Dynamic Radiation Force Research Articles

Vibro-magnetometry: Theoretical aspects and simulations

In this article, we introduce the theory for vibro-magnetometry (VM) with computational simulations for an idealized experimental setup. A method based on acoustic radiation force and magnetic measurement has been proposed for interrogating the mechanical vibrations of a target immersed in fluid medium. In this method, ultrasound radiation is used to exert a low-frequency (in kHz range) force on a rigid magnetized target immersed in a viscoelastic medium. In response, the target vibrates sinusoidally in a pattern determined by viscoelastic properties of the medium. The magnetic field resulting from target vibration is related to both the ultrasonic and low-frequency (kHz range) mechanical characteristics of the medium. We report the relationship between the magnetic field signal and the incident ultrasonic pressure field in terms of the mechanical parameters of the medium. Simulations were conducted to demonstrate a simple approach based on using amplitude-modulated ultrasound to generate a dynamic acoustic radiation force on a magnetic target. The magnetic field generated by vibration of this target is then obtained and used to estimate the radiation-force-induced displacement as a function of time. It was observed that the intensity of the dynamic component of the magnetic field caused by the acoustic excitation is high enough to be registered by a conventional magnetic sensor. When a low stress is applied on a reactive magnetic target embedded in the medium, the subsequent oscillating magnetic field is measured by a dedicated magnetic sensor, yielding the applicable mechanical information of the host medium. The proposed methodology presents a powerful tool for evaluation of acoustic radiation force as well as the mechanical properties of soft materials.

Acousto-magnetometry: A new vibrometery based on acoustic radiation force and magnetic measurement.

This work introduces a new method based on acoustic radiation force and magnetic measurement for interrogating the mechanical properties of fluid and biological tissues. In this method, ultrasound radiation is used to exert a low-frequency (in kHz range) force on a rigid magnetized target immersed in a viscoelastic medium. In response, the target vibrates in a pattern determined by viscoelastic properties of medium. We report the relation between the magnetic field signal and the incident ultrasonic pressure field in terms of the mechanical parameters of the medium. Simulations were conducted to demonstrate a simple approach based on using amplitude-modulated ultrasound to generate a dynamic acoustic radiation force on a magnetic target. The magnetic field generated by vibration of this target is then obtained and used to estimate the radiation-force-induced displacement as a function of time. It was observed that the intensity of the dynamic component of the magnetic field caused by the acoustic excitation is high enough to be registered by a conventional magnetic sensor. This proposed methodology presents a powerful tool for evaluation of acoustic radiation force as well as the mechanical properties of soft material.

Propagation of shear waves generated by a modulated finite amplitude radiation force in a viscoelastic medium

An effective way to generate localized narrowband low-frequency shear waves within tissue noninvasively, is by the modulated radiation force, resulting from the interference of two confocal quasi-CW ultrasound beams of slightly different frequencies. By using approximate viscoelastic Green's functions, investigations of the properties of the propagated shear-field component at the fundamental modulation frequency were previously reported by our group. However, high-amplitude source excitations may be needed to increase the signal-to-noise-ratio for shear-wave detection in tissue. This paper reports a study of the generation and propagation of dynamic radiation force components at harmonics of the modulation frequency for conditions that generally correspond to diagnostic safety standards. We describe the propagation characteristics of the resulting harmonic shear waves and discuss how they depend on the parameters of nonlinearity, focusing gain, and absorption. For conditions of high viscosity (believed to be characteristic of soft tissue) and higher modulation frequencies, the approximate shear wave Green's function is inappropriate. A more exact viscoelastic Green's function is derived in k-space, and using this, it is shown that the lowpass and dispersive effects, associated with a Voigt model of tissue, are more accurately represented. Finally, it is shown how the viscoelastic properties of the propagating medium can be estimated, based on several spectral components of the shearwave spectrum.

Harmonic motion detection in a vibrating scattering medium

Elasticity imaging is an emerging medical imaging modality that seeks to map the spatial distribution of tissue stiffness. Ultrasound radiation force excitation and motion tracking using pulse-echo ultrasound have been used in numerous methods. Dynamic radiation force is used in vibrometry to cause an object or tissue to vibrate, and the vibration amplitude and phase can be measured with exceptional accuracy. This paper presents a model that simulates harmonic motion detection in a vibrating scattering medium incorporating 3-D beam shapes for radiation force excitation and motion tracking. A parameterized analysis using this model provides a platform to optimize motion detection for vibrometry applications in tissue. An experimental method that produces a multifrequency radiation force is also presented. Experimental harmonic motion detection of simultaneous multifrequency vibration is demonstrated using a single transducer. This method can accurately detect motion with displacement amplitude as low as 100 to 200 nm in bovine muscle. Vibration phase can be measured within 10 degrees or less. The experimental results validate the conclusions observed from the model and show multifrequency vibration induction and measurements can be performed simultaneously.

Simulations of lesion detection using a combined phased array LHMI-technique

Ultrasound based elasticity imaging techniques have been developed during the past decades. Some of these techniques are based on an internal radiation force stimulation in which a transient or dynamic radiation force is produced by using a single or dual-frequency sonication. In addition, sonication and data acquisition can be implemented using combined or separate transducers. In this simulation study of lesion detection using localized harmonic motion imaging (LHMI), we used a combined phased array designed for simultaneous thermal ablation and lesion detection. In the sonication mode, a focused single-frequency amplitude-modulated sonication is used to induce harmonic motion and in the tracking mode, some of the array elements are used for pulse-echo tracking of the induced displacements. The results showed that the size of the lesion affected the induced displacement around the sonication point. The displacement tracking simulations demonstrated that these changes in the displacement distributions can be detected using only a few of the array elements in the tracking mode but the exact size of the lesion can not be detected accurately. The simulations also showed that two lesions having the radius of 2.5 mm can be distinguished if distance between these lesions is at least 2.5 mm.

Harmonic pulsed excitation and motion detection of a vibrating reflective target

Elasticity imaging is an emerging medical imaging modality. Methods involving acoustic radiation force excitation and pulse-echo ultrasound motion detection have been investigated to assess the mechanical response of tissue. In this work new methods for dynamic radiation force excitation and motion detection are presented. The theory and model for harmonic motion detection of a vibrating reflective target are presented. The model incorporates processing of radio frequency data acquired using pulse-echo ultrasound to measure harmonic motion with amplitudes ranging from 100 to 10,000 nm. A numerical study was performed to assess the effects of different parameters on the accuracy and precision of displacement amplitude and phase estimation and showed how estimation errors could be minimized. Harmonic pulsed excitation is introduced as a multifrequency radiation force excitation method that utilizes ultrasound tonebursts repeated at a rate f(r). The radiation force, consisting of frequency components at multiples of f(r), is generated using 3.0 MHz ultrasound, and motion detection is performed simultaneously with 9.0 MHz pulse-echo ultrasound. A parameterized experimental analysis showed that displacement can be measured with small errors for motion with amplitudes as low as 100 nm. The parameterized numerical and experimental analyses provide insight into how to optimize acquisition parameters to minimize measurement errors.

Simultaneous sum-frequency and vibro-acoustography imaging for nondestructive evaluation and testing applications

High-resolution ultrasound imaging systems for inspection of defects and flaws in materials are of great demand in many industries. Among these systems, Vibro-acoustography (VA) has shown excellent capabilities as a noncontact method for nondestructive high-resolution imaging applications. This method consists of mixing two confocal ultrasound beams, slightly shifted in frequency, to produce a dynamic (oscillatory) radiation force in the region of their intersection. This force vibrates the object placed at the focus of the confocal transducer. As a result of the applied force, an acoustic emission field at the difference frequency of the primary incident ultrasound beams is produced. In addition to the difference frequency acoustic emission signal, there exists another signal at the sum frequency, formed in the intersection region of the two primary beams. The goal of this study is to investigate the formation of high-resolution images using the sum frequency of ultrasound waves in VA while concurrently forming the conventional difference-frequency VA image, thereby increasing the amount of information acquired during a single scan. A theoretical model describing the sum-frequency wave propagation, including beam forming and image formation in the confocal configuration, is developed and verified experimentally. Moreover, sample experiments are performed on a flawed fiber-reinforced ceramic composite plate. Images at both the difference and sum frequencies are compared and discussed. Results show that the sum-frequency image produces a high-resolution C scan of the plate by which the flaws and structural details of the plate can be detected.

Modulated ultrasound and multifrequency radiation force

Modulating ultrasound can create dynamic ultrasound radiation force to induce local tissue vibration. Using different types of modulating signals produces radiation force with weighted multifrequency components. Modulation signals with frequency fr produce force with components at multiples of fr. Both amplitude modulation (AM) and double sideband suppressed carrier (DSB-SC) amplitude modulation were explored. Different waveforms were investigated such as sine, square, triangle, and sawtooth for modulating continuous wave ultrasound. A 3.0 MHz transducer produced ultrasound which was measured with a needle hydrophone and used to derive and analyze the spectrum of the radiation force function. The modulated ultrasound was used to vibrate a steel sphere in a gelatin phantom, and the motion was measured using a laser vibrometer. The measured spectra were used to find the frequency response of the sphere. Different modulating signals were used to produce multifrequency radiation force. The sphere frequency response was recovered using different modulating signals. Weighted multifrequency radiation force was produced by modulating ultrasound with different signals. Application of multifrequency radiation force can be used to measure the frequency response of objects or tissue. [This work was supported in part by grants EB002167, EB002640, and CA091956 from NIH.]

Phase aberration correction using ultrasound radiation force and vibrometry optimization

We describe a phase aberration correction method that uses dynamic ultrasound radiation force to harmonically vibrate an object using amplitude modulated continuous wave ultrasound. The phase of each element of an annular array transducer is adjusted to maximize the radiation force and obtain optimal focus of the ultrasound beam. The maximization of the radiation force is performed by monitoring the velocity of scatterers in the focus region. We present theory that shows focal optimization with radiation force has a well-behaved cost function. Experimental validation is shown by correction of manual defocusing of an annular array as well as correcting for a lens-shaped aberrator placed near the transducer. A Doppler laser vibrometer and a pulse-echo Doppler ultrasound method were used to monitor the velocity of a sphere used as a target for the transducer. By maximizing the radiation force-induced vibration of scatterers in the focal region, the resolution of the ultrasound beam can be recovered after aberration defocusing.

Multifrequency radiation force of acoustic waves in fluids

In this article we introduce the concept of multifrequency radiation force produced by a polychromatic acoustic beam propagating in a fluid. This force is a generalization of dynamic radiation force due to a bichromatic wave. We analyse the force exerted on a rigid sphere by a plane wave with N frequency components. Our approach is based on solving the related scattering problem, taking into account the nonlinearity of the fluid. The radiation force is calculated by integrating the excess of pressure in the quasilinear approximation over the surface of the sphere. Results reveal that the spectrum of the multifrequency radiation force is composed of up to N ( N − 1 ) / 2 distinct frequency components. In addition, the radiation force generated by plane progressive waves is predominantly caused by parametric amplification. This is a phenomenon due to the nonlinear nature of wave propagation in fluids.

Harmonic motion detection in a vibrating scattering medium

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.

Dynamic Radiation Force of a Pulsed Gaussian Beam Acting on Rayleigh Dielectric Sphere

We investigate the dynamic evolution of the radiation forces produced by the pulsed Gaussian beams acting on a Rayleigh dielectric sphere. We derive the analytical expressions for the scattering force and all components of the pondermotive force induced by the pulsed Gaussian beam. Our analysis shows that the radiation force can be greatly enhanced due to the effect of the short pulse duration, which leads to the enhancement of both the transverse and longitudinal radiation forces. And it is found that for the pulse with large pulse duration, it can be used for the stable trapping and manipulating the particle, while for the pulse with short pulse duration it may be used for guiding and moving the small dielectric particle. Finally we discuss the stability condition of the effectively trapping and manipulating the particle by the pulsed beam.

Dynamic radiation force of acoustic waves on solid elastic spheres

The present study concerns the dynamic radiation force on solid elastic spheres exerted by a plane wave with two frequencies (bichromatic wave) considering the nonlinearity of the fluid. Our approach is based on solving the wave scattering for the sphere in the quasilinear approximation within the preshock wave range. The dynamic radiation force is then obtained by integrating the component of the momentum flux tensor at the difference of the primary frequencies over the boundary of the sphere. Effects of the fluid nonlinearity play a major role in dynamic radiation force, leading it to a regime of parametric amplification. The developed theory is used to calculate the dynamic radiation force on three different solid spheres (aluminum, silver, and tungsten). The obtained spectrum of dynamic radiation force presents resonances with larger amplitude and better shape than those exhibited in static radiation force. Applications of the results to some elasticity imaging techniques based on dynamic radiation force will be presented.

Using the ultrasound standing wave in vibroacoustography for surface roughness imaging applications

The surface roughness (of about 20 microns) of an acrylic block immersed in water was measured using the acoustic emission pressure field (in the kHz range) induced by the dynamic radiation force of ultrasound (2 MHz). The dynamic radiation force is produced by mixing two beams of different frequencies to excite the probed object. The acoustic emission is a result of object vibration at the difference frequency of the incident ultrasound beams and is detected by a low-frequency hydrophone placed nearby the block. Due to the presence of the block, an ultrasound standing wave field is generated as a result of multiple reflections between the transducer and the block’s surface. The acoustic emission by the block’s surface varies according to its relative position to the transducer. This variation is used to form an image of the surface roughness at two difference frequencies Δf=9.9 and 22.4 kHz. To have a one-to-one map between the surface roughness and the image, the surface variation has to lie within the distance from a maximum to its nearest minimum in the standing wave. Images obtained here demonstrate that vibroacoustography may be used as a powerful tool for the nondestructive inspection and imaging of surface roughness [Mitri et al., Appl. Phys. Lett. 88, 234105 (2006)]. [Work supported by NIH.]

Phase aberration correction for a linear array transducer using ultrasound radiation force and vibrometry optimization: Simulation study

Diagnostic ultrasound images suffer from degradation due to tissues with sound speed inhomogeneities causing phase shifts of propagating waves. These phase shifts defocus the ultrasound beam, reducing spatial resolution and image contrast in the resulting image. We describe a phase aberration correction method that uses dynamic ultrasound radiation force to harmonically excite a medium using amplitude-modulated continuous wave ultrasound created by summing two ultrasound frequencies at f0=3.0 MHz and f0+Δf=3.0005 MHz. The phase of each element of a linear array transducer is sequentially adjusted to maximize the radiation force and obtain optimal focus of the ultrasound beam. The optimization is performed by monitoring the harmonic amplitude of the scatterer velocity in the desired focal region using Doppler techniques. Simulation results show the ability to regain a 3.0-MHz focused field after applying a phase screen with an rms time delay of 95.4 ns. The radiation force magnitude increased by 22 dB and the resolution of the field was regained. Simulation results show that the focus of the beam can be qualitatively and quantitatively improved with this method. [This study was supported in part by Grants EB002640 and EB002167 from the NIH.]

Dynamic radiation force of acoustic waves on solid elastic spheres

The present study concerns the dynamic radiation force on solid elastic spheres exerted by a plane wave with two frequencies (bichromatic wave) considering the nonlinearity of the fluid. Our approach is based on solving the wave scattering for the sphere in the quasilinear approximation within the preshock wave range. The dynamic radiation force is then obtained by integrating the component of the momentum flux tensor at the difference of the primary frequencies over the boundary of the sphere. Results reveal that effects of the nonlinearity of the fluid play a major role in dynamic radiation force leading it to a parametric amplification regime. The developed theory is used to calculate the dynamic radiation force on three different solid spheres (aluminum, silver, and tungsten). Resonances are observed in the spectrum of the force on the spheres. They have larger amplitude and better shape than resonances present in static radiation force.

Simulations of localized harmonic motions on a blood vessel wall induced by an acoustic radiation force used in ultrasound elastography

Many noninvasive techniques have been developed recently to explore the mechanical properties of soft tissue. In this paper, dynamic acoustic radiation force induced vibrations on a blood vessel wall were simulated using different stimulation frequencies and stiffness parameters for the vessel wall. The stimulation frequency was varied between 20 Hz and 20 kHz and the stiffness parameter (Young's modulus) was varied between 60 kPa and 360 kPa. The vibration simulations were computed using a finite-element method in a 3D geometry that contained a vessel wall surrounded by soft tissue. The results indicate that vibrations caused by acoustic stimulation are sensitive to the changes in mechanical properties of the vessel wall and that the vibrations are highly dependent on the stimulation frequency and target structure. Therefore, measurements of absolute stiffness parameters may not be accurately achieved because this method is so dependent on the whole target structure, whereas the monitoring of changes during some process may be feasible.

Parametric Amplification of the Dynamic Radiation Force of Acoustic Waves in Fluids

We report on parametric amplification in dynamic radiation force produced by a bichromatic acoustic beam in a fluid. To explain this effect we develop a theory taking into account the nonlinearity of the fluid. The theory is validated through an experiment to measure the dynamic radiation force on an acrylic sphere. Results exhibit an amplification of 66 dB in water and 80 dB in alcohol as the difference of the frequencies is increased from 10 Hz to 240 kHz.

Surface roughness imaging using the acoustic emission induced by the dynamic radiation force of ultrasound

High frequency ultrasound imaging systems are traditionally used in industry to obtain high resolution images of solid surfaces, and in some cases, to evaluate surface roughness. In this study we show that imaging fine surface roughness in the order of few microns is achievable at audio range frequencies (kilohertz range) by using the vibroacoustography (VA) technique. This technique allows one to image surface roughness on the basis of the ultrasound radiation force stimulated acoustic emission in a standing ultrasound wave field. Images obtained here demonstrate that VA may be used as a powerful tool for nondestructive inspection and imaging of surface roughness.

Stimulation of collagen production with low‐intensity acoustics

Low‐intensity pulsed ultrasound is a commonly prescribed therapy for delayed unions and nonunions after fractures. Several prospective double‐blind clinical trials have shown that a 1.5‐MHz ultrasound signal at a 200‐s tone burst repeating at 1 kHz shortens the time to clinically evaluated healing by 30%. We have shown in vitro that pulsed ultrasound increases aggrecan gene expression and aggrecan production in chondrocytes, a key cell in the fracture healing process. Because the square wave pulsed 1.5‐MHz signal produces radiation force vibration at 1 kHz, we tested the hypothesis that dynamic radiation force, not ultrasound, is responsible for the biological effect of the signal. Experiments showed that a 1‐kHz acoustic square wave, simulating the radiation force caused by the clinically used signal, induced chondrogenesis similarly to pulsed ultrasound treatment in ATDC5 cells. These results may have implications for remote ultrasound or acoustic stimulation of different types of strain‐sensitive cells in addition to those responsible for fracture healing.