Dong‐Lai Liu

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.

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.

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.

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.

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.

About the application of the van Cittert-Zernike theorem in ultrasonic imaging

The specific circumstances under which the van Cittert-Zernike theorem applies in ultrasonic imaging systems are examined through analysis and computations. Expressions are obtained for the mutual coherence function of an incoherent source when the signals are discrete in time and space and have finite lengths. Expressions are also obtained for statistics and effective signal-to-noise ratios that describe the error in the assumption of an incoherent source with finite signal lengths. Images of a one-dimensional source are reconstructed for different signal lengths and different pulse windows. The results show that ultrasonic signals with a relatively long effective length are needed to satisfy the incoherence requirement for image reconstruction based on the van Cittert-Zernike theorem. Consequently, although the van Cittert-Zernike theorem may be used to estimate the coherence length of ultrasonic signals in the aperture of an imaging system, special data acquisition techniques are needed for satisfactory reconstruction of ultrasonic images when depth resolution like that in current b-scans is required.<<ETX>>

A comparison of ultrasonic wavefront distortion and compensation in one-dimensional and two-dimensional apertures

A comparison of wavefront distortion and compensation in one-dimensional and two-dimensional apertures is made using two-dimensional transmission measurements through 14 different specimens of human abdominal wall. The measurements were employed to emulate data in one dimension by summing waveforms in the elevation direction after a geometric correction was performed using a fourth-order polynomial fit to the surface of arrival time. Distortion calculation and time-shift compensation were performed independently on waveforms in the one-dimensional and two-dimensional apertures and the waveforms were focussed using a Fourier transform method to obtain the point-spread function in the central elevation plane. The results show that distortion is smoothed increasingly by one-dimensional apertures as the elevation dimension grows and that the smoothing is substantial for elevations similar to those employed in present clinical imagers. The results also show that one-dimensional compensation becomes less effective than two-dimensional compensation as the size of the elevation increases but that one-dimensional compensation performs almost as well as two-dimensional compensation in apertures with elevations like those in current imaging systems.<<ETX>>

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.

An ultrasonic ring transducer system for studies of scattering and imaging

A novel ultrasonic ring transducer and special control electronics have been developed for scattering and imaging studies. The transducer contains 2048 rectangular elements with a center frequency of 2.4 MHz and a −6‐dB bandwidth of 70%. At the center frequency, the element size is 0.29 wavelength ×40 wavelength and the spacing is 0.37 wavelength. A multiplexer provides access to any contiguous 128 elements for transmission and any contiguous 16 elements for simultaneous reception. The transmit electronics have independently programmable waveforms. The receive electronics have time‐varied gain functions independently programmable over the range 15–55 dB. Each receive channel includes a 20‐MHz, 12‐bit A/D converter. The electronics permit synthesis of arbitrary transmit and receive apertures. A novel ultrasonic wavefront design method has been implemented to determine element excitations using backpropagation of a user‐specified field pattern. Pulse‐echo compound images using constant f/1.0 transmit and receive apertures have been obtained for model scattering objects and an anthropomorphic breast phantom. Scattering measurements have been analyzed to obtain frequency‐ and angle‐dependent average differential scattering cross sections of random media. The system is a useful facility for measurements of ultrasonic scattering for characterization of tissue, development of adaptive beam‐formation techniques, and implementation of quantitative image reconstruction methods.

Compensation for array nonidealities by electronics

Array elements usually have nonuniform characteristics in terms of element position, sensitivity, and waveform shape. Crosstalk caused by acoustic and electrical coupling limits the directivity of individual elements. These array nonidealities can be compensated by using pulser electronics with programmable transmit waveforms. Experiments were performed with a 2048‐element ring transducer and a 3×3 test block for a 64×64‐element 2‐D array. With the ring transducer, a thin wire was suspended at the center of the ring, and single‐element, pulse–echo data were collected for each element. To derive the one‐way inverse response for each element, the two‐way response was deconvolved using FFT, with special attention to phase unwrapping. Implementation of the inverse filtering reduced element arrival time fluctuation from 47 to 0.9 ns, energy level fluctuation from 1.2 to 0.4 dB, and increased the waveform similarity from 0.94 to 0.99. With the 3×3 test block, cancellation of crosstalk was performed by exciting neighboring elements with an opposing signal. The opposing signal was obtained by multiplying the original signal with a decoupling coefficient. Experimental results show that, with the particular test block, a decoupling coefficient of −0.08 extended the −6 dB half‐angle from 10.8 to 14.8 deg, with a corresponding decrease of 4.5 dB in sensitivity.