Urban, Matthew W

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.

New vibration pulses are proposed to increase the power of shear waves induced by ultrasound radiation force in a tissue region with a preferred spectral distribution. The new pulses are sparsely sampled from an orthogonal frequency wave composed of several sinusoidal signals. Those sinusoidal signals have different frequencies and are orthogonal to each other. The phase and amplitude of each sinusoidal signal are adjusted to control the shape of the orthogonal frequency wave. Amplitude of the sinusoidal signal is increased as its frequency increases to compensate for higher loss at higher frequency in the tissue region. The new vibration pulses and detection pulses can be interleaved for array transducer applications. The experimental results show that the new vibration pulses significantly increases induced tissue vibration with the same peak ultrasound intensity, compared with the binary vibration pulses.

In the past several decades, the fields of ultrasound and magnetic resonance elastography have shown promising results in noninvasive estimates of mechanical properties of soft tissues. These techniques often rely on measuring shear wave velocity due to an external or internal source of force and relating the velocity to viscoelasticity of the tissue. The mathematical relationship between the measured velocity and material properties of the myocardial wall, arteries, and other organs with non-negligible boundary conditions is often complicated and computationally expensive. A simple relationship between the Lamb–Rayleigh dispersion and the shear wave dispersion is derived for both the velocity and attenuation. The relationship shows that the shear wave velocity is around 20% higher than the Lamb–Rayleigh velocity and that the shear wave attenuation is about 20% lower than the Lamb–Rayleigh attenuation. Results of numerical simulations in the frequency range 0–500 Hz are presented.

Tissue mechanical properties can be obtained by algebraic direct inversion (ADI) of the shear-wave motion differential equation, which is insensitive to reflection and geometry of the pushing beam. Shear waves normally generated by a focused ultrasound pushing beam have limited spatial extent in depth and are transient in time, leading to noisy and unstable ADI results. A comb-shape acoustic radiation force distribution can generate shear waves with longer spatial extent and time duration, facilitating more robust ADI. For 400 μs, a linear array transducer simultaneously transmitted four unfocused pushing beams (12 on elements for each pushing beam, 8 off elements between beams) into a tissue-mimicking phantom (∼1.5 kPa) with a cylindrical inclusion (∼4 kPa). The ultrasound system (Verasonics Inc.) then immediately switched to flash imaging mode (frame rate = 2 kHz, spatial resolution = 0.31 mm) to measure shear-wave displacements in a 38 mm by 30 mm domain that was used for ADI. The reconstructed 2D shear elasticity map provides accurate shear elasticity estimates (background = 1.5 kPa with 7% variance; inclusion = 3.9 kPa with 15% variance) and excellent contrast between the background and inclusion.

In the field of tissue engineering, monitoring the elasticity of developing tissue cultures is important for evaluating their growth and maturation. In this work, we used wave propagation methods to measure the elasticity of thin tissue-mimicking layers to test the feasibility of measuring the elasticity of developing tissue cultures. We developed finite element and analytical models for investigating this problem and found good agreement between the results from both models. We used ultrasound radiation force to induce propagating waves, and the waves are measured using high frame rate ultrasound imaging at 10 kHz. The wave modes were identified and compared with an analytic model for Rayleigh wave propagation in a thin elastic layer bound to a solid substrate. The same gelatin mixture was used to make phantoms 1, 4, and 50 mm thick, where the phantom with 50 mm thickness was used as control and evaluated with shear wave imaging methods. The analytic model was used to fit data from experiments in the large block and thin layers of 1 and 4 mm thick, and the measured shear moduli were 22.7, 21.8, and 22.5 kPa, respectively. These results provide a validation for measurement of elasticity in thin elastic layers.

This paper describes the principles and initial experimental results of a new Doppler method called vibro-acoustic Doppler (VAD). VAD uses acoustic response of a moving object to a highly localized dynamic radiation force of ultrasound to measure the velocity of the object. The low frequency radiation force is exerted by two co-focused ultrasound beams with slightly different frequencies. The acoustic response of the object is detected by a hydrophone. A formula that describes the relation between the Doppler frequency shift of the emitted acoustic field and the velocity of the moving object is reported. To verify the theory, experiments are conducted on a moving string and a fluid flow phantom. Results show that the error in velocity measurement is less than 9.1% for either phantom. An advantage of this method over the traditional ultrasound Doppler is that velocity measurement with VAD is almost independent of the angle between the ultrasound beam and motion direction. It is shows that in the worst case, the error is 10.3% for a ±30 deg angle variation. Potential biomedical applications of VAD will be discussed.

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.