Greenleaf, James F.

This paper presents a new method of inducing localized low-frequency acoustic energy in an object by remote sources. In this method two interacting high-power, high-frequency, ultrasound beams at two different frequencies are used. These beams are positioned to interact at the object’s surface (or any other impedance discontinuity inside the object). The result is a radiation force at the difference frequency, df, exerted in a small area defined by the beamwidths. Experiments are performed on a small steel needle and blocks of gelatin. To monitor the vibration, a high-frequency probing transducer is used in pulse echo mode with the beam aimed at the vibrating part of the object. This transducer shoots tone bursts at a rate much higher than df. Echoes are quadrature detected and the resulting in-phase and quadrature signals are recorded. These signals are used to calculate the phase of the returned echo which is shown to be proportional to the target displacement. In the experiments, the power beams were driven at 20 W each and df=10 Hz. Amplitude of the resulting vibrations were 5 μm for the gelatin block and 1.2 μm for the needle.

Log compression of A lines to produce B-scan images in clinical ultrasound imaging systems is a standard procedure to control the dynamic range of the images. The statistics of such compressed images in terms of underlying scatterer statistics have not been derived. The statistics are analyzed for partially formed speckle using a general K distribution model of envelope statistics to derive the density function for the log-compressed envelope. This density function is used to elucidate the relation between the moments of the compressed envelope, the compression parameters, and the statistics of the scatterers. The analysis shows that the mean of the log-compressed envelope is an increasing function of both the backscattered energy and the effective scatterer density. The variance of the log-compressed envelope is a decreasing function of the effective scatterer density and is independent of the backscattered energy.

Earlier studies [P. J. Westervelt, J. Acoust. Soc. Am. 29, 199–203, 934–935 (1957)] of the mutual nonlinear interaction of two plane waves of sound with each other are extended to include the viscous effect. The viscous effect is considered both from the equations of motion and the equation of state of the medium. An analytical solution to the lowest-order scattering process is obtained if the viscous effect of second order and higher can be neglected.

Acoustic radiation pressure exerted by an arbitrary acoustic wave in a three-dimensional lossy medium is calculated by extending an indirect approach developed by Chu and Apfel [B-T. Chu and R. E. Apfel, ‘‘Acoustic radiation pressure produced by a beam of sound,’’ J. Acoust. Soc. Am. 72, 1673–1687 (1982)]. Without appealing to the detailed solutions of equations governing fluid motion, a general analytic expression for the radiation pressure in lossy media with arbitrary waves is obtained. When an infinite lossy medium is considered, the expression states that the radiation pressure, to the lowest order of approximation (i.e., second order), is equal to corresponding total energy density. For a special class of confined spaces, the expression leads to a rather general formula for the radiation pressure, in which the radiation pressure is given in terms of various energy densities in the field. Furthermore, a relationship among these energy densities is generalized to the case of lossy media, which enables one to compute the radiation pressure in the class of spaces with the knowledge of the first-order perturbation solution only.

Modern commercial medical ultrasound instruments are capable of obtaining up to 40 real-time, two-dimensional images per second. One of the most difficult organs to evaluate with ultrasound is the heart. The heart is a complex organ that achieves its pumping function through cyclic motion of its chambers and valves. Computerized visualization of the heart is being developed to aid in training and to provide comprehensible images of this complex organ to the patient, the surgeon, and the researcher. To obtain the required data, the two-dimensional imaging plane of an ultrasound instrument is scanned through the heart from the surface of the chest, or more commonly, from within the esophagus. Sequences of digitized two-dimensional images taken at incremental positions through the heart are gated with the cardiac cycle and assembled by computer programs into volumetric images. Visualization methods of filtering, segmentation, and rendering are used to produce comprehensible, data dense, three-dimensional images of the heart. Sequences of the three-dimensional images obtained at sequential points through the cardiac cycle produce what are called ‘‘four’’-dimensional images. Mathematical projections of elements of these images onto selected two-dimensional planes can be recorded on videotape to produce movies of the structure or function of interest at various angles of view. Metrics such as distance, area, volume, or speed can be used on these data to produce quantitative measurements.

Theories on acoustic radiation pressure associated with plane acoustic waves and lossless media have been examined extensively. The radiation pressure produced by a non-plane wave in a lossy unbounded medium was analyzed. The distinction between Lagrangian and Eulerian pressure was used to clarify the understanding of radiation pressure. The radiation pressure exerted on a perfectly absorbing pointwise target by an arbitrary acoustic wave in an unbounded lossy medium was then considered. By using an indirect approach developed in Chu and Apfel [B.-T. Chu and R. E. Apfel, 1673–1687 (1982)], the radiation pressure was analyzed without appealing to the detailed solutions of the governing fluid dynamic equations. It was shown that even in lossy media with arbitrary waves, the radiation pressure experienced by a pointwise target is equal to the Langevin pressure which is the time average energy density at that point. The radiation pressure exerted on a specific target by an arbitrary acoustic wave in an infinite lossy medium was studied and a concise theoretical result was obtained. [The work was supported by grants CA 43920 and HL 41046 from the National Institutes of Health.]

The heart is a three-dimensional structure that performs its function by undergoing complex deformation. Current clinical evaluation of the heart is limited to silhouettes, outlines, projections, or tomograms, obligating the clinician or investigator to sequentially evaluate a series of two-dimensional images using mental assimulation of data. To provide more easily understandable three-dimensional images, techniques have been developed for acquiring data in sequential planes through the heart to display the beating heart in three dimensions. Analysis of such data on a user-friendly workstation can be accomplished using an extensive set of software tools developed at our institution. Three-dimensional imaging can be used as an effective means of teaching interrelationships of volume, contents, and function, in addition to the physiologic and anatomic interrelation-ships. Three-dimensional images of the beating human heart obtained in vivo using new data acquisition techniques will be shown. Evaluation of the method using balloons and excised hearts has shown that software and geometry of scanning are appropriate for high-accuracy measurements of surfaces.

On the basis of many measurements on attenuation, absorption, and speed of ultrasound in biological materials, one can make the following generalizations: (a) Biological tissues have high attenuation coefficients, about two to three orders greater than their major component, water; (b) the amplitude attenuation coefficient increases with frequency near-linearly in soft tissues and near-quadratically in fluids with frequency in the range 1 to 10 MHz, and possibly even up to 100 MHz; (c) speed dispersion is extremely small (∼0.1 to 1 m/s/ MHz); (d) absorption and attenuation coefficients either increase or decrease with an increase in temperature, depending on the nature of the tissue, and the frequency of irradiatiOn; (e) fluids containing proteins show a sharp increase in excess absorption in acidic and basic pH ranges, and finally; (f) at sufficiently high intensity of irradiation the absorption coefficient increases with intensity. Comprehensive models for the propagation of ultrasonic waves through lossy media should explain these experimental findings. We will review some of the current models and critically examine them in light of the definition of absorption in relation to attenuation and scattering. [Work supported by NIH CA 24085, CA 41324, and NSF 8310626.]

The validity of wave equations employed as system models in acoustical diffraction tomography is investigated using simulations and measurements of the scattering of plane ultrasound waves by cylinders. It is demonstrated by simulation and experiment that it can be appropriate to neglect density fluctuations and shear waves, implying that the commonly used form of the wave equation suitably describes scattering by fluctuations of acoustic speed and absorption. Diffraction tomographic reconstructions of simulated data reveal the importance of absorption, the behavior of the real and imaginary parts of the reconstructed refractive index, and the relative advantages and limitations of the Born and Rytov approximate transformations.

Changes in the nonlinear parameter B/A caused by the addition of monohydric alcohols to water have been investigated. The measurements, made by using an aqueous solution of n-propanol, isopropanol, and t-butanol, show that as the alcohol concentration is increased, B/A decreases to a minimum at approximately 10% concentration (by volume). Further increase in alcohol concentration raises B/A rapidly to a maximum at about 80% by volume. This complex variation in B/A is attributed to solute–solvent interaction which is believed to be due to an enhancement of water structure in the water-rich region. These results suggest that the magnitude of B/A may be closely related to the quasilattice structure of water, which to a first approximation can be expressed by relative amounts of bound and unbound water.