Noninvasive method for measuring velocityof leaky surface skimming compressional
wave propagating on bone surface
H. Asai, H. Kanai and N. Chubachi

Indexing terms: Acoustic wave velocity measurement, Biomedical
ultrasonics
The authors propose a new method, based on the microdefocusing
method [1], for transcutaneously measuring the velocity of leaky
surface skimming compressional waves (LSSCWs) propagating on
the surface of bone. The method is realised by an ultrasonicmeasurement system which is applicable to in vivo measurement
using ultrasound of 1MHz. The velocity of the LSSCW propagatingon the surface of a Bakelite sample is snccessfully determined in apreliminary experiment, and the principle of the proposed method isconfirmed.

Introduction: Since ultrasound-based diagnosis of osteoporosis does
not necessitate the use of x-rays, it is preferable to, and can be more
frequently applied than other diagnosis methods. Acoustic and elastic properties of bone obtained by ultrasonic-based methods arehighly useful in the direct evaluation of bone characteristics. Thus,
many methods and systems have been developed such as the acoustic
emission (AE) method [2], the apparent velocity of the ultrasound(AVU) method [3], and the speed of sound-broadband ultrasoundattenuation (SOS-BUA) method [4, 5]. It is, however, well known
that the propagation loss is large in bone even for ultrasound of1MHz and that it is difficult to transcutaneously measure the bone
thickness, which is essential to the evaluation of velocity and theattenuation per unit length. Thus, the ultrasonic reflection method ismore effective than the pulse transmission method. In this Letter, wepropose an ultrasonic reflection method, in which the velocity of theLSSCW propagating on the surface of bone is determined based on
the V(z) curve analysis used in acoustic microscopy. Since the propagation loss of the LSSCW is also large for bone, there are only a few
periods of ∆z due to interference between the LSSCW componentVI(z) and a wave component VL(z) reflected perpendicularly from thesample surface in the measurement of the V(z) curve of bovine bone
[6, 7]. Thus, periodical analysis, such as the fast Fourier transform(FFT) is not adequate for accurate velocity determination. In thisLetter, as an alternative, we propose a new method for the evaluationof the velocity of the LSSCW based on the microdefocusing method[1]. In the proposed method, only the VI(z) component is received bya pair of transducers. Phase θ(f0, z) of the VI(z) component at thecentre frequency, f0, of the transducers is measured for several valuesof the sample position z. From the phase characteristics θ(f0, z) ofVI(z), the velocity of the LSSCW is determined. From a preliminary
experiment using a measurement system constructed in our laboratory, the LSSCW velocity for a Bakelite sample, almost the same asthat of human bone, is successfully determined and the principle ofthe proposed method is confirmed.

Fig. 1 Block diagram of measurement system

ELECTRONICS LETTERS

21st November 1996

Principle: Fig. 1 shows a block diagram of a system for the measurement of the velocity of the LSSCW. There are two ultrasonic transducers, transducer (A) for transmitting and transducer (B) forreceiving. Transducer (A) is positioned so as to transmit an ultrasonic pulse. Its centre axis is almost the same as the critical angle
θLSSCW of the sample so that only the LSSCW component is excitedon the sample surface. The centre frequency of the transducer f0 is
1MHz, and the focal length is 95mm. Transducer (A) is driven by an
RF burst pulse wave of 1MHz, 50 µs in length. The ultrasonic wave
is transmitted from the transducer (A), as shown in Fig. 1, to thesample surface with its critical angle with the LSSCW being set atθLSSCW. The LSSCW is excited and propagates on the sample surface.
When the distance between the transducers and the sample isdecreased by changing the sample position z toward to the transducers, the leaky wave VB(z) which is re-transmitted from the sample
surface, is detected by transducer (B) for each sample position z, andis digitised by a digitising oscilloscope. The received signal is transferred to a workstation. The longitudinal velocity vW in water isdetermined from the temperature T measured by a resistance-type
thermometer sensor using the previously reported relation between
T and vW [8].
By calculating the phase spectrum θ(f, z) of the detected signalVB(z), the phase delay θ(f0, z) at the centre frequency f0 = 1MHz of
the received signal is determined for each sample position z. When
only one mode of the leaky waves (the LSSCW mode in this case) isexcited on the sample surface, the velocity of the LSSCW is determined by the microdefocusing method [1]. Since the acoustic path inFig. 1 is the same as that for the LSSCW component VI(z) of V(z)which is measured in the acoustic microscope, the change δθ of thephase delay caused by moving the sample closer to the transducer byδz is given by

where kW and kLSSCW are the wave number of the longitudinal wave inwater and the wave number of the LSSCW, respectively. Since thecritical angle θLSSCW for LSSCW is given byand vLSSCW = 2πf/ kLSSCW is the phase velocity of LSSCW, eqn. 1 issimplified as
The phase change δθ is measured for each sample position z while
the distance between the sample and the transducers is decreased.
The gradient ξ of the phase delay θ(f0, z) is given by

Substituting eqn. 4 into eqn. 2, the velocity vLSSCW of the LSSCW isdetermined byThus, the velocity vLSSCW of the LSSCW propagating on the sample
surface is determined by measuring the gradient ξ of phase changeδθ, due to the decrease of the distance δz between the sample and thetransducers.
Experimental results: To confirm the principle of the proposed
method, the velocity vLSSCW of the LSSCW is measured for a sampleof Bakelite. The critical angle θLSSCW for the Bakelite is ~24 °, assuming that vW is 1500m/s and the longitudinal velocity vL of the Bakeliteis 3718m/s which is measured in advance by the ultrasonic pulse
transmission method [9].
Fig. 2 shows the relationship between the phase delay θ(f0, z) of
the received signal, which is measured by reducing the distance
between the sample and the transducers. The temperature is 25.8 °,and vW is 1499m/s. The gradient ξ is determined as 7.583 × 103 by
applying the least mean square method to Fig. 2. Substituting theresultant values of vW and ξ into eqn. 5, the velocity vLSSCW ofLSSCW for the Bakelite sample is determined to be 3515m/s, which
is different from the longitudinal velocity vL = 3818m/s of Bakelite.
Thus, the LSSCW mode is successfully excited and detected by theproposed method and system.

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© IEE 1996
Electronics Letters Online No: 19961470

8 October 1996

H. Asai, H. Kanai and N. Chubachi (Department of ElectricalEngineering, Faculty of Engineering, Tohoku University, Sendai 980-77,Japan)

References
1234
Fig. 2 Phase change θ in received signal measured for Bakelite sample

ξ = dθ/dz = 7.583rad/mm

5Conclusions: In this Letter, we have proposed a new method for invivo measurement of the velocity of the LSSCW for human bone. A
system based on the microdefocusing method was constructed andfrom a preliminary experiment using a Bakelite sample, the principleof the proposed method was confirmed. By comparing the measured
velocity vLSSCW of the LSSCW with its longitudinal velocity vL, theLSSCW was successfully excited and its velocity was measured bythe microdefocusing method. To realise an in vivo system for humanbone, soft tissues surrounding the bone must be taken into accountin any analysis. Fortunately, since the velocity and acoustic impedance of soft tissues are close to those of water, the proposed system
and method of analysis are also applicable to human bone.

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KANAI, H.,

CHUBACHI, N., and SANNOMIYA, T.: ‘Microdefocusing
method for measuring acoustic properties using acoustic
microscope’, IEEE Trans. UFFC., 1992, 39, (5), pp. 643–652
YOON, H.S., CARACO, B., KAUR, H., and KATZ, J.L.: ‘Clinical applicationof acoustic emission techniques to bone abnormalities’. 1980 IEEEUltrason. Symp. Proc., 1980, Vol. 2, pp. 1067–1072 (Cat. No.
80CH1602-2)
HEANEY, R.P., AVIORI, L.V., CHESNUT III, C.H., LAPPE, J., RECKER, R.R., andBRANDENBURGER, G.H.: ‘Osteoporotic bone fragility detection byultrasound transmission velocity’, JMMA, 1989, 261, pp. 2986–2990
LANGTON, C.M., PALMER, S.B., and PORTER, R.W.: ‘The measurement ofbroadband ultrasonic attenuation in cancellous bone’, Eng. Med.,
1984, 2, pp. 89–91
BARAN, D.T.,
KELLY, A.M.,
KARELLAS, A.,
GIONET, M.,
PRICE, M.,
LEAHEY, D., STEUTERNIAN, S., McSHERRY, B., and ROCHE, J.: ‘Ultrasoundattenuation of the os calcis in women with osteoporosis and hip
fractures’, Calcif. Tissue Int., 1988, 43, pp. 138–142
CHUBACHI, N., SANNOMIYA, T., and ASAI, H.: ‘Measurement of boneproperties by ultrasound to develop diagnostic equipment’. 1990
Ultrason. Symp. Proc., 1990, 3, pp. 1367–1370CHUBACHI, N., ASAI, T., and SANNOMIYA, H.: ‘A new method to measurebone properties by means of leaky surface acoustic waves’, J. Acoust.
Soc. Jpn. (E), 1992, 13, (2), pp. 121–125
KROEBEL, W., and MAHRT, K.H.: ‘Recent results of absolute soundvelocity measurements in pure water and sea water at atmosphericpressure’, Acoustica, 1976, 35, (3), pp. 154–164
ASAI, H., and CHUBACHI, N.: ‘Experimental evaluation of effects ofbone shape on the detemination of SOS and BUA using ultrasonicpulse transmission technique’. Proc. Acoust. Soc. Jpn., 1996, pp.
881–882 (in Japanese)

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