Digital processing for improvement of ultrasonic abdominal images.

Digital processing that increases resolution by spatial deconvolution and histogram-based amplitude mapping has been used to improve ultrasonic abdominal image quality. The processing was applied to pulse-echo ultrasound data obtained from clinical imaging instrumentation modified to permit digital recording of signals in either RF or video forms for subsequent off-line analysis. Spatial deconvolution was accomplished both along the axis and across the width of the ultrasonic beam. Axial deconvolution was carried out on RF data with a point spread function derived from the echo of a wire target. Lateral deconvolution was performed on the video envelope placed in a matrix by an inverse filter with parameters that adjust themselves to the spatial frequency content of the image being processed. Resultant image amplitudes were mapped into a hyperbolic distribution to increase image contrast for improved demonstration of low amplitudes. The combination of processing produced resolution improvements to show boundaries more sharply and contrast changes to demonstrate more detail in the images.

Wave space interpretation of scattered ultrasound.

Wave space is described nonmathematically for design and interpretation of ultrasound scattering experiments. By considering ultrasound scattering from a variety of targets and geometries, the wave space approach is shown to describe target characteristics in terms of spatial frequencies and their amplitudes. Experimental limitations for determining effective spacing of scattering structures and scattering medium anisotropy are discussed.

In vivo and in vitro ultrasound beam distortion measurements of a large aperture and a conventional aperture focussed transducer.

Ultrasound focussing through human tissue of thicknesses varying from 10 mm to 35 mm has been measured for two transducers with diameters 50 mm and 19 mm both focussed at 50 mm (f/1 and f/2.6, respectively). Comparisons are made between the two-way focal depth beam patterns obtained in water and those obtained after passage through tissue to study the degrading effects of frequency-dependent attenuation and inhomogeneities, and their dependence on aperture size. The effects of frequency-dependent attenuation is to broaden the beam and shorten the focal distance. Inhomogeneities mainly increase the sidelobe levels and cause deviations from the central beam axis. A direct comparison of the beam patterns of the two transducers after passage through the same tissue samples shows that the resolution is improved by using the larger aperture. The use of the larger transducer in the in vitro measurements on three human liver specimens demonstrated an average improvement in the -6 dB beamwidth, over the smaller transducer, of 42% (standard deviation +/- 3%). The average improvement in the in vivo measurements on ten female breasts was 34% (standard deviation +/- 5%). The measured improvement in water was 52%. Therefore, the measured resolution improvement in tissue is approximately 2/3 of that obtained in water. The results indicate that for an f/1 transducer with a focal depth of 50 mm the upper limit of maximum useful aperture size has not been reached.

Representations of rapidly oscillating structures on the Doppler display.

In cardiovascular applications of Doppler ultrasound, oscillating structures are at times within the sample volume of the transducer. When the period of oscillation is shorter than the time window of the Fourier transform, the velocities of the structure are not resolved in time by the frequency analyzer. The resulting display can differ considerably from that obtained from structures with linear velocities. The investigation characterizes this phenomenon with the use of theoretical relations, mechanical model experiments and patient data. The results demonstrate that the representations of rapidly oscillating structures on the Doppler display can be interpreted in terms of frequency of oscillation and also, to some extent, in terms of maximum displacement of the structure.

Doppler ultrasound in aortic stenosis: in vitro studies of pressure gradient determination.

Torricelli's equation expresses a simple relationship between fluid velocity and pressure gradient in orifice flow and is currently used in conjunction with noninvasive Doppler ultrasound to determine gradients in mitral stenosis, and aortic stenosis, as well as other cardiovascular orifices. In theory, however, the Torricelli equation overestimates the gradient in aortic stenosis and the Borda equation should be more applicable. A brief tutorial derivation of the Borda and Torricelli equations is presented. The applicability of Torricelli's equation in aortic stenosis was studied experimentally with a rigid wall, pulsatile flow analogue. Doppler ultrasound and manometric data were collected simultaneously. Percent stenosis, peak flow rate and fluid viscosity were varied. The results demonstrated that the Torricelli equation consistently overestimated the pressure gradient. At 61% area stenosis, the overestimation exceeded 100%. In vivo studies are required to determine the relevance of the observations to clinical situations.

The use of frequency mixing to distinguish size distributions of gas-filled micropores.

The presence of difference frequencies produced by frequency mixing from the nonlinear resonance of gas bodies has been employed to detect gas in porous hydrophobic membranes and to distinguish between gas bodies in the membranes with pore sizes. Calculations based on measured pore sizes were used to predict the range of frequencies over which resonance may be expected and also to predict that the two different nominal pore sizes in this study would have distinguishable resonance characteristics. Measurements of porous and nonporous membrane scattering characteristics before and after membrane pressurization and measurements of receiver linearity indicate that resonance of the gas bodies in the membranes is the origin of the observed difference-frequency amplitudes. Difference-frequency amplitudes in the spectra of signals scattered from the membranes with smaller pores are found to peak at excitation frequencies higher than difference-frequency amplitudes produced by membranes with larger pores and generally follow the predictions of the calculations. The results show that a two-frequency mixing technique is capable of detecting and distinguishing sizes of gas bodies that may exist in vivo and serve as cavitation nuclei.

In-vivo measurements of ultrasound attenuation in normal or diseased liver.

Ultrasonic attenuation coefficients of liver have been derived from echoes received by a modified commercial B-scan imaging instrument. Values have been measured from selected regions within liver scans of 59 individuals, of which 15 cases were presumed normal (based on medical histories), and the remainder were involved with diffuse liver disease such as alcoholic cirrhosis, chemotherapy toxicity, chronic hepatitis, and liver metastases. Medical histories on most individuals include the results of serum liver function enzymes, conventional B-scan examinations, and exposure to drugs and alcohol. The results of CT abdominal scans (N = 13) and/or liver biopsy (N = 12) were also available. The results show that normal attenuation values for human liver are 0.054 +/- 0.009 Np/cm-MHz (0.47 dB/cm-MHz) with a frequency dependence of fn, where n = 1.05 +/- 0.25, in agreement with in vitro studies of mammalian liver. In diffuse liver disease, no relationship was found between the attenuation coefficient and the results of CT or conventional ultrasonic examination. A trend towards higher attenuation with increased fibrosis and fat, as graded from liver biopsies, was noted, but the results were generally not statistically significant. However, a significant correlation was found between high values of attenuation and abnormal liver function tests. High attenuation is also found with ingestion of alcohol, chemotherapeutic agents, and steroids, all of which may affect liver composition.

Doppler ultrasound in orifice flow. In vitro studies of the relationship between pressure difference and fluid velocity.

The validity of an orifice equation (Torricelli's law) which expresses a simple relationship between the pressure difference across an orifice and the maximum fluid velocity in the orifice was tested in vitro. An aqueous suspension of barium sulfate particles with a polymer added to attain variations in viscosity, was forced through orifices which ranged in diameter from 0.4 to 4.7 mm. The pressure difference across the orifice was determined with a transducer and the maximum fluid velocity in the orifice was determined with Doppler ultrasound. Tests were performed at Reynolds numbers, fluid viscosities, and pressure differences that spanned the following ranges: 400-25,000, 1-5 cP, and 3-100 mmHg, respectively. At pressure differences larger than 3 mmHg and fluid viscosity 3 cP (approximate viscosity of in vivo blood), Torricelli's law was demonstrated to be valid for orifice diameters larger than 1.6 mm. The validity of the law was found to be relatively insensitive to variations in orifice length.

Nonlinear receiver compression effects on the amplitude distribution of backscattered ultrasonic signals.

Nonlinear receiver compression effects on the amplitude distribution of backscattered ultrasonic signals are investigated by using digitized RF signals that have been compressed in a commercially made ultrasonic B-scan imaging instrument. Amplitude distributions of compressed RF and video signals were obtained from regions of B-scan images that correspond to approximately the same physical region in a random medium model with known backscatter amplitude characteristics. The amplitude distribution of the signal before compression was obtained by using a table constructed from measurements of the imaging instrument compression characteristics as a function of time gain compensation. While the results indicate the general form of the decompressed data agrees with single parameter model curves that are predicted by a widely employed Gaussian random process model, the signal-to-noise ratios of the decompressed envelope vary up to 20% from the 1.91 value predicted that model. This implies that effects such as nonlinearities, envelope smoothing, and noise which all may be present in varying degrees in practical ultrasonic imaging instrumentation can cause appreciable departures from theoretical data even under highly controlled conditions.

Time-shift estimation and focusing through distributed aberration using multirow arrays.

The effects of element height on time-shift estimation and transmit focus compensation are demonstrated experimentally. Multirow ultrasonic transducer arrays were emulated by combining adjacent elements of a 3.0-MHz, 0.6-mm pitch, two-dimensional array to define larger virtual elements. Pulse-echo data were acquired through tissue-mimicking distributed aberrators, and time-shift maps estimated from those data were used for transmit focus compensation. Compensated beams formed by arrays with fine row pitches were similar, but focus restoration was significantly less effective for "1.75-D" arrays with a coarse row pitch. For example, when focus compensation was derived from strongly aberrated random scattering data [70-ns nominal rms arrival time fluctuation with 7 mm FWHM (full-width at half-maximum) correlation length], the mean -20 dB lateral beamwidths were 5.2 mm for f/2.0 arrays with 0.6- and 1.8-mm row pitches and 9.5 mm for an f/2.0 array with 5.4-mm pitch. Time-shift maps estimated from random scattering data acquired with 5.4-mm pitch arrays included large discontinuities caused by low correlation of signals received on vertically and diagonally adjacent emulated elements. The results indicate that multirow arrays designed for use with aberration correction should have element dimensions much less than 75% of the correlation length of the aberration and perhaps as small as 25 to 30% of the correlation length.

Propagation and backpropagation for ultrasonic wavefront design.

Wave backpropagation is a concept that can be used to calculate the excitation signals for an array with programmable transmit waveforms to produce a specified field that has no significant evanescent wave components. This concept can also be used to find the field at a distance away from an aperture based on measurements made in the aperture. For a uniform medium, three methods exist for the calculation of wave propagation and backpropagation: the diffraction integral method, the angular spectrum method, and the shift-and-add method. The boundary conditions that are usually implicitly assumed by these methods are analyzed, and the relationship between these methods are explored. The application of the angular spectrum method to other kinds of boundary conditions is discussed, as is the relationship between wave backpropagation, phase conjugation, and the time-reversal mirror. Wave backpropagation is used, as an example, to calculate the excitation signals for a ring transducer to produce a specified pulsatile plane wave with a limited spatial extent.

Estimation and correction of ultrasonic wavefront distortion using pulse-echo data received in a two-dimensional aperture.

Pulse-echo measurements from random scattering and from a point target have been used to quantify transmitter beam size effects and isoplanatic patch size as well as to evaluate the performance of different aberration compensation techniques. Measurements were made using a single-element transmitter with a diameter of 1/2 in., 1 in., or 2 in., each focused at 3 in. A tissue-mimicking scattering phantom or a point target was used to produce echoes that were received in a two-dimensional aperture synthesized by scanning a linear array. A specimen of abdominal wall was placed in the reception path to produce aberration. B-scan images were formed with no compensation, with time-shift compensation in the receiving aperture, and with backpropagation followed by time-shift compensation. The isoplanatic patch size was estimated by compensating the focus of a test point target with the parameters estimated for an original point target position, and observing the deterioration of compensation effects with increasing distance between the test and the original point targets. The results of the measurements using different transmitter diameters quantify the improvement of time-delay estimation with the increase in wavefront coherence that accompanies decreased transmitter beam size. For seven specimens, the average isoplanatic patch size determined from a 10% increase in the -10 dB effective diameter was 16.7 mm in the azimuthal direction and 39.0 mm in the range direction. These sizes increased after backpropagation to 19.0 mm and 41.4 mm, respectively. For the 1/2 in., 1 in., and 2 in. diameter transmitters, the average contrast ratio improvement was 2.0 dB, 2.1 dB, and 2.8 dB, respectively, with time-shift compensation, and 2.3 dB, 2.7 dB, and 3.5 dB, respectively, with backpropagation of 20 mm followed by time-delay estimation and compensation. The investigation indicates that a tightly focused transmitter beam is necessary to create a scattered wavefront satisfactory for time-shift estimation, the isoplanatic patch is about twice as long in the range direction as in the azimuthal direction, and backpropagation followed by time-shift compensation provides better compensation of distortion than time-shift compensation alone.

A k-space method for large-scale models of wave propagation in tissue.

Large-scale simulation of ultrasonic pulse propagation in inhomogeneous tissue is important for the study of ultrasound-tissue interaction as well as for development of new imaging methods. Typical scales of interest span hundreds of wavelengths; most current two-dimensional methods, such as finite-difference and finite-element methods, are unable to compute propagation on this scale with the efficiency needed for imaging studies. Furthermore, for most available methods of simulating ultrasonic propagation, large-scale, three-dimensional computations of ultrasonic scattering are infeasible. Some of these difficulties have been overcome by previous pseudospectral and k-space methods, which allow substantial portions of the necessary computations to be executed using fast Fourier transforms. This paper presents a simplified derivation of the k-space method for a medium of variable sound speed and density; the derivation clearly shows the relationship of this k-space method to both past k-space methods and pseudospectral methods. In the present method, the spatial differential equations are solved by a simple Fourier transform method, and temporal iteration is performed using a k-t space propagator. The temporal iteration procedure is shown to be exact for homogeneous media, unconditionally stable for "slow" (c(x) < or = c0) media, and highly accurate for general weakly scattering media. The applicability of the k-space method to large-scale soft tissue modeling is shown by simulating two-dimensional propagation of an incident plane wave through several tissue-mimicking cylinders as well as a model chest wall cross section. A three-dimensional implementation of the k-space method is also employed for the example problem of propagation through a tissue-mimicking sphere. Numerical results indicate that the k-space method is accurate for large-scale soft tissue computations with much greater efficiency than that of an analogous leapfrog pseudospectral method or a 2-4 finite difference time-domain method. However, numerical results also indicate that the k-space method is less accurate than the finite-difference method for a high contrast scatterer with bone-like properties, although qualitative results can still be obtained by the k-space method with high efficiency. Possible extensions to the method, including representation of absorption effects, absorbing boundary conditions, elastic-wave propagation, and acoustic nonlinearity, are discussed.

Compensation for receiver bandpass effects on ultrasonic backscatter power spectra using a random medium reference.

A linear model of an ultrasonic pulse-echo system is used to express the measured power spectrum as the product of a scattering medium power spectrum and a transfer function accounting for system effects. Transfer functions are experimentally determined for multiple ranges using a random medium reference. Measured power spectra normalized by these functions are shown to be in close agreement with theoretical power spectra both in shape and absolute magnitude. The results indicate that the model allows scattering media to be distinguished when the media backscatter characteristics differ in the bandwidth of the measurement system.