- Email: [email protected]
Ultrasonic sound velocity measurement in samples of soft materials through under-resonance excitation
Ultrasound in Med. & Biol., Vol. 31, No. 4, pp. 485– 491, 2005 Copyright © 2005 World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/05/$–see front matter
doi:10.1016/j.ultrasmedbio.2004.12.021
● Original Contribution ULTRASONIC SOUND VELOCITY MEASUREMENT IN SAMPLES OF SOFT MATERIALS THROUGH UNDER-RESONANCE EXCITATION JEAN-JACQUES AMMANN,*† VICTOR APABLAZA,* BELFOR GALAZ,* and CAROLINA FLORES* *Physics Department, Universidad de Santiago de Chile, Santiago, Chile; and †CIMAT, Santiago, Chile (Received 26 August 2004, revised 29 November 2004, accepted 17 December 2004)
Abstract—Ultrasound (US) velocity determination is a valuable characterization technique, providing important information on elastic properties of materials. Sound velocity can be obtained accurately in the pulsed method if the thickness of the specimen is precisely known. This is clearly not easily achievable for soft materials, such as biologic soft tissues or tissue-mimicking phantoms. From this consideration, previous works have established that sound velocity can be determined in through-transmission configuration without thickness measurement through the time-of-flight determination of specimen-reflected echoes in plane parallel-surfaced specimens. It is shown here that the amplitude and shape of these specimen echoes can be significantly improved by working in the tone-burst mode at an excitation frequency below the transducer resonance. This is particularly valuable for materials presenting a low acoustic contrast with the surrounding medium, usually water, such as tissuemimicking materials and water-based phantoms, making the specimen echo time-of-flights and, consequently, the sound velocity determination, more reliable. (E-mail: [email protected]) © 2005 World Federation for Ultrasound in Medicine & Biology. Key Words: Ultrasound, Sound velocity, Materials characterization, Gelatin, Tissue-mimicking materials.
values obtained by several recognized US laboratories on identical materials. If no explanation is proposed for this “unexpectedly large range of propagation speed,” thickness determination required by most evaluations is clearly a potential source of error for soft tissue–mimicking materials. Therefore, a new technique, based on a through-transmission configuration has been developed (Ammann et al. 2003; Ammann and Galaz 2003). This method, inspired by a previous work by Kroebel and Mahrt (1976) for determining sound velocity in liquid, substitutes the need for thickness measurement by the accurate measurement of the time-of-flight of the echoes generated by the reflection of the main pulse at the specimen surfaces, which must be plane and parallel. Indeed, while propagating from the excitation to the reception transducer in through-transmission configuration, the acoustic pulse is partially reflected at each of the two specimen surfaces (Fig. 1). This effect gives rise to the so-called intermediate or specimen echoes Sij appearing between the main successive transducers echoes E1 and E2 after being reflected back at the excitation transducer. The same scheme occurs for the main echo traveling toward the excitation transducer after being reflected at the reception
INTRODUCTION Elastic properties are of central interest for biologic tissue characterization and quantitative echography (Bamber 1998). Their potential significantly improved with the development of elastography as a new biomedical diagnostic tool (Hall et al. 1997; Ophir et al. 1999). The characterization of soft material elasticity is, therefore, of prime importance to correctly evaluate this new approach. Ultrasound (US) velocity measurement is a wellknown and efficient technique to access elastic coefficients of materials (Achenbach 1984). It is a relatively simple procedure, known for decades, and is performed by pulsed or continuous waves (Papadakis 1990). It usually requires the specimen thickness to be determined accurately by another way and is very accurate in hard materials such as ceramics and metallic alloys (Truscott and Strekitzki 1998). Surprisingly enough, however, a recent assessment of the velocity determination accuracy in tissue-mimicking specimens by Madsen et al. (1999) has pointed out a quite large variation (1.7%) among the Address correspondence to: Jean-Jacques Ammann, Physics Dept., Universidad de Santiago de Chile, Ecuador 3493, Santiago, Chile. E-mail: [email protected] 485
486
Ultrasound in Medicine and Biology
Fig. 1. Space-time plot of the burst propagation in the throughtransmission configuration with partial reflection at the specimen surfaces. The corresponding experimental RF trace in the lower part exhibits two main echoes (E1 and E2) (here truncated) and four intermediate echoes from a specimen presenting two parallel surfaces perpendicular to the acoustic beam.
transducer. In this way, each specimen surface produces, on the signal trace, a pair of intermediate echoes between two main transducer echoes. Echoes that undergo multiple reflections at the specimen surfaces are usually not observed on the radiofrequency (RF) trace when the medium and specimen exhibit similar acoustic impedances (Ammann et al. 2003) and will be neglected in the present study. By writing down the propagation equations of the echoes reflected at the specimen-medium interfaces according to Fig. 1, the sound velocity in the specimen cs can be written as a function of the respective time-offlight Ti, taking the sound velocity in the medium cw (here, water) as a reference:
冋
cs ⫽ cw 1 ⫹
册
2(TE2,ref ⫺ TE2) ⫺ (TE1,ref ⫺ TE1) , (1) 关(TSrf ⫺ TSef) ⫺ (TSeb ⫺ TSrb)兴
where the subscripts “e” and “r” denote that the specimen surface is facing the excitation or reception transducers, respectively, subscripts “f” and “b” stand for echoes reflected from a tone-burst propagating in the forward direction (toward the reception transducer) or
Volume 31, Number 4, 2005
backward direction (toward the excitation transducer), respectively, and the subscript “ref” refers to the main echoes of a reference trace obtained by removing the specimen from the acoustic path. Relying essentially on the intermediate echoes’ time-of-flight Tsij, the success of this method depends on a clear detection and characterization of these echoes. This aspect is particularly critical when the acoustic contrast between the specimen and the medium (usually water) is low, as it is commonly the case for biologic specimens or tissue-mimicking phantoms (Selfridge 1985). Indeed, in such cases, the impedance of the specimen is similar to that of the medium and the reflection coefficient of the medium/specimen interface is low. In such cases, the amplitude of the intermediate echoes is significantly reduced and the accuracy of the time-of-flight measurement is lowered by the electronic noise. To guarantee a reliable time-of-flight measurement, experimental conditions must be adequately selected. Although shock excitation is commonly used in pulseecho techniques, we are demonstrating here that working in the tone-burst mode offers significant advantages in through-transmission, when the intermediate echoes must be clearly observed. Additionally, this work evaluates the effects of excitation frequency on both amplitude and shape of the echoes and indicates a way to optimize the experimental parameters for reliable timeof-flight determination. If the specimen is assumed to present parallel surfaces, it is expected that the present method could account for a limited lack of parallelism of the surfaces and further studies are under way to address this point. The sound velocities determined according to the under-resonance condition are presented for gelatin specimens of various compositions. MATERIALS AND METHODS Experimental setup The through-transmission configuration adopted in this work consists in locating the specimen between a pair of facing coaxial transducers of similar frequency characteristics, here denominated excitation (E) and reception (R) transducers (Fig. 2) (Ammann and Galaz 2003). The whole system is immersed in a thermally controlled water-tank for accurate temperature control. The transducer spacing is significantly larger than the specimen, so that no contact occurs between the specimen and the transducers (stress-free condition), allowing a free alignment and positioning of the specimen along the acoustic beam. By keeping the specimen at a distance from the transducers equivalent to its near field limit, in our case 30 mm, this configuration also avoids any diffraction
Under-resonance sound velocity ● J-J. AMMANN et al.
Fig. 2. Through-transmission assembly, showing two coaxial excitation (E) and reception (R) transducers.
effect (Droin et al. 1988) and significantly reduces possible interference of the signal with transducer trailing noise. The excitation chain is composed of a signal generator (Wavetek, model 80, now Fluke Corp., Everett, WA) in sine burst mode attached to a power amplifier (ENI-325LA, ENI, Rochester, NY) that feeds the tone-burst signal to the 5-MHz broadband excitation transducer (Panametrics, Crescent St., Waltham, MA; 5.05-MHz peak frequency, 72.9% band width at ⫺6 dB and 6-mm diameter, quarter-wave matched), as illustrated in Fig. 2. The acquisition chain is composed of a similar broadband transducer (5.60 MHz peak frequency, 71.9% band width at ⫺6 dB) connected to a 500-MHz DSO oscilloscope (LT344, LeCroy, Chestnut Ridge, NY). Note that, considering the large band width of the transducers, the difference between the peak frequencies of the two excitation and reception transducers used here does not significantly affect the behavior of the described technique. The experimental RF trace obtained from the reception transducer is acquired at 500 MS/s. Triggering the oscilloscope on the signal delivered by the power amplifier allows a reliable and accurate averaging of the signal (100⫻) and a digitization at 11 bits before being transferred to a personal computer (PC) for processing. The length of the acoustic tone-burst can be chosen to narrow the frequency spectrum of the echoes and make them less sensitive to velocity dispersion. For transfer function determination, a Panametrics pulser-receiver (model 5800PR) is used in through-transmission mode feeding directly the excitation transducer (energy: 100 J, damping: 25 ⍀, gain: 40 dB) and delivering the amplified signal to the DSO. The specimen is fixed in a five degrees-of-freedom holder allowing accurate orientation and positioning along the ultrasonic beam. The two facing transducers, excitation (E) and reception (R), are mounted on an
487
independent support. After a convenient alignment of the specimen, the four intermediate echoes can be observed on the RF trace. Performing a slight shift of the specimen along the acoustic beam allows clear identification of the two forward echoes Sef and Srf shortening their time-offlight while increasing the distance between the specimen and the reception transducer; the backward echoes Seb and Srb behave in the opposite way. Then, having identified forward and backward echoes, Sef clearly reaches the reception transducer before Srf and Srb before Seb (refer to Fig. 1). An adequate positioning of the specimen along the acoustic beam allows avoiding a possible overlapping of some of the intermediate echoes on the RF trace. The velocity determination through eqn (1) relies exclusively on the time-of-flight difference of similar echoes (Ammann and Galaz 2003). This makes the cross-correlation processing a wise choice for determining the echo position on the time scale. In this processing, a segment of the RF trace containing one of the echoes to be analyzed is extracted and used as the crosscorrelation reference signal. Using the conventional method, the cross-correlation is performed on the whole trace and its envelope is obtained through the Hilbert transform (Ammann and Galaz 2003), exhibiting a single peak for each of the echoes. The time-of-flight of each echo is taken as the maximum of the corresponding peak and is determined with a resolution better than the sampling interval. Through-transmission transfer functions Because the transducers, medium and specimen have slightly different acoustic impedances, the acoustic tone-burst undergoes a partial reflection at each interface. After suffering two reflections, the tone-burst eventually reaches the reception transducer and is recorded on the RF trace. Ideally, at each transducer surface, the amplitude of the reflected and transmitted tone-bursts, ER and ET, respectively, are related to the incident wave Ei through the transmission and reflection coefficients of the transducer, TT() and TR(), respectively: ER ⫽ Ei ⫻ TR() and ET ⫽ Ei ⫻ TT(), with TR() ⫹ TT()⫽ 1. Due to the intrinsic behavior of the transducer, both TT() and TR() are strongly frequency-dependent close to the resonance frequency. In this context, the frequency-dependence of the transmission and reflection coefficients of the specimen, TST and TSR, respectively, can be considered to be negligible. In the scope of this paper, these parameters will be considered as constant and TST ⬇ 1 and TSR << 1. Then, the power spectrum of each echo can be related to the excitation signal E0 by considering the
488
Ultrasound in Medicine and Biology
Volume 31, Number 4, 2005
specific transmissions and reflections the tone-burst undergoes (Fig. 1), so: E1() ⫽ E0 ⫻ T2T(), E2() ⫽ E0 ⫻ T2T() ⫻ TR2() ⫽ E1() ⫻ TR2() Sij() ⫽ E0 ⫻ T2T() ⫻ TSR ⫻ TR() ⫽ E1 () ⫻ TR() (2a) with E1 ⫽ E1() ⫻ TSR
(2b)
Assuming a simple Gaussian model for the transmission transfer function of the transducers with a 0.9 maximum efficiency at res, Fig. 3 illustrates the major trends of the main and intermediate echo amplitudes. As expected, because the transmission transfer function (TT) is maximum at the resonance frequency res, the first main echo E1 goes through a strong maximum at res. However, the reflection transfer function TR is minimum at res and the echoes undergoing reflection at the transducer surfaces, both E2 and the intermediate echo Sij, present a relative minimum at that frequency, with two side maxima below and above the transducer resonance frequency (Fig. 3). It can be considered, therefore, that the signals undergoing reflections at the transducer surfaces suffer a significant “absorption” by part of the transducers, and their amplitude is strongly reduced at the resonance frequency. It is worth observing that the side maxima for the intermediate echoes Sij are closer to res and of higher amplitude than the second main echo E2. It can be shown, through a simple calculation based on the basic equations presented above, that the second main echo E2 goes through its maximum amplitude when the transmission transfer function is TT ⫽ 1/2. Similarly, intermediate echoes undergo one transducer reflection only and pass through their maximum when TT ⫽ 2/3. Then, the optimum choice of the working frequency, in the through-transmission configuration when main and intermediate echoes are to be observed, will be closely related to the shape of the transducer transfer functions. Materials The specimen material is prepared by adding from 4 to 15%wt gelatin (type B/225 Blum, Sigma) to distilled water at 60 to 70°C, using 0.02% sodium azide (Riedel de Haën, Seelze, Germany) as a fungus inhibitor. After homogenization, the gelatin is slowly cooled down, to allow possible air bubbles to escape, and gelified at room temperature. It is then liquefied at 40°C and poured in a mold built by fixing a PVC tube (30 mm in diameter ⫻ 20 mm long) on top of a glass plate. After gelling, the
Fig. 3. Gaussian model for the transducer transfer functions TT (—), TR ( · · · · ) and corresponding echoes spectrum of E1 (—–), E2 (- · - · - · ) and intermediate Sij (- · · - · · -).
glass plate is removed by gently heating its base, exposing two opposite free specimen surfaces. It is worth noting here that the specimen thickness does not appear explicitly in the sound velocity determination, eqn (1) but, on the contrary, can be deduced afterward through the generic relation ds ⫽ 1/2 cs⌬Ts. Therefore, the sound velocity measurement will not be affected, in this specific case, by a possible swelling of the gelatin, which represents a significant advantage of this approach. RESULTS AND DISCUSSION Transfer function and echo shape and amplitude The experimental aspect of the under-resonance improvement of sound velocity determination is illustrated on the water-based gelatin specimen. Gelatin being mostly composed of water (85 to 96 wt%), its impedance is expected to be close to the impedance of water (Povey 1989). When adequately aligned between the two transducers, the gelatin specimens exhibit an acoustic trace similar to the one shown in Fig. 1 with four specimen echoes bracketed between the main E1 and E2 transducer echoes. The amplitudes of the first and second main echoes (E1 and E2) are directly related through the transducer reflection function TR() that can be deduced from the frequency spectrum of these two echoes (Fig. 4): TR() ⫽
冑
E2 E1
(3a)
and TT() ⫽ 1 ⫺ TR.
(3b)
To determine TT() and TR() experimentally, a shock excitation, generated by the pulser-receiver, has
Under-resonance sound velocity ● J-J. AMMANN et al.
Fig. 4. Experimental transfer functions obtained through shock excitation TT (—), TR (- - - - - -) and echoes E1 (- · - · - · ) and E2 ( · · · · ).
been used. As expected, TT exhibits the characteristic resonance peak of the transducers. The top-hat–shaped maximum observed on the TT peak is due to the slightly different resonance frequencies of the two transducers (5.1 and 5.6 MHz), causing the maximum of each transfer function TTe and TTr to appear at slightly different frequencies. The E1 amplitude in eqn (2a), then becomes: E1 ⫽ E0 * TTe * TTr. As expected, the amplitude of the main echo E2 peaks below the resonance frequency at ⫽ 3.9 MHz, close to the predicted frequency for TR ⫽ 1/2 ( ⫽ 4.2 MHz). A similar behavior is observed at frequencies higher than res, in spite of additional distortion of the transfer functions due to higher harmonics. The effect of the TT transfer function on the E2 amplitude is illustrated in tone-burst mode in Fig. 5 for
Fig. 5. RF traces of the E2 main echo plotted against the excitation frequency. The peak-to-peak amplitude plot exhibits a clear depression around the transducer resonance frequency (res ⫽ 5 MHz).
489
Fig. 6. Frequency spectra of the second main echo E2 as a function of excitation frequency. A deep depression appears at the transducer resonance frequency independently of exc, significantly altering the main lobe of the Fourier transforms of tonebursts emitted close to the transducer frequency (frequencies in MHz). The frame indicates the spectrum location corresponding to an excitation at the transducer resonance frequency.
excitation frequencies between 2.0 and 7.0 MHz. This figure shows that the overall shape of the E2 echo is significantly distorted and depressed when the excitation frequency is close to res; here, 5 MHz. This is highlighted by the superimposed peak-to-peak plot of E2 amplitude, exhibiting a clear minimum at the transducer resonance frequency. Close to the resonance frequency, the transducer transfer function TR presents a narrow minimum and the E2 echo frequency spectrum, modulated by TR, is highly distorted. Indeed, when looking at the power spectra of E2 taken at several excitation frequencies exc (Fig. 6), the alteration due to the transducer appears as a deep trench at res. The distortion is critical when altering the main lobe of the tone-burst Fourier transform, reflecting the distortion of the tone-burst shape observed in Fig. 5. Introducing a specimen between the transducers produces intermediate echoes on the RF trace (Fig. 1). The effects of the transducer transfer function on the shape and amplitude of these intermediate echoes are similar to the ones described above. However, because they undergo only one reflection at a transducer surface, the alteration introduced on their shape is reduced; see eqn (1). The time-of-flight and sound velocity The time-of-flight determination is performed by selecting the maximum of the echo cross-correlation envelope obtained through the Hilbert transform. The cross-correlation envelope of an intermediate echo using a different intermediate echo as reference is exhibited in
490
Ultrasound in Medicine and Biology
Fig. 7, for various excitation frequencies between 1.0 and 6.0 MHz. Clearly, the maximum of the cross-correlation envelope is obtained for frequencies under the transducer resonance frequency; here, this is 4 MHz for res of 5 MHz. Additionally, the smoothness and symmetry of the Hilbert peak decrease significantly under and above 4 MHz, degrading the accuracy and reliability of the time-of-flight determination. For the optimal condition (exc ⬇ 4 MHz), the time-of-flight is determined with a precision close to the sampling interval (2 ns). As mentioned above, the optimum excitation frequencies for the second main echo and the intermediate specimen echoes depend on the transducer transfer function. Determined on a trial basis, it corresponds, in this case, to exc ⫽ 0.8 res. The sound velocity has been determined using the presented method in eqn (1) at exc ⫽ 4 MHz and, according to the experimental conditions discussed in this paper, is presented below for gelatin of 4, 6, 10 and 15 wt%. Sound velocity in water cw is taken as 1482 m/s for a temperature stabilized at 20.0°C (Krautkrämer and Krautkrämer 1991). An experimental trace appears in Fig. 1, and Fig. 8 exhibits the linear dependency of the sound velocity cs against the gelatin weight content C%: cs ⫽ cgel ⫽ cw ⫹ 3.56 C%
(4)
Although the method does not require the determination of the specimen thickness, it is still affected by the lack of parallelism of the specimen faces, and additional studies are underway to assess this important issue and possibly to account for this effect.
Volume 31, Number 4, 2005
Fig. 8. Sound velocity in gelatin specimen as a function of weight concentration.
SUMMARY Soft-tissue–mimicking materials often have uncertainties in thickness that introduce inaccuracy in traditional acoustic velocity measurements. It has been shown that using the specimen-induced intermediate echoes in the through-transmission configuration allows determination of the sound velocity in plane parallel-sided samples without requiring determination of the specimen thickness. However, the acoustic impedance of these materials being similar to that of water, commonly used as measurement medium, makes both the detection of intermediate echoes and the accurate measurement of their timeof-flight more difficult. Working in tone-burst mode at an excitation frequency lower than the transducer resonance frequency significantly improves the amplitude of the specimen and transducer echoes. In addition, the shape of the echoes is better preserved and the time-of-flight determination performed by cross-correlation and the Hilbert transform is made more efficient and reliable. Time-of-flight precisions similar to the digitizing interval of the acquisition chain are achieved, significantly improving the sound velocity measurement accuracy. The optimal excitation frequency choice depends on the transducer’s transfer functions. Acknowledgements—This work is supported by Fondecyt (project No. 1040206), Chile, ECOS-Conicyt (project no C01E01)(Chile-France), Fondap (project No. 11980002) and Dicyt/USACH, Chile.
REFERENCES
Fig. 7. Cross-correlation envelope (Hilbert transform) of an intermediate echo Sij for various excitation frequencies: 1.0 (), 2.0 (●), 3.0 (‘), 4.0 (’), 5.0 (⽧) and 6.0 MHz (°) for a resonance frequency of res ⫽ 5 MHz.
Achenbach JD. Wave propagation in elastic solids. Amsterdam: NorthHolland, 1984. Ammann JJ, Galaz BA. Sound velocity determination in gel-based emulsions. Ultrasonics 2003;41:569 –579. Ammann JJ, Galaz BA, Hentzschel F. Tissue-mimicking materials assessment through ultrasound velocity measurement. In: Walker
Under-resonance sound velocity ● J-J. AMMANN et al. WF, Insana MF, eds. Ultrasonic imaging and signal processing. San Diego: SPIE-Medical Imaging 2003;5035:440 – 451. Bamber JC. Ultrasonic properties of tissues. In: Duck FA, Baker AC, Starrit HC, eds. Ultrasound in medicine. Bristol: Inst. of Physics, 1998;57– 88. Droin P, Berger G, Laugier P. Velocity dispersion of acoustic waves in cancellous bone. IEEE Trans Ultrason Ferroelec Freq Control 1988; 45:581–592. Hall TJ, Bilgen M, Insana MF, Krouskop TH. Phantom materials for elastography, IEEE Trans Ultrason Ferroelec Freq Control 1997; 44:1355–1365. Krautkrämer J, Krautkrämer H. Ultrasonic testing of materials. Berlin: Springer-Verlag, 1991. Kroebel W, Mahrt KH. Recent results of absolute sound velocity measurements in pure water and sea water at atmospheric pressure. Acustica 1976;35:154 –164.
491
Madsen EL, Dong F, Frank GR, et al. Interlaboratory comparison of ultrasonic backscatter, attenuation and speed measurements. J Ultrasound Med 1999;18:615– 631. Ophir J, Alam SK, Garra B, Kallel F, et al., Elastography: Ultrasonic estimation and imaging of the elastic properties of tissues. Proc Inst Mech Eng 1999;213:203–233. Papadakis EP. The measurement of ultrasonic velocity. In: Thurston RN, ed. Ultrasonic measurement methods, physical acoustic. Vol. 19. New York: Academic Press, 1990:107–155. Povey MJW. Ultrasonics in food engineering Part II: Applications. J Food Eng 1989;9:1–20. Selfridge AR. Approximate material properties in isotropic materials. IEEE Trans Son Ultrason 1985;SU-32:381–394. Truscott JG, Strekitzki R. Challenges in the ultrasonic measurement of bone. In: Duck FA, Baker AC, Starrit HC, eds. Ultrasound in medicine. Bristol: Inst. of Physics, 1998:287–306.
doi:10.1016/j.ultrasmedbio.2004.12.021
● Original Contribution ULTRASONIC SOUND VELOCITY MEASUREMENT IN SAMPLES OF SOFT MATERIALS THROUGH UNDER-RESONANCE EXCITATION JEAN-JACQUES AMMANN,*† VICTOR APABLAZA,* BELFOR GALAZ,* and CAROLINA FLORES* *Physics Department, Universidad de Santiago de Chile, Santiago, Chile; and †CIMAT, Santiago, Chile (Received 26 August 2004, revised 29 November 2004, accepted 17 December 2004)
Abstract—Ultrasound (US) velocity determination is a valuable characterization technique, providing important information on elastic properties of materials. Sound velocity can be obtained accurately in the pulsed method if the thickness of the specimen is precisely known. This is clearly not easily achievable for soft materials, such as biologic soft tissues or tissue-mimicking phantoms. From this consideration, previous works have established that sound velocity can be determined in through-transmission configuration without thickness measurement through the time-of-flight determination of specimen-reflected echoes in plane parallel-surfaced specimens. It is shown here that the amplitude and shape of these specimen echoes can be significantly improved by working in the tone-burst mode at an excitation frequency below the transducer resonance. This is particularly valuable for materials presenting a low acoustic contrast with the surrounding medium, usually water, such as tissuemimicking materials and water-based phantoms, making the specimen echo time-of-flights and, consequently, the sound velocity determination, more reliable. (E-mail: [email protected]) © 2005 World Federation for Ultrasound in Medicine & Biology. Key Words: Ultrasound, Sound velocity, Materials characterization, Gelatin, Tissue-mimicking materials.
values obtained by several recognized US laboratories on identical materials. If no explanation is proposed for this “unexpectedly large range of propagation speed,” thickness determination required by most evaluations is clearly a potential source of error for soft tissue–mimicking materials. Therefore, a new technique, based on a through-transmission configuration has been developed (Ammann et al. 2003; Ammann and Galaz 2003). This method, inspired by a previous work by Kroebel and Mahrt (1976) for determining sound velocity in liquid, substitutes the need for thickness measurement by the accurate measurement of the time-of-flight of the echoes generated by the reflection of the main pulse at the specimen surfaces, which must be plane and parallel. Indeed, while propagating from the excitation to the reception transducer in through-transmission configuration, the acoustic pulse is partially reflected at each of the two specimen surfaces (Fig. 1). This effect gives rise to the so-called intermediate or specimen echoes Sij appearing between the main successive transducers echoes E1 and E2 after being reflected back at the excitation transducer. The same scheme occurs for the main echo traveling toward the excitation transducer after being reflected at the reception
INTRODUCTION Elastic properties are of central interest for biologic tissue characterization and quantitative echography (Bamber 1998). Their potential significantly improved with the development of elastography as a new biomedical diagnostic tool (Hall et al. 1997; Ophir et al. 1999). The characterization of soft material elasticity is, therefore, of prime importance to correctly evaluate this new approach. Ultrasound (US) velocity measurement is a wellknown and efficient technique to access elastic coefficients of materials (Achenbach 1984). It is a relatively simple procedure, known for decades, and is performed by pulsed or continuous waves (Papadakis 1990). It usually requires the specimen thickness to be determined accurately by another way and is very accurate in hard materials such as ceramics and metallic alloys (Truscott and Strekitzki 1998). Surprisingly enough, however, a recent assessment of the velocity determination accuracy in tissue-mimicking specimens by Madsen et al. (1999) has pointed out a quite large variation (1.7%) among the Address correspondence to: Jean-Jacques Ammann, Physics Dept., Universidad de Santiago de Chile, Ecuador 3493, Santiago, Chile. E-mail: [email protected] 485
486
Ultrasound in Medicine and Biology
Fig. 1. Space-time plot of the burst propagation in the throughtransmission configuration with partial reflection at the specimen surfaces. The corresponding experimental RF trace in the lower part exhibits two main echoes (E1 and E2) (here truncated) and four intermediate echoes from a specimen presenting two parallel surfaces perpendicular to the acoustic beam.
transducer. In this way, each specimen surface produces, on the signal trace, a pair of intermediate echoes between two main transducer echoes. Echoes that undergo multiple reflections at the specimen surfaces are usually not observed on the radiofrequency (RF) trace when the medium and specimen exhibit similar acoustic impedances (Ammann et al. 2003) and will be neglected in the present study. By writing down the propagation equations of the echoes reflected at the specimen-medium interfaces according to Fig. 1, the sound velocity in the specimen cs can be written as a function of the respective time-offlight Ti, taking the sound velocity in the medium cw (here, water) as a reference:
冋
cs ⫽ cw 1 ⫹
册
2(TE2,ref ⫺ TE2) ⫺ (TE1,ref ⫺ TE1) , (1) 关(TSrf ⫺ TSef) ⫺ (TSeb ⫺ TSrb)兴
where the subscripts “e” and “r” denote that the specimen surface is facing the excitation or reception transducers, respectively, subscripts “f” and “b” stand for echoes reflected from a tone-burst propagating in the forward direction (toward the reception transducer) or
Volume 31, Number 4, 2005
backward direction (toward the excitation transducer), respectively, and the subscript “ref” refers to the main echoes of a reference trace obtained by removing the specimen from the acoustic path. Relying essentially on the intermediate echoes’ time-of-flight Tsij, the success of this method depends on a clear detection and characterization of these echoes. This aspect is particularly critical when the acoustic contrast between the specimen and the medium (usually water) is low, as it is commonly the case for biologic specimens or tissue-mimicking phantoms (Selfridge 1985). Indeed, in such cases, the impedance of the specimen is similar to that of the medium and the reflection coefficient of the medium/specimen interface is low. In such cases, the amplitude of the intermediate echoes is significantly reduced and the accuracy of the time-of-flight measurement is lowered by the electronic noise. To guarantee a reliable time-of-flight measurement, experimental conditions must be adequately selected. Although shock excitation is commonly used in pulseecho techniques, we are demonstrating here that working in the tone-burst mode offers significant advantages in through-transmission, when the intermediate echoes must be clearly observed. Additionally, this work evaluates the effects of excitation frequency on both amplitude and shape of the echoes and indicates a way to optimize the experimental parameters for reliable timeof-flight determination. If the specimen is assumed to present parallel surfaces, it is expected that the present method could account for a limited lack of parallelism of the surfaces and further studies are under way to address this point. The sound velocities determined according to the under-resonance condition are presented for gelatin specimens of various compositions. MATERIALS AND METHODS Experimental setup The through-transmission configuration adopted in this work consists in locating the specimen between a pair of facing coaxial transducers of similar frequency characteristics, here denominated excitation (E) and reception (R) transducers (Fig. 2) (Ammann and Galaz 2003). The whole system is immersed in a thermally controlled water-tank for accurate temperature control. The transducer spacing is significantly larger than the specimen, so that no contact occurs between the specimen and the transducers (stress-free condition), allowing a free alignment and positioning of the specimen along the acoustic beam. By keeping the specimen at a distance from the transducers equivalent to its near field limit, in our case 30 mm, this configuration also avoids any diffraction
Under-resonance sound velocity ● J-J. AMMANN et al.
Fig. 2. Through-transmission assembly, showing two coaxial excitation (E) and reception (R) transducers.
effect (Droin et al. 1988) and significantly reduces possible interference of the signal with transducer trailing noise. The excitation chain is composed of a signal generator (Wavetek, model 80, now Fluke Corp., Everett, WA) in sine burst mode attached to a power amplifier (ENI-325LA, ENI, Rochester, NY) that feeds the tone-burst signal to the 5-MHz broadband excitation transducer (Panametrics, Crescent St., Waltham, MA; 5.05-MHz peak frequency, 72.9% band width at ⫺6 dB and 6-mm diameter, quarter-wave matched), as illustrated in Fig. 2. The acquisition chain is composed of a similar broadband transducer (5.60 MHz peak frequency, 71.9% band width at ⫺6 dB) connected to a 500-MHz DSO oscilloscope (LT344, LeCroy, Chestnut Ridge, NY). Note that, considering the large band width of the transducers, the difference between the peak frequencies of the two excitation and reception transducers used here does not significantly affect the behavior of the described technique. The experimental RF trace obtained from the reception transducer is acquired at 500 MS/s. Triggering the oscilloscope on the signal delivered by the power amplifier allows a reliable and accurate averaging of the signal (100⫻) and a digitization at 11 bits before being transferred to a personal computer (PC) for processing. The length of the acoustic tone-burst can be chosen to narrow the frequency spectrum of the echoes and make them less sensitive to velocity dispersion. For transfer function determination, a Panametrics pulser-receiver (model 5800PR) is used in through-transmission mode feeding directly the excitation transducer (energy: 100 J, damping: 25 ⍀, gain: 40 dB) and delivering the amplified signal to the DSO. The specimen is fixed in a five degrees-of-freedom holder allowing accurate orientation and positioning along the ultrasonic beam. The two facing transducers, excitation (E) and reception (R), are mounted on an
487
independent support. After a convenient alignment of the specimen, the four intermediate echoes can be observed on the RF trace. Performing a slight shift of the specimen along the acoustic beam allows clear identification of the two forward echoes Sef and Srf shortening their time-offlight while increasing the distance between the specimen and the reception transducer; the backward echoes Seb and Srb behave in the opposite way. Then, having identified forward and backward echoes, Sef clearly reaches the reception transducer before Srf and Srb before Seb (refer to Fig. 1). An adequate positioning of the specimen along the acoustic beam allows avoiding a possible overlapping of some of the intermediate echoes on the RF trace. The velocity determination through eqn (1) relies exclusively on the time-of-flight difference of similar echoes (Ammann and Galaz 2003). This makes the cross-correlation processing a wise choice for determining the echo position on the time scale. In this processing, a segment of the RF trace containing one of the echoes to be analyzed is extracted and used as the crosscorrelation reference signal. Using the conventional method, the cross-correlation is performed on the whole trace and its envelope is obtained through the Hilbert transform (Ammann and Galaz 2003), exhibiting a single peak for each of the echoes. The time-of-flight of each echo is taken as the maximum of the corresponding peak and is determined with a resolution better than the sampling interval. Through-transmission transfer functions Because the transducers, medium and specimen have slightly different acoustic impedances, the acoustic tone-burst undergoes a partial reflection at each interface. After suffering two reflections, the tone-burst eventually reaches the reception transducer and is recorded on the RF trace. Ideally, at each transducer surface, the amplitude of the reflected and transmitted tone-bursts, ER and ET, respectively, are related to the incident wave Ei through the transmission and reflection coefficients of the transducer, TT() and TR(), respectively: ER ⫽ Ei ⫻ TR() and ET ⫽ Ei ⫻ TT(), with TR() ⫹ TT()⫽ 1. Due to the intrinsic behavior of the transducer, both TT() and TR() are strongly frequency-dependent close to the resonance frequency. In this context, the frequency-dependence of the transmission and reflection coefficients of the specimen, TST and TSR, respectively, can be considered to be negligible. In the scope of this paper, these parameters will be considered as constant and TST ⬇ 1 and TSR << 1. Then, the power spectrum of each echo can be related to the excitation signal E0 by considering the
488
Ultrasound in Medicine and Biology
Volume 31, Number 4, 2005
specific transmissions and reflections the tone-burst undergoes (Fig. 1), so: E1() ⫽ E0 ⫻ T2T(), E2() ⫽ E0 ⫻ T2T() ⫻ TR2() ⫽ E1() ⫻ TR2() Sij() ⫽ E0 ⫻ T2T() ⫻ TSR ⫻ TR() ⫽ E1 () ⫻ TR() (2a) with E1 ⫽ E1() ⫻ TSR
(2b)
Assuming a simple Gaussian model for the transmission transfer function of the transducers with a 0.9 maximum efficiency at res, Fig. 3 illustrates the major trends of the main and intermediate echo amplitudes. As expected, because the transmission transfer function (TT) is maximum at the resonance frequency res, the first main echo E1 goes through a strong maximum at res. However, the reflection transfer function TR is minimum at res and the echoes undergoing reflection at the transducer surfaces, both E2 and the intermediate echo Sij, present a relative minimum at that frequency, with two side maxima below and above the transducer resonance frequency (Fig. 3). It can be considered, therefore, that the signals undergoing reflections at the transducer surfaces suffer a significant “absorption” by part of the transducers, and their amplitude is strongly reduced at the resonance frequency. It is worth observing that the side maxima for the intermediate echoes Sij are closer to res and of higher amplitude than the second main echo E2. It can be shown, through a simple calculation based on the basic equations presented above, that the second main echo E2 goes through its maximum amplitude when the transmission transfer function is TT ⫽ 1/2. Similarly, intermediate echoes undergo one transducer reflection only and pass through their maximum when TT ⫽ 2/3. Then, the optimum choice of the working frequency, in the through-transmission configuration when main and intermediate echoes are to be observed, will be closely related to the shape of the transducer transfer functions. Materials The specimen material is prepared by adding from 4 to 15%wt gelatin (type B/225 Blum, Sigma) to distilled water at 60 to 70°C, using 0.02% sodium azide (Riedel de Haën, Seelze, Germany) as a fungus inhibitor. After homogenization, the gelatin is slowly cooled down, to allow possible air bubbles to escape, and gelified at room temperature. It is then liquefied at 40°C and poured in a mold built by fixing a PVC tube (30 mm in diameter ⫻ 20 mm long) on top of a glass plate. After gelling, the
Fig. 3. Gaussian model for the transducer transfer functions TT (—), TR ( · · · · ) and corresponding echoes spectrum of E1 (—–), E2 (- · - · - · ) and intermediate Sij (- · · - · · -).
glass plate is removed by gently heating its base, exposing two opposite free specimen surfaces. It is worth noting here that the specimen thickness does not appear explicitly in the sound velocity determination, eqn (1) but, on the contrary, can be deduced afterward through the generic relation ds ⫽ 1/2 cs⌬Ts. Therefore, the sound velocity measurement will not be affected, in this specific case, by a possible swelling of the gelatin, which represents a significant advantage of this approach. RESULTS AND DISCUSSION Transfer function and echo shape and amplitude The experimental aspect of the under-resonance improvement of sound velocity determination is illustrated on the water-based gelatin specimen. Gelatin being mostly composed of water (85 to 96 wt%), its impedance is expected to be close to the impedance of water (Povey 1989). When adequately aligned between the two transducers, the gelatin specimens exhibit an acoustic trace similar to the one shown in Fig. 1 with four specimen echoes bracketed between the main E1 and E2 transducer echoes. The amplitudes of the first and second main echoes (E1 and E2) are directly related through the transducer reflection function TR() that can be deduced from the frequency spectrum of these two echoes (Fig. 4): TR() ⫽
冑
E2 E1
(3a)
and TT() ⫽ 1 ⫺ TR.
(3b)
To determine TT() and TR() experimentally, a shock excitation, generated by the pulser-receiver, has
Under-resonance sound velocity ● J-J. AMMANN et al.
Fig. 4. Experimental transfer functions obtained through shock excitation TT (—), TR (- - - - - -) and echoes E1 (- · - · - · ) and E2 ( · · · · ).
been used. As expected, TT exhibits the characteristic resonance peak of the transducers. The top-hat–shaped maximum observed on the TT peak is due to the slightly different resonance frequencies of the two transducers (5.1 and 5.6 MHz), causing the maximum of each transfer function TTe and TTr to appear at slightly different frequencies. The E1 amplitude in eqn (2a), then becomes: E1 ⫽ E0 * TTe * TTr. As expected, the amplitude of the main echo E2 peaks below the resonance frequency at ⫽ 3.9 MHz, close to the predicted frequency for TR ⫽ 1/2 ( ⫽ 4.2 MHz). A similar behavior is observed at frequencies higher than res, in spite of additional distortion of the transfer functions due to higher harmonics. The effect of the TT transfer function on the E2 amplitude is illustrated in tone-burst mode in Fig. 5 for
Fig. 5. RF traces of the E2 main echo plotted against the excitation frequency. The peak-to-peak amplitude plot exhibits a clear depression around the transducer resonance frequency (res ⫽ 5 MHz).
489
Fig. 6. Frequency spectra of the second main echo E2 as a function of excitation frequency. A deep depression appears at the transducer resonance frequency independently of exc, significantly altering the main lobe of the Fourier transforms of tonebursts emitted close to the transducer frequency (frequencies in MHz). The frame indicates the spectrum location corresponding to an excitation at the transducer resonance frequency.
excitation frequencies between 2.0 and 7.0 MHz. This figure shows that the overall shape of the E2 echo is significantly distorted and depressed when the excitation frequency is close to res; here, 5 MHz. This is highlighted by the superimposed peak-to-peak plot of E2 amplitude, exhibiting a clear minimum at the transducer resonance frequency. Close to the resonance frequency, the transducer transfer function TR presents a narrow minimum and the E2 echo frequency spectrum, modulated by TR, is highly distorted. Indeed, when looking at the power spectra of E2 taken at several excitation frequencies exc (Fig. 6), the alteration due to the transducer appears as a deep trench at res. The distortion is critical when altering the main lobe of the tone-burst Fourier transform, reflecting the distortion of the tone-burst shape observed in Fig. 5. Introducing a specimen between the transducers produces intermediate echoes on the RF trace (Fig. 1). The effects of the transducer transfer function on the shape and amplitude of these intermediate echoes are similar to the ones described above. However, because they undergo only one reflection at a transducer surface, the alteration introduced on their shape is reduced; see eqn (1). The time-of-flight and sound velocity The time-of-flight determination is performed by selecting the maximum of the echo cross-correlation envelope obtained through the Hilbert transform. The cross-correlation envelope of an intermediate echo using a different intermediate echo as reference is exhibited in
490
Ultrasound in Medicine and Biology
Fig. 7, for various excitation frequencies between 1.0 and 6.0 MHz. Clearly, the maximum of the cross-correlation envelope is obtained for frequencies under the transducer resonance frequency; here, this is 4 MHz for res of 5 MHz. Additionally, the smoothness and symmetry of the Hilbert peak decrease significantly under and above 4 MHz, degrading the accuracy and reliability of the time-of-flight determination. For the optimal condition (exc ⬇ 4 MHz), the time-of-flight is determined with a precision close to the sampling interval (2 ns). As mentioned above, the optimum excitation frequencies for the second main echo and the intermediate specimen echoes depend on the transducer transfer function. Determined on a trial basis, it corresponds, in this case, to exc ⫽ 0.8 res. The sound velocity has been determined using the presented method in eqn (1) at exc ⫽ 4 MHz and, according to the experimental conditions discussed in this paper, is presented below for gelatin of 4, 6, 10 and 15 wt%. Sound velocity in water cw is taken as 1482 m/s for a temperature stabilized at 20.0°C (Krautkrämer and Krautkrämer 1991). An experimental trace appears in Fig. 1, and Fig. 8 exhibits the linear dependency of the sound velocity cs against the gelatin weight content C%: cs ⫽ cgel ⫽ cw ⫹ 3.56 C%
(4)
Although the method does not require the determination of the specimen thickness, it is still affected by the lack of parallelism of the specimen faces, and additional studies are underway to assess this important issue and possibly to account for this effect.
Volume 31, Number 4, 2005
Fig. 8. Sound velocity in gelatin specimen as a function of weight concentration.
SUMMARY Soft-tissue–mimicking materials often have uncertainties in thickness that introduce inaccuracy in traditional acoustic velocity measurements. It has been shown that using the specimen-induced intermediate echoes in the through-transmission configuration allows determination of the sound velocity in plane parallel-sided samples without requiring determination of the specimen thickness. However, the acoustic impedance of these materials being similar to that of water, commonly used as measurement medium, makes both the detection of intermediate echoes and the accurate measurement of their timeof-flight more difficult. Working in tone-burst mode at an excitation frequency lower than the transducer resonance frequency significantly improves the amplitude of the specimen and transducer echoes. In addition, the shape of the echoes is better preserved and the time-of-flight determination performed by cross-correlation and the Hilbert transform is made more efficient and reliable. Time-of-flight precisions similar to the digitizing interval of the acquisition chain are achieved, significantly improving the sound velocity measurement accuracy. The optimal excitation frequency choice depends on the transducer’s transfer functions. Acknowledgements—This work is supported by Fondecyt (project No. 1040206), Chile, ECOS-Conicyt (project no C01E01)(Chile-France), Fondap (project No. 11980002) and Dicyt/USACH, Chile.
REFERENCES
Fig. 7. Cross-correlation envelope (Hilbert transform) of an intermediate echo Sij for various excitation frequencies: 1.0 (), 2.0 (●), 3.0 (‘), 4.0 (’), 5.0 (⽧) and 6.0 MHz (°) for a resonance frequency of res ⫽ 5 MHz.
Achenbach JD. Wave propagation in elastic solids. Amsterdam: NorthHolland, 1984. Ammann JJ, Galaz BA. Sound velocity determination in gel-based emulsions. Ultrasonics 2003;41:569 –579. Ammann JJ, Galaz BA, Hentzschel F. Tissue-mimicking materials assessment through ultrasound velocity measurement. In: Walker
Under-resonance sound velocity ● J-J. AMMANN et al. WF, Insana MF, eds. Ultrasonic imaging and signal processing. San Diego: SPIE-Medical Imaging 2003;5035:440 – 451. Bamber JC. Ultrasonic properties of tissues. In: Duck FA, Baker AC, Starrit HC, eds. Ultrasound in medicine. Bristol: Inst. of Physics, 1998;57– 88. Droin P, Berger G, Laugier P. Velocity dispersion of acoustic waves in cancellous bone. IEEE Trans Ultrason Ferroelec Freq Control 1988; 45:581–592. Hall TJ, Bilgen M, Insana MF, Krouskop TH. Phantom materials for elastography, IEEE Trans Ultrason Ferroelec Freq Control 1997; 44:1355–1365. Krautkrämer J, Krautkrämer H. Ultrasonic testing of materials. Berlin: Springer-Verlag, 1991. Kroebel W, Mahrt KH. Recent results of absolute sound velocity measurements in pure water and sea water at atmospheric pressure. Acustica 1976;35:154 –164.
491
Madsen EL, Dong F, Frank GR, et al. Interlaboratory comparison of ultrasonic backscatter, attenuation and speed measurements. J Ultrasound Med 1999;18:615– 631. Ophir J, Alam SK, Garra B, Kallel F, et al., Elastography: Ultrasonic estimation and imaging of the elastic properties of tissues. Proc Inst Mech Eng 1999;213:203–233. Papadakis EP. The measurement of ultrasonic velocity. In: Thurston RN, ed. Ultrasonic measurement methods, physical acoustic. Vol. 19. New York: Academic Press, 1990:107–155. Povey MJW. Ultrasonics in food engineering Part II: Applications. J Food Eng 1989;9:1–20. Selfridge AR. Approximate material properties in isotropic materials. IEEE Trans Son Ultrason 1985;SU-32:381–394. Truscott JG, Strekitzki R. Challenges in the ultrasonic measurement of bone. In: Duck FA, Baker AC, Starrit HC, eds. Ultrasound in medicine. Bristol: Inst. of Physics, 1998:287–306.