapsular bone strength are still not well understood.
The relative contributions of cortical versus trabecular
bone to bone strength have been revisited recently. It was
shown by Holzer et al. that trabecular bone loss at the
femoral neck could only explain 10% of the loss in bone
strength [3], suggesting a major contribution of the corti-
cal shell to the neck mechanical stability. The mechani-
cal competence of cortical bone is determined by micro-
structural and material properties. Granke et al. [4] have
shown that Haversian porosity of the femoral mid-shaft is
the most important determinant of cortical bone elasticity
at the millimeter scale. Bell et al. examined osteoporotic
changes in cortical bone at the femoral neck ex vivo and
found a decrease in cortical thickness (Ct.Th) and an in-
crease in cortical porosity (Ct.Po). The latter could be ex-
plained by a growing number of larger pores [5], [6]. These
studies indicate that the cortical bone microstructure at
the femoral neck might carry fracture relevant informa-
tion.
Despite being the recommended method and current
gold standard for fracture risk assessment, dual X-ray
absorptiometry (DXA) has some limitations when used
for the assessment of the mechanical competence of the
femoral neck cortex. Because of its projection technique,
whereby an areal density in grams per square centimeter
is measured, DXA is not appropriate to provide direct
and reliable quantitative measurements on cortical bone.
Quantitative computed tomography (QCT) of the hip is
able to yield estimates of Ct.Th and bone mineral den-
sity of cortical bone when high-resolution protocols are
applied. However, because of limited spatial resolution,
measurements are not able to separate between density
variations caused by changes in mineralization and chang-
es caused by increased Ct.Po. High-resolution peripheral
quantitative computed tomography (HR-pQCT) can mea-
sure both Ct.Th and Ct.Po, albeit with large accuracy
errors [7], but is only available for measurements at distal
sites.
Noninvasive diagnostic tools with the ability to assess
cortical bone properties would be beneficial. Quantita-
Manuscript received July 19, 2013; accepted October 16, 2013. This in-
vestigation is partly funded by the EU within the program Interreg IVA
(project Cross-border improvement of the situation of osteoporosis pa-
tients) and was performed within the frameworks of the Baltic network
Quantitative Imaging of Functional Competence of the Musculoskeletal
System (QUIMUS) and the French/German Laboratoire Européen As-
socié–Ultrasound-based Assessment of Bone (LEA-ULAB) network.
K. Rohde, C.-C. Glüer, and R. Barkmann are with the Sektion Bio-
medizinische Bildgebung, Klinik für Radiologie, Universitätsklinikum
Schleswig-Holstein, Campus Kiel, Kiel, Germany (e-mail: k.rohde@rad.
uni-kiel.de).
D. Rohrbach and K. Raum are with the Julius Wolff Institute and
Berlin-Brandenburg School for Regenerative Therapies, Charité-Univer-
sitätsmedizin Berlin, Berlin, Germany.
P. Laugier and Q. Grimal are with CNRS, UMR 7623, Laboratoire
d’Imagerie Paramétrique (LIP), Paris, France, and the Université Pierre
et Marie Curie, University of Paris 6, UMR 7623, LIP, Paris, France.
DOI http://dx.doi.org/10.1109/TUFFC.2014.2910