Citations

Propagating shear waves in tissue can be measured with high frame rate Doppler or correlation methods. The measured characteristics of the shear waves, such as speed versus frequency, can be used to deduce material properties such as complex viscoelastic modulus using physics models appropriate to the geometry and properties of the tissue. This inverse problem is characterized by calculating the storage and loss modulus as a function of frequency and requires appropriate tissue motion, which in turn requires optimized dynamic radiation force distributions. We will discuss novel radiation force distributions that provide enhanced tissue motions appropriate to dealing with the inverse problem of determining tissue material properties from ultrasonically measured tissue motion.

The response of an embedded sphere in a viscoelastic medium excited by acoustic radiation force has been studied in both the time- and frequency-domains. This model is important because it can be used to characterize the viscoelastic properties of the medium by fitting the response to the theoretical model. The Kelvin–Voigt model has been used exclusively in these models. An extension to the previously reported models is described so that any viscoelastic rheological model can be used. This theoretical development describes the generalized embedded sphere response both in the time and frequency domains. Comparing the results from derivations in both domains showed very good agreement with a median absolute error (MAE) ranging from 0.0044 to 0.0072. Good agreement is demonstrated with finite element model simulations and the theory with a MAE of 0.006. Lastly, results for characterization of gelatin and rubber materials with the new theory are shown where the MAE values were used to determine which rheological model best describes the measured responses.

Arterial elasticity has been proposed as an independent predictor of cardiovascular diseases and mortality. Identification of the different propagating modes in thin shells can be used to characterize the elastic properties. Ultrasound radiation force was used to generate local mechanical waves in the wall of a urethane tube or an excised pig carotid artery. The waves were tracked using pulse-echo ultrasound. A modal analysis using two-dimensional discrete fast Fourier transform was performed on the time–space signal. This allowed the visualization of different modes of propagation and characterization of dispersion curves for both structures. The urethane tube/artery was mounted in a metallic frame, embedded in tissue-mimicking gelatin, cannulated, and pressurized over a range of 10–100 mmHg. The k-space and the dispersion curves of the urethane tube showed one mode of propagation, with no effect of transmural pressure. Fitting of a Lamb wave model estimated Young’s modulus in the urethane tube around 560 kPa. Young’s modulus of the artery ranged from 72 to 134 kPa at 10 and 100 mmHg, respectively. The changes observed in the artery dispersion curves suggest that this methodology of exciting mechanical waves and characterizing the modes of propagation has potential for studying arterial elasticity.

Arterial elasticity has gained importance in the past decades as it has been shown to be an independent predictor of cardiovascular diseases. Ultrasound radiation force has been used to excite propagating waves in arterial vessels in order to measure the wave speeds and characterize the elastic properties of the vessels. Excised pig carotid arteries were excited with impulsive radiation force using 3-MHz tonebursts of length 200, and the propagating waves were measured along the length of the artery over a distance of 2 cm. A 2-D fast Fourier transform was performed on the spatiotemporal data for identification of several propagating modes in the vessel. Multiple propagating modes could be visualized from the spatiotemporal data that varied with the transmural pressure of the artery under investigation over a range of 10–100 mm Hg. The modes present in the data were fitted with a theoretical model to estimate the elasticity of the arteries. The comparison with the model provides insight into characterizing the elastic properties of the artery. [This work was supported in part by NIH Grant no. EB002640.]

Vibro-acoustography with rectilinear raster scanning using confocal or linear array transducers have been reported before. Endo-cavity imaging requires a different type of scanning due to space limitation. This paper describes 3-D endo-cavity vibro-acoustography by a rotating linear array that scans the volume of interest. In this configuration a linear array is used to steer the beam electronically, which is combined with the rotational motion of the transducer to scan the beam in a cylindrical volume. This particular geometry produces special artifacts in the image. One such artifact is non-uniformity in signal power due to angular variations with respect to the hydrophone. Another artifact is related to the geometrical distortion in the image. In this paper, we will present examples of vibro-acoustography images with linear and rotational scanning and describe image characteristics and methods to reduce the artifacts. [Work supported by NIH Grant P50 CA91956P2.]

Characterization of viscoelastic soft tissues and materials has been a subject of active research for the past two decades. Techniques involving measuring the motion of embedded spheres in viscoelastic media have been employed to measure the viscoelastic material properties of the media surrounding the sphere. The published work using this technique has been restricted to using the Kelvin–Voigt model, which has worked for gelatin-based materials. We report an extension of this method using different viscoelastic rheological models such as the Maxwell, generalized Maxwell, Zener, and Kelvin–Voigt fractional derivative models. We performed experiments using a focused 3-MHz transducer to produce radiation force and a 7.5-MHz pulse-echo transducer to measure the sphere motion. Two phantoms were tested; one made of gelatin and another made of rubber with stainless steel spheres embedded in the materials. The response was fitted with the generalized theoretical model to find the material properties over bandwidths of 25–3000 Hz. The median absolute errors ranged from 0.0036–0.0421 and 0.0365–0.0879 for the gelatin and rubber phantoms, respectively. This generalized method offers added flexibility to characterize different types of viscoelastic materials using the most appropriate rheological model. [Work supported in part by NIH Grant nos. EB002167 and DK082408.]

Rapid calculations of the intensity are required for models of the radiation force generated by linear ultrasound phased arrays. To determine the computation times and numerical errors produced by two medical ultrasound simulation packages, namely, FIELD II and FOCUS, comparisons of the calculated pressures and intensities are performed using a simulated Vermon L5 phased array probe with 128 active elements. In these simulations, the array generates a fixed focus 25 mm from the array for a 5-MHz excitation, and the pressure field is computed on a 133 × 133 × 261 rectilinear grid that is centered at the focus. Half wavelength sampling is employed in all three directions. In FIELD II, this calculation takes approximately 4 h on a 64-bit laptop running Linux, and in FOCUS, the same calculation takes less than 4 min on the same computer. The numerical errors are also much smaller with FOCUS. Details of the simulation approaches employed for this transducer model will be presented, including selection of FIELD II and FOCUS simulation parameters and calculations of the reference pressure field for error evaluations. The impact of numerical errors on shear wave calculations will also be discussed.

Vibro-acoustography is an ultrasound-based imaging modality that maps the acoustic response of an object induced by acoustic radiation force. The method employs two ultrasound beams with frequencies separated by a small difference, typically in the kilohertz range. Using a 1.75D array transducer, which has multiple rows of elements, offers an advantage over linear array transducers because it allows for focusing in the elevation direction. We have performed simulations of different arrangements for the apertures assigned to the two ultrasound frequencies and evaluated resolution and sidelobe levels for different arrangements. However, the large size of the elements produces grating lobes in the transmitted fields. We will describe metrics for evaluating grating lobe levels compared to the main lobe of the transmitted field as a quantitative approach to optimize aperture design. We present experimental measurements of the transmitted field and compare with simulation results. Finally, we present imaging results from phantom experiments. This beamforming study is directed toward improving vibro-acoustography image formation using a General Electric Vivid 7 scanner for breast and thyroid imaging. [Mayo Clinic and two of the authors have potential financial interest related to devices or technology referenced above. Work supported by NIH Grant No. R21CA121579 and AIUM Award No. AIUM-EER#1.]

Multiple methods have been proposed to characterize the viscoelastic material properties of soft tissues to differentiate normal from pathological tissue. Shearwave dispersion ultrasound vibrometry is a method that uses the dispersion of the shear wave velocity to characterize tissue shear elasticity and viscosity. It has recently been shown [M. W. Urban and J. F. Greenleaf, Phys. Med. Biol. 54, 5919–5933 (2009)] that the Kramers–Kronig relationships can be applied to shear wave measurements in ex vivo skeletal muscle over a frequency bandwidth of 100–600 Hz. We will describe this process where shear wave attenuation is modeled using a power law, and the shear wave velocity dispersion is predicted by applying the Kramers–Kronig relationships. In this study, we apply this method to shear wave propagation measurements made in different soft tissues such as ex vivo porcine skeletal muscle and kidney and in vivo porcine liver. The shear wave velocity predictions using the Kramers–Kronig relationships agree with the velocity measurements. The mean square error for these tissues ranged from 0.0024–0.0625 m2/s2. The Kramers–Kronig relationships can be used in shear wave propagation measurements in different types of soft tissues. [This work was supported in part by NIH Grants Nos. EB002167 and DK082408.]