Ultrasound shear wave imaging for bone

Ultrasound in Med. & Biol., Vol. 26, No. 5, pp. 833– 837, 2000 Copyright © 2000 World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/00/$–see front matter

PII S0301-5629(00)00214-3

● Original Contribution ULTRASOUND SHEAR WAVE IMAGING FOR BONE SHIGONG YE,* JUNRU WU† and JOHN PEACH‡ *Institute of Acoustics and State Key Laboratory of Modern Acoustics, Nanjing University, Nanjing 210093 China; † Departments of Physics and ‡Mechanical Engineering, University of Vermont, Burlington, VT 05405 USA (Received 22 December 1999; in final form 29 February 2000)

Abstract—Recently, a computer-controlled scanning ultrasound (US) imaging system was developed in our laboratory. It includes a pair of broadband 48-MHz focusing copolymer transducers. The apertures of the transducers and their f-numbers were identically equal to 2 mm and 2.25, respectively. A specimen can be moved in a 10-␮m increment in its plane and its normal direction can be rotated along the US propagation direction. It can be used to produce transmission-mode images of shear waves, as well as longitudinal waves for solid specimens. Shear waves in solids were generated by mode conversion. The results of the longitudinal and shear-wave US images for a piece of compact bovine bone obtained using this system are presented. Shear-wave images combined with longitudinal images can provide a more complete mechanical characterization of bone. © 2000 World Federation for Ultrasound in Medicine & Biology. Key Words: Shear waves, Longitudinal waves, Compact bone, Acoustic imaging.

INTRODUCTION

ported that there is a correlation between the US propagation velocity and attenuation vs. the density, elasticity and mechanical strength of bone (Lees et al. 1983; Langton et al. 1984; Tavakoli and Evans 1992). The attenuation coefficient of bone for longitudinal waves has been used as a method for diagnosis osteoporosis (Langton et al. 1984; Laugier et al. 1994). Different measurement methods were proposed to determine the propagation velocity, attenuation and backscattering coefficients; most of these were limited to the low megahertz frequency range (Kremkau et al. 1981; Tavakoli and Evans 1992; Wu and Cubberley 1997; Wear and Gara 1998). The US imaging has been used both in vivo and in vitro in biomedical applications (Briggs 1992, 1995; Briggs and Arnold 1996; Kaufman et al. 1992; Callens et al. 1997). Conventionally, a US longitudinal wave is the choice of obtaining a US image due to its simplicity. Because the longitudinal wave velocity is a function of both bulk modulus and shear modulus (see Results and Discussion sections), it can not be used to give a complete evaluation of elastic moduli of bone. Recently, US shear-wave imaging has been explored as an alternative imaging method. The properties of shear waves, including propagation velocity and attenuation coefficient, are extremely sensitive to pathological conditions of tissues (Sarvazyan 1996; Andreev et al. 1996). Ultrasound shear wave imaging can provide additional shear properties of bone that may be very valuable for diagnostic purposes. It has been reported that

In general, there are two categories of mammalian bone: compact (or cortical) and cancellous (or trabecular). The compact bone, most abundant in the shaft of long bone, appears to be hard and dense, and cancellous bone, appearing at the ends of long bone, seems to be porous and spongy. The constituents of bone include hydroxyapatite, Ca10(PO4)6(OH)2, protein (principally collagen), water and polysaccarides. The human bone strength in vivo can be affected by, among other things, exercise, environment (e.g., in space flight) and diseases (e.g., osteoporosis). Bone strength is also dependent on its microstructure, orientation and composition, as well as the external load. Macroscopically, bone can be considered as a viscoelastic and nonlinear medium; its mechanical properties are frequency and displacement-amplitude dependence (Lakes 1999). Ultrasound (US), used as a tool to generate images and study mechanical properties of bone, has its unique advantages because the time periods associated with ultrasonic waves are much shorter than the relaxation times of viscoelastic effects, and the displacement caused by US is so small that the nonlinear effects can be neglected. Furthermore, it has been re-

Address correspondence to: Junru Wu, Department of Physics, University of Vermont, Burlington, VT 05405 USA. 833

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the shear waves in soft materials were generated by the acoustic radiation force of a focused sound wave (Andreev et al. 1996) or by a shock pulse produced by a focused laser (Pishchal’nikov et al. 1998). A scanning, high-frequency US imaging system was recently developed in our laboratory. A specimen can be moved in a 10-␮m increment in its plane, and its normal direction can be rotated along the US propagation direction. It can be used to produce longitudinal-wave and shear-wave images of solid specimens. Shear waves in solids were generated by mode conversion. In this paper, we report the results of the longitudinal and shearwave US images for a piece of compact bovine bone obtained using this system. EXPERIMENTAL PROCEDURE Bone sample treatment The bone sample used in the experiment was taken from long bovine femur bone obtained from a local supermarket. The sample was cut from the compact portion into a thin disk with its normal in parallel with the bone axis and polished. The thickness and the diameter of the bone specimen were measured using a caliper to be 400 ␮m and 1.1 cm, respectively. The diameter of the disk was much larger than the US beam diameter in situ. The weight of the bone sample was measured using an electronic balance capable of measurements to 0.1 mg (model AE163, Mettler Instruments AG, Switzerland) and the calculated density was 1.9 g/cm3. The cutting process was as follows: The bone was mounted in an ENCO milling machine, and a 0.25-inch (6.35 mm) diameter coring bit (Starlite, Rosemont, PA) was attached to the drill head. The long axis of the coring bit was aligned so that it was in the transverse plane of the bone. The drill speed was set to 1300 rpm. During the drilling process, the bone was bathed in distilled water to keep the bone cool and wash debris away. After the coring operation, the cylindrical bone sample was approximately 1 cm deep. To machine the bone into thin disks, a mounting device was needed. Therefore, approximately one half of the bone was potted in a small tube filled with epoxy. The epoxy was allowed to harden, and the mounted sample was placed in a Buehler Isomet 2000 saw. A diamond-wafering blade (Buehler, series 15 LC Diamond, Chicago, IL) with an angular velocity of 1500 rpm was used to cut the bone. During the cutting process, the bone and blade were continuously sprayed with a jet of water. A cutting force of 100 g was used to prevent deflection of the blade so that both surfaces were parallel. After bone specimens were prepared, they were stored at 4°C in 0.15 M sodium chloride solution. Experimental system and theoretical background A block diagram of the experimental system is shown in Fig. 1. A pair of 48-MHz focusing copolymer

Fig. 1. A block diagram of the imaging system.

transducers made by the Department of Biophysics, University of Toronto, Ontario, Canada, was used in this study; one was used as the transmitter and the other as the receiver. The apertures of the transducers and their f-numbers were identically equal to 2 mm and 2.25, respectively. A bone sample was taken from the saline solution and placed in a sample holder that was mounted on a rotatable scanning platform between a US transmit-

Fig. 2. The relative orientation of the sample with respect to the transducers.

Shear wave imaging ● S. YE et al.

ter and a receiver. The transducers and the sample holder were immersed in a distilled water bath whose temperature was regulated to be 37°C. The bone sample was in water-saturated condition. The insertion-substitution method was used to generate both amplitude and propagation velocity images. The transmitter was driven by a pulser/receiver (Panametrics, Model 5900PR, Waltham, MA). A short ultrasonic pulse was generated by the transmitter. After passing through the sample, the ultrasonic pulse was received by the receiver. The radiofrequency (RF) signal corresponding to the received pulse was amplified by the same pulser/receiver. The specimen was scanned in a raster fashion, 10 ␮m per step, by a stepper motor 2-axis precision motion system (Newport MM3000, Newport Inc, Irvine, CA). The data acquisition and the sample scan were controlled by a personal computer (PC) (OptiPlex XmT-5100, Dell system, Roundock, TX, USA). Data acquisition was coordinated with the scan by counting motor steps. An image of 128 ⫻ 128 grids corresponding to physical dimensions of 1.28 mm ⫻ 1.28 mm was generated. The amplitude of the received RF signal was obtained by using a gated peak detector (Panametrics, Model 5600, Waltham, MA). A 25-ns window of gate width was used to detect the peak value of the amplified

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RF signal. The detected peak values were digitized using a 12-bit A/D board (Lab-PC⫹, National Instruments, Austin, TX) and was stored in the PC for later data manipulation when the data collection was completed. The amplitude within the time window is used to detect spatial variations in received amplitude with position. For longitudinal-wave imaging, the front surfaces of the transmitter and the receiver were aligned perpendicularly to the US propagation direction (UPD) before the specimen was introduced. This can be achieved by maximizing the received RF signal shown on the oscilloscope. Then, the sample was introduced between the transducers. The normal incident orientation of the sample was secured by rotating the sample orientation until the RF signals corresponding to longitudinal waves reached the maximum. To get the best imaging quality, it was important to move the transmitter and the receiver relative to the sample along UPD until the sample was placed at the confocal position of the pair of focused transducers. The propagation velocity of longitudinal wave, cL, was calculated by (Kremkau et al. 1981; Wu 1996; Wu and Cubberley 1997): cL ⫽

c wd , 共d ⫺ c w⌬t兲

Fig. 3. Waveforms of a transmitted signal from the bone. L. W ⫽ longitudinal waves; S. W ⫽ shear waves.

(1)

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where d is the thickness of the sample, cw is the sound speed in water at 37°C, and the ⌬t is the difference between arrival times, measured at the first zero-crossing of the waveforms, when the sample was inserted, and that when the sample was absent. To generate shear waves in a bone sample, the normal of the sample was rotated around the US wave propagation direction (Fig. 2). In this case, the US beam impinges upon a solid sample from water with an incident angle of ␪i ⫽ 0. Thus, not only a refracted longitudinal wave, but also a shear wave will propagate in the sample by the mode conversion (Wu 1996). During the rotation, the longitudinal wave signals gradually decreased and shear wave signals shown at a later time on the oscilloscope increased (Fig. 3). When ␪i ⬎ ␪cr, where ␪cr is the critical angle corresponding to the incident angle of the longitudinal wave, only the shear wave was propagated through the sample. The propagation velocity of shear wave cs was calculated by: cs ⫽

冑

冉

cw

c w⌬t sin ␪ i ⫹ cos␪ i ⫺ d 2

冊

2

,

(2)

where cw, d and the ⌬t have been defined above. When the shear-wave amplitude reached the maximum, the

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incident angle ␪i was recorded. Usually, ␪i was near 37° for our bone specimen. For propagation velocity measurement, the received RF waveforms were recorded with a 500-MHz bandwidth, 2 Gsa/s sampling rate and 8-bit digital oscilloscope (Hewlett Packard 54616B, ). The digitized signals were transferred via an IEEE-488 to the PC for further processing. The waveform amplitude and the propagation velocity of the same region were used as imaging parameters. Four US images were generated. They, respectively, are: the longitudinal-wave amplitude image, the shear-wave amplitude image, the longitudinal-wave velocity image and the shear-wave velocity image, as shown in Fig. 4. RESULTS AND DISCUSSION As shown in Fig. 4, the velocity variation both for longitudinal and shear waves was in the range of about 10%, but the variation in amplitude was in the range of about 80%. It suggested that amplitude used as a parameter of imaging may be more sensitive to a microscopic change of constituents and structure in bone. In Fig. 4, the Harversian canal structure of compact bone tissue, where a large variation of amplitude and propagation velocity takes place, can be seen especially from the amplitude image of longi-

Fig. 4. Acoustic images of a thin compact bone disk of thickness 400 ␮m. The scales used for amplitude images are relative scales.

Shear wave imaging ● S. YE et al.

Fig. 5. Acoustic images of a thin disk of a polymer material used as a US transducer backing material provided by Hewlett Packard Co (commercial name of the material was not provided). The thickness of the disk is 1 mm, diameter is 2.5 cm and density is 1.24 g/cm3.

tudinal and shear waves. It is also shown from the wave velocity images that, both for longitudinal and shear wave velocities in bone, they were far from single-valued. They varied spatially because the mechanical properties, structure and the density of the bone were nonuniform. From Fig. 4, it is also clear for both imaging cases that the higher the velocity, the smaller the amplitude. For comparison, acoustic images of longitudinal waves for a disk made of a polymer material used as a backing material of ultrasonic transducers of medical scanners were generated shown in Fig. 5. This disk appeared to be more uniform, and this was verified by the images in Fig. 5. The variation of the velocity shown by the image on the left was less than 4% and that of the amplitude shown on the right was less than 40%. It is still true that the location where the velocity is higher has smaller amplitude. Another observation is that the resolution of shearwave imaging turned out to be worse than its longitudinal counterpart, although its wavelength is shorter for the same frequency. This is because the attenuation coefficient is generally an increasing function of frequency, and it is much higher for shear wave than for longitudinal wave in bone (Wu and Cubberley 1997). Thus, the center frequency of the broadband pulse after its transmission through the bone specimen became only about 10 MHz in the case of shear wave because it was near 40 MHz in the case of the longitudinal wave. The ratio of the wavelength of longitudinal waves to that of shear waves was actually 0.4. In addition, because the attenuation of bone is much lower for longitudinal waves than for shear waves, the signal/noise was better for longitudinal wave images, as well. Therefore, the resolution of the longitudinal-wave image was better compared to its shear-wave counterpart. However, as the velocities of longitudinal and shear waves are, respectively, given by eqns (3) and (4): c L ⫽ 冑共B ⫹ 4 ␮ /3兲/ ␳ ,

(3)

c s ⫽ 冑␮ / ␳ ,

(4)

where B is the bulk modulus, ␮ is the shear modulus and ␳ is the density of bone, the longitudinal wave image

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alone cannot evaluate elastic moduli completely. In this sense, shear-wave images are complementary to longitudinal images. One advantage of the shear-wave generation by the mode conversion is elimination of shear-wave transducers and associated coupling gel and, therefore, the reproducibility improves (Wu 1996). One of the disadvantages in this is that the sample is tilted because the angle of incidence is not zero. Therefore, the image plane in this case is not exactly the same as that of the longitudinal image. Because the sample was very thin, it may not be a serious problem. Finally, although the proposed shear-wave imaging technique cannot directly be used as a clinical diagnostic tool, biomechanical information obtained by the method should be important for understanding bone diseases. REFERENCES Andreev V, Pishalnikov Y, Rudenko O, Sapozhnikov O, Dmitriev V, Sarvazyan A. Excitation of shear waves inside of rubberlike material by focused ultrasound. J Acoust Soc Am 1996;100(2):2647. Briggs A. Acoustic microscopy. New York: Oxford University Press, 1992. Briggs A, ed. Advances in acoustic microscopy. Vol. 1. New York, London: Plenum Press, 1995. Briggs A, Arnold W, eds. Advances in acoustic microscopy. Vol. 2. New York, London: Plenum Press, 1996. Callens D, Lefebvre F, Pernod P, Nongaillard B. Nondestructive evaluation of osteoprogenitor cell cultures using high frequency acoustical imaging and imaging processing. Acoust Imaging 1997;23: 151–156. Kaufman JJ, A.Chiabrera A, Fallot S, Alves JM, Hermann G, Siffert RS, Grabowski G. Ultrasonic bone tissue characterization in gaucher disease type I. Acoust Imaging 1992;19:399 – 402. Kremkau FW, Barnes RW, McGrew CP. Ultrasonic attenuation and propagation velocity in normal human brain. J Acoust Am 1981; 70:29 –38. Laker RS. Viscoelastic solids. Boca Radon, FL: CRC Press, 1999. Langton CM, Palmer SB, Porter RW. The measurement of broadband ultrasonic attenuation in cancellous bone. Eng Med 1984;13:89 –91. Laugier P, Giat P, Berger G. Broadband ultrasonic attenuation imaging: a new imaging technique of Os Calcis. Calcif Tissue Int 1994;54: 83– 86. Lees S, Ahern JM, Leonard M. Parameters influencing the sonic velocity in compact calcified tissues of various species. J Acoust Soc Am 1983;74:28 –33. Pishchal’nikov Y, Andreev V, Rudenko O, Sapozhnikov O, Sarvazyan A. Shear wave excitation in rubber-like medium by focused shock pulse. Proceedings of the 16th International Congress on Acoustics and 135th Meeting of Acoustical Society of America. Acoust Soc Am 1998;3:1857–1858. Sarvazyan AP. Remotely induced shear acoustic waves in tissues by radiation force of focused ultrasound. J Acoust Soc Am 1996;99: 2465. Tavakoli MB, Evans JA. The effect of bone structure on ultrasonic attenuation and velocity. Ultrasonics 1992;30:389 –395. Wear KA, Garra BS. Assessment of bone density using ultrasonic backscatter. Ultrasound Med Biol 1998;24:689 – 695. Wu J. Determination of velocity and attenuation of shear waves using ultrasonic spectroscopy. J Acoust Soc 1996;99:2871–2875. Wu J, Cubberley F. Measurement of velocity and attenuation of shear waves in bone using ultrasonic spectroscopy. Ultrasound Med Biol 1997;23:29 –134.