A Method for Characterization of Tissue Elastic Properties Combining Ultrasonic Computed Tomography With Elastography

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1 Technical Advance A Method for Characterization of Tissue Elastic Properties Combining Ultrasonic Computed Tomography With Elastography Tanya Glozman, MSc, Haim Azhari, DSc Objective. The correlation between various diseases and the change in the local mechanical properties of soft tissues has been long known. Over the past 20 years, there have been increasing research efforts to characterize mechanical properties of biological tissues using ultrasonic elastography. However, most of these works were based on characterization of only 1 type of waves (longitudinal or shear). The goal of this work was to devise a comprehensive ultrasound-based imaging method capable of measuring elastic parameters by combining both backscattered elastography and throughtransmitted ultrasonic computed tomography. Methods. Our suggested technique provides measurements of both longitudinal and shear wave velocities. This enables the noninvasive computation of several tissue elasticity parameters such as Young s and shear moduli, Poisson s ratio, and, more importantly, the bulk modulus, the determination of which requires both wave velocities. Four different phantom types were examined: agar-gelatin based phantoms and porcine fat tissue, turkey breast tissue, and bovine liver tissue in vitro specimens. The values of Young s modulus, the shear modulus, and Poisson s ratio were estimated and were consistent with values published in the literature. Results. The average bulk modulus values of the phantoms ± SD were 2.83 ± 0.001, 2.25 ± 0.01, 2.48 ± 0.01, and 2.53 ± 0.02 GPa, respectively. A statistically significant difference (P <.001) in the values of the bulk modulus of the different phantoms was found. Conclusions. The bulk modulus is suitable for differentiation between different tissue types. The obtained results show the feasibility of using a comprehensive ultrasonic imaging technique for noninvasive quantitative tissue characterization. Key words: bulk modulus; computed tomography; elastic parameters; elastography; tissue characterization; wave velocity. Abbreviations CT, computed tomography; TOF, time of flight; UCT, ultrasonic computed tomography Received August 25, 2009, from the Department of Biomedical Engineering, Technion, Israel Institute of Technology, Haifa, Israel. Revision requested September 3, Revised manuscript accepted for publication September 15, We thank Aharon Alfasi for valuable technical support and Dr Yoav Levy for helpful discussions. Address correspondence to Haim Azhari, DSc, Department of Biomedical Engineering, Technion, Israel Institute of Technology, Haifa, Israel. haim@bm.technion.ac.il For centuries, physicians have used palpation as a daily diagnostic tool. The efficacy of palpation is based on the fact that pathologic changes may alter the stiffness of tissues. 1 Moreover, the mechanical properties of malignant lesions are different than those of benign lesions. 2 However, in many cases, the small size of a pathologic lesion or its location deep in the body makes its detection and evaluation by palpation difficult or impossible. Furthermore, palpation is nonquantitative and lacks accuracy in locating the lesion by the American Institute of Ultrasound in Medicine J Ultrasound Med 2010; 29: /10/$3.50

2 Characterization of Tissue Elastic Properties The range of the elastic moduli of normal soft tissues spans over as much as 4 orders of magnitude. 3 The numbers are even greater when comparing normal tissue with malignant or benign lesions. 1 This has led to the development of the field of elastography. Although magnetic resonance elastography has been extensively investigated, 4,5 the modality prevailing in the field is ultrasound. In conventional ultrasonic imaging, stiffer tissue does not necessarily depict the substantial change in its sonographic properties. For example, prostate and breast tumors are substantially stiffer than the embedding tissue, yet in many cases, they do not depict sufficient contrast on standard ultrasound examinations. 6 Also, in diffused diseases such as liver cirrhosis, the overall stiffness of the liver changes, yet the sonogram may appear normal. 6 Thus, indirect elasticity measurements are commonly needed. A wide range of elastographic methods currently exist. Elasticity imaging methods all combine some form of tissue deformation technique with methods for detection of the corresponding tissue response. In the field of ultrasonic imaging, there are roughly 3 types of elastographic methods. The first is compression elastography or strain imaging, extensively researched by Ophir et al, 7 in which tissue is imaged before and after compression. The precompression and postcompression echo signals are compared using correlation techniques, and the tissue s strain map is calculated. The second is transient elastography, 8 12 in which low-frequency transient vibration is used to generate motion in the tissue. Tissue displacements are detected using pulse-echo ultrasound. The third method is vibrational sonoelastography, 13 in which Doppler techniques are used to image the propagation of low-frequency shear waves (<1 KHz) induced in the tissue by an external vibrator. A variation on the latest is the harmonic motion imaging technique, 14 in which a remote harmonically variable radiation force is applied to generate harmonic motion deep within the tissue, and the resulting harmonic displacements are estimated using cross-correlation techniques. The rationale behind all of these techniques is that a stiffer tissue will generally experience less strain than a softer one. Hence, it should be possible to detect a stiffer inclusion from the strain image or vibration pattern image. To the best of our knowledge, most ultrasoundbased elastography research has thus far been focused almost exclusively on analysis of back - scattered data and estimation of the shear modulus (or Young s modulus) alone by measuring the shear wave velocity, C S. These techniques are based on the assumption that the tissue is an incompressible material with a Poisson s ratio of 0.5. Assuming total incompressibility, the relation (1) is valid, where µ is the shear modulus, and E is the Young s modulus. In these studies, the tissue stiffness property is assessed by its shear or Young s modulus alone. The shear modulus describes the material response to shear stress, and Young s modulus describes its response to axial stress. These parameters are most suitable for describing the elasticity of isotropic solids and solidlike materials. They have been used extensively and successfully for measuring, modeling, and predicting the mechanical response of tissues such as skin, ligaments, cartilage, bones, and teeth. 3 However, soft tissues such as muscle, fat, and liver do not have a simple mechanical nature. Thus, there is no single parameter that can fully describe their elastic behavior. In this context, shear and Young s moduli are equivalent in the aspect that they both measure tissue response to a 1-dimensional stress. Furthermore, considering the fact that Poisson s ratio for soft tissues is about 0.5, measuring one or the other makes no difference because these parameters are related by Equation 1. Hence, the mechanical information provided by the bulk modulus is most important in 2 aspects: 1. The material property expressed by the bulk modulus is essentially different from the properties measured by either Young s or shear moduli: the bulk modulus describes the material resistance to uniform compression (see Equation 10). It should also be noted that the mechanical property expressed by the bulk modulus, material resistance to uniform compression, is somewhat related to what is felt in palpation examinations where the pressure on the tissue is applied from several directions. 388 J Ultrasound Med 2010; 29:

3 Glozman and Azhari 2. As shown below, the dynamic range of shear and Young s moduli is rather small, which makes statistical differentiation between different tissue types challenging. For the bulk modulus, however, our results show clear statistical significance in differentiation between different tissue types. Thus, the information embodied in the bulk modulus adds further insight on soft tissue s mechanical nature. Hence, the bulk modulus is important both as a standalone parameter and as additional information to the shear/young s modulus. Furthermore, elastography research has thus far focused mainly on measuring the shear wave velocity, whereas the longitudinal wave velocity was neglected. However, several recent articles prove the clinical merit of the longitudinal velocity for differentiation between different tissue types. Here are few examples: 1. Abdelwahab and Meziri 15 studied the potential usefulness of longitudinal sound wave velocity and attenuation for evaluation of hepatic diseases. Their conclusion, based on experimental results was The ultrasonic parameters (speed of sound and α1) exhibited a discriminating power to differentiate between healthy and pathological samples as well as between different pathological subgroups. This suggests a potential usefulness of the method for diagnosing. 2. Cuiping et al 16 used an ultrasonic computed tomography (UCT) device to measure longitudinal sound speed and attenuation in the breast tissue of more than 180 patients and concluded that Statistically, the malignant masses have elevated values of sound speed and attenuation parameters relative to the surrounding tissue. 3. Glide et al 17 used UCT to study the correlation between sound speed and density of the breast and found that dense breasts generally have high sound speeds. Therefore, they concluded that whole-breast sound speed can be used as an overall indicator of breast density, which is an important risk factor for breast cancer. In light of these studies, it is clear that longitudinal wave velocity is a clinically important parameter. Here, we propose a comprehensive approach to the soft tissue elasticity estimation problem that uses both backscattered and through-transmission data. We introduce a method by which the bulk modulus as well as shear and Young s moduli can be estimated and used as sources for tissue characterization. Specifically, we suggest using both UCT and transient elastography to measure both longitudinal wave velocity and shear wave velocity in tissue. We prove the feasibility of this approach and present our experimental results. Theoretical Background The theory of the transient and vibration elastographic methods is mainly based on the propagation of shear waves through elastic materials. Considering the complex properties of biological tissues, ie, their nonhomogeneity, nonlinearity, viscoelasticity, complex shape, and boundary conditions, a closed analytical general solution of such problems does not exist. However, ignoring these complexities and applying simplifying assumptions, the governing equation for a linear (elastic and isotropic) medium, considering small deformations and neglecting the effects of body forces (such as gravity), is given by 18 (2) where ρ is the density; u is the displacement vector; and λ and µ are the Lamè constants. The shear wave equation can be easily obtained from the above equation by noting that the term ( u) = 0 because there is no volume change in shear mode. From the remaining equation, µ 2 u = ρü, the corresponding wave equation is derived: (3) or J Ultrasound Med 2010; 29:

4 Characterization of Tissue Elastic Properties where the shear wave velocity is given by (4) To derive the equation for the longitudinal (pressure) wave, a potential function ψ, which fulfills the relation ψ = u is first defined. Then, using the vector identity 2 u = u u, and noting that u = 0 (which implies that the pressure wave is irrotational), we can obtain the wave equation for ψ: (5) (6) which leads to Thus, it can be noted that if both wave velocities, C S and C L, and the density of the medium are known, the 2 Lamè constants, λ and µ, can be calculated using the following equations derived from Equations 4 and 6: (9) The bulk modulus of a substance is defined by the following equation: P meaning K = V, V that it equals the pressure increase, P, required for a given relative change in volume, V. V The bulk modulus measures the compressibility of a substance. The values of the shear wave velocity, C S, for soft tissues are substantially smaller by orders of magnitude than the values of the longitudinal wave velocity, C L ; The C S values for soft tissues are typically in the range of 1 to 10 m/s, whereas typical C L values for soft tissues are around 1500 m/s. Accounting for this large difference between C S and C L, Equation set 9 can be approximated by (7) (10) Knowing the Lamè constants, the following elastic properties can be derived 19 : (8) where K *, E *, and υ* are the approximate bulk modulus, Young s modulus, and Poisson s ratio, respectively. It is clear, therefore, that both the longitudinal wave velocity and shear wave velocity are required to fully characterize the elasticity properties of a tissue. Materials and Methods where K is the bulk modulus; E is Young s modulus; and υ is Poisson s ratio. Expressed as a function of C S and C L alone, these equations become As explained above, if both wave velocities, C S and C L, and the density of the medium are known, the 2 Lamè constants, λ and µ, can be calculated (under the approximations stated above). From these constants, the other elastic parameters can be derived. The approach suggested here is therefore to use through-transmission UCT for 390 J Ultrasound Med 2010; 29:

5 Glozman and Azhari measuring C L and pulse-echo transient elastography for measuring C S. To achieve this goal, 2 experimental systems were devised: a UCT system for measuring C L and a transient elastography system for measuring C S. The data acquired from each system were processed separately, and the elastic parameters of interest were derived by integrating the results. Ultrasonic Computed Tomography System Ultrasonic computed tomography was first suggested by Greenleaf et al 20 in It mimics the configuration of x-ray computed tomography (CT) by using through-transmission acoustic projection. The UCT system built in our laboratory is schematically depicted in Figure 1. The system is composed of a pair of focused transducers (Panametrics, Austin, TX; central frequency of 5 MHz, diameter of 12.7 mm, and focal length of 10.2 cm) submerged in a water tank. The distance between the transducers is about twice the focal length. The transducers are set up on a mechanical assembly with 3 of freedom of movement controlled by software developed at our laboratory. The system can scan a user-defined cylindrical volume (up to 15 cm in height and 20 cm in diameter) at the center of the water tank. Two Panametrics 5800 pulser/ receivers were used for longitudinal wave through- transmission measurements. The pulse repetition frequency was 500 Hz, and the ultrasonic signals were sampled at 100 MHz. In the imaging configuration used here, the object is scanned using a planar CT mode (even though the system allows for volume imaging by spiral CT scanning, 21 only 1 plane was scanned in this study to simplify the experiments and data management). An acoustic time of flight (TOF) projection is acquired every 3 over 180. This yields a radon transform of 60 projections. The scanning resolution was set to mm ( 1 wavelength of the central frequency). The obtained raw data were first bandpass filtered to reduce measurement noise. Then the corresponding TOF sinogram (radon transform) was extracted. A typical TOF sinogram is shown in Figure 2. Each horizontal line in the sinogram represents a projection taken at a different angle. Each pixel corresponds to a different lateral position (the total length of the scan was 170 mm Figure 1. Computed tomography system: experimental setup. An object is placed in a water tank between 2 ultrasonic transducers. A signal is transmitted from 1 transducer and detected by the other. An analog to digital (A/D) sampling card samples the data. An image is obtained by scanning the object in the planar CT mode. [567 pixels using the specified resolution of 0.3 mm]). After acquisition, the ordered subsets expectation maximization algorithm 22 was applied for image reconstruction. The output from this step is a reconstructed cross-sectional image of the scanned object in which each pixel value represents the corresponding longitudinal wave speed C L in that pixel. Figure 2. Example of a TOF sinogram obtained from UCT projection data of a turkey breast submerged in water. Each pixel value in the sinogram depicts the TOF for the corresponding acoustic ray. Brighter gray levels correspond to a short TOF (faster speed of sound). J Ultrasound Med 2010; 29:

6 Characterization of Tissue Elastic Properties Transient Elastography System The transient elastography system used for generating and measuring the shear wave velocity is schematically depicted in Figure 3. The system is basically composed of 2 main elements: a shear wave generator and a pulse-echo system for registering the backscattered waves in the M-mode. The shear wave source was a bimorph made from 2 piezoelectric beams (QuickPack type 15w piezoelectric actuator; Midé, Medford, MA) set in contact with the object. The actuator was activated by applying a short pulse of low-frequency voltage to the beams. The low-frequency pulse consisted of 1 cycle of an 8-Hz square wave. It was generated by a Tabor 8026 arbitrary waveform generator (Tabor Electronics Ltd, Tel Hanan, Israel) and amplified by a Horizon Electronics amplifier (Horizon Electronics, Inc, Hays, KS). The M-mode monitoring subsystem was composed of a computerized pulser/receiver ultrasonic box (Panametrics 5800) connected to a focused transducer (Panametrics; central frequency of 5 MHz, diameter of 12.7 mm, and focal length of 10.2 cm) submerged in a water tank. The transducer operated in the pulse-echo mode with a pulse repetition frequency of 800 Hz. The ultrasonic signals were sampled at a sampling rate of 100 MHz. Figure 3. Elastography system: experimental setup: A piezoelectric shear wave source is in close contact with the object. Arrows indicating the motion vector. Tissue displacement is detected using an ultrasound transducer. A/D indicates analog to digital; and I/O, input/output. Tissue displacements caused by the propagating shear wave were imaged by the M-mode monitoring subsystem. The vibrator pulse was synchronized with the signal acquisition initiation by a digital input/output card (National Instruments, Austin, TX). The transducer scanned the object along the z-axis. Five M-mode scans were acquired at each height along the z-axis with 1-mm steps. Because the shear wave propagation direction is from the top of the phantom (at z = 0), where the actuator is located, to the bottom, we expected to find increasing wave arrival times in scans of lower image planes (at z > 0). The signals were analyzed for shear wave propagation detection and measurement of shear wave speed by the following steps: The raw data were first bandpass filtered to reduce noise. A cross-correlation algorithm was then applied on each scan to measure the displacement pattern of each pixel along the axial direction (Figure 3, y-axis). To improve signal to noise ratio, 5 consecutive scans were averaged at each height along the z-axis. These steps were repeated for each height level. At this stage of the algorithm, a pattern of the displacements caused by the shear wave at every height (z-axis) and at every location along the y-axis was obtained. From these data, the arrival times, τ a, of the wavefronts were derived. The corresponding propagation speed for the shear wave, C S, was then obtained by applying linear regression to τ a versus z. The shear wave velocity is simply the inverse of the slope of that graph. Phantoms Experiments were performed on 3 different types of tissues (in vitro): turkey breast, bovine liver, and porcine fat. All tissues were bought at a local butcher several hours before the experiment. All tissue specimens were cut and prepared to be as homogenous as possible. Each phantom type was measured several times to verify reproducibility of the results: there were a total of 8 liver samples, 8 turkey breast samples, 11 porcine fat samples, and 3 agar samples. In addition, tissue-mimicking agar-gelatin based phantoms were prepared and examined. These were prepared by mixing 3% agar (Difco Laboratories, Detroit, MI) and 6% gelatin (type A; Sigma-Aldrich Corp, St Louis, MO) with deionized 392 J Ultrasound Med 2010; 29:

7 Glozman and Azhari boiling water. A 0.25-g/mL silicon carbide powder (Buehler, Lake Bluff, IL) was added to the mixture before cooling to enhance the echogenic properties of the phantom. The preparation process was as follows: first, the deionized water was heated atop a magnetic stirrer until the boiling point was reached, and then the agar and gelatin powders were slowly added while stirring. The mixture was then left at room temperature for 0.5 hour while stirring; the carbon powder was then added; and then the mixture was poured into a box-shaped plastic mold with dimensions of cm and was left for 1 additional hour to cool. Results The first 2 subsections below describe the results obtained from each technique (longitudinal wave velocity from UCT and shear wave velocity from transient elastography). Finally, the results obtained by integrating these 2 techniques for estimation of the elastic constants are described in the final subsection. Ultrasonic Computed Tomography An exemplary TOF sinogram obtained for a turkey breast tissue specimen using the UCT system is presented in Figure 2. Each line in the sinogram represents a projection taken at a different angle. As noted above, projections were acquired over 180 with an angular increment of 3. Each pixel value in the sinogram depicts the TOF for the corresponding acoustic ray. Brighter gray levels correspond to a shorter TOF (faster speed of sound). Typical UCT cross-sectional reconstruction images depicting the longitudinal wave velocity (C L ) maps for the 4 different phantoms are shown in Figure 4. Brighter gray levels correspond to a higher speed of sound. The gray scale range has been adjusted to enhance the contrast of the images to allow better visualization of the phantoms on the surrounding background; hence, the gray scale range for the 2 upper images (turkey breast tissue and bovine liver tissue phantoms) displays sound velocities between 1450 and 1620 m/s, and the gray scale range for the 2 lower images (porcine fat tissue and agar-gelatin phantom) displays sound velocities between 1450 and 1520 m/s. (The streak artifacts that appear on these images stem from the fact that only 60 projections were used, ie, undersampling). The characteristic values of the longitudinal wave velocity for each phantom were obtained by calculating the average values within several selected regions of interest within the object. The longitudinal velocity values for the different phantoms are summarized at Table 1. Transient Elastography A typical tissue displacements map obtained using the transient elastographic technique is presented in Figure 5. This image depicts the displacements induced in the turkey breast tissue by the shear wave propagation along a vertical line at a specific y location chosen at the middle of the phantom. These displacements are plotted as a function of time (x-axis) and the distance from the shear wave source (y-axis). The shear wave pulse was given at time t = 0 seconds, and the vibrator is located at the top surface of the phantom (z = 0 mm). Two observations can be noted when inspecting this image: first, the arrival time of the shear wavefront (at the left side of the image) is linearly related to the distance from the top of the phantom, forming a slanted strip. Second, the wave is attenuated as it progresses through the tissue. This is manifested by the drop of the displacement amplitude over depth. The arrival time vector, τ a, for each scan was calculated using a cross-correlation based algorithm as explained in Materials and Methods under Transient Elastography System. The shear wave velocity was derived by finding the linear fit of the arrival times versus the distance from the vibrator. An example of such data is shown in Figure 6. The shear wave velocity is simply the inverse of the slope of that graph. Integration of the Results Table 1 summarizes the average and SD values for C S and C L of all phantoms. The measured C L and C S values for all samples and phantom types are also graphically depicted in Figure 7. The C S values for the different phantoms are plotted at the average C L value and vice versa. The ellipses indicate an area of 1 SD; the horizontal radius of J Ultrasound Med 2010; 29:

8 Characterization of Tissue Elastic Properties the ellipses is equal to the SD of the corresponding C S, and the vertical radius is equal to the SD of the corresponding C L. Several important points arise when inspecting Figure 7 and Table 1: 1. Most of the measured values for C S fall in the range 1 to 10 m/s. This is consistent with the values reported in the literature (Bercoff et al, 8 Catheline et al, 9,10 and Gennisson et al 12 ). The values measured for C L were also consistent with the values reported in the literature The SD for C S values of the different phantoms is rather large. Furthermore, the averages for C S of all phantom types except fat were very close. To check the statistical significance, a t test was performed on the shear wave velocity data. The P value was calculated for each phantom pair, and the results were as follows: it was found that the differences between C S values of all phantom types except fat were not statistically significant (P >.1). As for the fat tissue phantoms, although the scatter for C S of fat was rather large, its values were significantly different from those of the other tissue types (P <.001). This is consistent with previous reports, such as that of Gennison et al. 12 The difference between the C S values measured for the different phantoms was not statistically significant. This is also consistent with previous reports, such as that of Gennisson et al, 12 Figure 4. Longitudinal wave velocity images obtained from UCT. A, Turkey breast tissue phantom. B, Bovine liver tissue phantom. C, Porcine fat tissue phantom. D, Agar-gelatin based phantom. Brighter gray levels correspond to a higher speed of sound. Note that the gray scale is different for A, B, C, and D to allow better detail visualization. A B C D 394 J Ultrasound Med 2010; 29:

9 Glozman and Azhari Table 1. Average and SD Values of Longitudinal and Shear Wave Velocities for the Different Phantoms Velocity Agar Porcine Fat Turkey Breast Bovine Liver C L, m/s ± ± ± ± 7.0 C S, m/s 2.6 ± ± ± ± 0.4 who showed that the shear wave velocity values of soft tissues vary extensively (up to a ratio of 4 between the smallest and the highest measured values for the same tissue specimen) because of their strong heterogeneity. This implies that it is not possible to differentiate these phantom types on the basis of measurements of C S alone. Contrary to C S variance, it was found that the discrepancy in the C L values for the different phantoms was very high and statistically significant. It can be concluded that the longitudinal wave velocity can serve as a better discriminator between different tissue types. 3. There exists a clear difference in the C L values of the different phantom types. To verify this observation and prove statistical significance of the differences, a t-test was performed on the C L values of the different phantoms. It was found that all tested phantom types differed significantly from each other (p-value < 0.001). Estimation of the Elastic Constants Equation set 9 was used to estimate the value of the elastic constants from the measured longitudinal and shear wave velocities (C L and C S ). Because the density values that appear in these equations cannot be measured directly in a noninvasive manner, an average density of 1000 kg/m 3 was taken for all tissue specimens. For the agar-gelatin phantom, the actual measured value of 1277 kg/m 3 was used. Table 2 summarizes the average and SD values for Young s modulus, the shear modulus, and the bulk modulus of all phantom types. It can be noted from that table that the differences in Young s and shear moduli between the different phantom types were not statistically significant. In fact, P values for the differences in the Young s and shear modulus values for turkey breast tissue, bovine liver tissue, and agar-gelatin phantoms were greater than.25. A statistically significant difference was noted only between Young s and shear modulus values of porcine fat tissue and all other phantom types (P <.01). As was expected, the value of Poisson s ratio for all phantom types was 0.5 (with an accuracy of up to the fifth decimal point). Contrary to that, there was a clear difference between the values of the bulk moduli for the different tissue types. Moreover, the SDs were small, and the values of the bulk moduli for each tissue type were well localized. To verify this and prove statistical significance of the differences, a t test was performed on the bulk modulus values of the different phantoms. It was found that all tested phantom types differed significantly from each other (P <.001). Bulk modulus values for the different phantoms are graphically displayed in Figure 8. These results indicate that the bulk modulus is a distinctive parameter and can be used as a potential source of contrast for ultrasonic imaging and tissue characterization. Figure 5. Displacements induced in turkey breast tissue by the shear wave pulse as a function of the distance from the shear wave source (which is located at z = 0 mm; top) versus time. Brighter grey levels correspond to a larger displacement amplitude. J Ultrasound Med 2010; 29:

10 Characterization of Tissue Elastic Properties Figure 6. Wavefront arrival time as a function of depth: original data and a linear fit. Discussion In this study, the feasibility of a combined method for measuring tissue elasticity was shown. The suggested method uses both UCT and transient ultrasonic elastography to measure both longitudinal and shear wave velocities, C L Figure 7. Shear wave velocity (C S ) and longitudinal wave velocity (C L ) graph for all samples and phantom types. The C S values for the different phantoms are plotted at the average C L value and vice versa. The surrounding ellipses denote an area of 1 SD; the horizontal radius of the ellipses is equal to the SD of the corresponding C S, and the vertical radius is equal to the SD of the corresponding C L. and C S, in the same experimental setup. Using this method, it is possible to estimate all elastic parameters through equations of linear elasticity. This includes Young s and shear moduli, which can also be measured by other previously introduced elastographic techniques. 1,5,6,9,12,13 More importantly, however, it also enables the determination of Poisson s ratio and the bulk modulus, whose values can only be determined by using both velocities. This provides a comprehensive characterization of the mechanical properties for the examined soft tissue. To the best of our knowledge, the ultrasonic determination of these 2 parameters has not been reported previously. The measured values for C S and C L were consistent with the values reported in the literature (eg, Bercoff et al, 8 Catheline et al, 9,10 Gennisson et al, 12 Bishop et al, 23 and Duck 3 ) with the exception of the shear wave velocity values measured for fat. The values found here (7.2 ± 2.5 m/s) were significantly higher than those reported previously 23 of about 1 m/s. This discrepancy may be attributed to 2 possible reasons: The measurements in the other studies were done for fat at a temperature of 37 C, whereas our experiments were held at room temperature ( 25 C). It is well known that fat has a strong dependence of longitudinal wave velocity on temperature. For example, Bamber and Hill 24 reported a drop of about 100 m/s in the longitudinal wave velocity for bovine fat as the temperature rises from 21 C to 37 C. It is reasonable to assume that the increase in velocity as temperature decreases is characteristic of shear waves as well. Bishop et al 23 measured shear wave velocity at frequencies of 125 and 250 Hz, whereas the shear wave frequency in our experiments was only 8 Hz. Catheline et al 10 reported that there is a global increase in velocity when the frequency decreases. Thus, shear wave dispersion may have also contributed to the relatively high values of the velocities measured in our experimental setup. The resulting values calculated for shear and Young s moduli were consistent with the literature as well (eg, Duck 3 ). All Poisson s ratios experimentally obtained here complied with the incompressibility assumption (eg, Gao et al 6 ), yielding a value of 0.5 up to the fifth decimal point. 396 J Ultrasound Med 2010; 29:

11 Glozman and Azhari Table 2. Average and SD Values of the Young s Modulus, Shear Modulus, Bulk Modulus, and Poisson Ratio Young s Modulus Shear Modulus Bulk Modulus Poisson Ratio Phantom (D), kpa (G), kpa (K), GPa (υ) Agar-gelatin 26.8 ± ± ± ± 4.8e 007 Porcine fat tissue ± ± ± ± 5e 006 Turkey breast tissue 31.9 ± ± ± ± 1e 006 Bovine liver tissue 31.1 ± ± ± ± 3e 007 The differences in Young s and shear moduli obtained for the different phantom types examined here were not statistically significant. P values for the turkey breast tissue, bovine liver tissue, and agar-gelatin phantoms were greater than.25. A statistically significant difference was noted only between the Young s and shear moduli values of porcine fat tissue and all other phantom types (P <.01). Contrary to those findings, bulk modulus values obtained for all examined tissue types were significantly different. The average bulk modulus values for the agar-gelatin phantoms, porcine fat tissue, turkey breast tissue, and bovine liver tissue were 2.83 ± 0.001, 2.25 ± 0.01, 2.48 ± 0.01, and 2.53 ± 0.02 GPa, respectively (corresponding P <.001). This clearly indicates the potential use of the bulk modulus for tissue differentiation and classification. As noted, the bulk modulus can be determined only by combining both longitudinal and shear wave velocity measurements. Hence, these results indicate the usefulness of combining UCT with elastography for noninvasive estimation of the mechanical properties of soft tissues. In this study, we have used an actuator set in direct contact with the tissue. Because of the accessibility and setup limitations, the suggested method may have potential clinical applications mainly in breast tumor ultrasonic imaging because the breast is accessible for both UCT and mechanical actuator stimulation, as in the setup used here. The suggested technique may potentially serve as a diagnostic screening tool for breast cancer detection and ultimately serve as a complementary method to mammography. Furthermore, it is conceivable to use remote actuation for measuring shear wave velocity by applying acoustic radiation force impulse 25 or harmonic motion imaging. 14 This may allow application of this method for internal or less accessible organs as well. Figure 8. Bulk modulus values for the different phantoms, calculated assuming density of 1000 kg/m 3 for all tissue specimens. For the agar phantom, density was measured directly, and the value was 1277 kg/m 3. Error bars denote a range of 1 SD around the average. J Ultrasound Med 2010; 29:

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