Biomedical subjects

R C Waag

Publications and source records attributed to R C Waag.

At least 19 recordsLinked to original sources

PubMed1997

Harmonic amplitude distribution in a wideband ultrasonic wavefront after propagation through human abdominal wall and breast specimens.

The amplitude characteristics of ultrasonic wavefront distortion produced by transmission through the abdominal wall and breast is described. Ultrasonic pulses were recorded in a two-dimensional aperture after transmission through specimens of abdominal wall or breast. After the pulse arrival times were corrected for geometric path differences, the pulses were temporally Fourier transformed and two-dimensional maps of harmonic amplitudes in the measurement aperture were computed. The results indicate that, as the temporal frequency increases, the fluctuation in harmonic amplitudes increases but the spatial scale of the fluctuation decreases. The normalized second-order and third-order moments of the amplitude distribution also increase with temporal frequency. The wide range variation of these distribution characteristics could not be covered by the Rayleigh, Rician, or K-distribution because of their limited flexibility. However, the Weibull distribution and especially the generalized K-distribution provide better fits to the data. In the fit of the generalized K-distribution, a decrease of its parameter alpha with increasing temporal frequency was observed, as predicted by analysis based on a phase screen model.

Abdomen↗

PubMed1997

Measurements of ultrasonic pulse distortion produced by human chest wall.

Ultrasonic wavefront distortion produced by transmission through human chest wall specimens was measured over a two-dimensional aperture. Measured pulse wavefronts were sometimes disrupted by secondary wavefronts produced by interaction between the transmitted pulses and the bone and cartilage structures of the rib cage. The secondary wavefronts produced large distortions in the received waveforms and interfered with the determination of the wavefront distortion caused by soft-tissue inhomogeneities. The effects of secondary wavefronts were minimized by reducing the region of analysis. Differences in arrival time and energy level between these restricted regions and references that account for geometric delay and spreading were computed. Spectral changes were assessed by calculating a waveform similarity factor that is decreased from 1.0 by changes in waveform shape. For 16 different intercostal spaces, the arrival time fluctuations of the measured waveforms had an average (+/-s.d.) rms value of 21.3 (+/-8.4) ns and an average correlation length of 2.50 (+/-0.62) mm. The energy level fluctuations had an average rms value of 1.57 (+/-0.45) dB and an average correlation length of 1.98 (+/-0.33) mm, and the average waveform similarity factor was 0.964 (+/-0.012). For soft-tissue inhomogeneities in chest wall specimens, the average rms arrival time and energy level fluctuations were less than half those measured for the abdominal wall. However, although the average correlation length of the arrival time fluctuations was less than half that found for the abdominal wall, the average correlation length of the energy level fluctuations was similar to that of the abdominal wall.

Aged↗

PubMed1997

Focusing and imaging using eigenfunctions of the scattering operator.

An inverse scattering method that uses eigenfunctions of the scattering operator is presented. This approach provides a unified framework that encompasses eigenfunction methods of focusing and quantitative image reconstruction in arbitrary media. Scattered acoustic fields are described using a compact, normal operator. The eigenfunctions of this operator are shown to correspond to the far-field patterns of source distributions that are directly proportional to the position-dependent contrast of a scattering object. Conversely, the eigenfunctions of the scattering operator specify incident-wave patterns that focus on these effective source distributions. These focusing properties are employed in a new inverse scattering method that represents unknown scattering media using products of numerically calculated fields of eigenfunctions. A regularized solution to the nonlinear inverse scattering problem is shown to result from combinations of these products, so that the products comprise a natural basis for efficient and accurate reconstructions of unknown inhomogeneities. The corresponding linearized problem is solved analytically, resulting in a simple formula for the low-pass-filtered scattering potential. The linear formula is analytically equivalent to known filtered-backpropagation formulas for Born inversion, and, at least in the case of small scattering objects, has advantages of computational simplicity and efficiency. A similarly efficient and simple formula is derived for the nonlinear problem in which the total acoustic pressure can be determined based on an estimate of the medium. Computational results illustrate focusing of eigenfunctions on discrete and distributed scattering media, quantitative imaging of inhomogeneous media using products of retransmitted eigenfunctions, inverse scattering in an inhomogeneous background medium, and reconstructions for data corrupted by noise.

Humans↗

PubMed1997

Simulation of ultrasonic pulse propagation through the abdominal wall.

Ultrasonic pulse propagation through the abdominal wall has been simulated using a model for two-dimensional propagation through anatomically realistic tissue cross sections. The time-domain equations for wave propagation in a medium of variable sound speed and density were discretized to obtain a set of coupled finite-difference equations. These difference equations were solved numerically using a two-step MacCormack scheme that is fourth-order accurate in space and second-order accurate in time. The inhomogeneous tissue of the abdominal wall was represented by two-dimensional matrices of sound speed and density values. These values were determined by processing scanned images of abdominal wall cross sections stained to identify connective tissue, muscle, and fat, each of which was assumed to have a constant sound speed and density. The computational configuration was chosen to simulate that of wavefront distortion measurements performed on the same specimens. Qualitative agreement was found between those measurements and the results of the present computations, indicating that the computational model correctly depicts the salient characteristics of ultrasonic wavefront distortion in vivo. However, quantitative agreement was limited by the two-dimensionality of the computation and the absence of detailed tissue microstructure. Calculations performed using an asymptotic straight-ray approximation showed good agreement with time-shift aberrations predicted by the full-wave method, but did not explain the amplitude fluctuations and waveform distortion found in the experiments and the full-wave calculations. Visualization of computed wave propagation within tissue cross sections suggests that amplitude fluctuations and waveform distortion observed in ultrasonic propagation through the abdominal wall are associated with scattering from internal inhomogeneities such as septa within the subcutaneous fat. These observations, as well as statistical analysis of computed and observed amplitude fluctuations, suggest that weak fluctuation models do not fully describe ultrasonic wavefront distortion caused by the abdominal wall.

Abdomen↗

PubMed1995

Measurement and correction of ultrasonic pulse distortion produced by the human breast.

Ultrasonic wavefront distortion produced by transmission through breast tissue specimens was measured in a two-dimensional aperture. Differences in arrival time and energy level between the measured waveforms and references that account for geometric delay and spreading were calculated. Also calculated was a waveform similarity factor that is decreased from 1.0 by changes in waveform shape. For nine different breast specimens, the arrival time fluctuations had an average (+/- s.d.) rms value of 66.8 (+/- 12.6) ns and an associated correlation length of 4.3 (+/- 1.1) mm, while the energy level fluctuations had an average rms value of 5.0 (+/- 0.5) dB and a correlation length of 3.4 (+/- 0.8) mm. The corresponding waveform similarity factor was 0.910 (+/- 0.023). The effect of the wavefront distortion on focusing and the ability of time-shift compensation to remove the distortion were evaluated by comparing parameters such as the -30-dB effective radius, the -10-dB peripheral energy ratio, and the level at which the effective radius departs from an ideal by 10% for the focus obtained without compensation, with time-shift estimation and compensation in the aperture, and with time-shift estimation and compensation performed after backpropagation. For the nine specimens, the average -10-dB peripheral energy ratio of the focused beams fell from 3.82 (+/- 1.83) for the uncompensated data to 0.96 (+/- 0.18) with time-shift compensation in the aperture and to 0.63 (+/- 0.07) with time-shift compensation after backpropagation. The average -30-dB effective radius and average 10% deviation level were 4.5 (+/- 0.8) mm and -19.2 (+/- 3.5) dB, respectively, for compensation in the aperture and 3.2 (+/- 0.7) mm and -22.8 (+/- 2.8) dB, respectively, for compensation after backpropagation. The corresponding radius for the uncompensated data was not meaningful because the dynamic range of the focus was generally less than 30 dB in the elevation direction, while the average 10% deviation level for the uncompensated data was -4.9 (+/- 4.1) dB. The results indicate that wavefront distortion produced by breast significantly degrades ultrasonic focus in the low MHz frequency range and that much of this degradation can be eliminated using wavefront backpropagation and time-shift compensation.

Adolescent↗

PubMed1995

Wave space resolution in ultrasonic scattering measurements.

The spatial-frequency spectra of the spatial properties of a scattering medium can be determined from measurements of scattering over a number of angles or frequencies. In such measurements, the spatial localization associated with transducer beam patterns and time gates causes an uncertainty in the measured spatial-frequency domain properties of the scatterer. This uncertainty is analyzed using an analytic and computational model in which system effects are represented by a spatial-frequency domain function. Wave space resolution in a particular direction is shown to be inversely proportional to the spatial-frequency spread of the system function in that direction. In the backscatter case, wave space resolution is limited in the direction of the scattering vector by a convolution of the emitted pulse and the detector time gate, and resolution in the lateral direction depends mainly on the transducer aperture, increasing approximately in proportion to the aperture diameter. In the case of backscatter measurements, smooth aperture apodization improves lateral resolution somewhat but has little effect on resolution in the direction of the scattering vector. For angular scattering measurements, resolution in all directions depends on both the aperture size and (for sufficiently short time gates) on the time gates employed. Illustration of the practical importance of wave space resolution is provided using analysis of two previously published tissue characterization experiments.

Acoustics↗

PubMed1994

Measurements of ultrasonic pulse arrival time and energy level variations produced by propagation through abdominal wall.

Ultrasonic pulse arrival time and energy level variations introduced by propagation through human abdominal wall specimens have been measured. A hemispheric transducer transmitted an ultrasonic pulse that was detected by a linear array transducer after propagation through an abdominal wall section. The array was translated in the elevation direction to collect data over a two-dimensional aperture. Differences in arrival time and energy level between the measured waveforms and calculated references that account for geometric delay and spreading were found. Plots of waveforms compensated for geometric path, maps of time delay differences and energy level fluctuations, and statistics derived from these for water paths and tissue paths characterize the measurement system and describe the time delay differences and energy level fluctuations caused by 14 different human abdominal wall specimens. Repeated measurements using the same specimens show that individual tissue path measurements are reproducible, the results depend on specimen position, and frozen storage of a specimen for three months does not appear to alter the time delay differences and energy level fluctuations produced by the specimen. Comparison of measurements at room and body temperature indicates that appreciably higher time delay differences occur at body temperature while energy level fluctuations and time delay difference patterns are less affected. For the 14 different abdominal wall specimens, the rms time delay differences and energy level fluctuations have average values of 43.0 ns and 3.30 dB, respectively, and the associated correlation lengths of the time delay differences and energy level fluctuations are 7.90 and 2.28 mm, respectively. The spatial patterns of time delay difference and energy level fluctuation in the reception plane appear largely uncorrelated, although some background variations in energy level fluctuation are similar to features in time delay difference maps. The results provide important new information about the variety and range of ultrasonic wave front arrival and energy variations caused by transmission through abdominal wall.

Abdominal Muscles↗

PubMed1994

Time-shift compensation of ultrasonic pulse focus degradation using least-mean-square error estimates of arrival time.

Focus degradation produced by abdominal wall has been compensated using a least-mean-square error estimate of arrival time. The compensation was performed on data from measurements of ultrasonic pulses from a curved transducer that emits a hemispheric wave and simulates a point source. The pulse waveforms were measured in a two-dimensional aperture after propagation through a water path and after propagation through 14 different specimens of human abdominal wall. Time histories of the virtual point source were reconstructed by removing the time delays produced by geometric path differences and also removing time shifts produced by propagation inhomogeneities in the case of compensation, finding the complex amplitudes of the Fourier harmonics across the aperture, calculating the Fraunhofer diffraction pattern of each harmonic, and summing the patterns. This process used a least-mean-square error solution for the relative delay expressed in terms of the arrival time differences between neighboring points and included an algorithm to determine arrival time differences when correlation based estimates were unsatisfactory due to dissimilarity of neighboring waveforms. Comparisons of reconstructed time histories in the image plane show that the -10-dB effective radius of the focus for reception through abdominal wall without compensation for inhomogeneities averaged 48% greater than the corresponding average effective radius for ideal waveforms, while time-shift compensation reduced the average -10-dB effective radius to a value that is only 4% greater than for reception of ideal waveforms. The comparisons also indicate that the average ratio of energy outside an ellipsoid defined by the -10-dB effective widths to the energy inside that ellipsoid is 1.81 for uncompensated tissue path data and that time-shift compensation reduced this average to 0.93, while the corresponding average for ideal waveforms was found to be 0.35. These results show that time-shift compensation yields a significant improvement over the uncompensated case although other factors must be considered to achieve an ideal diffraction limited focus.

Abdominal Muscles↗

PubMed1994

Correction of ultrasonic wavefront distortion using backpropagation and a reference waveform method for time-shift compensation.

A model is introduced to describe ultrasonic pulse amplitude and shape distortion as well as arrival time fluctuation produced by propagation through specimens of human abdominal wall. In the model, amplitude and shape distortion develops as the wavefront propagates in a uniform medium after passing through a phase screen that only causes time shifts. This distortion is compensated by a backpropagation of the wavefront using the angular spectrum method. The compensation employed waveforms emitted by a pointlike source and measured after propagation through the tissue. The waveforms were first corrected for geometric path and then were backpropagated over a sequence of increasing distances. At each distance, a waveform similarity factor was calculated to find the backpropagation distance at which the waveforms were most similar. A new method was devised to estimate pulse arrival time for geometric correction as well as to perform time-shift compensation. The method adaptively derives a reference waveform that is then cross correlated with all the waveforms in the aperture to obtain a surface of arrival times. The surface was smoothed iteratively to remove outlying points due to waveform distortion. The mean (+/- s.d.) of the waveform similarity factor for 14 specimens was found to be 0.938 (+/- 0.025) initially. After backpropagation of waveforms to the distance of maximum waveform similarity for each specimen, the waveform similarity factor improved to 0.967 (+/- 0.015). The corresponding energy level fluctuation in the wavefront was 4.2 (+/- 0.4) dB initially and became 3.3 (+/- 0.3) dB after backpropagation. For wavefronts focused at 180 mm, the -30 dB mean (+/- s.d.) effective radius of the focus was 4.2 (+/- 1.2) mm with time-shift compensation in the aperture and became 2.5 (+/- 0.5) mm with backpropagation followed by time-shift compensation. These results indicate that a phase screen placed some distance away from the aperture is an improved model for the description of wavefront distortion produced by human abdominal wall and that wavefront backpropagation followed by time-shift estimation and compensation is an effective method to compensate for such distortion.

Abdominal Muscles↗

PubMed1992

Analysis and computations of measurement system effects in ultrasonic scattering experiments.

A model that characterizes the effects of beams and waveforms on the measurement of ultrasonic scattering is analyzed in detail. The analysis obtains a wideband expression for the system function in terms of an integration over spatial- and temporal-frequency variables. The temporal-frequency integration is reduced to a convolution in the direction of the scattering vector when the temporal frequencies are concentrated in a narrow band around a central frequency. The spatial-frequency integration is simplified to a straight line path when the spatial frequencies in the angular spectra of the emitter are concentrated around a point on the axis of the emitter and the spatial frequencies of the detector sensitivity pattern are similarly concentrated around a point on the axis of the detector. Expressions that result from the temporal and spatial approximations are evaluated analytically for circularly symmetric Gaussian spatial apertures and Gaussian temporal waveforms. In addition, numerical results are obtained to compare the effects of circularly symmetric Gaussian, exponential, and uniform spatial aperture functions on the weight that beam patterns have on measurements of scattering. The results may be used to design experiments from which intrinsic parameters of scattering media can be obtained by an appropriate normalization to remove measurement system effects from the data.

Humans↗

PubMed1991

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.

Gases↗

PubMed1991

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.

Data Collection↗

PubMed1991

Measurements of ultrasonic pulse arrival time differences produced by abdominal wall specimens.

The influence of propagation medium inhomogeneities on pulsatile ultrasonic fields has been investigated experimentally. The study employed a special curved transducer to produce a hemispherical wave pulse and a linear array to measure the resulting field along a line in a plane. Translation of the array in the elevation direction yielded data over a two-dimensional aperture. Time delay across the aperture was calculated by adding delay differences obtained by cross-correlating signals on adjacent elements and noting the position of the cross-correlation peaks. Received waveforms were shifted an amount given by the difference between the actual arrival time and a calculated geometric delay to isolate arrival time differences due to propagation path inhomogeneities. Waveform and time delay difference plots as well as histograms and statistics derived from them for propagation through a water path and for propagation through five specimens of human abdominal wall indicate that arrival time fluctuations in the presence of human abdominal wall specimens are significantly greater than for a water path and that degradation in focusing through human abdominal wall can be expected in ultrasonic imaging systems that operate in the low megahertz range and employ a relatively large aperture.

Abdominal Muscles↗

PubMed1990

Characterization of measurement system effects in ultrasonic scattering experiments.

A general model is developed to characterize the effect of an ultrasonic measurement system on the experimental determination of ultrasonic scattering as a function of angle and frequency. The model includes arbitrary emitter beams and detector apertures as angular spectra of plane waves. Arbitrary emitted pulses and detector time gates are incorporated through frequency spectra of temporal harmonics. A transformation of variables is employed to express the spectrum of the measured pressure as a product in wave space of a system function and the Fourier transform of the medium variations. The mean-square value of the measured pressure spectrum is similarly expressed as a product of the squared magnitude of the system function and the power spectrum of the medium variations. The measured quantities are shown to become scaled values of intrinsic scattering characteristics when the system function weight is concentrated relative to the medium characteristics in wave space. The assumption of an indefinitely long detector gate is used to represent the system function as a product in which one factor is a beam function dependent on spatial frequency and the other factors are dependent on temporal frequency. Beam-function calculations as well as calculations of second moments and overall beam weight are made for identical Gaussian-shaped emitter and detector apertures to illustrate the blurring and weighting effects of measurement system beam patterns as a function of scattering angle. The moment calculations are shown to identify circumstances when the medium variation function can be factored out from under the integral and the measurement represented as a simple product of the medium properties and a measurement system weight. The results may be used to design scattering experiments in which degradations due to system effects are within acceptable limits.

Computer Simulation↗

PubMed1989

Estimates of wave front distortion from measurements of scattering by model random media and calf liver.

An expression based on a perturbation method is employed to estimate the correlation of path length difference in a plane normal to the direction of wave propagation from measurements of ultrasonic scattering by model random media and calf liver. The expression gives the correlation function of path length difference in terms of an integral of the correlation function of the medium variations or an equivalent integral of the power spectrum of medium variations, both for a scattering angle of zero degrees. Power spectra derived from measurements of average differential scattering cross section over a spatial-frequency window are used to fit analytic functions that extend over all spatial frequencies. The results for the windowed and unwindowed data yield correlation functions and corresponding power spectra that are used to estimate the correlation function of path length difference. The results suggest that the correlation length in calf liver is less than 100 microns and that a root-mean-square path length variation of about 20 microns results from propagation through a 100-mm calf liver path.

Animals↗

PubMed1989

Spectral power determinations of compressibility and density variations in model media and calf liver using ultrasound.

A model of scattering is used to relate average differential scattering cross section and power spectra of scattering medium variations. The model expresses the average differential scattering cross section as a sum of the power spectrum of medium compressibility variations, the power spectrum of density variations weighted by the square of the cosine of the scattering angle, and the cross-power spectrum of compressibility and density variations weighted by twice the cosine of the scattering angle. Known values of the average differential scattering cross section at a minimum of three different scattering angles and temporal frequencies corresponding to the same spatial frequency are used to calculate each of the three power spectra. Since noise and statistical fluctuations are present in actual measurements of average differential scattering cross section, the calculations of power spectra are obtained from an overdetermined set of equations to which a solution is found by using a singular value decomposition. Data derived from a model for scattering from a cloud of correlated particles are employed to show the influence of additive noise. Calculations are also made from measurements of scattering from three suspensions of particles that have a different average radius in each suspension but are similarly modeled by scattering from a cloud. Additionally, the calculations are applied to measurements of average differential scattering cross section of calf liver. The results show that determination of the power spectra of scattering medium variations can be made under practical conditions, and also imply that density variations contribute significantly to scattering by calf liver.

Animals↗

PubMed1989

Sequential topographical portrayal of myocardial blood flow.

Methods to portray myocardial blood flow in a two-dimensional continuum are advantageous in that they allow blood flow history to be overlaid on histological or histochemical descriptions of the consequences of ischemia. We describe here autoradiographic methods that allow such portrayals at three separate times during the evolution of ischemic injury. A computer-based image-analysis system was used to derive such flow maps by taking advantage of the physical characteristics of radioactive isotopes.

Animals↗

PubMed1988

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.

Animals↗