Frequency Dependence of Ultrasonic Attenuation in Bovine Cortical Bone: An In Vitro Study

Ultrasound in Med. & Biol., Vol. 33, No. 12, pp. 1933–1942, 2007 Copyright © 2007 World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/07/$–see front matter

doi:10.1016/j.ultrasmedbio.2007.05.022

● Original Contribution FREQUENCY DEPENDENCE OF ULTRASONIC ATTENUATION IN BOVINE CORTICAL BONE: AN IN VITRO STUDY MAGALI SASSO,* GUILLAUME HAÏAT,* YU YAMATO,† SALAH NAILI,* and MAMI MATSUKAWA‡ *Université Paris 12, Laboratoire de Mécanique Physique, Créteil, France; †Orthopaedic Surgery, Hamamatsu University School of Medicine, Hamamatsu, Shizuoka, Japan; and ‡Laboratory of Ultrasonic Electronics, Faculty of Engineering, Doshisha University, Kyotanabe, Kyoto-fu, Japan (Received 9 January 2007; revised 11 May 2007; in final form 24 May 2007)

Abstract—Recent progress in quantitative ultrasonic (QUS) techniques enables the in vivo evaluation of cortical bone, which is determinant in bone fragility. However, the interaction between ultrasound and cortical bone remains poorly understood. Most ultrasonic studies have been confined to longitudinal wave speed analysis and the frequency dependence of ultrasonic wave attenuation in this complex multiscale structure has not been extensively investigated. Our objective was to evaluate in vitro the frequency dependence of attenuation in bovine femoral cortical bone samples obtained from three specimens at different anatomical locations along the diaphysis axis and around the circumference. The frequency-dependent attenuation coefficient was evaluated after correction of transmission effects using a transmission device operating at 10 MHz. Attenuation exhibits a non linear variation versus frequency. However, the quasi-linearity of attenuation on a 1 MHz restricted bandwidth around 4 MHz enables broadband ultrasonic attenuation (BUA) evaluation. Our study demonstrates the feasibility of BUA measurements in the three directions (axial, radial and tangential) with reasonable precision (standardized coefficient of variation: 10% to 12%). Significant differences in BUA are obtained according to the anatomical location. BUA values are higher in the distal and proximal parts of the bone than in the midshaft and in the posterior and lateral parts than in the medial and anterior parts. Findings are consistent with results previously obtained and may be explained primarily by scattering phenomena but also by bone viscoelasticity. (E-mail: [email protected]) © 2007 World Federation for Ultrasound in Medicine & Biology. Key Words: Quantitative ultrasound (QUS) techniques, Cortical bone, Frequency dependent attenuation, Broadband ultrasonic attenuation (BUA).

mass: bone mineral density (BMD). Although the loss of bone mass is related to an increase in fracture risk (Kanis 2002), other characteristics such as microarchitecture or material properties playing an important role in bone strength cannot be assessed with DXA. Ultrasound has the ability to go beyond this limitation since the elastic wave propagation is likely to be sensitive to bone structural and material properties. Currently, the two main parameters measured by QUS techniques are the wave velocity (speed of sound, SOS) and the slope of the frequency-dependent attenuation curve (broadband ultrasonic attenuation, BUA) (Langton et al. 1984; Ragozzino 1981). The development of QUS is still limited (Cadossi et al. 2000) since information potentially available in transmitted ultrasound is not fully analyzed and parameters such as bone material properties or microstructural parameters cannot currently

INTRODUCTION Bone quantitative ultrasound (QUS) techniques play a gradually increasing role in the assessment of osteoporosis and in fracture risk prediction since the 1990s (Laugier 2006). Osteoporosis is recognized (World Health Organization 1994) as a systemic disease of the skeleton characterized by a loss of bone mass and by microarchitectural deterioration of bone tissue, with a consequent increase in bone fragility and susceptibility to fracture. The gold standard for osteoporosis diagnosis (Cullum et al. 1989) is dual-energy X-ray absorptiometry (DXA) which measures information related to bone

Address correspondence to: Guillaume Haïat, Laboratoire de Biomécanique et Biomatériaux Ostéo-Articulaires, Université Paris XII-UMR CNRS 7052, 61 avenue du Général de Gaulle, 94010 Créteil, France. E-mail: [email protected] 1933

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be recovered. The interaction between ultrasound and bone remains poorly understood due to the complex nature of cortical bone, which has a viscoelastic porous microstructure spanning many length scales (Cowin 2001). Initially, most applications of QUS techniques in bone have been confined to cancellous bone characterization (Langton et al. 1984; Laugier et al. 1994; Nicholson and Njeh 1999). However, more interest should be placed in cortical bone exploration (Rico 1997) since it accounts for 80% of the skeleton, supports most of the load of the body and is mainly involved in many osteoporotic fractures. Furthermore, cortical bone is affected by age-related bone resorption and osteoporosis (Cowin 2001). It undergoes an increase in porosity as well as a cortical shell thinning, which has recently been shown to be determinant in fracture risk (Mayhew et al. 2005). In addition, mineralization of cortical bone increases with age or disease (Grynpas 1993), leading to an increased stiffness (Currey 1969) and fragility. The development of new QUS devices enables the in vivo cortical bone evaluation with specific devices such as the axial transmission technique. This technique allows the assessment of the cortical layer of the mid tibia (Foldes et al. 1995), distal radius (Bossy et al. 2004) and of several sites including ulna, finger phalanxes, metacarpal or metatarsus (Barkmann et al. 2000a). The transverse transmission technique may also be used for both cortical and trabecular bone evaluation on sites such as wrist bones or phalanx (Barkmann et al. 2000b; Mano et al. 2006). However, QUS for cortical bone evaluation is mainly confined to SOS analysis and numerous in vitro studies (see for example [Ashman et al. 1984; Bensamoun et al. 2004a, 2004b; Lee et al. 1997]) focused on the understanding of ultrasonic wave propagation in cortical bone and on its relation to bone physical parameters through wave velocity analysis. In comparison with trabecular bone studies, only a few studies have reported attenuation measurements in cortical bone. Han et al. (1996) and Serpe and Rho (1996) have reported BUA values around 0.5 MHz in bovine cortical bone. Langton et al. (1990) have reported in vivo BUA values in the same frequency range on horse. Lakes et al. (1986) have investigated attenuation in wet cortical bone over a large frequency range (1 to 16 MHz). Lees and Klopholz (1992) have also evaluated ultrasonic attenuation in wet cortical bone but on a larger frequency range (5 to 100 MHz). Saulgozis et al. (1996) and Vilks et al. (1977) have shown on human tibiae in vivo that attenuation can be related to fracture healing. However, no systematic study has been found in the literature about the frequency dependence of attenuation in cortical bone around 4 MHz. At these frequencies, the wavelength in cortical bone is around 1 mm, which is

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Fig. 1. Schematic representation of the spatial repartition of the bone samples. (a) Locations where the intact femur was cut to obtain the five cortical rings. (b) Quadrant positions of the eight parallelepipedic samples around each cortical ring. (c) Illustration of the orientation of the three directions.

higher but of the same order of magnitude than the typical size of the main structures (osteons, lamellae). A study of attenuation measurements on different bone samples is of interest since it can lead to a better understanding of the interaction between ultrasound and the complex and multiscale bone structure. The present study focuses on the evaluation of the frequency dependent attenuation in bovine cortical bone. The first objective of this article is to appraise the linearity of the frequency-dependent attenuation in bovine cortical bone to evaluate the feasibility of BUA measurements around 4 MHz. The second objective is to investigate the dependence of BUA on the anatomical position and on the direction of propagation relatively to bone axis. Parallelepipedic cortical bone samples were therefore cut from three bovine femurs along the diaphysis axis and circumference and were then analyzed using an ultrasonic transmission device. MATERIALS AND METHODS Sample Preparation Three intact left femurs from 36-mo-old bovines were obtained at the public abattoir. From each femur, five ring shaped cortical bones were cut (1) in the distal part at 50 mm and 30 mm from the center of the bone, (2) at the center of the bone, and (3) in the proximal part at 30 mm and 50 mm from the center of the bone. From each ring, eight parallelepipedic samples were cut in the anterior, posterior, medial, lateral and in the four oblique parts as shown in Fig. 1. Bone was cut using a precision table top cut-off and a grinding machine Accutom-50 (Stuers, Ballerup, Denmark). The samples were carefully

Ultrasonic attenuation in bovine cortical bone ● M. SASSO et al.

Fig. 2. Schematic representation of the experimental set-up.

polished into rectangular parallelepipeds with sides comprised between 4 and 11 mm. Thickness measurements were performed using a digital micrometer (Mitsutoyo, Tokyo, Japan). The samples were kept in a freezer at ⫺20°C for conservation and unfrozen before ultrasonic measurement. According to Turner and Burr (1993), freezing at this temperature does not significantly impact bone mechanical properties. Ultrasonic Experimental Set-Up Measurements were performed in a normal saline solution (NSS) stabilized at 25.0 ⫾ 0.1°C using an external control temperature system. Temperatures closer to body temperature would be more interesting for in vivo applications. However, a deterioration of our self-made transducer has been observed due to the loss of adherence between the polyvinylidene fluoride (PVDF) films and the backing material with increasing temperature. All bone samples and NSS were carefully degassed with a vacuum pump to remove air bubbles. The ultrasonic experimental set-up is shown in Fig. 2. A pair of self-made broadband PVDF transducers described in detail by Nakamura and Otani (1993) was used. Both sensors are planar with a diameter of 8 mm and supported by cylindrical brass backing. PVDF films are located on the inner ends of the rods as depicted in Fig. 2 with a thin gold layer of a few microns (corresponding to the electrode), which also protect the transducer against corrosion. The emitter and receiver were coaxially aligned and operated in transmission. The emitter was driven by a function generator 33250A manufac-

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tured by Agilent Technologies (Palo Alto, CA, USA) using a single sinusoidal cycle of 10 MHz with a voltage of 10 V peak to peak. Our self-made transducers are not used in the resonant frequency region, which is expected to be higher than 30 MHz, due to the thickness of the PVDF film (40 ␮m). Therefore, the frequency response of the transducer is almost flat as reported by Nakamura and Otani (1993) in the frequency bandwidth of interest. The transmitted waveform is different from the excited sinusoidal electric signal, due to the diffraction effect at the edge of transducer surface. Received signals were amplified using a wide-band amplifier BX-31A from NF Electronic Instruments (Yokohama, Japan) and digitized at a sampling rate of 500 MS.s⫺1 by a digital oscilloscope TDS520C made by Tektronix Ltd. (Bracknell, UK) with eight-bit vertical resolution and 2048 times averaging. Each received signal was then transferred to a personal computer for off-line analysis. To avoid interferences between the transmitted pulse and echoes due to multiple reflections between the bone sample and the receiver’s surface, samples were placed at a minimal distance of 1.5 mm from the receiver. For each sample, ultrasonic measurements were performed in the three directions: axial, radial and tangential by rotating the sample accordingly. Frequency-Dependent Attenuation Ultrasonic measurements were performed using a substitution method. A broadband ultrasonic pulse was received first without and then with the sample positioned between the transducers. High frequency noise was filtered using a low pass filter with a 20 MHz cut-off frequency. The frequency-dependent attenuation coefficient ␣(f) can be derived from the ratio of the magnitude spectrum of the measured pulse |Ab共f兲| with the magnitude spectrum of the reference wave |Ar共f兲| (Droin et al. 1998). Magnitude spectra were obtained using a fast Fourier transform algorithm (FFT). The quantity ␣(f) expressed in decibel, is given by:

␣(f) ⫽ 20log10(e)

冉

ⱍ ⱍ

冊

ⱍ ⱍ

1 Ab(f) ⫹ ln(T(f)) , ln L Ar(f)

(1)

where L is the sample length in cm in the considered measurement direction. The term T(f) is introduced to correct for losses due to transmission effects at bone/ NSS interfaces and corresponds to the transmission coefficient of the pulse through the sample: T(f) ⫽

ⱍ

4Zr(f)Zb(f) , Zr(f) ⫹ Zb(f) 2

ⱍ

(2)

where Zr(f) ⫽ ␳rVr(f) and Zb(f) ⫽ ␳bVb(f) are respectively the acoustic impedance of the reference medium (NSS)

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and of the bone sample. The quantities ␳r and Vr(f) designate respectively the mass density and the velocity in the reference medium, ␳b and Vb(f) are respectively the mass density and the phase velocity in the bone sample. Here, the values of the phase velocity Vb(f) are determined for each sample and each direction. The difference ␾(f) between the phase of the reference signal and the phase of the signal transmitted through the bone sample is first computed. The phase difference is then unwrapped and the phase velocity is given by: Vb(f) ⫽

1 1 ␾(f) ⫺ Vr(f) 2␲ fL

.

(3)

The phase velocity Vb(4 MHz) is equal to 4116 ⫾ 176 m.s⫺1 in the axial direction, 3305 ⫾ 199 m.s⫺1 in the radial direction and 3548 ⫾ 172 m.s⫺1 in the tangential direction. The mass density ␳b is measured for each sample using Archimedes’ principle (2.06 ⫾ 0.05 g.cm⫺3). The velocity in NSS is assumed to be independent of frequency. The velocity Vr is derived from the time of flight difference, ⌬t, between the wave received in distilled water and in NSS using: Vr ⫽

Vwd , d ⫺ ⌬tVw

(4)

where d is the inter-sensors distance and Vw is the temperature-dependent wave velocity in distilled water given by (Kaye and Laby 1973): Vw ⫽ 1402.9 ⫹ 4.835T ⫺ 0.047016T2 ⫺ 0.00012725T3, (5) where T is the temperature in Celsius. At 25°C, Vw ⫽ 1496.4 m.s⫺1 and Vr ⫽ 1508 m.s⫺1. The mass density of NSS ␳r ⫽ 1.0028 g.cm⫺3 is given by the manufacturer (Wakenyaku Co. Ltd., Kyoto, Japan). BUA is then defined as the slope of the frequency dependent attenuation curve whose relation is given by Eq. (1) (Langton et al. 1984) and is evaluated using a least-square linear regression. For all bone samples, the measured attenuation coefficient showed a quasi-linear variation with frequency in a 1 MHz-wide frequency bandwidth comprised between 3.5 and 4.5 MHz. BUA could therefore be evaluated in this frequency range. Short-Term Reproducibility To evaluate the reproducibility, four measurements were performed with repositioning for each sample in each direction. Between each measurement, the bone sample was removed from the emitter/receiver’s axis and repositioned. The first two measurements were per-

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formed on the same side of a given sample and for a given direction. The last two measurements were performed on the other side in the same direction, after rotating the sample. The short-term reproducibility was evaluated on BUA measurements as described hereafter. The individual short term precision SDnd was evaluated as the standard deviation (SD) of the four measurements for the sample n in the direction d. Then, the technique precision error for a given direction was determined by the root-mean-square (rms) average of the individual precision errors using the procedure described by Glüer et al. (1995) and Njeh et al. (1999):

P ⫽ d

冑

N

兺

n⫽1

2

SDnd , N

(6)

where N is the total number of samples. Finally, to express the precision on a percentage basis and in a standardized way, the technique standardized precision error was computed for each direction using (Miller et al. 1993): d ⫽ PsCV

Pd R5⫺95 pc

,

(7)

where R5⫺95pc is the 5 to 95 percentile range. The global technique standardized precision error PsCV is computed by the root-mean-square average of the three values of d PsCV corresponding to the three directions. The quantities d PsCV and PsCV are standardized coefficients of variation and do not depend on the mean value of the considered measurement. Standardized coefficients of variation therefore enable the comparison between the three directions although each of them has a different mean value. Interspecimen Variability For each anatomical location a and each direction d, the inter-specimen short term variability Pad was evaluated as the standard deviation of the three BUA values corresponding to the three specimens. Then, the interspecimen variability Vd for a given direction d was obtained by the root-mean-square average of the individual inter-specimen variability for all the 40 anatomical locations:

Vd ⫽

冑

1 40

40

兺 (SD ) , d 2 a

(8)

a⫽1

Finally, to express the precision on a percentage basis, results were normalized by the 5 to 95 percentile range, R 5⫺95pc:

Ultrasonic attenuation in bovine cortical bone ● M. SASSO et al.

Fig. 3. Example of normalized radio-frequency signals. The reference waveform is obtained through NSS (solid line). (a) Typical waveform through bone sample with high attenuation (dashed line). (b) Typical waveform through bone sample with low attenuation (dotted line). The ratio between the maximum amplitude of the waveform obtained through bone and through NSS is of 4 ⫻ 10⫺3 in (a) and of 0.14 in (b). Both samples were assessed in the radial direction. The low attenuation sample was taken from the postero-distal part at 5 cm from the center on the diaphysis. The high attenuation sample was taken from the antero-proximal part at 5 cm from the center of the diaphysis.

d VsCV ⫽

Vd R5⫺95pc

,

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sitioning are equal to 12% in the axial and tangential directions and to 10% in the radial direction. The values of the standardized coefficient of variation PsCV is equal d to 11.4%. The values of inter-specimen variability VsCV for the three specimens are equal to 25% in the axial and tangential directions and to 20% in the radial direction. The values of the standardized coefficient of variation VsCV is equal to 23.4%. Typical normalized waveforms obtained through bone with high and low attenuation values are plotted respectively in Fig. 3a with a dashed line and in Fig. 3b with a dotted line. The reference waveform obtained through NSS is plotted on these figures with a solid line. The corresponding normalized amplitude spectra are plotted in Fig. 4 for the NSS (solid line), high attenuation sample (dashed line) and low attenuation sample (dotted line). Here, the ⫺10 dB bandwidth of the amplitude spectrum of the initial pulse through NSS (without bone sample) ranges between 2.4 and 10.9 MHz. The ⫺10 dB bandwidths of the wave through bone range between 1.2 and 6.7 MHz for the high attenuation sample and 1.7 and 8.8 MHz for the low attenuation sample. The variation of the attenuation coefficient ␣(f) corresponding to the waveforms depicted in Fig. 3a and Fig. 3b is shown respectively with a dashed and dotted line in Fig. 5a. In spite of the nonlinear behavior of the attenuation coefficient over the whole frequency bandwidth, its behavior is quasi linear over the 1 MHz restricted frequency bandwidth around 4 MHz. The variation of the attenuation coefficient in the 3.5 to 4.5 MHz bandwidth together with its least-square linear regression is shown in Fig. 5b.1 for the high attenuation sample (waveform in Fig. 3a) and in Fig. 5b.2 for the low attenuation sample (waveform in Fig. 3b). A linear regression analysis was performed in this restricted bandwidth for each measurement obtained for all samples and all directions. The values of the correlation coefficients (r) range from 0.996

(9)

The global inter-specimen variability VsCV was evaluated as the root-mean-square average of the three values of d VsCV corresponding to the three directions. Statistical Analysis Analysis of variance (ANOVA) and TuckeyKramer multiple comparison tests were performed using MatLab software (The MathWorks Inc, Natick, MA, USA) to test the significance of BUA variations as a function of the measurement direction and anatomical location. RESULTS The values of the standardized coefficient of variad tion PsCV obtained for the four measurements with repo-

Fig. 4. Normalized amplitude spectra for the signal transmitted in water (solid line), for the signals shown in Fig 3a (high attenuation sample: dashed line) and for the signals shown in Fig. 3b (low attenuation sample: dotted line).

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Fig. 6. Mean BUA values and standard deviation (solid line on the bar diagram) as a function of the position along the bone axis. Pro5 and pro3 correspond to the cortical rings in the proximal part at 5 and 3 cm from the central part of the shaft. Mid corresponds to the cortical ring at the center part of the shaft. Dis5 and dis3 corresponds to the cortical rings in the distal part at 5 and 3 cm, respectively from the central part of the shaft.

Fig. 5. Variation of the frequency dependent attenuation coefficient as a function of frequency (a) over the entire frequency bandwidth for a sample with high attenuation (dashed line) and a sample with low attenuation (dotted line), (b) over the restricted 1 MHz wide frequency bandwidth for the sample with high attenuation in (b.1) and with low attenuation in (b.2). The corresponding linear regression fit (solid line) and correlation coefficient (r) are shown in (b). High attenuation and low attenuation samples correspond to the radio frequency signals and amplitude spectra shown in Fig. 3 and Fig. 4, respectively.

to 1 with a mean value equal to 0.999 ⫾ 0.001. The corresponding relative rms error (RMSE) ranges from 0.07 to 3.20% with a mean value equal to 0.80 ⫾ 0.46%. Average, standard deviation, minimal and maximal values of BUA obtained for the three directions of propagation are summarized in Table 1. BUA values obtained

Table 1. Average, standard deviation, minimal and maximal values of BUA values for the three measurement directions: axial, radial and tangential. BUA is evaluated between 3.5 and 4.5 MHz. BUA (dB · cm⫺1 · MHz⫺1)

axial radial tangential

in the axial direction are significantly smaller than BUA values obtained in the radial and tangential directions. ANOVA revealed a significant directional effect (p ⬍ 0.002). Tuckey-Kramer multiple comparisons revealed significant differences between axial and radial direction and between axial and tangential directions. However, no significant difference was found between radial and tangential directions. To assess the influence of the anatomical position on BUA values, results were first averaged according to the quadrant position and then, to the position along the bone axis. The behavior of BUA values as a function of the position along the bone axis (proximal, medial or distal position) is summarized in Fig. 6 for the three directions of propagation. The highest BUA values are obtained in the distal part of the bone whereas the smallest BUA values can be found in the centero-proximal part of the bone. The behavior of BUA values (averaged according to the position along the bone axis) as a function of the quadrant position are summarized in Fig. 7 for the three measurement directions. BUA values are the highest in the postero-lateral position and the smallest in the antero-medial part. ANOVA test revealed a significant anatomical position effect (p ⬍ 0.005) for the quadrant and cortical ring position for each of the three directions.

mean

SD

min

max

DISCUSSION

3.2 4.2 4.4

2.0 2.4 2.9

0.8 1.7 1.5

10.6 12.8 16.6

The present work represents the first extensive study of the frequency dependent attenuation in bovine cortical bone around 4 MHz.

Ultrasonic attenuation in bovine cortical bone ● M. SASSO et al.

Fig. 7. Mean BUA values and standard deviation (solid line on the bar diagram) as a function of the quadrant position. L is lateral quadrant, AL is antero-lateral quadrant, A is anterior quadrant, AM is antero-medial quadrant, M is medial quadrant, PM is postero-medial quadrant, P is posterior quadrant, and PL is postero-lateral quadrant.

Bandwidth Determination The attenuation coefficient exhibits a highly non linear behavior over a large bandwidth (cf. Fig. 5a). This result is consistent with a previous study of Lakes et al. (1986) performed on a comparable but slightly larger frequency range using a continuous wave technique. The peaks at approximately 1, 9 and 12 MHz for the high attenuation sample (in Fig. 5a) and at 12 MHz for the low attenuation sample (in Fig. 5a) are due to the fact that the amplitude spectra of the signal transmitted in bone (cf. Fig. 4) have local minima. These peaks do not carry any physical information on bone and the attenuation coefficient should not be considered outside the intersection of the ⫺10 dB bandwidths of both reference spectrum and spectrum through bone. Any information outside the intersection of both bandwidths might be mixed up with noise. The quasi-linear variation of the attenuation coefficient in the fixed 1 MHz-wide bandwidth centered at 4 MHz enables BUA evaluation. Similarly as in trabecular

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bone studies (see for example [Strelitzki and Evans 1996]), BUA was evaluated in a fixed bandwidth for all samples. On the 1 MHz restricted bandwidth, the correlation coefficients of the attenuation versus frequency are comparable with values observed for trabecular bone at different frequencies. For instance, Droin et al. (1998) found correlation coefficients always greater that 0.97 on 15 trabecular samples and Wear (2001) found r ⫽ 0.999 for 16 trabecular samples. In several studies (Haïat et al. 2006; Padilla et al. 2004), a data acceptance criterion based on a linear variation of the attenuation coefficient was devised with a value of the threshold for the correlation coefficient given by r ⫽ 0.97, which is lower than the minimal value of the correlation coefficient found in this study. The choice of the center frequency of the bandwidth used for BUA determination is a compromise between a sufficiently small wavelength to be sensitive to bone heterogeneities, and the requirement of an acceptable signal-to-noise ratio for all samples and all directions. The -10 dB bandwidths range in average between 1.6 to 8.2 MHz for the axial direction, 1.5 to 7.8 MHz for the radial direction and 1.4 to 7.0 MHz for the tangential direction. The center frequencies of received pulses through bone samples are equal to 4.4, 4.2 and 4 MHz respectively for the axial, radial and tangential directions, which justify the choice of 4 MHz for the center frequency of the bandwidth used for BUA evaluation. The choice of the frequency range for BUA evaluation is a compromise between a satisfactory linear variation of the attenuation coefficient versus frequency for all samples (together with an acceptable goodness-of-fit of the linear regression analysis) and a sufficient amount of information contained in the bandwidth. To justify the choice of the frequency range and to compare the results reported here with those generated by a similar analysis over different frequency ranges, Table 2 shows both correlation coefficient (r) and relative rms error (RMSE) obtained from a linear regression analysis between the attenuation coefficient and the frequency, for different

Table 2. Correlation coefficient (r) obtained from the linear regression analysis of the attenuation coefficient versus frequency for different bandwidths centered around 4 MHz. Values of the relative root mean square error RMSE are also shown. r

relative RMSE (%)

bandwidth (MHz)

mean

SD

min

max

mean

SD

min

max

0.5 1 1.5 2 3 4

1 0.999 0.999 0.998 0.996 0.993

0.001 0.001 0.002 0.003 0.004 0.006

0.995 0.996 0.985 0.979 0.967 0.954

1 1 1 1 1 1

0.21 0.80 1.88 3.21 7.22 12.92

0.12 0.46 1.16 1.62 3.24 4.84

0.04 0.07 0.13 0.25 1.08 2.25

0.92 3.20 12.97 11.80 22.54 36.10

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Table 3. Results obtained from attenuation measurements in various cortical bone specimens by previous authors.

Reference

Precision (%)

Lakes et al. (1986)

10–15 (attenuation coefficient)

Type of bone

Number of samples

human femur

4

bovine femur

1

Frequency range (MHz) 2–7 8–16 1–7 8–16

Langton et al. (1990) Lees and Klopholtz (1992)

6.3 (CV) —

horse metacarpal bovine femur

Han et al. (1996) Serpe and Rho (1996)

4.8 (CV) 4 (CV)

bovine femur bovine femur

bandwidths centered around 4 MHz. For bandwidths up to 2 MHz wide, r always fall under the acceptance threshold r ⫽ 0.97 used in trabecular bone studies (Haïat et al. 2006; Padilla et al. 2004). In addition, we verified that slight modifications of the center frequency (from 3.5 up to 4.5 MHz) and of the amplitude of the bandwidth (from 0.5 up to 1.5 MHz) do not significantly impact the results obtained in this study (data not shown). Reproducibility and Variability The averaged BUA short-term precision expressed in terms of sCV was found to be around 12% in the axial and tangential directions and 10% in the radial direction. Other investigators found lower coefficient of variation at lower frequency, as summarized in Table 3. Around the frequencies used in the present study, Lakes et al. (1986) found an error for the attenuation coefficient comprised between 10% and 15%, which is comparable with our results. BUA values summarized in Table 1 are comparable with previously reported values in cortical bone, which are summarized in Table 3. In particular, Lakes et al. (1986) have measured attenuation versus frequency for one bovine femoral sample in the three directions. BUA values evaluated between 1 and 7 MHz are similar to the results found in the present study. Lees and Klopholtz (1992) also evaluated attenuation versus frequency for four bovine femoral samples in the axial and radial directions. Their results match the averaged values found in the present study in the axial (⬃3 dB.cm⫺1.MHz⫺1) and radial directions (⬃4 dB.cm⫺1.MHz⫺1). The inter-specimen reproducibility shows variations of the BUA value according to the specimen two times greater than the measurement precision, even although the three bovine specimens have the same age. The interpretation of the data on inter-specimen reproducibil-

—(in vivo) 4 4 5 2

0.2–0.6 0–25 0–30 0.3–0.7 0.2–0.6

Direction

BUA (dB · cm⫺1 · MHz⫺1)

axial axial axial radial tangential axial radial tangential — axial radial radial —

⬃3 ⬃9 ⬃2 ⬃3 ⬃3 ⬃3 ⬃7 ⬃7 6.1 ⬃3 ⬃4 5–12 10–18

ity should be considered very carefully because only three different bovine specimens were used in this study. Further measurements and analysis including more specimens should be carried out to draw definitive conclusions about the inter specimen variability. Effect of the Direction For all anatomical positions, BUA values obtained in the axial direction were the smallest. This is consistent with the tendency observed by Lakes et al. (1986) (see Table 3). Scattering effects can be a reason that might explain the dependence of BUA on the direction of propagation. In trabecular bone, finite difference time domain (FDTD) simulations have recently shown that scattering effects are responsible for the linear frequency dependence of attenuation (Bossy et al. 2005) and that BUA is highly correlated with BMD (Haïat et al. 2006, 2007). This study shows that scattering effects may also help to understand ultrasonic wave attenuation phenomena in cortical bone. In bovine cortical bone, lamellae and osteons are aligned in the axial direction. Therefore, the wave crosses more pores when it propagates perpendicular to the axial direction (i.e., in the radial or tangential directions) and, is therefore, more attenuated. The lamellae structure also seems to induce scattering and multiple reflections at the interfaces due to the small difference in the acoustic impedance (Katz et al. 1997). The results found in the present study on the dependence of BUA on the direction of propagation can be compared with those found in the study of Yamato et al. (2005, 2006) where SOS measurements were performed with the same samples in the three directions of propagation. In their papers, Yamato et al. (2005, 2006) found that SOS values obtained in the axial direction are significantly higher than those obtained in the tangential direction, which were significantly higher than those obtained in the radial direction. Their results, together with our

Ultrasonic attenuation in bovine cortical bone ● M. SASSO et al.

results can be explained qualitatively by the relative orientation of the direction of propagation and of the main direction of the pores. In the axial direction, ultrasonic waves always propagate parallel to the lamellae and osteonal structures. They are then less affected by the pores and interfaces than in the radial or tangential directions, which results in the higher velocities. Effect of the Position Similarly, the dependence of BUA values on the anatomical position may be analyzed by considering the dependence of wave velocity measurements. Yamato et al. (Yamato et al. 2005, 2006) showed for the same samples that ultrasonic wave velocity was higher in the anterior positions than in the posterior positions. Similar results have been obtained by Bensamoun et al. (2004a, 2004b) in a study where a cartography of the axial ultrasonic wave velocity was performed. Lower porosity values were invoked to explain the higher velocity obtained in the medial and anterior quadrants. Lower porosities also induce lesser scattering effects which are responsible for a decrease of BUA values in the medial and anterior positions. The significant difference of BUA values as a function of the anatomical positions and the corresponding results obtained for velocity measurements seems to suggest that BUA values may be sensitive to microstructural differences. As reported by Yamato et al. (2005, 2006), various microstructures in the posterior positions can be found, whereas only plate-like lamellae (plexiform) structure was found in the anterior positions. This complex distribution of microstructures seems to result in the large dispersion of BUA values in the posterior parts (PM-P-PL). Therefore, further work including an analysis of the microstructure and of the distribution of pores needs to be performed to investigate the attenuation in cortical bone tissue. Effect of Viscoelasticity Other physical causes of ultrasonic wave attenuation may be considered like viscous absorption or non linear effects. Viscous absorption can be caused by viscoelasticity of the bone solid matrix or by viscous losses due to fluid circulation in this biphasic medium. Cortical bone is known to exhibit viscoelastic properties (Cowin 2001) modeled in different studies (Iyo et al. 2004, 2006; Sasaki et al. 1993), which results from multiple processes occurring at different scales (Lakes and Katz 1979). At lower scales, collagen fibers in bone matrix may exhibit significant anisotropic viscoelastic behavior (Lakes and Katz 1979; Sasaki et al. 1993). The part between osteons in Haversian structure and lamellae in plexiform structure, which is delimited by a thin layer called cement surface is known to have a viscoelastic behavior (Lakes and Katz 1979; Lakes and Saha 1979).

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Moreover, viscoelastic dissipation due to fluid flow in bone’s pores has also been described and is likely to be significant particularly over 1 MHz (Buechner et al. 2001; Garner et al. 2000). Fluid flow should be the most important in the axial direction because the mean axis of the pores is aligned with the direction of propagation. However, BUA is found to be smaller in the axial direction than in the two other directions, which might indicate that fluid flow remains a phenomenon of the second order for ultrasonic attenuation. Acknowledgments—Part of this study was supported by the Academic Frontier Research Project on “New Frontier of Biomedical Engineering Research” of Doshisha University. Mami Matsukawa would like to thank the “SAKURA” program of JSPS and CNRS for financial support. Magali Sasso would like to thank the University Paris 12 – Val de Marne (“Conseil Scientifique”) for support during her stay at the Laboratory of Ultrasonic Electronics, Doshisha University, Japan.

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