To develop an ultrasound elastography method for imaging a layered tissue structure, a plate-like single-layer tissue-mimicking phantom was made of synthetic gelatin (#0, Humimic Medical, Greenville, SC, United States) with 0.4w/v% silica gel (Product Number 288500, Sigma-Aldrich, Co., St. Louis, MO, United States) as scatters. In the meantime, a bulk phantom, in which both shear and surface waves can be generated, was also made of the same materials to compare the shear and surface waves to the wave generated in this single-layer structure. Instead of conventional gelatin from porcine skin, synthetic gelatin was chosen as the phantom material because this synthesis gelatin performs much better in handling tension and compression. With higher durability than the gelatin from porcine skin, synthesis gelatin can easily retain its shape after tension or compression, which makes it more suitable for mimicking muscles, including myocardium—the tissue of interest in this study. In addition, the thickness of the single-layer gelatin phantom was made to be 3.5 mm, the same as the average thickness of the rat heart thickness. The thickness of the bulk gelatin phantom is 40 mm, thick enough to allow for the generation of surface acoustic waves and shear waves.

A rat left ventricular tissue specimen was prepared to test the feasibility of the developed ultrasonic guided wave elastography method (for imaging layered tissue structures) in characterizing the elasticity of myocardial tissue for rodent models. To ensure the material properties of the specimen are similar to its in vivo status, the specimen was excised from the rat and tested within 2 hours after preparation. The left ventricular free wall was excised from the whole heart to prepare the specimen, cutting along the inter-ventricular septum from the base to the apex. The thickness of the tissue was measured in a minimum of three locations using a digital micrometer (2097A12, McMaster-Carr, Elmhurst, IL, United States), and the average value was 3.5 mm. The prepared specimen was nearly circular in shape, having an effective testing region of 6 mm by 6 mm for ultrasound elastography and mechanical testing.

In ultrasound elastography, two types of methods, i.e., group velocity-based method and phased velocity-based method, are available for deriving wave speeds and further evaluating tissue elasticity. Group velocity refers to the velocity of the overall wave envelope (containing many frequency components) generated by ARFI and propagating in the target tissue. In contrast, phase velocity refers to the velocity of each component wave propagating at their respective frequencies. For a non-dispersive medium, group velocity is the same as phase velocity. However, for a dispersive medium, which is the case for most soft tissues, group velocity differs from phase velocity.

In shear wave elastography, the primary method of ultrasound elastography, the velocity of group shear wave ( c s h e a r ) is normally acquired using the time-of-flight based method from the recorded wave propagation data. The corresponding tissue elasticity, evaluated either by shear modulus ( G ) or Young’s modulus ( E ), can be calculated using the following equations. In this study, mass density ρ for both gelatin phantoms and rat heart tissue was taken as 1,000 kg/m³, a typical value used in ultrasound elastography for convenience. G = ρ c s h e a r 2 (1) E ≈ 3 G (2)

Theoretically, the phase velocity-based method should be used to acquire accurate wave speed for the tissue of interest because most soft tissues are dispersive. However, the group velocity-based method is still the most frequently used way to extract wave speed and estimate tissue elasticity. The following are the main reasons. First, applying the phase velocity-based method requires that the tissue under test has relatively homogeneous mechanical properties throughout the region under test. This requirement is needed to ensure that the generated wave’s dispersion (which requires a path of propagation to develop fully) originates from the tissue under test only, not induced by any potential inhomogeneous composition of the tissue. This requirement can be satisfied locally in the region of interest in imaging the tissues, such as the cornea. (Tanter et al., 2009), artery wall (Couade et al., 2010), and human tendon (Helfenstein-Didier et al., 2016). But in many cases, when the target tissue is composed of more than one type of tissue (e.g., a tumor in healthy tissue), this requirement cannot be met, and the group velocity-based method must be used. Second, the group velocity-based method is capable of characterizing tissue inhomogeneity. In contrast with the phase velocity-based method, the group velocity-based method is not only capable of characterizing tissue inhomogeneity but also in favor of it. The group velocity-based method is highly preferred for applications in which tissue elasticity difference is used as a contrast mechanism to distinguish tissues of different types, and the actual elasticity value is not important. Even for cases where the value of tissue elasticity matters (but is not crucial), the group velocity method is also preferred due to its capability of mapping a large field of view instead of evaluating tissue elasticity of a relative small region.

In this study, both group velocity-based and phase velocity-based methods are used to process the experimental data obtained from the two tissue-mimicking phantoms to help develop an ultrasonic guided wave elastography technique for imaging layered tissue structures. With the established method, only the phase velocity-based method was used to process the data acquired from the rat heart tissue.

Phase velocity-based method contains two steps to derive wave speeds for the target tissue: first, a dispersion curve is extracted from the recorded wave, and then wave speed at differenct frequenicies are retrieved from the dispersion curve.

Mechanical testing was also performed on the same heart tissue specimen to examine the reliability and accuracy of the developed ultrasonic guided wave elastography method in evaluating the elasticity of rat heart tissue. Since mechanical testing is currently the gold standard method for assessing the mechanical properties of biomaterials, in this study, the elastic modulus obtained from mechanical testing was used as reference values to determine the reliability of the measurements obtained from ultrasound elastography.

The plate-like single-layer tissue-mimicking gelatin phantom was tested first to check the feasibility of the proposed experimental setup shown in Figure 1A for imaging layered tissue structures. It was confirmed that acoustic radiation force impulse (ARFI) can generate propagating waves in this phantom. Since the energy of such acoustic waves is mainly confined within the layered structure during propagation, these waves are commonly called guided waves. In this study, the speed of the guided wave generated in the single-layer gelatin phantom was evaluated by tracking its propagation using the group velocity-based method. Figure 4A shows the speed map of the generated guided wave acquired in the rectangular area of 2 mm by 4 mm, which is marked in the B-mode image of the single-layer gelatin phantom. For comparison, the surface wave speed map and shear wave speed map of the same size evaluated for the regions marked in the B-mode image of the bulk gelatin phantom are shown in Figure 4B. The average speeds of these speed maps and their standard deviations were computed and listed in Table 1 and plotted in Figure 4C.

Table 1; Figure 4C readily show that the speed of the guided wave is the smallest of the three, 25% smaller than the surface wave speed and 43% smaller than the shear wave speed. Because these three waves are generated in the same material with different geometric conditions, the influence of medium geometry (or boundary condition) on wave speed can be clearly observed.

The phase velocity-based method was applied to first evaluate the phase velocities of all three types of waves (guided wave, surface wave, and shear wave) investigated in this study and then to calculate the guided wave’s corresponding shear wave speed based on its phase velocity. The reason for retrieving the shear wave speed from the guided wave generated in the single-layer gelatin phantom is to perform tissue elasticity evaluation. This is because shear wave speed is a material property not affected by sample geometry, but guided wave speed is affected not only by material property but also sample geometry.

The first step in obtaining the phase velocity of the waves is to perform dispersion analysis. Different from the group velocity-based method, in which a group velocity can be evaluated for every position (pixel) of the field of view, the phase velocity-based method can only provide a dispersion curve and corresponding phase velocities for each axial position (corresponding to a lateral-time data set). Figure 5A shows an example of choosing an axial position for the dispersion analysis of each wave, in which the dashed line indicates the path of each wave’s propagation.

Before evaluating the phase velocity from a dispersion curve using Equation 3, the effective frequency range of the data under analysis should be found. Figure 5B shows the 2DFFT of the lateral-time domain data chosen from the single-layer gelatin phantom with only the top 1% intensity shown. From this figure, the effective frequency range was identified as from 160 Hz to 580 Hz, and the average and standard deviation of the dispersion curve within this range were computed as the estimate of the phase velocity of the guided wave and its standard deviation. The same operations were also done for the surface wave and the shear wave, and the results were listed in Table 2 and compared in Figure 5C. For comparison, the group wave velocities of these three wave types were also depicted in Figure 5C.

By comparing the ratios between the average and the standard deviation of the wave speeds evaluated over the range of effective frequency ( δ / c ¯ ) listed in Table 2, it can be readily seen that the ratio for the guided wave (20.55%) is much larger than those for the surface wave (3.07%) and shear wave (3.51%). This suggests that the phase velocity of the guided wave experiences a significant variation over the range of effective frequency (160 Hz–580 Hz). In contrast, those of the surface and shear waves are relatively consistent. The main reason for this phenomenon is that the guided wave in the layer gelatin phantom is dispersive, but the surface wave and shear wave in the bulk gelatin phantom are not. The comparison between the group velocities and the phase velocities in Figure 5C confirms this reasoning: for both the surface wave and shear wave, their phase velocities are very close to their group velocities (with a difference of 2% for the surface wave and 1% for shear wave), and so they are not dispersive; for the guided wave, this difference is as much as 24%, and so it is dispersive.

For evaluating the elasticity of a layered tissue structure, the corresponding shear wave speed should be retrieved from the dispersion curve of the guided wave. This can be accomplished by applying Equation 2 to the phase velocities over the range of effective frequencies. Figure 6 depicts these calculated values of shear wave speed over the effective frequency range; for comparison, it also depicts the dispersion curve. To obtain an estimate of the shear wave speed of the gelatin material (material property not affected by sample geometry), the average and standard deviation of the shear wave speeds retrieved shown in Figure 6 were calculated, and they are 6.61 m/s and 0.31 m/s, respectively.

To assess the reliability of shear wave speed evaluation using the phase velocity-based method applied to guided wave measurement (PVM-GW), Table 3 compares the average and standard derivation of shear wave speed evaluated from Figure 6 with those measured using the group velocity-based method (GVM) as in Table 1 and the phase velocity-based method applied to shear wave measurement (PVM-SW) as in Table 2. The ratios between average speed and standard derivation ( δ / c ¯ ) in Table 3 shows PVM-GW has similar consistency to PVM-SW in evaluating shear wave speed at effective different frequencies, both of which are much more consistent than GVM. More importantly, the average speed obtained using PVM-GW has a difference of −7.29% and −6.37% from those obtained using PVM-SW and GVM, respectively. In the field of ultrasound elastography, such differences are acceptable, and they confirms the feasibility of the phase velocity-based method (including Equation 4) in evaluating the shear wave speed of a layered tissue structure.

Thus, the proposed ultrasonic guided wave elastography method, including the experimental setup in Figure 1A and the phase velocity-based method for shear wave speed evaluation, was established as a reliable elastography method for imaging layered tissue structures and was ready to characterize the elasticity of the rat heart tissue in this study.

The phase velocity-based method was applied to evaluate the shear wave speeds of the rat heart tissue under different mechanical (stress and strain) states during the mechanical testing. The evaluation was executed on the guided wave elastography measurements, which were acquired during the stretching process of these three cycles (Cycles 6–8) of mechanical testing. Figure 7 shows the resultant shear wave speed estimates at their corresponding measurement times. Because data acquisition was done manually, the temporal gaps between two consecutive shear wave speeds retrieved is not the same.

Figure 7 shows that the retrieved shear wave speed increases as the mechanical stretching progresses for all three cycles. This speed variation trend is expected because the heart tissue becomes increasly stiffer along with stretching. Although the maximum and minimum speed values are different among different cycles (they were not obtained at the same relative time in each cycle), they approximately fall into the range of 6.5 m/s to 17 m/s. Applying Equation 1 and Equation 2, Young’s moduli of the rat heart tissue corresponding to these retrieved shear wave speeds can be obtained and discussed later.

The mechanical testing results of the rat heart tissue specimen are summarized in Figure 8. The stress-strain curves were obtained by averaging the measurements of three cycles (Cycle 9 to Cycle 11) in both circumferential and longitudinal directions, as in Figure 8A. Since the ultrasonic-guided wave elastography was performed in the longitudinal direction, only the stress-strain measurements obtained in the longitudinal direction were processed. To provide a general reference on the elasticity of the rat heart tissue for assessing the performance of the proposed ultrasonic guided wave elastography method, the longitudinal stress-strain curve was divided into three sections (low, middle, and high sections in Figure 8A), and linear regression was applied to these three sections for calculating Young’s moduli. The resultant Young’s moduli and their standard deviations are depicted in Figure 8B. From Figure 8B, we can see that Young’s modulus of the heart tissue increases as the tissue is stretching.

Based on the retrieved shear wave speeds of the rat heart tissue obtained from the guided wave elastography shown in Figure 7, Young’s moduli of the tissue were computed using Equations 1, 2 and depicted in Figure 9. To assess the accuracy of the elasticity measurements by ultrasonic guided wave elastography, the measurements by mechanical testing shown in Figure 8B were repeated in Figure 9 in the format of elasticity ranges for the low, middle, and high stress-strain states defined in Figure 8A. It can be readily observed that most of the data points obtained by ultrasound elastography fall between the upper boundary of the high stress-strain state and the lower boundary of the low stress-strain state. Since the measurements by mechanical testing are treated as actual values of tissue elasticity in this study, this observation suggests that the proposed ultrasonic guided wave elastography method could provide relatively reliable measurements for rat heart tissue.

Although this pilot study of cardiac elastography supports the feasibility of ultrasonic guided wave elastography in characterizing heart tissue elasticity, further studies of the developed method are needed to improve its reliability.

One of the further studies is to investigate the accuracy of converting the measured guided wave speed to shear wave speed. Currently, we used the empirical relationship in Equation 4 without examining its reliability. In future studies, both numerical and experimental investigations should be performed to evaluate the accuracy of this relationship. Considering the significant effect of sample thickness on the guided wave properties, a thorough investigation of the impact of sample thickness should be emphasized.

Because the major goal of this study is to check the feasibility of the developed method, a limited number of data sets were acquired and processed for both guided wave elastography and mechanical testing. For a more strict evaluation of the proposed ultrasound method, a detailed comparison of measurements between the two methods should be obtained. Taking the mechanical testing measurements as the actual values of tissue elasticity, the accuracy or error of the ultrasound-based measurements should be evaluated. If such a further comparison reaches the same conclusion as this study, the technology developed in this work will be ready for in vivo study.

With the feasibility of the developed ultrasonic guided wave elastography confirmed in this ex vivo study, the logical next step is to test its feasibility in vivo cardiac imaging in a rodent model. In such endeavors, challenges may occur, and adjustments to the developed method will be necessary.

One of the challenges is guided wave excitation. In this study, guided waves were excited in heart tissue using a very high frequency (15 MHz), which may not be effective for in vivo studies due to the high attenuation and the corresponding low penetration of high-frequency sound. To address this challenge, the single-transducer ultrasound elastography approach, in which elastic wave generation and tracking are performed by the same transducer, may be replaced by a dual-transducer approach, in which a low-frequency transducer is used to generate elastic waves and a high-frequency transducer to track the generated waves. Our preliminary in vivo studies show it is feasible to use a 5 MHz pencil case transducer to generate guided waves and use the high-frequency transducer, i.e., L22-14vLF, to track the generated waves. Another solution to this problem is to choose a relatively high-frequency transducer, such as a 10 MHz transducer, which can provide decent wave excitation power as well as high-resolution imaging for in vivo studies while using the single-transducer approach.

Another challenge is the selection of a coupling medium for ultrasound transmission. Water was used in this ex vivo study, but it is inconvenient for in vivo studies. To address this issue, typical ultrasound gel can replace water without affecting the wave properties, as confirmed in our investigation of surface acoustic wave elastography (Liu et al., 2023).