Urban, Matthew W.

The objective of this study was to analyze and optimize the ultrasound radiation force source for creating shear waves for quantitative elasticity and viscosity measurements. A simulation model based on work by Bercoff et al., [IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 51(11), 1523–34 (2004)] was utilized to examine the shear wave propagation from a spatiotemporal impulsive force and the simulated radiation force generated from a linear array transducer. Parameters such as aperture size, F-number of the transducer, and medium shear elasticity and viscosity were varied to analyze how the shear wave amplitude and shape changes. The wave attenuation and group and phase velocities were evaluated. The aperture size and the F-number of the transducer affected the spatial distribution of the propagating shear wave significantly. The influence of the coupling term between the bulk and shear waves was analyzed spatially and temporally by evaluating parameters such as shear wave amplitude, wave attenuation, and the group and phase velocities. This simulation model provides insight for making shear wave propagation measurements from the perspective of optimizing the spatial and temporal characteristics of induced shear wave motion from an applied radiation force. [This work was supported in part by Grant EB002167 from NIH.]

Diastolic dysfunction is the impaired ability of the left ventricle (LV) to passively fill during diastole and maintain its stroke volume at physiologic filling pressures and is associated with impaired relaxation and reduced compliance of LV. Knowledge of the quantitative values of the myocardial viscoelastic properties would improve the clinician’s ability to evaluate diastolic dysfunction in patients. To gain better understanding of the viscoelastic properties of the LV as a function of geometry, we studied Lamb wave propagation in different directions in excised porcine free-wall myocardium. The phantom consisting of a dissected porcine LV free-wall embedded in gelatin was fixed in a water tank. A mechanical shaker was used for harmonic excitation over a range of 40–500 Hz and a 7.5 MHz ultrasound transducer was used for motion measurements. Motion amplitude and phase at different depths of the sample were analyzed to obtain dispersion curves in four orthogonal directions. The data were fitted to the Lamb wave equations and shear elasticity and viscosity coefficients were estimated. The values of μ1 and μ2 were 13.75 ± 0.96 and 5.86 ± 0.75 Pa s. Our results suggest that the viscoelastic characteristics of the porcine LV free-wall in orthogonal directions were similar.

The objective of this study was to assess the potential for noninvasively identifying viscoelastic material properties in arterial vessels using ultrasound radiation force and modern computational inverse problem techniques. A rubber tube embedded in gelatin was excited at different points along the axis using impulsive ultrasound radiation force. The resulting mechanical waves were measured using a laser vibrometer and pulse-echo ultrasound. The inverse problem was cast as an optimization problem, in which the discrepancy between the measured dynamic response and the computed finite element model response was minimized with respect to viscoelastic material parameters. The model was very sensitive to the tube’s viscoelastic parameters and relatively insensitive to those of the gelatin. The viscoelastic properties of the tube obtained from the inverse problem were compared to the results obtained from a dynamic mechanical analyzer (DMA). For the overlapping range of frequencies (130–190 Hz), the results of the inverse problem gave an equivalent modulus that range from 7.3–8.5 MPa, while the DMA values range from 6.0–9.2 MPa. These results have important implications for using ultrasound radiation force in noninvasive characterization of the viscoelastic properties of arteries in vivo. [This work was supported in part by Grant No. EB002640 from NIH.]

Dynamic ultrasound radiation force can induce local tissue vibration. To understand the tissue response, we developed a method to ultrasonically measure the induced motion. We present a model for motion detection in a vibrating scattering medium. We developed a harmonic pulsed excitation method using tonebursts repeated at frequency fr. This excitation method creates a multifrequency force with components at harmonics of fr. We use pulse-echo ultrasound and narrowband Kalman filtering to perform multifrequency motion detection. In an experiment, a 3.0 MHz air-backed transducer was used to create the radiation force, and with the same transducer performed pulse-echo motion detection at 9.0 MHz. Bovine muscle was used for radiation force excitation and motion detection. We present simulation results for a parameterized model of motion detection in a scattering medium. We show experimental measurements of vibration displacement and phase for motion with amplitude of 0.1–10 μm. Our simulation model provides a platform to optimize detection of small harmonic motion in a scattering medium. Multifrequency harmonic pulsed excitation and detection methods are presented that induce and measure very small amplitude harmonic motion.

Vibro-acoustography is a method that uses ultrasound radiation force to investigate the mechanical response of an object [Fatemi and Greenleaf, ‘‘Ultrasound-stimulated vibro-acoustic spectrography,’’ Science, 280, 82–85 (1998)]. The dynamic radiation force causes the object to vibrate within the focal region of the transducer, which creates a sound field called acoustic emission measured by a hydrophone. To gain a better understanding of the objects investigated with vibro-acoustography, a method is proposed that measures the displacement of the local vibration. A pulse-echo ultrasound method is implemented with the same transducer used to create the radiation force to measure the displacement of the object. A Kalman filter approach is used to process the pulse-echo data to obtain estimates of the local displacement [Zheng et al., ‘‘Kalman filter motion detection for vibroacoustography using pulse-echo ultrasond,’’ 2003 IEEE Ultrasonics Symposium, pp. 1812–1815 (2003)]. Results using this ultrasound method to measure vibration of a metal beam compare well with laser vibrometer results. This method can reliably measure displacements with amplitudes of 120–2000 nm with error less than 9%. A pulse-echo method is described that provides displacement detection with simultaneous radiation force generation for vibro-acoustography applications using a single transducer. [Work supported by Grants EB002640 and EB002167 from NIH.]

Vibro-acoustography is a method that uses the dynamic radiation force (stress) of ultrasound to locally excite an object at low frequency [Fatemi and Greenleaf, Science 280, 82]. A multifrequency vibro-acoustography method is proposed that uses a multifrequency radiation stress produced by an array transducer driven with N ultrasound frequencies. A multifrequency image at the different N(N−1)/2 frequencies is produced with one scan of the region of interest, increasing the information yield by a factor of N(N−1)/2. Image formation theory is presented for multifrequency vibro-acoustography using an annular array transducer. Simulations of the stress field were performed for a 20-element, 3.5-MHz annular array transducer. Four ultrasound frequencies produce six unique low-frequency components in the point spread function. Computer phantoms with small spheres are used to demonstrate the usefulness of multifrequency vibro-acoustography for microcalcification detection in breast imaging. The lateral and axial width of the main lobe at −6 dB is 0.68 and 6.47 mm, respectively. The lateral and axial sidelobe levels are −27.8 and −16.8 dB, respectively. The proposed method holds the potential for large gains of information with good spatial resolution and no increase in scanning time. [Work supported by Grant EB00535-03 from NIH.]

Elasticity imaging methods have been used to study tissue mechanical properties and have demonstrated that tissue elasticity changes with disease state. Quantitative mechanical properties can be measured in a model independent manner if both shear wave speed and attenuation are known. However, measuring shear wave speed attenuation is challenging in the field of elasticity imaging. Typically, only shear wave speed is measured and rheological models, such as Kelvin-Voigt, Maxwell and Standard Linear Solid, are used to solve for shear viscoelastic complex modulus. Acoustic radiation force has been used to study quasi-static viscoelastic properties of tissue during creep and relaxation conditions, however, as with shear wave propagation methods, a rheological model needs to be fit to the creep or relaxation experimental data to solve for viscoelastic parameters. This paper presents a method to quantify viscoelastic properties in a model-independent way by estimating complex shear elastic modulus over a wide frequency range using time-dependent creep response induced by acoustic radiation force. The acoustic radiation force induced creep (RFIC) method uses a conversion formula that is the analytic solution of the constitutive equation relating time dependent stress and time dependent strain. The RFIC method in combination with shear wave propagation is used to measure the complex shear modulus so that knowledge of the applied radiation force magnitude is not necessary. Numerical simulation of creep strain and compliance using the Kelvin-Voigt model shown that the conversion formula is sensitive to sampling frequency, the first reliable measure in time and the long term viscosity approximation. Experimental data are obtained in homogeneous tissue mimicking phantoms and excised swine kidneys.

Many methods in the field of elasticity imaging use shear waves to investigate the material properties of various soft tissues. The accurate and robust measurement of the shear wave speed is necessary for reliable clinical measurements. We propose using the Radon transformation on the spatiotemporal shear wave data to estimate the shear wave speed. A similar algorithm called the Radon sum transformation was proposed by Rouze, et al (IEEE Trans. Ultrasonics Ferroelectr. Freq. Control. 2010. pp. 2662-70), but this algorithm requires different input parameters that can affect the results. The use of the full Radon transform allows for the differentiation of waves that are traveling in different directions, thus this method can be used as a directional filter. We will also demonstrate the connection between estimating shear wave speeds in the Radon transform domain and estimating shear wave speeds from Fourier transform k-space. Results from shear wave measurements using shear waves induced by ultrasound radiation force will be shown. We will examine the accuracy of measurements made in calibrated elasticity phantoms, and show examples of shear wave speed estimation in arteries and kidneys. [This research was supported in part by NIH grants EB002640 and DK082408.]

Acoustoelasticity is a technique that allows quantification of the elastic nonlinearity coefficients (the so-called third-order moduli) of a material by measuring the variation of the sound speed in different directions (and/or polarizations) versus the applied uniaxial static stress. When dealing with nominally isotropic solids, the variation of the shear wave speed in two orthogonal directions with the applied stress permits the computation of two out of three independent nonlinearity coefficients. To generate the shear wave in an experimental setting, the acoustic radiation force pulse was applied to uniaxially deformed phantoms with strains of up to 30%. The results demonstrate that the compressional-shear coefficient C, which governs the variation of the (linear) shear modulus with hydrostatic pressure was found to vary substantially from one phantom to another, with the highest value observed in an agarose-based phantom. The importance of this nonlinearity parameter resides in the fact that the magnitude of the acoustic radiation force (ARF) in soft solids is proportional to C-1. For consistency, the values of C obtained from the acoustoelasticity experiment are compared to those deduced from the shear wave amplitude via its relationship to the magnitude of the ARF used to generate the shear wave.

Elasticity imaging is a medical imaging modality that measures tissue elasticity to aid in diagnosis of certain diseases. Shear wave-based methods have been developed to perform elasticity measurements in soft tissue. Hybrid beamforming applies both the conventional spherical and axicon focusing to produce a beam for generating a shear wave with increased depth-of-field so that measurements can be made with a plane-like shear wave. We present our aperture design and beam optimization performed using Field II simulations. We varied the number of elements devoted to spherical and axicon focusing as well as the opening angle used for axicon focusing. We tested hybrid beamforming in three elastic phantoms and an excised kidney. We evaluated the shear wave speed measurements accuracy in the phantoms as well as the depth-of-field for each hybrid beam. We compared our results with those from using beams generated using spherical and axicon focusing. Our results show that hybrid beamforming is capable of producing a long narrow beam that performs well when among the 128 elements of transducer, 48 elements are allocated to each axicon portion and 32 elements for spherical aperture while the angle of the axicon aperture is set less than 20.