Oscillatory Radiation Force Research Articles

Amplitude and time-dependence of ultrasonic radiation force on modulation frequency computed from specular reflection contributions

Ever since the late 1970s, there has been interest in the modulated radiation pressure of double sideband suppressed carrier (DSSC) ultrasound, because the associated radiation pressure oscillates at a single low frequency. Recent research considers situations, where the radius of curvature of the illuminated objects greatly exceeds the wavelength at the implicit carrier frequency of the ultrasonic illumination [Marston et al., J. Acoust. Soc. Am. 149, 3042–3051 (2021); 150, 25–28 (2021)]. Furthermore, the objects of interest, cylinders, and spheres in water are taken to be sufficiently highly reflecting that the radiation force can be shown to be dominated by contributions associated with specular reflection. In such cases, it is helpful to geometrically analyze the amplitude and time dependence of the oscillatory radiation force for perfectly reflecting objects, where the relevant integrals of the stress projections can be carried out analytically. The results are expressed using Bessel and Struve functions. They explain how the amplitude and phase of the force depends on the DSSC modulation frequency in agreement with partial-wave-series based calculations. The approach is relevant in other situations. [Work supported by the U. S. Office of Naval Research.]

Dynamic oscillatory powers, cross sections, and energy efficiencies in coherent optical heterodyning.

In a recent analysis [J. Quant. Spectrosc. Radiat. Transfer250, 106994 (2020)JQSRAE0022-407310.1016/j.jqsrt.2020.106994], the emergence of a dynamic oscillatory radiation force in coherent optical/electromagnetic (EM) heterodyning has been demonstrated for TM- and TE-polarized amplitude-modulated (AM) plane waves interacting with a lossless dielectric circular cylinder. A dynamic oscillatory component of the EM radiation force emerged at the beat frequency of two interfering fully correlated wave fields driven at slightly different frequencies. This work extends the scope of that analysis to examine the oscillatory behavior of energy-related physical observables from the standpoint of energy conservation applied to scattering. Partial-wave series for the oscillatory scattering, extinction and absorption powers, cross sections, and energy efficiencies are derived in cylindrical coordinates for a circular homogeneous cylinder material using the short-term time averaging (STTA) procedure and Poynting's theorem. AM plane progressive waves incident upon a lossless dielectric cylinder with arbitrary radius are considered. Numerical computations of the oscillatory scattering and extinction energy efficiencies illustrate the theory. A criterion based on computing and quantifying accurately the percentage (or relative) error between the dynamic (oscillatory) extinction and scattering efficiencies is developed and numerically evaluated. This benchmark tool provides physical validation and verification of the results from the standpoint of energy conservation. The results show that the percent (relative) error increases at the resonances of the dielectric cylinder as its refractive index increases. Far from the resonances, the oscillatory component of the STTA remains appropriate because the percent (relative) error does not exceed 0.05%, provided the beating difference frequency is much smaller than that of the primary waves. The case of an absorptive dielectric cylinder is also illustrated and discussed. The present analysis is of fundamental importance in order to validate dynamic radiation force computational results from the standpoint of energy conservation in the development, design, and optimization of oscillatory optical heterodyne tweezers and tractor beams in related applications in particle manipulation.

Dynamic oscillatory radiation force in optical heterodyning

In contrast with the optical radiation force induced by conventional lasers of continuous mono-frequency wave-fields, a dynamic or oscillatory mode arises when a beating effect caused by intensity changes over time (i.e., amplitude modulation) occurs. The purpose of this analysis is directed toward examining theoretically the dynamic (oscillatory) radiation force in optical heterodyning, caused by interfering/mixing two electromagnetic/optical plane waves driven at slightly different frequencies. The example of a dielectric cylinder material having a circular geometric cross-section is considered. Based on the integration of Maxwell's stress tensor over the surface of the object in the near-field, the modal expansion method in cylindrical coordinates is used in conjunction with the short-term time average to obtain mathematical series for the longitudinal dynamic optical radiation force per-length (i.e. acting along the direction of wave propagation). The cases of incident TM and TE polarized plane progressive waves are considered. Numerical illustrative results for the dimensionless dynamic radiation force function are performed with particular emphasis on changing the size parameter of the cylinder as well as the normalized difference-frequency and time parameters. The results show that the total force is not the mere sum of the components originated by the primary waves. There is an additional cross-term factor related to the dynamic component which cannot be neglected, suggesting that the radiation force phenomenon using beating optical waves is slowly time-varying (oscillatory). Moreover, a resonance splitting effect in the plots of the dynamic radiation force is observed and discussed. The present analysis has the potential to open a novel method in the development of dynamic/oscillatory optical heterodyne tweezers and tractor beams for particle manipulation and characterization.

Tumor characterization and treatment monitoring of postsurgical human breast specimens using harmonic motion imaging (HMI).

BackgroundHigh-intensity focused ultrasound (HIFU) is a noninvasive technique used in the treatment of early-stage breast cancer and benign tumors. To facilitate its translation to the clinic, there is a need for a simple, cost-effective device that can reliably monitor HIFU treatment. We have developed harmonic motion imaging (HMI), which can be used seamlessly in conjunction with HIFU for tumor ablation monitoring, namely harmonic motion imaging for focused ultrasound (HMIFU). The overall objective of this study was to develop an all ultrasound-based system for real-time imaging and ablation monitoring in the human breast in vivo.MethodsHMI was performed in 36 specimens (19 normal, 15 invasive ductal carcinomas, and 2 fibroadenomas) immediately after surgical removal. The specimens were securely embedded in a tissue-mimicking agar gel matrix and submerged in degassed phosphate-buffered saline to mimic in vivo environment. The HMI setup consisted of a HIFU transducer confocally aligned with an imaging transducer to induce an oscillatory radiation force and estimate the resulting displacement.Results3D HMI displacement maps were reconstructed to represent the relative tissue stiffness in 3D. The average peak-to-peak displacement was found to be significantly different (p = 0.003) between normal breast tissue and invasive ductal carcinoma. There were also significant differences before and after HMIFU ablation in both the normal (53.84 % decrease) and invasive ductal carcinoma (44.69 % decrease) specimens.ConclusionsHMI can be used to map and differentiate relative stiffness in postsurgical normal and pathological breast tissues. HMIFU can also successfully monitor thermal ablations in normal and pathological human breast specimens. This HMI technique may lead to a new clinical tool for breast tumor imaging and HIFU treatment monitoring.

High-intensity focused ultrasound monitoring using harmonic motion imaging for focused ultrasound (HMIFU) under boiling or slow denaturation conditions.

Harmonic motion imaging for focused ultrasound (HMIFU) is a recently developed high-intensity focused ultrasound (HIFU) treatment monitoring method that utilizes an amplitude-modulated therapeutic ultrasound beam to induce an oscillatory radiation force at the HIFU focus and estimates the focal tissue displacement to monitor the HIFU thermal treatment. In this study, the performance of HMIFU under acoustic, thermal, and mechanical effects was investigated. The performance of HMIFU was assessed in ex vivo canine liver specimens (n = 13) under slow denaturation or boiling regimes. A passive cavitation detector (PCD) was used to assess the acoustic cavitation activity, and a bare-wire thermocouple was used to monitor the focal temperature change. During lesioning with slow denaturation, high quality displacements (correlation coefficient above 0.97) were observed under minimum cavitation noise, indicating the tissue initial-softening-then- stiffening property change. During HIFU with boiling, HMIFU monitored a consistent change in lesion-to-background displacement contrast (0.46 ± 0.37) despite the presence of strong cavitation noise due to boiling during lesion formation. Therefore, HMIFU effectively monitored softening-then-stiffening during lesioning under slow denaturation, and detected lesioning under boiling with a distinct change in displacement contrast under boiling in the presence of cavitation. In conclusion, HMIFU was shown under both boiling and slow denaturation regimes to be effective in HIFU monitoring and lesioning identification without being significantly affected by cavitation noise.

Performance Assessment of HIFU Lesion Detection by Harmonic Motion Imaging for Focused Ultrasound (HMIFU): A 3-D Finite-Element-Based Framework with Experimental Validation

Harmonic motion imaging for focused ultrasound (HMIFU) is a novel high-intensity focused ultrasound (HIFU) therapy monitoring method with feasibilities demonstrated in vitro, ex vivo and in vivo. Its principle is based on amplitude-modulated (AM) - harmonic motion imaging (HMI), an oscillatory radiation force used for imaging the tissue mechanical response during thermal ablation. In this study, a theoretical framework of HMIFU is presented, comprising a customized nonlinear wave propagation model, a finite-element (FE) analysis module and an image-formation model. The objective of this study is to develop such a framework to (1) assess the fundamental performance of HMIFU in detecting HIFU lesions based on the change in tissue apparent elasticity, i.e., the increasing Young’s modulus, and the HIFU lesion size with respect to the HIFU exposure time and (2) validate the simulation findings ex vivo. The same HMI and HMIFU parameters as in the experimental studies were used, i.e., 4.5-MHz HIFU frequency and 25 Hz AM frequency. For a lesion-to-background Young’s modulus ratio of 3, 6 and 9, the FE and estimated HMI displacement ratios were equal to 1.83, 3.69 and 5.39 and 1.65, 3.19 and 4.59, respectively. In experiments, the HMI displacement followed a similar increasing trend of 1.19, 1.28 and 1.78 at 10-s, 20-s and 30-s HIFU exposure, respectively. In addition, moderate agreement in lesion size growth was found in both simulations (16.2, 73.1 and 334.7 mm 2) and experiments (26.2, 94.2 and 206.2 mm 2). Therefore, the feasibility of HMIFU for HIFU lesion detection based on the underlying tissue elasticity changes was verified through the developed theoretical framework, i.e., validation of the fundamental performance of the HMIFU system for lesion detection, localization and quantification, was demonstrated both theoretically and ex vivo.

Experimental validation of the amplitude‐modulated harmonic motion imaging for tissues stiffness estimation

It has been previously shown that amplitude‐modulated harmonic motion imaging (AM‐HMI) has the capability of induce and image tissue displacement during the application of an oscillatory radiation force. Here, we aim at validating theoretical HMI findings with experimental results on similar phantoms. A finite‐element‐method (FEM) was first used to model a dynamic response of phantoms with inclusions at different stiffnesses and sizes. The FEM and experimental results were compared and used to describe the behavior of the locally displaced tissue. The radiation force was generated by a 4.68 MHz FUS transducer modulated at 50 Hz with acoustic pressure levels varied between 1.2 and 4 MPa. A 7.5 MHz pulse‐echo transducer was placed through the center of the FUS transducer and used to image the displaced tissue. A 1D‐cross‐correlation method on successive RF signals was used to estimate the axial‐displacement. The FEM and experimental results displayed good agreement in displacement patterns, i.e., the highes...

Comparison of Stress Field Forming Methods for Vibro-acoustography

Vibro-acoustography is a method that produces images of the acoustic response of a material to a localized harmonic motion generated by ultrasound radiation force. The low-frequency, oscillatory radiation force (e.g., 10 kHz) is produced by amplitude modulating a single ultrasound beam, or by interfering two beams of slightly different frequencies. Proper beam forming for the stress field of the probing ultrasound is very important because it determines the resolution of the imaging system. Three beam-forming geometries are studied: amplitude modulation, confocal, and x-focal. The amplitude of radiation force on a unit point target is calculated from the ultrasound energy density averaged over a short period of time. The profiles of radiation stress amplitude oil the focal plane and on the beam axis are derived. The theory is validated by experiments using a small sphere as a point target. A laser vibrometer is used to measure the velocity of the sphere, which is proportional to the radiation stress exerted on the target as the transducer is scanned over the focal plane or along the beam axis. The measured velocity profiles match the theory. The theory and experimental technique may be useful in future transducer design for vibro-acoustography.

Comparison of stress field forming methods for vibro-acoustography

Vibro-acoustography is a method that produces images of the acoustic response of a material to a localized harmonic motion generated by ultrasound radiation force. The low-frequency, oscillatory radiation force (e.g., 10 kHz) is produced by amplitude modulating a single ultrasound beam, or by interfering two beams of slightly different frequencies. Proper beam forming for the stress field of the probing ultrasound is very important because it determines the resolution of the imaging system. Three beam-forming geometries are studied: amplitude modulation, confocal, and x-focal. The amplitude of radiation force on a unit point target is calculated from the ultrasound energy density averaged over a short period of time. The profiles of radiation stress amplitude on the focal plane and on the beam axis are derived. The theory is validated by experiments using a small sphere as a point target. A laser vibrometer is used to measure the velocity of the sphere, which is proportional to the radiation stress exerted on the target as the transducer is scanned over the focal plane or along the beam axis. The measured velocity profiles match the theory. The theory and experimental technique may be useful in future transducer design for vibro-acoustography.

Mode excitation and imaging by the radiation force of ultrasound

A method for noncontact excitation and displaying the vibration mode shapes in solids is introduced. This method utilizes the radiation force of amplitude-modulated focused ultrasound to remotely excite a resonant mode in the object. The ultrasound transducer is driven by a sinusoidally modulated continuous wave signal to produce an oscillatory radiation force on the object and drive it into one of its natural resonance modes. The acoustic field resulting from object vibration is detected by a hydrophone. A theoretical model has been developed that describes the relationship between the force, mode shape, and the acoustic field. It is shown that the acoustic field amplitude is proportional to the value of the mode shape at the focal point of the ultrasound beam. By scanning the ultrasound beam across the object it is possible to map the acoustic data into an image that represents the mode shape of the object. Experiments have been conducted on small steel, aluminum, and glass beams. The first five resonant modes were excited and imaged by the present method. Experimental results have shown remarkable agreement with the theory and computer simulation. Beam deflections in the order of tens of nanometers can be detected by this method.

Vibro-acoustography of small spheres

Vibro-acoustography is a method for imaging the acoustic energy emitted from objects in response to an oscillatory radiation force produced by two interfering focused beams of ultrasound [M. Fatemi and J. F. Greenleaf, Science 280, 82–85 (1998)]. To facilitate quantitative study, a model is presented that describes the behavior of an elastic sphere in two plane ultrasound waves of slightly different frequencies. The vibrating velocity and the resulting acoustic emission of the sphere at the difference frequency are derived from the radiation force and the impedance of the sphere. For small steel spheres in water, the velocity and emission are predicted to have a simple relationship with the difference frequency and the size of the sphere. Experiments on small stainless steel spheres of different size are carried out for a number of difference frequencies, with a laser interferometer to measure the velocity of the sphere and a calibrated hydrophone to measure the acoustic emission from the sphere. The experimental results fit the model description well. This means that vibro-acoustography may be useful in quantitative measurement.

Ultrasound-stimulated vibro-acoustic spectrography.

An ultrasound method based on radiation force is presented for imaging the acoustic response of a material to mechanical excitation. Acoustic energy was emitted from solids and tissues in response to an oscillatory radiation force produced by interfering focused beams of ultrasound. Frequency spectra of ultrasound-stimulated acoustic emission exhibited object resonances. Raster-scanning the radiation force over the object and recording the amplitude and phase of the emitted sound resulted in data from which images related to the elastic compositions of the acoustically emitting objects could be computed. Acoustic emission signals distinguished tuning-fork resonances, submillimeter glass spheres, and calcification in excised arteries and detected object motions on the order of nanometers.