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Acoustic speed and attenuation coefficient in sheep aorta measured at 5-9 MHz
Ultrasound in Med. & Biol., Vol. 32, No. 6, pp. 971–980, 2006 Copyright © 2006 World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/06/$–see front matter
doi:10.1016/j.ultrasmedbio.2006.02.1417
● Original Contribution ACOUSTIC SPEED AND ATTENUATION COEFFICIENT IN SHEEP AORTA MEASURED AT 5-9 MHZ KATHARINE H. FRASER,* TAMIE L. POEPPING,* ALAN MCNEILLY,† IAN L. MEGSON,‡ and PETER R. HOSKINS* *Medical Physics; †MRC Human Reproductive Sciences Unit; and ‡Centre for Cardiovascular Science, University of Edinburgh, Edinburgh, Scotland (Received 19 September 2005, revised 23 January 2006, in final form 2 February 2006)
Abstract—B-mode ultrasound (US) images from blood vessels in vivo differ significantly from vascular flow phantom images. Phantoms with acoustic properties more closely matched to those of in vivo arteries may give better images. A method was developed for measuring the speed and attenuation coefficient of US over the range 5 to 9 MHz in samples of sheep aorta using a pulse-echo technique. The times-of-flight method was used with envelope functions to identify the reference points. The method was tested with samples of tissue-mimicking material of known acoustic properties. The tissue samples were stored in Krebs physiologic buffer solution and measured over a range of temperatures. At 37°C, the acoustic speed and attenuation coefficient as a function of frequency in MHz were 1600 ⴞ 50 ms–1 and 1.5 ⴞ 4f 0.94 ⴞ 1.3 dB cm–1, respectively. (E-mail: kate.fraser@ ed.ac.uk) © 2006 World Federation for Ultrasound in Medicine & Biology. Key Words: Acoustic speed, Attenuation coefficient, Scanning acoustic macroscope, Artery, Aorta, B-mode, Phantom, Segmentation.
geometry can be patient-specific and obtained from a 3-D image dataset. To create the 3-D surface geometry of the vessel, the relevant shape must be marked out, or segmented from, the 3-D image data. This segmentation is challenging in US imaging due to both the nonisotropic nature of the image and the presence of speckling. Validation of segmentation using a phantom is desirable. The authors’ experience of using a conventional wallless phantom for this purpose is that the vessel edge may easily be identified at the points of perpendicular insonation as expected, but, unlike the in vivo scenario, the lateral locations of the wall are also easily identified. This indicates that the image from such a phantom is not representative of an image from a human artery and that it provides limited information when used to test the effectiveness of vessel segmentation routines. One possibility is that, in real arteries, there is a mismatch in acoustic velocity between the arterial wall and the blood. If this is the case, then vascular phantom design for B-mode imaging should ideally reproduce this mismatch. The aim of this study is to provide information on acoustic properties of arteries to inform the design of a vascular phantom suitable for B-mode imaging. To build such a phantom, it is necessary to know the acoustic properties of arteries at the frequencies used in clinical US scanners and in conditions found in vivo.
INTRODUCTION Vascular ultrasound (US) phantoms have mostly been used in studies testing the accuracy of velocity measurements made using Doppler US. Previously reported Doppler phantoms use either a thin-walled vessel (Poepping et al. 2004) or are wall-less (Ramnarine et al. 2001). Although much effort has been expended on the design and characterisation of these phantoms for Doppler US studies, phantom design for B-mode studies has received little attention. When imaged in cross-section, B-mode images of arteries in humans demonstrate a bright echo at the points on the wall nearest to and furthest from the transducer, that is, the points of perpendicular insonation, with substantial loss of image quality at the lateral borders. This nonisotropic image appearance makes it difficult to identify the vessel boundary. Vessel geometry is of interest in, for example, image-guided modelling, where a computational model of blood flow is used to provide three-dimensional (3-D) time-varying flow field data (Glor et al. 2005). This requires specification of boundary conditions, usually the 3-D surface geometry of the vessel along with inlet and outlet flow. The surface Address correspondence to: Katharine H. Fraser, The Chancellor’s Building, 49 Little France Crescent, Edinburgh, EH16 4SB, Scotland. E-mail: [email protected] 971
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There have been many measurements of acoustic properties of different tissues summarized in the comprehensive work by Duck (1990), as well as Goss et al. (1978, 1980) and Chivers and Parry (1978), updated in Hill et al. (2004), and some more recent studies on blood vessels at intravascular US frequencies, for example (Lockwood et al. 1991; Marsh et al. 2004). However, few groups have studied blood vessels at transcutaneous frequencies. Greenleaf et al. (1974, 1975) recorded transmitted, reflected and scattered 10 MHz US in diseased human vessels using a scanning system. Their samples were placed between lucite blocks, enabling the sample thickness to be measured accurately but not allowing for variation in thickness across the sample. Shung and Reid (1978) and Geleskie and Shung (1982) measured the velocity at 22°C in bovine blood vessels using aluminium buffer rods as a solid transmission medium for 5 MHz US. Again, the solid rods did not allow for variation in thickness across the sample. Hughes and Snyder (1980) measured the speed of 10 MHz US in dog aorta over a range of temperatures, both in Ringer’s lactate solution and fixed with formalin. Rooney et al. (1982) studied velocity and attenuation in human and canine arteries at 37°C, taking measurements at 20 to 30 sites in each of 17 arteries. They attribute the dominant error in their technique to the precision (⫾0.1 mm) of the tissue thickness measurement, for which they used calipers. In this work, a method was developed for measuring the acoustic speed and attenuation coefficient of thin tissue samples without the need for a separate tool to measure thickness. Similar methods have been used by others (Geleskie and Shung 1982; Hughes and Snyder 1980; Shung and Reid 1978), but these papers do not describe from which part of the waveform they measured their times. The pulse shape is distorted as it propagates through the medium and sample (Hill et al. 2004), which can lead to errors in time measurements, depending on which point in the waveform is used. In the work described, this error has been minimised by using an envelope function. The thickness is then measured at the same sample site as that at which the acoustic speed and attenuation coefficient data are recorded, thus also minimising error. The method was tested by measuring the properties of thin samples of tissue-mimicking material (TMM) and then used to measure the acoustic speed and attenuation coefficient of samples of sheep aorta. MATERIALS AND METHODS Measurement of Sample Thickness, Acoustic Speed and Attenuation Coefficient The acoustic speed and attenuation coefficient of the samples were measured using the pulse-echo substitution method (Browne et al. 2003), with the incorpora-
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Fig. 1. Distances involved in calculations.
tion of the times-of-flight (TOF) method (Kuo et al. 1990) to measure the sample thickness. All measurements were made using a scanning acoustic macroscope (SAM) (Ultrasonic Sciences Limited, Fleet, UK) (Foster et al. 1984; Moran et al. 1995). The SAM allows measurements to be made over a defined area of the sample for spatial averaging. The SAM system comprised an 8-bit, 100-MHz, analog-to-digital input/output personal computer (PC) board, a 1- to 20 MHz pulse receiver and a stepper motor control system, all controlled by a PC. One transducer acted as both transmitter and receiver, and the pulse was transmitted through the surrounding medium, either deionized water or Krebs, a solution that contains all nutrients required to keep cells alive for several days, and reflected from a highly-polished flat steel plate. The centre frequency of the transducer was 7 MHz, the 6 dB bandwidth was 71%, the focal length was 50 mm, the crystal diameter was 11.8 mm and the – 6 dB diameter at the focal length was 0.86 mm. An area of 16 ⫻ 15.5 mm was scanned in increments of 1 ⫻ 0.5 mm. At each position, the reflected radio-frequency signal from the steel reflector was digitised at a sampling rate of 100 MHz and stored for offline analysis. Each sample required three scans: a reference scan, which was a scan without the sample; a sample scan; and a reflection scan, which was to detect the small signals reflected from the interfaces of the sample and the medium. The difference in apparatus for these scans is shown in Fig. 1. The driving voltage was set at the relatively low value of 100 V (Browne et al. 2003) to minimise nonlinear propagation effects (Zeqiri 1992) for both the reference scan and sample scan, whereas for the reflection scan, it was 300 V, which allowed the much smaller signals to be located. The signals were analysed using in-house code developed in MATLAB (MathWorks Inc., Natick, MA, USA). Example signals are shown in Fig. 2. With a very large signal-to-noise ratio, the times TS, the return time to the reflector with the sample, and TR, the return time to
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the nonlinearly-generated harmonics and the fundamental causes the change in pulse shape. Reference points on the pulse that use thresholding result in errors in the TOF measurement as a result of frequency-dependent attenuation (Weir 2001) but, by using an envelope function, the reference point is unaffected by these changes in signal shape. The susceptibility of the envelope function to changes in the pulse shape due to nonlinear propagation was assessed by examining the position of the reference point with respect to the predicted position as the propagation distance was increased. The effect was found to be negligible because the mean error was ⬍0.1 mm, the accuracy to which the distances could be measured. The sample thickness, dS, was calculated from VK, the acoustic speed in the immersion medium, TR, TS, T1 and T2:
Reference
Sample
dS ⫽ dT ⫺ d1 ⫺ d2 ⫽
Reflection
T
1
T
2
T
S
T
R
Fig. 2. The three signals required: reference, sample and reflection and the time points needed for thickness and speed calculations. Signals are shown with solid lines, signal envelopes are shown in dashed lines and dotted lines show the time points required for thickness and acoustic speed calculations. The reflection signal is used to obtain times T1 and T2, the reflections from the upper and lower surfaces of the sample, respectively. The sample signal is used to obtain TS, the reflection from the highly-polished reflector in the presence of the sample, and the reference signal is used to obtain TR, the reflection from the highly-polished reflector without the sample.
the reflector without the sample, were easy to define. Butterworth filters were applied to the sample and reference signals and the peak amplitudes of these filtered signals were used as the reference points. The times T1, the return time to the upper surface of the sample, and T2, the return time to the lower surface of the sample, were harder to define because the signal-to-noise ratios at these times were small. The short-time Fourier transform of the reflection signal was taken with an interval of 0.32 s and used to plot the magnitude of the signal at 7 MHz (centre frequency of the transducer). The peaks in this plot of the signal power at 7 MHz were then used to define times T1 and T2. The two main effects that cause the pulse shape to change are frequency-dependent attenuation and nonlinear propagation (Hill et al. 2004). Higher frequencies are attenuated more, thus narrowing the bandwidth and causing the signal to lengthen in time. In nonlinear propagation, the phase relationship between
VK T ⫺ T1 ⫺ TS ⫹ T2兲 2共 r
(1)
where dT is the distance from transducer to reflector, d1 is the distance from transducer to upper sample surface and d2 is the distance from lower sample surface to reflector (Kuo et al. 1990). These distances are shown in Fig 1. The acoustic speed in the sample VS was then calculated as: VS ⫽
2dS T2 ⫺ T1
(2)
The acoustic speed was calculated for all 496 locations in the 16 ⫻ 15.5-mm scan area and the mean of these was calculated to obtain the sample acoustic speed. When measuring the attenuation coefficient of samples by the insertion technique, power is also lost through reflection at the tissue-medium interfaces, and this is included in the attenuation coefficient measurement (Hill et al. 2004). These insertion losses, compared with the attenuation due to absorption and scattering, will be relatively larger in thin samples than in thicker ones. By considering the geometry of the apparatus and using equations for transmission and attenuation, an equation for the attenuation coefficient including interface losses was derived. If I is the incident intensity, T is the intensity transmitted at an interface between two media with impedances z1 and z2, and A is the intensity after attenuation through a medium with thickness d and attenuation coefficient ␣, then
冉 冊
2z2 T ⫽ I z1 ⫹ z2
A ⫽ 10⫺d␣⁄10. I
2
(3)
Accounting for transmission at all four interfaces gives
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the following equation for the intensity transmitted after the return journey through the sample of thickness dS: T4 ⫽ I
冉
冉
256z14z24 共z1⫹z2兲8 attenuation coefficient:
Setting K ⫽
冊
256z14z24 10⫺2dS␣⁄10. 共z1 ⫹ z2兲8
冊
␣共 f 兲 ⫽
(4)
leads to an equation for the
IK 10 log10 . 2dS T4
(5)
The reference and sample signals were fast-Fouriertransformed to give their frequency spectra, which were then squared to give I and T4. Acoustic impedances z1 and z2 were calculated using VK and VS as above, density of the medium K ⫽ 1016 kg m–3 and density of the sample, S ⫽ 1062 kg m–3 (Shung and Reid 1978). The attenuation coefficient of the sample was the mean of the attenuation coefficients at each location in the scan area. Preparation and Measurement of Acoustic Speed of Krebs Solution To prevent alteration in acoustic properties postmortem, the aorta were stored in Krebs solution. This provided all nutrients necessary to keep the cells alive for a few days when refrigerated and consisted of NaCl 118 mM, d-glucose 5.6 mM, HEPES 25 mM, KCl 4.7 mM, MgSO4.7H2O 1.18 mM, KH2PO4 1.18 mM, CaCl2.2H2O 2.5 mM and penicillin 2 M units l⫺1. To contract the smooth muscle cells, 4.7 mM KCl was replaced with 118 mM KCl to make a high potassium ion (K⫹) Krebs solution. For the pulse-echo technique, it is necessary to know the acoustic velocity in the medium surrounding the sample, that is, the Krebs solution. This was determined using the pulse-echo technique described above and with a fluid cell containing Krebs solution immersed in a tank of degassed, deionized water. The acoustic speed of the water used was a function of temperature and is given by Bilaniuk and Wong (1993, 1996). To degas the solution, it was made the day before the experiments and refrigerated overnight. Measurements were made over the temperature range 6 to 42°C and, to test for batch-to-batch variability, three different batches were tested. The acoustic velocity in the high K⫹ Krebs was assumed to be the same as in the standard Krebs, within measurement error. Test Samples The above method for calculating sample thickness, acoustic speed and attenuation coefficient was tested on three samples of TMM. The TMM was an agar-based material made as described by Ramnarine et al. (2001) and it was then poured into three flat dishes to different
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depths to create three thin samples (0.8 to 1.5 mm) with three different uniform thicknesses. After solidifying, the samples were covered with a layer of 10% glycerol in water solution (to prevent them drying out or the glycerol diffusing out) and stored at room temperature. Measurements of thickness, acoustic speed and attenuation coefficient were made as described above, using deionized water as the medium. The water was degassed by boiling and left overnight to cool to room temperature. The TMM samples were kept in water for the minimum time to minimise diffusion of glycerol out of them, which would reduce the acoustic speed. After measuring the acoustic properties, the thickness of each of the thin samples was measured at 40 different points using calipers (error ⫽ ⫾0.01 mm). Aorta Samples The aorta samples were obtained immediately after death from the abdominal section of freshly excised sheep aortas obtained from sheep killed with an overdose of sodium pentobarbitone (Euthetal; Rhone-Merieux Ltd., Harlow, Essex, UK) at the Marshall Building, Roslin, Edinburgh, UK. The procedures were conducted in accordance with the Home Office Animals (Scientific Procedures) Act 1996 of the United Kingdom. Each aorta was dissected and immediately placed in Krebs solution for transport to the laboratory. All experiments were carried out within 7 h of the excision, with the exception of the experiment to determine the effects of storage, which took 9 h. The aortas were cleaned of connective tissue and fat, cut into ⬇3 cm lengths and sliced open longitudinally. Each sample was spread flat with the inner endothelium uppermost and attached to a stainless steel ring (inner diameter 31 mm, outer diameter 54 mm, thickness 2 mm). A needle was used to push a piece of sewing thread through each corner of the sample at the point where the sample overlapped the ring and these threads were then knotted onto the ring. It was then impossible to increase the tension in the tissue, as either the sample or thread would slip back to its original position. The ring was on top of the sample and this weighed it down while in the solution, held it flat and enabled easy handling. Altogether, 25 samples were obtained from 15 aortas. Fresh samples at room temperature. Eight samples from six aortas were measured fresh and at room temperature (20 to 22°C). One sample was excluded from further analysis because it was visually observed to be calcified severely, leaving a total of seven samples. The attenuation coefficient of this diseased sample was above 60 dB cm–1. Comparison with Greenleaf et al. (1974), who reported the attenuation coefficient of calcified le-
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sions to be above 45 dB cm–1, confirms that it was calcified. Effect of storage on the acoustic properties. The possibility of change in properties, acoustic speed and attenuation coefficient in the aorta over storage time was investigated with further studies on four samples from above. After the first measurement, these were stored in the refrigerator to minimise degradation and then placed in the room temperature solution before being scanned. A simple calculation was performed to determine how long the samples should be left to equilibrate to room temperature. Because the Biot number—the nondimensional ratio of convection to conduction—is small, the lumped capacitance method can be used to solve the transient conduction problem (Incropera and de Witt 1990) and can be shown that the time taken for the sample to reach a final temperature TF is given by:
冉
t ⫽ ⫺ln
冊
TF ⫺ To kd . TF ⫺ To ␣h
(6)
where TF is the final tissue temperature, To is the temperature of the Krebs solution, T1 is the initial tissue temperature, k is the thermal conductivity, d is the sample thickness, ␣ is the thermal diffusivity and h is the convective heat transfer coefficient. For TF ⫽ 21.01°C, To ⫽ 21.0°C, T1 ⫽ 6°C, k ⫽ 0.476 W m⫺1 K–1 (Duck 1990), d ⫽ 1 mm, ␣ ⫽ 0.127 m 2 s ⫺ 1 (Duck 1990) and h of the order 50 W m –2 K –1 (Incropera and De Witt 1990), the time taken is of the order of 1 ms. The sample was left to equilibrate for 10 min to be certain. Each sample was measured three or four times over 5.4 h. Effect of contraction on acoustic properties. Because arteries in vivo spend much of their time contracted, the properties of contracted aorta were examined by placing samples directly into high K⫹ Krebs solution after excision. When the K⫹ concentration is increased, K⫹ is driven into the cell, upsetting the ionic intracellular concentration. The membrane potential depolarizes, becoming more positive, because of the increase in positive charge inside the cell. Depolarisation of the membrane opens voltage sensitive Ca2⫹ channels in the cell membrane, which allows Ca2⫹ to flow from its higher concentration outside the cells to the lower concentration inside. Ca2⫹ is essential for contraction because it causes phosphorylation of critical proteins in the contractile machinery through activation of myosin light-chain kinase. The artery samples were stored in this high K⫹ Krebs solution for transport to the laboratory and then immersed in fresh high K⫹ Krebs solution during measurements. Five samples from three aortas were studied at room temperature (20 to 22°C). The results from these
Fig. 3. Acoustic speed in Krebs solution for temperatures 5 to 45°C. Error bars on the data points are the standard deviations in these measurements. The data were fitted with a quadratic VK ⫽ 1426 ⫹ 4.109t ⫺ 0.03312t2 and the 95% confidence intervals for this fit are shown with dashed lines. The acoustic speed in pure water is shown as a dotted line (Bilaniuk and Wong 1993, 1996).
samples were then compared with those from the fresh samples at room temperature. Effect of temperature on acoustic properties. In addition to the samples measured at room temperature, six samples, two from each of three aortas, were measured both at refrigerator temperature (6 to 11°C) and at body temperature (36 to 41°C). Because body temperature is of greater interest and relevancy, a further four samples were measured only at this temperature. These results, obtained at different temperatures, were then compared with the fresh samples at room temperature. RESULTS Krebs Solution Figure 3 shows the variation of acoustic speed in Krebs with temperature. Each data point is the mean acoustic speed of the 496 measurements in the scan and the error bars give the standard deviation. Measurements from all three batches of the solution were plotted and fit to a quadratic, VK ⫽ 1426 ⫹ 4.109t ⫺ 0.03312t2, using MATLAB (Mathworks, Inc.). Also plotted are the 95% confidence intervals for this quadratic fit and the acoustic speed in water as measured by Bilaniuk and Wong (1993, 1996). Test samples. Thicknesses of the three TMM test samples measured ultrasonically were (mean ⫾ standard deviation (SD)): 0.88 ⫾ 0.05, 1.24 ⫾ 0.05 and 1.50 ⫾ 0.05 mm.
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20 18
attenuation /dB cm
−1
16 14 12 10 8 6 4 2 0 5
5.5
6
6.5
7
7.5
8
8.5
9
frequency /MHz
Fig. 4. Variation in sample attenuation coefficient with frequency at room temperature. Data points represent the mean of measurements made on seven samples, and the error bars are the standard deviation in this mean; every fifth point has been plotted for clarity. An exponential was fitted to the mean, ␣ ⫽ 0.35f1.7 and this fit is shown with the solid line.
These are well within the standard deviations of the thicknesses measured using calipers (mean ⫾ SD): 0.79 ⫾ 0.20, 1.27 ⫾ 0.25 and 1.62 ⫾ 0.20 mm. The acoustic speeds were (mean ⫾ SD) 1538 ⫾ 8, 1559 ⫾ 8 and 1544 ⫾ 5 m s–1, which are within 18 m s–1 of the value 1541 ⫾ 3 m s–1 given by (Ramnarine et al. 2001) and so imply a measurement error of 1%. The attenuation coefficient measured in the three samples over the range 5 to 9 MHz was 0.52f ⫹ 0.58, 0.58f ⫹ 0.28 and 0.54f ⫹ 0.10 dB cm–1, where f is the frequency in MHz. Comparison with the published value for this TMM given by Ramnarine et al. (2001), 0.50f ⫹ 0.00 dB cm–1, shows there is a 24% measurement error at 7 MHz. Sheep Aorta Fresh samples at room temperature. Figure 4 shows the mean variation in attenuation coefficient for seven samples measured fresh and at room temperature (mean ⫾ SD ⫽ 20.9 ⫾ 0.6°C) and the exponential fit (␣ ⫽ 0.35f1.7) to these data. The exponent of the frequency is
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1.7, which is 70% larger than the value of 1, which is often assumed for soft tissues but is within the range of values for all soft tissues (Duck 1990). Although the range of frequencies used in this study was 5 to 9 MHz, the empirical fit can be extrapolated for the purposes of comparison with published data and the value of the attenuation coefficient at 10 MHz is found to be 17.5 dB cm–1. This is almost three times the 6.1 dB cm–1 reported by Greenleaf et al. (1974) for normal human aorta. The acoustic speed results for the seven samples measured at room temperature and considered to be normal and nonpathologic are shown in Table 1. The mean acoustic speed, 1570 m s–1, is 4% higher than that reported for the human aorta by Greenleaf et al. (1974), which was 1501 m s–1, is 1.6% higher than the 1545 m s–1 reported by Hughes and Snyder (1980) for canine aorta, but is just 0.3% lower than the value 1575.3 m s–1 found by Geleskie and Shung (1982) in bovine aorta. Effect of storage on the acoustic properties. Figure 5 shows the mean attenuation coefficient at 7 MHz in each sample and the time at which it was measured. Paired t-tests on the differences in attenuation coefficient between first and second measurements (p ⫽ 0.5), second and third measurements (p ⫽ 0.5) and first and third measurements (p ⫽ 0.5) show there is no significant change in the attenuation coefficient of the samples over the time period investigated. In addition, the variation in attenuation coefficient with frequency did not change with time, being approximately linear for each sample and at each time (if ␣ ⫽ af b, b is (mean ⫾ SD) 1.3 ⫾ 0.3). Figure 6 shows the mean acoustic speed in each sample and the time at which it was measured. The acoustic speed increases with storage time and a linear best fit to the normal nondiseased samples was produced with VS ⫽ 1549t ⫹ 0.0534t2, where t is in minutes. Paired t-tests on the difference in acoustic speed between first and second measurements (p ⫽ 0.5), second and third measurements (p ⫽ 0.1) and first and third measurements (p ⫽ 0.05) show that the acoustic speed differences up to the time of the second measurements (270 min) are insignificant, whereas later measurements show a significant change in the samples. These results suggest
Table 1. Summary of acoustic properties Acoustic speed /m s⫺1
Relaxed samples at room temperature (21°C) High K⫹ samples at room temperature (21°C) Relaxed samples at body temperature (37°C)
Attenuation coefficient at 7 MHz/dB cm⫺1
Samples
Mean ⫾ SD
Range
Mean ⫾ SD
Range
7 5 10
1570 ⫾ 30 1578 ⫾ 9 1600 ⫾ 50
1550–1600 1570–1590 1550–1670
9⫾2 8⫾3 9⫾3
6–12 6–14 3–14
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Effect of contraction on acoustic properties. The effect of contraction on the acoustic properties was determined by placing five samples from three aortas in Krebs solution with 128 mM K⫹, rather than the standard 4.7 mM, which caused the smooth muscle cells to contract. The acoustic properties of the contracted samples are given in Table 1 and can be compared with the fresh room-temperature samples. These results showed that, although the arteries were visually observed to contract and were noticeably stiffer during handling, the differences in the acoustic properties of the contracted and relaxed samples were not significant (Student’s t-tests for speed (p ⫽ 0.5) and attenuation coefficient (p ⫽ 0.5)).
140
attenuation /dB cm
−1
120 100 80 60 40 20 0 50
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100
150
200
250
300
350
400
450
time /minutes
Fig. 5. Variation in sample attenuation coefficient at 7 MHz with storage time. Each data point is the mean of all measurements in that sample scan, and error bars show the standard deviation in these means. The four different samples are represented by different symbols: cross, triangle, diamond and circle. The sample represented by the diamond is the diseased one.
that the Krebs solution maintained the samples for 4.5 h. Wilhjelm et al. (1997) and Bamber et al. (1979) found that some tissue preservation methods affected the acoustic properties, although Hughes and Snyder (1980) found that Ringer’s solution preserved their samples for 24 h.
Effect of temperature on acoustic properties. Figure 7 shows the variation in acoustic speed with temperature. A quadratic function was fitted to the data, VS ⫽ 1363 ⫹ 13.5T ⫺ 0.186T2, and this is shown along with the 95% confidence intervals. Comparison of the results in Table 1 shows the increase in acoustic speed for the body temperature samples compared with those at room temperature (mean ⫾ SD ⫽ 20.9 ⫾ 0.6°C). These results can be compared with those of Hughes and Snyder (1980), who found the acoustic speed in their canine aorta samples increased linearly from 1545 ⫾ 8 m s–1 at 23°C to 1590 ⫾ 10 m s⫺1 at 37° C. Figure 8 shows the results of the attenuation coefficient measurements over the range of temperatures. Although a linear best fit shows a small increase in attenuation coefficient with temperature (linear fit: VS ⫽ 7.1 ⫹ 0.063T), a paired t-test comparing samples at refrigerator and body temperatures showed that the difference in attenuation coefficient is not sig-
1800
1750 1700 1650 −1
1700
1650
speed /m s
speed /m s−1
1750
1600
1600 1550 1500 1450
1550
1400 1500 50
100
150
200
250
300
350
400
450
time /minutes
Fig. 6. Variation in acoustic speed with storage time. Each data point is the mean of all measurements in that sample scan, and error bars show the standard deviation in these means. The four different samples are represented by different symbols: cross, triangle, diamond and circle. The sample represented by the diamond is the diseased one. The normal nondiseased data points were fitted to a straight line, VS ⫽ 1549t ⫹ 0.0534t2, where t is in min, which is shown dashed on the graph.
1350 1300 5
10
15
20
25
30
35
40
o
temperature / C
Fig. 7. Variation in acoustic speed with sample temperature. Each data point is the mean of all measurements in that sample scan, and error bars show the standard deviation in these means. The data were fit to a quadratic, VS ⫽ 1363 ⫹ 13.5T ⫺ 0.186T2, and the dashed lines show the 95% confidence intervals for this fit.
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(Duck 1990). Six of the samples studied at body temperature were first studied at refrigerator temperature and so had been cooled before being heated to body temperature, whereas the other four samples were only measured at body temperature. There were no significant differences in either the acoustic speed or attenuation coefficient between these groups (p ⫽ 0.5 for both).
30 25 20 15 10
DISCUSSION
5
A method was developed for measuring the acoustic speed and attenuation coefficient in thin tissue samples. Based on measurements of TMM samples, the error in the acoustic speed measurement was just 1%, although the attenuation coefficient error was considerably larger at 24%. The transducer drive voltage of 100 V was chosen as a balance between obtaining measurable signals and reducing the effect of nonlinear propagation, but, for all finite amplitude waves, there will be some nonlinear distortion. The level of distortion can be described by the shock parameter which was calculated (Bacon 1984) for the focused beam on return to the transducer and found to be 1.0, which is on the threshold of a pressure discontinuity. As found by Zeqiri (1992), nonlinear propagation of the beam produces overestimates of the transmission coefficient. A simple experiment was performed to assess the order of magnitude of this error in the attenuation coefficient results. The power spectrum of the 100 V pulse was compared with that from a pulse of similar amplitude to that obtained with the tissue sample in place, which was 80 V. The 80 V power spectrum was
−5 5
10
15
20
25
30
35
40
temperature /oC
Fig. 8. Variation in sample attenuation coefficient at MHz with temperature. Each data point is the mean of all measurements in that sample scan, and error bars show the standard deviation in these means.
nificant (0.1 ⬍ p ⬍ 0.5) and unpaired t-tests on the difference between the groups (refrigerator and room p ⫽ 0.07, room and body p ⫽ 0.5, refrigerator and body p ⫽ 0.1) confirmed that they are insignificant. There was no significant change in the variation in attenuation coefficient with frequency as the temperature was increased with bmean ⫽ 1.4 and standard deviation ⫽ 0.6. Bamber and Hill (1979) measured the variation of attenuation coefficient with frequency in bovine and human soft tissues and found that, at 7 MHz, the attenuation coefficient decreased by about 21% from 20 to 37°C, whereas, above 40°C, the attenuation coefficient increased. Also, O’Donnell et al. (1977) presented measurements on canine myocardial tissue and showed that the attenuation coefficient decreased linearly with temperature, such that, at 37°C, it was 20% less than at 20°C. Relaxed samples at body temperature. The acoustic properties at body temperature 37°C are summarized in Table 1. The mean temperature used was (mean ⫾ SD ⫽ 38.5 ⫾ 1.4°C). However, the acoustic speed results have been corrected to find the acoustic speed at 37°C, using the equation for the variation with temperature found above. This results in an acoustic speed of 1600 ⫾ 50 m s–1. This is slightly higher than that reported by Hughes and Snyder (1980) for canine aorta at 37°C, which was 1586 ⫾ 7 m s–1, although Rooney et al. (1982) also found a wide range of acoustic speeds in their samples of human and canine arteries from 1550 m s–1 to 1660 m s–1. The variation in attenuation coefficient with frequency is shown in Fig. 9, along with the exponential fit (␣ ⫽ 1.5 ⫾ 4 f 0.94⫾1.3) to the data. The exponent of 0.94 is 6% off the value of 1 often assumed for soft tissues
20 18 16 −1
0
attenuation /dB cm
attenuation /dB cm−1
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14 12 10 8 6 4 2 0 5
5.5
6
6.5
7
7.5
8
8.5
9
frequency /MHz
Fig. 9. Variation in sample attenuation coefficient with frequency at body temperature. Data points represent the mean of measurements made on 10 samples, and the error bars are the standard deviation in this mean. An exponential was fitted to the mean, ␣ ⫽ 1.5f0.94, and this fit is shown with the solid line.
Arterial acoustic properties ● K. H. FRASER et al.
scaled by 1.252, and the difference in these spectra was then the difference in the nonlinear attenuation at the two voltages or the difference in the nonlinear attenuation with and without the sample. The difference in the spectra gave an approximate value for the underestimate in the attenuation coefficients. In this case, the signals were analysed after the entire return path length, whereas in the real experiment, the difference in signal amplitude only occurred after transmission through the tissue and so the difference in the nonlinear propagation occurred for just the return path length. A more accurate value is then half the value for the entire path length, which is 0.03 dB varying by 0.05 dB over the 5 to 9 MHz range. This is only an estimate of the size of the nonlinear error because the real reduction in signal depends on the sample and the scale factor depends on the linearity of the transducer’s response. Vessel-mimicking materials (VMMs), which are in use, along with their physical properties, are listed by Hoskins (1994). The VMMs with properties closest to those of the arterial samples measured here in terms of acoustic speed are norprene and latex rubber, with speeds of 1571 and 1566 m s–1, although their attenuation coefficients are 10 dB cm–1 MHz–1 and 7 dB cm–1 MHz–1, respectively, at 8 MHz. Best for attenuation coefficient is Perspex, with a value of 0.83 dB cm–1 MHz–1 at 8 MHz, but its acoustic speed is 2756 m s–1. For customisable geometries, Poepping et al. (2004) used a mouldable silicone elastomer with a range of concentrations of cellulose particles to give a range of properties. The variation with the closest acoustic properties to the ones measured here was the pure elastomer, with speed 1020 m s–1 and almost linear change in attenuation coefficient with frequency of 3.5 dB cm–1 MHz–1. None of the above VMMs have both acoustic speed and attenuation coefficient similar to the measurements made here. Polyvinyl alcohol is another mouldable VMM (Fromageau et al. 2003) commonly used and its ultrasonic properties were investigated by Surry et al. (2004). The properties vary with the number of freeze-thaw cycles, but the acoustic properties closest to those measured here are given by the material made with four cycles. With added enamel paint, the acoustic speed was 1542 m s–1 and the attenuation coefficient was 0.28 dB cm–1 MHz–1. Although weaker in general, standard tissue-mimicking materials have acoustic properties better matched to arteries. The acoustic properties of commonly used TMMs were assessed by Browne et al. (2003). The TMMs that were best matched for acoustic speed were the agar-based material, condensed milk gel 0.5 and condensed milk gel 0.7, which had acoustic speeds of 1550, 1555 and 1560 m s–1, respectively. For attenuation coefficient, the same three materials all had variations in attenuation coefficient with frequencies that
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were close to linear and, of these, condensed milk gel 0.7 was the best matched in magnitude, with 0.72 dB cm–1 MHz–1. CONCLUSIONS A method was developed for measuring the acoustic speed and attenuation coefficient in arterial samples at clinical frequencies. The mean acoustic speed in sheep aorta samples at 37°C was found to be 1600 ⫾ 50 m s–1, the mean attenuation coefficient at 7 MHz was 9 ⫾ 3 dB cm–1 and the attenuation coefficient in dB cm–1 as a function of frequency in MHz was described by ␣ ⫽ 1.5 f 0.94. Samples could be stored in Krebs solution for 4.5 h without significant changes in the acoustic speed. The effect of contraction on both acoustic speed and attenuation coefficient was not significant, which could be because the intra- and intersample variations in acoustic properties were large compared with the effect of this parameter. If an ideal vascular phantom VMM were to be produced with specific properties for the vessel wall, the speed of sound and attenuation coefficient should be higher than current TMMs by about 40 m s–1 and 0.6 dB cm–1 MHz–1, respectively. When compared with the best-matched current VMMs, speed and attenuation coefficient should be higher by about 60 m s–1 and 1.0 dB cm–1 MHz–1, respectively. Acknowledgments—The authors wish to thank Dr. S. Pye for helpful discussions and comments.The work was funded by the EPSRC GR/ R19793101.
REFERENCES Bacon DR. Finite amplitude distortion of the pulsed fields used in diagnostic ultrasound. Ultrasound Med Biol 1984;10:189 –195. Bamber JC, Hill CR. Ultrasonic attenuation and propagation speed in mammalian tissues as a function of temperature. Ultrasound Med Biol 1979;5:149 –157. Bamber JC, Hill CR, King JA, Dunn F. Ultrasonic propagation through fixed and unfixed tissues. Ultrasound Med Biol 1979;5:159 –165. Bilaniuk N, Wong GSK. Speed of sound in pure water as a function of temperature. J Acoust Soc Am 1993;93:1609 –1612. Bilaniuk N, Wong GSK. Erratum: Speed of sound in pure water as a function of temperature [J Acoust Soc Am 1993;93:1609 –1612]. J Acoust Soc Am 1996;99:3257. Browne JE, Ramnarine KV, Watson AJ, Hoskins PR. Assessment of the acoustic properties of common tissue mimicking test phantoms. Ultrasound Med Biol 2003;29:1053–1060. Chivers RC, Parry RJ. Ultrasonic velocity and attenuation in mammalian tissues. J Acoust Soc Am 1978;63:940 –953. Duck FA. Physical properties of tissue. London, UK: Academic Press Limited, 1990. Foster FS, Strban M, Austin G. The ultrasound macroscope—Initial studies of breast-tissue. Ultrasonic Imaging 1984;6:243–261. Fromageau J, Brusseau E, Vray D, Glimenez G, Delachartre P. Characterization of PVA cryogel for intravascular ultrasound elasticity imaging. IEEE T Ultrason Ferr 2003;50:1318 –1324. Geleskie JV, Shung KK. Further studies on acoustic impedance of major bovine blood vessel walls. J Acoust Soc Am 1982;71:467– 470.
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Glor FP, Ariff B, Hughes AD, et al. Operator dependence of 3-d ultrasound-based computational fluid dynamics for the carotid bifurcation. IEEE T Med Imaging 2005;24:451– 456. Goss SA, Johnston RL, Dunn F. Comprehensive compilation of empirical ultrasound properties of mammalian tissues. J Acoust Soc Am 1978;64:423– 430. Goss SA, Johnston RL, Dunn F. Compilation of empirical ultrasound properties of mammalian tissues 2. J Acoust Soc Am 1980;68:93–108. Greenleaf JF, Duck FA, Samayoa WF, Johnson SA. Ultrasonic data acquisition and processing system for atherosclerotic tissue characterization. Ultrasonics Symposium Proceedings 1974:738 –743. Greenleaf JF, Duck FA, Samayoa WF, Johnson SA. Ultrasonic data acquisition and processing system for atherosclerotic tissue characterization. IEEE T Son Ultrason 1975;3:218. Hill CR, Bamber JC, ter Haar GR. Physical principles of medical ultrasonics. Chicester, UK: John Wiley and Sons Ltd, 2004;93–186. Hoskins PR. Testing of Doppler Ultrasound Equipment. Chapter 2. In: Hoskins PR, Sherriff SB, Evans JA, eds. Review of the design and use of flow phantoms chapter. York, UK: Institute of Physical Sciences in Medicine, 1994; pp12–29. Hughes DJ, Snyder B. Speed of 10MHz sound in canine aortic wall: Effects of temperature, storage and formalin soaking. Med Biol Eng Comput 1980;18:220 –222. Incropera FP, de Witt DP. Fundamentals of heat and mass transfer. New York: John Wiley and Sons, 1990;226 –236. Kuo IY, Hete B, Shung KK. A novel method for the measurement of acoustic speed. J Acoust Soc Am 1990;88:1679 –1682. Lockwood GR, Ryan LK, Hunt JW, Foster FS. Measurement of the ultrasonic properties of vascular tissues and blood from 35– 65 MHz. Ultrasound Med Biol 1991;17:653– 666.
Volume 32, Number 6, 2006 Marsh JN, Takiuchi S, Lin SJ, et al. Ultrasonic delineation of aortic microstructure: The relative contribution of elastin and collagen to aortic microstructure. J Acoust Soc Am 2004;115:2032–2040. Moran CM, Bush NL, Bamber JC. Ultrasonic propagation properties of excised human skin. Ultrasound Med Biol 1995;21:1177– 1190. O’Donnell M, Mimbs JW, Sobel BE, Miller JG. Ultrasonic attenuation of myocardial tissue: Dependence on time after excision and on temperature. J Acoust Soc Am 1977;62:1054 –1057. Poepping TL, Nikolov HN, Thorne ML, Holdsworth DW. A thinwalled carotid vessel phantom for Doppler ultrasound flow studies. Ultrasound Med Biol 2004;30:1067–1078. Ramnarine KV, Anderson T, Hoskins PR. Construction and geometric stability of physiological flow rate wall-less stenosis phantoms. Ultrasound Med Biol 2001;27:245–250. Rooney JA, Gammell PM, Hestenes JD, Chin HP, Blankenhorn DH. Velocity and attenuation of sound in arterial tissues. J Acoust Soc Am 1982;71:462– 466. Shung KK, Reid JM. Ultrasound velocity in major bovine blood vessel walls. J Acoust Soc Am 1978;64:692– 694. Surry KJM, Austin HJB, Fenster A, Peters TM. Poly(vinyl alcohol) cryogel phantoms for use in ultrasound and mr imaging. Phys Med Biol 2004;49:5529 –5546. Weir KA. A numerical method to predict the effects of frequency dependent attenuation and dispersion on speed of sound estimates in cancellous bone. J Acoust Soc Am 2001;109:1213–1218. Wilhjelm JE, Vogt K, Jespersen SK, Sillesen H. Influence of tissue preservation methods on arterial geometry and echogenicity. Ultrasound Med Biol 1997;23:1071–1082. Zeqiri B. Errors in attenuation measurements due to nonlinear propagation effects. J Acoust Soc Am 1992;91:2585–2593.
doi:10.1016/j.ultrasmedbio.2006.02.1417
● Original Contribution ACOUSTIC SPEED AND ATTENUATION COEFFICIENT IN SHEEP AORTA MEASURED AT 5-9 MHZ KATHARINE H. FRASER,* TAMIE L. POEPPING,* ALAN MCNEILLY,† IAN L. MEGSON,‡ and PETER R. HOSKINS* *Medical Physics; †MRC Human Reproductive Sciences Unit; and ‡Centre for Cardiovascular Science, University of Edinburgh, Edinburgh, Scotland (Received 19 September 2005, revised 23 January 2006, in final form 2 February 2006)
Abstract—B-mode ultrasound (US) images from blood vessels in vivo differ significantly from vascular flow phantom images. Phantoms with acoustic properties more closely matched to those of in vivo arteries may give better images. A method was developed for measuring the speed and attenuation coefficient of US over the range 5 to 9 MHz in samples of sheep aorta using a pulse-echo technique. The times-of-flight method was used with envelope functions to identify the reference points. The method was tested with samples of tissue-mimicking material of known acoustic properties. The tissue samples were stored in Krebs physiologic buffer solution and measured over a range of temperatures. At 37°C, the acoustic speed and attenuation coefficient as a function of frequency in MHz were 1600 ⴞ 50 ms–1 and 1.5 ⴞ 4f 0.94 ⴞ 1.3 dB cm–1, respectively. (E-mail: kate.fraser@ ed.ac.uk) © 2006 World Federation for Ultrasound in Medicine & Biology. Key Words: Acoustic speed, Attenuation coefficient, Scanning acoustic macroscope, Artery, Aorta, B-mode, Phantom, Segmentation.
geometry can be patient-specific and obtained from a 3-D image dataset. To create the 3-D surface geometry of the vessel, the relevant shape must be marked out, or segmented from, the 3-D image data. This segmentation is challenging in US imaging due to both the nonisotropic nature of the image and the presence of speckling. Validation of segmentation using a phantom is desirable. The authors’ experience of using a conventional wallless phantom for this purpose is that the vessel edge may easily be identified at the points of perpendicular insonation as expected, but, unlike the in vivo scenario, the lateral locations of the wall are also easily identified. This indicates that the image from such a phantom is not representative of an image from a human artery and that it provides limited information when used to test the effectiveness of vessel segmentation routines. One possibility is that, in real arteries, there is a mismatch in acoustic velocity between the arterial wall and the blood. If this is the case, then vascular phantom design for B-mode imaging should ideally reproduce this mismatch. The aim of this study is to provide information on acoustic properties of arteries to inform the design of a vascular phantom suitable for B-mode imaging. To build such a phantom, it is necessary to know the acoustic properties of arteries at the frequencies used in clinical US scanners and in conditions found in vivo.
INTRODUCTION Vascular ultrasound (US) phantoms have mostly been used in studies testing the accuracy of velocity measurements made using Doppler US. Previously reported Doppler phantoms use either a thin-walled vessel (Poepping et al. 2004) or are wall-less (Ramnarine et al. 2001). Although much effort has been expended on the design and characterisation of these phantoms for Doppler US studies, phantom design for B-mode studies has received little attention. When imaged in cross-section, B-mode images of arteries in humans demonstrate a bright echo at the points on the wall nearest to and furthest from the transducer, that is, the points of perpendicular insonation, with substantial loss of image quality at the lateral borders. This nonisotropic image appearance makes it difficult to identify the vessel boundary. Vessel geometry is of interest in, for example, image-guided modelling, where a computational model of blood flow is used to provide three-dimensional (3-D) time-varying flow field data (Glor et al. 2005). This requires specification of boundary conditions, usually the 3-D surface geometry of the vessel along with inlet and outlet flow. The surface Address correspondence to: Katharine H. Fraser, The Chancellor’s Building, 49 Little France Crescent, Edinburgh, EH16 4SB, Scotland. E-mail: [email protected] 971
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There have been many measurements of acoustic properties of different tissues summarized in the comprehensive work by Duck (1990), as well as Goss et al. (1978, 1980) and Chivers and Parry (1978), updated in Hill et al. (2004), and some more recent studies on blood vessels at intravascular US frequencies, for example (Lockwood et al. 1991; Marsh et al. 2004). However, few groups have studied blood vessels at transcutaneous frequencies. Greenleaf et al. (1974, 1975) recorded transmitted, reflected and scattered 10 MHz US in diseased human vessels using a scanning system. Their samples were placed between lucite blocks, enabling the sample thickness to be measured accurately but not allowing for variation in thickness across the sample. Shung and Reid (1978) and Geleskie and Shung (1982) measured the velocity at 22°C in bovine blood vessels using aluminium buffer rods as a solid transmission medium for 5 MHz US. Again, the solid rods did not allow for variation in thickness across the sample. Hughes and Snyder (1980) measured the speed of 10 MHz US in dog aorta over a range of temperatures, both in Ringer’s lactate solution and fixed with formalin. Rooney et al. (1982) studied velocity and attenuation in human and canine arteries at 37°C, taking measurements at 20 to 30 sites in each of 17 arteries. They attribute the dominant error in their technique to the precision (⫾0.1 mm) of the tissue thickness measurement, for which they used calipers. In this work, a method was developed for measuring the acoustic speed and attenuation coefficient of thin tissue samples without the need for a separate tool to measure thickness. Similar methods have been used by others (Geleskie and Shung 1982; Hughes and Snyder 1980; Shung and Reid 1978), but these papers do not describe from which part of the waveform they measured their times. The pulse shape is distorted as it propagates through the medium and sample (Hill et al. 2004), which can lead to errors in time measurements, depending on which point in the waveform is used. In the work described, this error has been minimised by using an envelope function. The thickness is then measured at the same sample site as that at which the acoustic speed and attenuation coefficient data are recorded, thus also minimising error. The method was tested by measuring the properties of thin samples of tissue-mimicking material (TMM) and then used to measure the acoustic speed and attenuation coefficient of samples of sheep aorta. MATERIALS AND METHODS Measurement of Sample Thickness, Acoustic Speed and Attenuation Coefficient The acoustic speed and attenuation coefficient of the samples were measured using the pulse-echo substitution method (Browne et al. 2003), with the incorpora-
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Fig. 1. Distances involved in calculations.
tion of the times-of-flight (TOF) method (Kuo et al. 1990) to measure the sample thickness. All measurements were made using a scanning acoustic macroscope (SAM) (Ultrasonic Sciences Limited, Fleet, UK) (Foster et al. 1984; Moran et al. 1995). The SAM allows measurements to be made over a defined area of the sample for spatial averaging. The SAM system comprised an 8-bit, 100-MHz, analog-to-digital input/output personal computer (PC) board, a 1- to 20 MHz pulse receiver and a stepper motor control system, all controlled by a PC. One transducer acted as both transmitter and receiver, and the pulse was transmitted through the surrounding medium, either deionized water or Krebs, a solution that contains all nutrients required to keep cells alive for several days, and reflected from a highly-polished flat steel plate. The centre frequency of the transducer was 7 MHz, the 6 dB bandwidth was 71%, the focal length was 50 mm, the crystal diameter was 11.8 mm and the – 6 dB diameter at the focal length was 0.86 mm. An area of 16 ⫻ 15.5 mm was scanned in increments of 1 ⫻ 0.5 mm. At each position, the reflected radio-frequency signal from the steel reflector was digitised at a sampling rate of 100 MHz and stored for offline analysis. Each sample required three scans: a reference scan, which was a scan without the sample; a sample scan; and a reflection scan, which was to detect the small signals reflected from the interfaces of the sample and the medium. The difference in apparatus for these scans is shown in Fig. 1. The driving voltage was set at the relatively low value of 100 V (Browne et al. 2003) to minimise nonlinear propagation effects (Zeqiri 1992) for both the reference scan and sample scan, whereas for the reflection scan, it was 300 V, which allowed the much smaller signals to be located. The signals were analysed using in-house code developed in MATLAB (MathWorks Inc., Natick, MA, USA). Example signals are shown in Fig. 2. With a very large signal-to-noise ratio, the times TS, the return time to the reflector with the sample, and TR, the return time to
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the nonlinearly-generated harmonics and the fundamental causes the change in pulse shape. Reference points on the pulse that use thresholding result in errors in the TOF measurement as a result of frequency-dependent attenuation (Weir 2001) but, by using an envelope function, the reference point is unaffected by these changes in signal shape. The susceptibility of the envelope function to changes in the pulse shape due to nonlinear propagation was assessed by examining the position of the reference point with respect to the predicted position as the propagation distance was increased. The effect was found to be negligible because the mean error was ⬍0.1 mm, the accuracy to which the distances could be measured. The sample thickness, dS, was calculated from VK, the acoustic speed in the immersion medium, TR, TS, T1 and T2:
Reference
Sample
dS ⫽ dT ⫺ d1 ⫺ d2 ⫽
Reflection
T
1
T
2
T
S
T
R
Fig. 2. The three signals required: reference, sample and reflection and the time points needed for thickness and speed calculations. Signals are shown with solid lines, signal envelopes are shown in dashed lines and dotted lines show the time points required for thickness and acoustic speed calculations. The reflection signal is used to obtain times T1 and T2, the reflections from the upper and lower surfaces of the sample, respectively. The sample signal is used to obtain TS, the reflection from the highly-polished reflector in the presence of the sample, and the reference signal is used to obtain TR, the reflection from the highly-polished reflector without the sample.
the reflector without the sample, were easy to define. Butterworth filters were applied to the sample and reference signals and the peak amplitudes of these filtered signals were used as the reference points. The times T1, the return time to the upper surface of the sample, and T2, the return time to the lower surface of the sample, were harder to define because the signal-to-noise ratios at these times were small. The short-time Fourier transform of the reflection signal was taken with an interval of 0.32 s and used to plot the magnitude of the signal at 7 MHz (centre frequency of the transducer). The peaks in this plot of the signal power at 7 MHz were then used to define times T1 and T2. The two main effects that cause the pulse shape to change are frequency-dependent attenuation and nonlinear propagation (Hill et al. 2004). Higher frequencies are attenuated more, thus narrowing the bandwidth and causing the signal to lengthen in time. In nonlinear propagation, the phase relationship between
VK T ⫺ T1 ⫺ TS ⫹ T2兲 2共 r
(1)
where dT is the distance from transducer to reflector, d1 is the distance from transducer to upper sample surface and d2 is the distance from lower sample surface to reflector (Kuo et al. 1990). These distances are shown in Fig 1. The acoustic speed in the sample VS was then calculated as: VS ⫽
2dS T2 ⫺ T1
(2)
The acoustic speed was calculated for all 496 locations in the 16 ⫻ 15.5-mm scan area and the mean of these was calculated to obtain the sample acoustic speed. When measuring the attenuation coefficient of samples by the insertion technique, power is also lost through reflection at the tissue-medium interfaces, and this is included in the attenuation coefficient measurement (Hill et al. 2004). These insertion losses, compared with the attenuation due to absorption and scattering, will be relatively larger in thin samples than in thicker ones. By considering the geometry of the apparatus and using equations for transmission and attenuation, an equation for the attenuation coefficient including interface losses was derived. If I is the incident intensity, T is the intensity transmitted at an interface between two media with impedances z1 and z2, and A is the intensity after attenuation through a medium with thickness d and attenuation coefficient ␣, then
冉 冊
2z2 T ⫽ I z1 ⫹ z2
A ⫽ 10⫺d␣⁄10. I
2
(3)
Accounting for transmission at all four interfaces gives
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the following equation for the intensity transmitted after the return journey through the sample of thickness dS: T4 ⫽ I
冉
冉
256z14z24 共z1⫹z2兲8 attenuation coefficient:
Setting K ⫽
冊
256z14z24 10⫺2dS␣⁄10. 共z1 ⫹ z2兲8
冊
␣共 f 兲 ⫽
(4)
leads to an equation for the
IK 10 log10 . 2dS T4
(5)
The reference and sample signals were fast-Fouriertransformed to give their frequency spectra, which were then squared to give I and T4. Acoustic impedances z1 and z2 were calculated using VK and VS as above, density of the medium K ⫽ 1016 kg m–3 and density of the sample, S ⫽ 1062 kg m–3 (Shung and Reid 1978). The attenuation coefficient of the sample was the mean of the attenuation coefficients at each location in the scan area. Preparation and Measurement of Acoustic Speed of Krebs Solution To prevent alteration in acoustic properties postmortem, the aorta were stored in Krebs solution. This provided all nutrients necessary to keep the cells alive for a few days when refrigerated and consisted of NaCl 118 mM, d-glucose 5.6 mM, HEPES 25 mM, KCl 4.7 mM, MgSO4.7H2O 1.18 mM, KH2PO4 1.18 mM, CaCl2.2H2O 2.5 mM and penicillin 2 M units l⫺1. To contract the smooth muscle cells, 4.7 mM KCl was replaced with 118 mM KCl to make a high potassium ion (K⫹) Krebs solution. For the pulse-echo technique, it is necessary to know the acoustic velocity in the medium surrounding the sample, that is, the Krebs solution. This was determined using the pulse-echo technique described above and with a fluid cell containing Krebs solution immersed in a tank of degassed, deionized water. The acoustic speed of the water used was a function of temperature and is given by Bilaniuk and Wong (1993, 1996). To degas the solution, it was made the day before the experiments and refrigerated overnight. Measurements were made over the temperature range 6 to 42°C and, to test for batch-to-batch variability, three different batches were tested. The acoustic velocity in the high K⫹ Krebs was assumed to be the same as in the standard Krebs, within measurement error. Test Samples The above method for calculating sample thickness, acoustic speed and attenuation coefficient was tested on three samples of TMM. The TMM was an agar-based material made as described by Ramnarine et al. (2001) and it was then poured into three flat dishes to different
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depths to create three thin samples (0.8 to 1.5 mm) with three different uniform thicknesses. After solidifying, the samples were covered with a layer of 10% glycerol in water solution (to prevent them drying out or the glycerol diffusing out) and stored at room temperature. Measurements of thickness, acoustic speed and attenuation coefficient were made as described above, using deionized water as the medium. The water was degassed by boiling and left overnight to cool to room temperature. The TMM samples were kept in water for the minimum time to minimise diffusion of glycerol out of them, which would reduce the acoustic speed. After measuring the acoustic properties, the thickness of each of the thin samples was measured at 40 different points using calipers (error ⫽ ⫾0.01 mm). Aorta Samples The aorta samples were obtained immediately after death from the abdominal section of freshly excised sheep aortas obtained from sheep killed with an overdose of sodium pentobarbitone (Euthetal; Rhone-Merieux Ltd., Harlow, Essex, UK) at the Marshall Building, Roslin, Edinburgh, UK. The procedures were conducted in accordance with the Home Office Animals (Scientific Procedures) Act 1996 of the United Kingdom. Each aorta was dissected and immediately placed in Krebs solution for transport to the laboratory. All experiments were carried out within 7 h of the excision, with the exception of the experiment to determine the effects of storage, which took 9 h. The aortas were cleaned of connective tissue and fat, cut into ⬇3 cm lengths and sliced open longitudinally. Each sample was spread flat with the inner endothelium uppermost and attached to a stainless steel ring (inner diameter 31 mm, outer diameter 54 mm, thickness 2 mm). A needle was used to push a piece of sewing thread through each corner of the sample at the point where the sample overlapped the ring and these threads were then knotted onto the ring. It was then impossible to increase the tension in the tissue, as either the sample or thread would slip back to its original position. The ring was on top of the sample and this weighed it down while in the solution, held it flat and enabled easy handling. Altogether, 25 samples were obtained from 15 aortas. Fresh samples at room temperature. Eight samples from six aortas were measured fresh and at room temperature (20 to 22°C). One sample was excluded from further analysis because it was visually observed to be calcified severely, leaving a total of seven samples. The attenuation coefficient of this diseased sample was above 60 dB cm–1. Comparison with Greenleaf et al. (1974), who reported the attenuation coefficient of calcified le-
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sions to be above 45 dB cm–1, confirms that it was calcified. Effect of storage on the acoustic properties. The possibility of change in properties, acoustic speed and attenuation coefficient in the aorta over storage time was investigated with further studies on four samples from above. After the first measurement, these were stored in the refrigerator to minimise degradation and then placed in the room temperature solution before being scanned. A simple calculation was performed to determine how long the samples should be left to equilibrate to room temperature. Because the Biot number—the nondimensional ratio of convection to conduction—is small, the lumped capacitance method can be used to solve the transient conduction problem (Incropera and de Witt 1990) and can be shown that the time taken for the sample to reach a final temperature TF is given by:
冉
t ⫽ ⫺ln
冊
TF ⫺ To kd . TF ⫺ To ␣h
(6)
where TF is the final tissue temperature, To is the temperature of the Krebs solution, T1 is the initial tissue temperature, k is the thermal conductivity, d is the sample thickness, ␣ is the thermal diffusivity and h is the convective heat transfer coefficient. For TF ⫽ 21.01°C, To ⫽ 21.0°C, T1 ⫽ 6°C, k ⫽ 0.476 W m⫺1 K–1 (Duck 1990), d ⫽ 1 mm, ␣ ⫽ 0.127 m 2 s ⫺ 1 (Duck 1990) and h of the order 50 W m –2 K –1 (Incropera and De Witt 1990), the time taken is of the order of 1 ms. The sample was left to equilibrate for 10 min to be certain. Each sample was measured three or four times over 5.4 h. Effect of contraction on acoustic properties. Because arteries in vivo spend much of their time contracted, the properties of contracted aorta were examined by placing samples directly into high K⫹ Krebs solution after excision. When the K⫹ concentration is increased, K⫹ is driven into the cell, upsetting the ionic intracellular concentration. The membrane potential depolarizes, becoming more positive, because of the increase in positive charge inside the cell. Depolarisation of the membrane opens voltage sensitive Ca2⫹ channels in the cell membrane, which allows Ca2⫹ to flow from its higher concentration outside the cells to the lower concentration inside. Ca2⫹ is essential for contraction because it causes phosphorylation of critical proteins in the contractile machinery through activation of myosin light-chain kinase. The artery samples were stored in this high K⫹ Krebs solution for transport to the laboratory and then immersed in fresh high K⫹ Krebs solution during measurements. Five samples from three aortas were studied at room temperature (20 to 22°C). The results from these
Fig. 3. Acoustic speed in Krebs solution for temperatures 5 to 45°C. Error bars on the data points are the standard deviations in these measurements. The data were fitted with a quadratic VK ⫽ 1426 ⫹ 4.109t ⫺ 0.03312t2 and the 95% confidence intervals for this fit are shown with dashed lines. The acoustic speed in pure water is shown as a dotted line (Bilaniuk and Wong 1993, 1996).
samples were then compared with those from the fresh samples at room temperature. Effect of temperature on acoustic properties. In addition to the samples measured at room temperature, six samples, two from each of three aortas, were measured both at refrigerator temperature (6 to 11°C) and at body temperature (36 to 41°C). Because body temperature is of greater interest and relevancy, a further four samples were measured only at this temperature. These results, obtained at different temperatures, were then compared with the fresh samples at room temperature. RESULTS Krebs Solution Figure 3 shows the variation of acoustic speed in Krebs with temperature. Each data point is the mean acoustic speed of the 496 measurements in the scan and the error bars give the standard deviation. Measurements from all three batches of the solution were plotted and fit to a quadratic, VK ⫽ 1426 ⫹ 4.109t ⫺ 0.03312t2, using MATLAB (Mathworks, Inc.). Also plotted are the 95% confidence intervals for this quadratic fit and the acoustic speed in water as measured by Bilaniuk and Wong (1993, 1996). Test samples. Thicknesses of the three TMM test samples measured ultrasonically were (mean ⫾ standard deviation (SD)): 0.88 ⫾ 0.05, 1.24 ⫾ 0.05 and 1.50 ⫾ 0.05 mm.
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attenuation /dB cm
−1
16 14 12 10 8 6 4 2 0 5
5.5
6
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7
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8
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frequency /MHz
Fig. 4. Variation in sample attenuation coefficient with frequency at room temperature. Data points represent the mean of measurements made on seven samples, and the error bars are the standard deviation in this mean; every fifth point has been plotted for clarity. An exponential was fitted to the mean, ␣ ⫽ 0.35f1.7 and this fit is shown with the solid line.
These are well within the standard deviations of the thicknesses measured using calipers (mean ⫾ SD): 0.79 ⫾ 0.20, 1.27 ⫾ 0.25 and 1.62 ⫾ 0.20 mm. The acoustic speeds were (mean ⫾ SD) 1538 ⫾ 8, 1559 ⫾ 8 and 1544 ⫾ 5 m s–1, which are within 18 m s–1 of the value 1541 ⫾ 3 m s–1 given by (Ramnarine et al. 2001) and so imply a measurement error of 1%. The attenuation coefficient measured in the three samples over the range 5 to 9 MHz was 0.52f ⫹ 0.58, 0.58f ⫹ 0.28 and 0.54f ⫹ 0.10 dB cm–1, where f is the frequency in MHz. Comparison with the published value for this TMM given by Ramnarine et al. (2001), 0.50f ⫹ 0.00 dB cm–1, shows there is a 24% measurement error at 7 MHz. Sheep Aorta Fresh samples at room temperature. Figure 4 shows the mean variation in attenuation coefficient for seven samples measured fresh and at room temperature (mean ⫾ SD ⫽ 20.9 ⫾ 0.6°C) and the exponential fit (␣ ⫽ 0.35f1.7) to these data. The exponent of the frequency is
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1.7, which is 70% larger than the value of 1, which is often assumed for soft tissues but is within the range of values for all soft tissues (Duck 1990). Although the range of frequencies used in this study was 5 to 9 MHz, the empirical fit can be extrapolated for the purposes of comparison with published data and the value of the attenuation coefficient at 10 MHz is found to be 17.5 dB cm–1. This is almost three times the 6.1 dB cm–1 reported by Greenleaf et al. (1974) for normal human aorta. The acoustic speed results for the seven samples measured at room temperature and considered to be normal and nonpathologic are shown in Table 1. The mean acoustic speed, 1570 m s–1, is 4% higher than that reported for the human aorta by Greenleaf et al. (1974), which was 1501 m s–1, is 1.6% higher than the 1545 m s–1 reported by Hughes and Snyder (1980) for canine aorta, but is just 0.3% lower than the value 1575.3 m s–1 found by Geleskie and Shung (1982) in bovine aorta. Effect of storage on the acoustic properties. Figure 5 shows the mean attenuation coefficient at 7 MHz in each sample and the time at which it was measured. Paired t-tests on the differences in attenuation coefficient between first and second measurements (p ⫽ 0.5), second and third measurements (p ⫽ 0.5) and first and third measurements (p ⫽ 0.5) show there is no significant change in the attenuation coefficient of the samples over the time period investigated. In addition, the variation in attenuation coefficient with frequency did not change with time, being approximately linear for each sample and at each time (if ␣ ⫽ af b, b is (mean ⫾ SD) 1.3 ⫾ 0.3). Figure 6 shows the mean acoustic speed in each sample and the time at which it was measured. The acoustic speed increases with storage time and a linear best fit to the normal nondiseased samples was produced with VS ⫽ 1549t ⫹ 0.0534t2, where t is in minutes. Paired t-tests on the difference in acoustic speed between first and second measurements (p ⫽ 0.5), second and third measurements (p ⫽ 0.1) and first and third measurements (p ⫽ 0.05) show that the acoustic speed differences up to the time of the second measurements (270 min) are insignificant, whereas later measurements show a significant change in the samples. These results suggest
Table 1. Summary of acoustic properties Acoustic speed /m s⫺1
Relaxed samples at room temperature (21°C) High K⫹ samples at room temperature (21°C) Relaxed samples at body temperature (37°C)
Attenuation coefficient at 7 MHz/dB cm⫺1
Samples
Mean ⫾ SD
Range
Mean ⫾ SD
Range
7 5 10
1570 ⫾ 30 1578 ⫾ 9 1600 ⫾ 50
1550–1600 1570–1590 1550–1670
9⫾2 8⫾3 9⫾3
6–12 6–14 3–14
Arterial acoustic properties ● K. H. FRASER et al.
Effect of contraction on acoustic properties. The effect of contraction on the acoustic properties was determined by placing five samples from three aortas in Krebs solution with 128 mM K⫹, rather than the standard 4.7 mM, which caused the smooth muscle cells to contract. The acoustic properties of the contracted samples are given in Table 1 and can be compared with the fresh room-temperature samples. These results showed that, although the arteries were visually observed to contract and were noticeably stiffer during handling, the differences in the acoustic properties of the contracted and relaxed samples were not significant (Student’s t-tests for speed (p ⫽ 0.5) and attenuation coefficient (p ⫽ 0.5)).
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120 100 80 60 40 20 0 50
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100
150
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350
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time /minutes
Fig. 5. Variation in sample attenuation coefficient at 7 MHz with storage time. Each data point is the mean of all measurements in that sample scan, and error bars show the standard deviation in these means. The four different samples are represented by different symbols: cross, triangle, diamond and circle. The sample represented by the diamond is the diseased one.
that the Krebs solution maintained the samples for 4.5 h. Wilhjelm et al. (1997) and Bamber et al. (1979) found that some tissue preservation methods affected the acoustic properties, although Hughes and Snyder (1980) found that Ringer’s solution preserved their samples for 24 h.
Effect of temperature on acoustic properties. Figure 7 shows the variation in acoustic speed with temperature. A quadratic function was fitted to the data, VS ⫽ 1363 ⫹ 13.5T ⫺ 0.186T2, and this is shown along with the 95% confidence intervals. Comparison of the results in Table 1 shows the increase in acoustic speed for the body temperature samples compared with those at room temperature (mean ⫾ SD ⫽ 20.9 ⫾ 0.6°C). These results can be compared with those of Hughes and Snyder (1980), who found the acoustic speed in their canine aorta samples increased linearly from 1545 ⫾ 8 m s–1 at 23°C to 1590 ⫾ 10 m s⫺1 at 37° C. Figure 8 shows the results of the attenuation coefficient measurements over the range of temperatures. Although a linear best fit shows a small increase in attenuation coefficient with temperature (linear fit: VS ⫽ 7.1 ⫹ 0.063T), a paired t-test comparing samples at refrigerator and body temperatures showed that the difference in attenuation coefficient is not sig-
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speed /m s−1
1750
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1600 1550 1500 1450
1550
1400 1500 50
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time /minutes
Fig. 6. Variation in acoustic speed with storage time. Each data point is the mean of all measurements in that sample scan, and error bars show the standard deviation in these means. The four different samples are represented by different symbols: cross, triangle, diamond and circle. The sample represented by the diamond is the diseased one. The normal nondiseased data points were fitted to a straight line, VS ⫽ 1549t ⫹ 0.0534t2, where t is in min, which is shown dashed on the graph.
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40
o
temperature / C
Fig. 7. Variation in acoustic speed with sample temperature. Each data point is the mean of all measurements in that sample scan, and error bars show the standard deviation in these means. The data were fit to a quadratic, VS ⫽ 1363 ⫹ 13.5T ⫺ 0.186T2, and the dashed lines show the 95% confidence intervals for this fit.
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(Duck 1990). Six of the samples studied at body temperature were first studied at refrigerator temperature and so had been cooled before being heated to body temperature, whereas the other four samples were only measured at body temperature. There were no significant differences in either the acoustic speed or attenuation coefficient between these groups (p ⫽ 0.5 for both).
30 25 20 15 10
DISCUSSION
5
A method was developed for measuring the acoustic speed and attenuation coefficient in thin tissue samples. Based on measurements of TMM samples, the error in the acoustic speed measurement was just 1%, although the attenuation coefficient error was considerably larger at 24%. The transducer drive voltage of 100 V was chosen as a balance between obtaining measurable signals and reducing the effect of nonlinear propagation, but, for all finite amplitude waves, there will be some nonlinear distortion. The level of distortion can be described by the shock parameter which was calculated (Bacon 1984) for the focused beam on return to the transducer and found to be 1.0, which is on the threshold of a pressure discontinuity. As found by Zeqiri (1992), nonlinear propagation of the beam produces overestimates of the transmission coefficient. A simple experiment was performed to assess the order of magnitude of this error in the attenuation coefficient results. The power spectrum of the 100 V pulse was compared with that from a pulse of similar amplitude to that obtained with the tissue sample in place, which was 80 V. The 80 V power spectrum was
−5 5
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temperature /oC
Fig. 8. Variation in sample attenuation coefficient at MHz with temperature. Each data point is the mean of all measurements in that sample scan, and error bars show the standard deviation in these means.
nificant (0.1 ⬍ p ⬍ 0.5) and unpaired t-tests on the difference between the groups (refrigerator and room p ⫽ 0.07, room and body p ⫽ 0.5, refrigerator and body p ⫽ 0.1) confirmed that they are insignificant. There was no significant change in the variation in attenuation coefficient with frequency as the temperature was increased with bmean ⫽ 1.4 and standard deviation ⫽ 0.6. Bamber and Hill (1979) measured the variation of attenuation coefficient with frequency in bovine and human soft tissues and found that, at 7 MHz, the attenuation coefficient decreased by about 21% from 20 to 37°C, whereas, above 40°C, the attenuation coefficient increased. Also, O’Donnell et al. (1977) presented measurements on canine myocardial tissue and showed that the attenuation coefficient decreased linearly with temperature, such that, at 37°C, it was 20% less than at 20°C. Relaxed samples at body temperature. The acoustic properties at body temperature 37°C are summarized in Table 1. The mean temperature used was (mean ⫾ SD ⫽ 38.5 ⫾ 1.4°C). However, the acoustic speed results have been corrected to find the acoustic speed at 37°C, using the equation for the variation with temperature found above. This results in an acoustic speed of 1600 ⫾ 50 m s–1. This is slightly higher than that reported by Hughes and Snyder (1980) for canine aorta at 37°C, which was 1586 ⫾ 7 m s–1, although Rooney et al. (1982) also found a wide range of acoustic speeds in their samples of human and canine arteries from 1550 m s–1 to 1660 m s–1. The variation in attenuation coefficient with frequency is shown in Fig. 9, along with the exponential fit (␣ ⫽ 1.5 ⫾ 4 f 0.94⫾1.3) to the data. The exponent of 0.94 is 6% off the value of 1 often assumed for soft tissues
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6
6.5
7
7.5
8
8.5
9
frequency /MHz
Fig. 9. Variation in sample attenuation coefficient with frequency at body temperature. Data points represent the mean of measurements made on 10 samples, and the error bars are the standard deviation in this mean. An exponential was fitted to the mean, ␣ ⫽ 1.5f0.94, and this fit is shown with the solid line.
Arterial acoustic properties ● K. H. FRASER et al.
scaled by 1.252, and the difference in these spectra was then the difference in the nonlinear attenuation at the two voltages or the difference in the nonlinear attenuation with and without the sample. The difference in the spectra gave an approximate value for the underestimate in the attenuation coefficients. In this case, the signals were analysed after the entire return path length, whereas in the real experiment, the difference in signal amplitude only occurred after transmission through the tissue and so the difference in the nonlinear propagation occurred for just the return path length. A more accurate value is then half the value for the entire path length, which is 0.03 dB varying by 0.05 dB over the 5 to 9 MHz range. This is only an estimate of the size of the nonlinear error because the real reduction in signal depends on the sample and the scale factor depends on the linearity of the transducer’s response. Vessel-mimicking materials (VMMs), which are in use, along with their physical properties, are listed by Hoskins (1994). The VMMs with properties closest to those of the arterial samples measured here in terms of acoustic speed are norprene and latex rubber, with speeds of 1571 and 1566 m s–1, although their attenuation coefficients are 10 dB cm–1 MHz–1 and 7 dB cm–1 MHz–1, respectively, at 8 MHz. Best for attenuation coefficient is Perspex, with a value of 0.83 dB cm–1 MHz–1 at 8 MHz, but its acoustic speed is 2756 m s–1. For customisable geometries, Poepping et al. (2004) used a mouldable silicone elastomer with a range of concentrations of cellulose particles to give a range of properties. The variation with the closest acoustic properties to the ones measured here was the pure elastomer, with speed 1020 m s–1 and almost linear change in attenuation coefficient with frequency of 3.5 dB cm–1 MHz–1. None of the above VMMs have both acoustic speed and attenuation coefficient similar to the measurements made here. Polyvinyl alcohol is another mouldable VMM (Fromageau et al. 2003) commonly used and its ultrasonic properties were investigated by Surry et al. (2004). The properties vary with the number of freeze-thaw cycles, but the acoustic properties closest to those measured here are given by the material made with four cycles. With added enamel paint, the acoustic speed was 1542 m s–1 and the attenuation coefficient was 0.28 dB cm–1 MHz–1. Although weaker in general, standard tissue-mimicking materials have acoustic properties better matched to arteries. The acoustic properties of commonly used TMMs were assessed by Browne et al. (2003). The TMMs that were best matched for acoustic speed were the agar-based material, condensed milk gel 0.5 and condensed milk gel 0.7, which had acoustic speeds of 1550, 1555 and 1560 m s–1, respectively. For attenuation coefficient, the same three materials all had variations in attenuation coefficient with frequencies that
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were close to linear and, of these, condensed milk gel 0.7 was the best matched in magnitude, with 0.72 dB cm–1 MHz–1. CONCLUSIONS A method was developed for measuring the acoustic speed and attenuation coefficient in arterial samples at clinical frequencies. The mean acoustic speed in sheep aorta samples at 37°C was found to be 1600 ⫾ 50 m s–1, the mean attenuation coefficient at 7 MHz was 9 ⫾ 3 dB cm–1 and the attenuation coefficient in dB cm–1 as a function of frequency in MHz was described by ␣ ⫽ 1.5 f 0.94. Samples could be stored in Krebs solution for 4.5 h without significant changes in the acoustic speed. The effect of contraction on both acoustic speed and attenuation coefficient was not significant, which could be because the intra- and intersample variations in acoustic properties were large compared with the effect of this parameter. If an ideal vascular phantom VMM were to be produced with specific properties for the vessel wall, the speed of sound and attenuation coefficient should be higher than current TMMs by about 40 m s–1 and 0.6 dB cm–1 MHz–1, respectively. When compared with the best-matched current VMMs, speed and attenuation coefficient should be higher by about 60 m s–1 and 1.0 dB cm–1 MHz–1, respectively. Acknowledgments—The authors wish to thank Dr. S. Pye for helpful discussions and comments.The work was funded by the EPSRC GR/ R19793101.
REFERENCES Bacon DR. Finite amplitude distortion of the pulsed fields used in diagnostic ultrasound. Ultrasound Med Biol 1984;10:189 –195. Bamber JC, Hill CR. Ultrasonic attenuation and propagation speed in mammalian tissues as a function of temperature. Ultrasound Med Biol 1979;5:149 –157. Bamber JC, Hill CR, King JA, Dunn F. Ultrasonic propagation through fixed and unfixed tissues. Ultrasound Med Biol 1979;5:159 –165. Bilaniuk N, Wong GSK. Speed of sound in pure water as a function of temperature. J Acoust Soc Am 1993;93:1609 –1612. Bilaniuk N, Wong GSK. Erratum: Speed of sound in pure water as a function of temperature [J Acoust Soc Am 1993;93:1609 –1612]. J Acoust Soc Am 1996;99:3257. Browne JE, Ramnarine KV, Watson AJ, Hoskins PR. Assessment of the acoustic properties of common tissue mimicking test phantoms. Ultrasound Med Biol 2003;29:1053–1060. Chivers RC, Parry RJ. Ultrasonic velocity and attenuation in mammalian tissues. J Acoust Soc Am 1978;63:940 –953. Duck FA. Physical properties of tissue. London, UK: Academic Press Limited, 1990. Foster FS, Strban M, Austin G. The ultrasound macroscope—Initial studies of breast-tissue. Ultrasonic Imaging 1984;6:243–261. Fromageau J, Brusseau E, Vray D, Glimenez G, Delachartre P. Characterization of PVA cryogel for intravascular ultrasound elasticity imaging. IEEE T Ultrason Ferr 2003;50:1318 –1324. Geleskie JV, Shung KK. Further studies on acoustic impedance of major bovine blood vessel walls. J Acoust Soc Am 1982;71:467– 470.
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Glor FP, Ariff B, Hughes AD, et al. Operator dependence of 3-d ultrasound-based computational fluid dynamics for the carotid bifurcation. IEEE T Med Imaging 2005;24:451– 456. Goss SA, Johnston RL, Dunn F. Comprehensive compilation of empirical ultrasound properties of mammalian tissues. J Acoust Soc Am 1978;64:423– 430. Goss SA, Johnston RL, Dunn F. Compilation of empirical ultrasound properties of mammalian tissues 2. J Acoust Soc Am 1980;68:93–108. Greenleaf JF, Duck FA, Samayoa WF, Johnson SA. Ultrasonic data acquisition and processing system for atherosclerotic tissue characterization. Ultrasonics Symposium Proceedings 1974:738 –743. Greenleaf JF, Duck FA, Samayoa WF, Johnson SA. Ultrasonic data acquisition and processing system for atherosclerotic tissue characterization. IEEE T Son Ultrason 1975;3:218. Hill CR, Bamber JC, ter Haar GR. Physical principles of medical ultrasonics. Chicester, UK: John Wiley and Sons Ltd, 2004;93–186. Hoskins PR. Testing of Doppler Ultrasound Equipment. Chapter 2. In: Hoskins PR, Sherriff SB, Evans JA, eds. Review of the design and use of flow phantoms chapter. York, UK: Institute of Physical Sciences in Medicine, 1994; pp12–29. Hughes DJ, Snyder B. Speed of 10MHz sound in canine aortic wall: Effects of temperature, storage and formalin soaking. Med Biol Eng Comput 1980;18:220 –222. Incropera FP, de Witt DP. Fundamentals of heat and mass transfer. New York: John Wiley and Sons, 1990;226 –236. Kuo IY, Hete B, Shung KK. A novel method for the measurement of acoustic speed. J Acoust Soc Am 1990;88:1679 –1682. Lockwood GR, Ryan LK, Hunt JW, Foster FS. Measurement of the ultrasonic properties of vascular tissues and blood from 35– 65 MHz. Ultrasound Med Biol 1991;17:653– 666.
Volume 32, Number 6, 2006 Marsh JN, Takiuchi S, Lin SJ, et al. Ultrasonic delineation of aortic microstructure: The relative contribution of elastin and collagen to aortic microstructure. J Acoust Soc Am 2004;115:2032–2040. Moran CM, Bush NL, Bamber JC. Ultrasonic propagation properties of excised human skin. Ultrasound Med Biol 1995;21:1177– 1190. O’Donnell M, Mimbs JW, Sobel BE, Miller JG. Ultrasonic attenuation of myocardial tissue: Dependence on time after excision and on temperature. J Acoust Soc Am 1977;62:1054 –1057. Poepping TL, Nikolov HN, Thorne ML, Holdsworth DW. A thinwalled carotid vessel phantom for Doppler ultrasound flow studies. Ultrasound Med Biol 2004;30:1067–1078. Ramnarine KV, Anderson T, Hoskins PR. Construction and geometric stability of physiological flow rate wall-less stenosis phantoms. Ultrasound Med Biol 2001;27:245–250. Rooney JA, Gammell PM, Hestenes JD, Chin HP, Blankenhorn DH. Velocity and attenuation of sound in arterial tissues. J Acoust Soc Am 1982;71:462– 466. Shung KK, Reid JM. Ultrasound velocity in major bovine blood vessel walls. J Acoust Soc Am 1978;64:692– 694. Surry KJM, Austin HJB, Fenster A, Peters TM. Poly(vinyl alcohol) cryogel phantoms for use in ultrasound and mr imaging. Phys Med Biol 2004;49:5529 –5546. Weir KA. A numerical method to predict the effects of frequency dependent attenuation and dispersion on speed of sound estimates in cancellous bone. J Acoust Soc Am 2001;109:1213–1218. Wilhjelm JE, Vogt K, Jespersen SK, Sillesen H. Influence of tissue preservation methods on arterial geometry and echogenicity. Ultrasound Med Biol 1997;23:1071–1082. Zeqiri B. Errors in attenuation measurements due to nonlinear propagation effects. J Acoust Soc Am 1992;91:2585–2593.