Wavefront amplitude distribution in the female breast

Speed of sound ultrasound transmission tomography image reconstruction based on Bézier curves

Speed of Sound (SoS) maps from ultrasound tomography (UST) provide valuable quantitative information for soft tissue characterization and identification of lesions, making this technique interesting for breast cancer detection. However, due to the complexity of the processes that characterize the interaction of ultrasonic waves with matter, classic and fast tomographic algorithms such as back-projection are not suitable. Consequently, the image reconstruction process in UST is generally slow compared to other more conventional medical tomography modalities. With the aim of facilitating the translation of this technique into real clinical practice, several reconstruction algorithms are being proposed to make image reconstruction in UST to be a fast and accurate process. The geometrical acoustic approximation is often used to reconstruct SoS with less computational burden in comparison with full-wave inversion methods. In this work, we propose a simple formulation to perform on-the-flight reconstruction for UST using geometrical acoustics with refraction correction based on quadratic Bézier polynomials. Here we demonstrate that the trajectories created with these polynomials are an accurate approximation to reproduce the refracted acoustic paths connecting the emitter and receiver transducers. The method is faster than typical acquisition times in UST. Thus, it can be considered a step towards real-time reconstructions, which may contribute to its future clinical translation.

Can acoustic structural quantification be used to characterize the ultrasound echotexture of the peripheral zone of breast lesions?

BACKGROUND:

Besides mammography, breast ultrasound is the most important imaging modality for women with suspected breast cancer. New software tools bear high potential for improved detectability and specification of malignant breast lesions.

OBJECTIVE:

To compare the halo depicted around malignant breast lesions by ultrasound using Acoustic Structure Quantification (ASQ) of raw image data with the echogenic rim seen in B-mode ultrasound.

METHODS:

This retrospective study included 37 women for whom conventional B-mode ultrasound of the breast and ASQ were available as well as histopathology findings for comparison. Software tools were used to measure the halo area or echogenic rim and tumor area and calculate halo-to-lesion ratios for the two ultrasound modes. Six inexperienced readers characterized the breast lesions based on this information. Specificity, sensitivity, positive predictive value (PPV), and negative predictive value (NPV) were determined. ANOVA, the Wilcoxon test, and ROC curve analysis were performed.

RESULTS:

There was a linear relationship between ASQ-based and B-mode-based halo-to-lesion ratios; however, a systematic error was also noted. ASQ-derived ratios tended to be higher for breast lesions with lymphangioinvasion (p = 0.051, n.s.) and higher N-stages (p > 0.925, n.s.), while there was no correlation with other markers. Because of the significantly greater conspicuity of peritumoral halos in the ASQ mode, inexperienced readers achieved greater sensitivity (78% vs. 74%) and specificity (75% vs. 71%) and higher NPVs (75% vs. 71%) and PPVs (78% vs. 74%) compared with B-mode images. Greater halo conspicuity affected the identification of malignant lesions with both modes; ASQ was found to be particularly well suited (F_Bimage (1,100) = 19.253, p < 0.001; F_ASQ (1,100) = 52.338, p < 0.001). The inexperienced readers were significantly more confident about their diagnosis using the ASQ maps (z = –3.023, p = 0.003).

CONCLUSIONS:

We conclude that the halo in ASQ and the echogenic rim in B-mode ultrasound are attributable to different morphologic correlates. ASQ improves diagnostic accuracy and confidence of inexperienced examiners because of improved halo visibility.

Refraction corrected transmission ultrasound computed tomography for application in breast imaging

PURPOSE

We present an iterative framework for CT reconstruction from transmission ultrasound data which accurately and efficiently models the strong refraction effects that occur in our target application: Imaging the female breast.

METHODS

Our refractive ray tracing framework has its foundation in the fast marching method (FNMM) and it allows an accurate as well as efficient modeling of curved rays. We also describe a novel regularization scheme that yields further significant reconstruction quality improvements. A final contribution is the development of a realistic anthropomorphic digital breast phantom based on the NIH Visible Female data set.

RESULTS

Our system is able to resolve very fine details even in the presence of significant noise, and it reconstructs both sound speed and attenuation data. Excellent correspondence with a traditional, but significantly more computationally expensive wave equation solver is achieved.

CONCLUSIONS

Apart from the accurate modeling of curved rays, decisive factors have also been our regularization scheme and the high-quality interpolation filter we have used. An added benefit of our framework is that it accelerates well on GPUs where we have shown that clinical 3D reconstruction speeds on the order of minutes are possible.

Effects of cochlear implant processing and fundamental frequency on the intelligibility of competing sentences

Speech perception in the presence of another competing voice is one of the most challenging tasks for cochlear implant users. Several studies have shown that (1) the fundamental frequency (F0) is a useful cue for segregating competing speech sounds and (2) the F0 is better represented by the temporal fine structure than by the temporal envelope. However, current cochlear implant speech processing algorithms emphasize temporal envelope information and discard the temporal fine structure. In this study, speech recognition was measured as a function of the F0 separation of the target and competing sentence in normal-hearing and cochlear implant listeners. For the normal-hearing listeners, the combined sentences were processed through either a standard implant simulation or a new algorithm which additionally extracts a slowed-down version of the temporal fine structure (called Frequency-Amplitude-Modulation-Encoding). The results showed no benefit of increasing F0 separation for the cochlear implant or simulation groups. In contrast, the new algorithm resulted in gradual improvements with increasing F0 separation, similar to that found with unprocessed sentences. These results emphasize the importance of temporal fine structure for speech perception and demonstrate a potential remedy for difficulty in the perceptual segregation of competing speech sounds.

Computer simulation of forward wave propagation in soft tissue

A method for simulating forward wavefront propagation in heterogeneous tissue is discussed. The intended application of this method is for the study of aberration produced when performing ultrasound imaging through a layer of soft tissue. A one-way wave equation that permits smooth variation in all acoustically important variables is derived. This equation also describes tissue exhibiting nonlinear elasticity and arbitrary frequency-dependent relaxation. A numerical solution to this equation is found by means of operator splitting and propagation along the spatial depth coordinate. The numerical solution is accurate when compared to analytical solutions for special cases, and when compared to numerical solutions of the full wave equation by other methods. The presented implementation provides a fast numerical method for studying the impact of aberration in medical ultrasound imaging through soft tissue--both on the transmitted beam and the nonlinearly generated harmonic beam.

Simulations of optoacoustic wave propagation in light-absorbing media using a finite-difference time-domain method

Optoacoustic (OA) imaging is an emerging technology that combines the high optical contrast of tissues with the high spatial resolution of ultrasound. Taking full advantage of OA imaging requires a better understanding of OA wave propagation in light-absorbing media. Current simulation methods are mainly based on simplified conditions such as thermal confinement, negligible viscosity, and homogeneous acoustic properties throughout the image object. In this study a new numerical approach is proposed based on a finite-difference time-domain (FDTD) method to solve the general OA equations, comprising the continuity, Navier-Stokes, and heat-conduction equations. The FDTD code was validated using a benchmark problem that has an approximate analytical solution. OA experiments were also conducted and data were in good agreement with those predicted by the FDTD method. Characteristics of simulated OA waveforms and OA images were discussed. The simulator was also employed to study wavefront distortion in OA breast imaging.

Comparisons of lesion detectability in ultrasound images acquired using time-shift compensation and spatial compounding

The effects of aberration, time-shift compensation, and spatial compounding on the discrimination of positive-contrast lesions in ultrasound b-scan images are investigated using a two-dimensional (2-D) array system and tissue-mimicking phantoms. Images were acquired within an 8.8 x 12-mm2 field of view centered on one of four statistically similar 4-mm diameter spherical lesions. Each lesion was imaged in four planes offset by successive 45 degree rotations about the central scan line. Images of the lesions were acquired using conventional geometric focusing through a water path, geometric focusing through a 35-mm thick distributed aberration phantom, and time-shift compensated transmit and receive focusing through the aberration phantom. The views of each lesion were averaged to form sets of water path, aberrated, and time-shift compensated 4:1 compound images and 16:1 compound images. The contrast ratio and detectability index of each image were computed to assess lesion differentiation. In the presence of aberration representative of breast or abdominal wall tissue, time-shift compensation provided statistically significant improvements of contrast ratio but did not consistently affect the detectability index, and spatial compounding significantly increased the detectability index but did not alter the contrast ratio. Time-shift compensation and spatial compounding thus provide complementary benefits to lesion detection.

Spectral estimation for characterization of acoustic aberration

Spectral estimation based on acoustic backscatter from a motionless stochastic medium is described for characterization of aberration in ultrasonic imaging. The underlying assumptions for the estimation are: The correlation length of the medium is short compared to the length of the transmitted acoustic pulse, an isoplanatic region of sufficient size exists around the focal point, and the backscatter can be modeled as an ergodic stochastic process. The motivation for this work is ultrasonic imaging with aberration correction. Measurements were performed using a two-dimensional array system with 80 x 80 transducer elements and an element pitch of 0.6 mm. The f number for the measurements was 1.2 and the center frequency was 3.0 MHz with a 53% bandwidth. Relative phase of aberration was extracted from estimated cross spectra using a robust least-mean-square-error method based on an orthogonal expansion of the phase differences of neighboring wave forms as a function of frequency. Estimates of cross-spectrum phase from measurements of random scattering through a tissue-mimicking aberrator have confidence bands approximately +/- 5 degrees wide. Both phase and magnitude are in good agreement with a reference characterization obtained from a point scatterer.

Analysis and correction of ultrasonic wavefront distortion based on a multilayer phase-screen model

A model is introduced that incorporates the cumulative wavefront distortion effects caused by spatial heterogeneities along the path of propagation, and a corresponding model-based wavefront distortion-correction method is presented. In the proposed model, a distributed heterogeneous medium is lumped into a series of parallel phase screens. The distortion effects can be compensated--without a priori knowledge of the distorting structure--by backpropagation of received wavefronts through hypothetical multiple phase screens located between the imaging system and targets, while each pointwise time shift is adjusted iteratively to maximize a specified image quality factor at the final layer. Theoretical analyses indicate that the mean speckle brightness decreases monotonically with the root-mean-square value of distributed phase distortions; therefore, the speckle brightness can be used as an image quality factor. Experimental one-dimensional (1-D) array data with simulated distortion effects based on a real 2-D abdominal-tissue map were used to evaluate the performance of the proposed method and existing aberration-correction techniques. The simulated characteristics of wavefront distortion and relative performance of existing correction techniques were similar to reports based on abdominal-wall data and breast data. This investigation shows that the proposed method provides better compensation for wavefront distortion.

Estimation and compensation of ultrasonic wavefront distortion using a blind system identification method

A common random input filter model is described for estimation and correction of wavefront aberration in ultrasonic b-scan imaging. In the model, aberration between the focus and the transducer elements is represented by the response of a linear filter bank to a common random signal. The response of each filter in the bank is found using a two-level extension of an existing subspace method for blind system identification. The receive waveforms are compensated using an inverse filter, and the transmit waveforms are predistorted using time reversal. To test the model, experiments were conducted using a two-dimensional array system to obtain echoes from a point reflector and from a random medium in each case through an aberrator. The aberrator is a phantom that mimics wavefront distortion produced by human abdominal wall, and the random medium is made to mimic ultrasonic characteristics of human liver. The results indicate the method can improve both the transmit and the receive focus and can outperform time-shift estimation and compensation as well as the method of backpropagation followed by timeshift estimation and compensation.

A comparison of material classification techniques for ultrasound inverse imaging

The conjugate gradient method with edge preserving regularization (CGEP) is applied to the ultrasound inverse scattering problem for the early detection of breast tumors. To accelerate image reconstruction, several different pattern classification schemes are introduced into the CGEP algorithm. These classification techniques are compared for a full-sized, two-dimensional breast model. One of these techniques uses two parameters, the sound speed and attenuation, simultaneously to perform classification based on a Bayesian classifier and is called bivariate material classification (BMC). The other two techniques, presented in earlier work, are univariate material classification (UMC) and neural network (NN) classification. BMC is an extension of UMC, the latter using attenuation alone to perform classification, and NN classification uses a neural network. Both noiseless and noisy cases are considered. For the noiseless case, numerical simulations show that the CGEP-BMC method requires 40% fewer iterations than the CGEP method, and the CGEP-NN method requires 55% fewer. The CGEP-BMC and CGEP-NN methods yield more accurate reconstructions than the CGEP method. A quantitative comparison of the CGEP-BMC, CGEP-NN, and GN-UMC methods shows that the CGEP-BMC and CGEP-NN methods are more robust to noise than the GN-UMC method, while all three are similar in computational complexity.

The direct estimation of sound speed using pulse-echo ultrasound

A method for the direct estimation of the longitudinal speed of sound in a medium is presented. This estimator derives the speed of sound through analysis of pulse-echo data received across a single transducer array following a single transmission, and is analogous to methods used in exploration seismology. A potential application of this estimator is the dynamic correction of beamforming errors in medical imaging that result from discrepancy between the assumed and actual biological tissue velocities. The theoretical basis of this estimator is described and its function demonstrated in phantom experiments. Using a wire target, sound-speed estimates in water, methanol, ethanol, and n-butanol are compared to published values. Sound-speed estimates in two speckle-generating phantoms are also compared to expected values. The mean relative errors of these estimates are all less than 0.4%, and under the most ideal experimental conditions are less than 0.1%. The relative errors of estimates based on independent regions of speckle-generating phantoms have a standard deviation on the order of 0.5%. Simulation results showing the relative significance of potential sources of estimate error are presented. The impact of sound-speed errors on imaging and the potential of this estimator for phase aberration correction and tissue characterization are also discussed.

Inverse imaging of the breast with a material classification technique

In recent publications [Chew et al., IEEE Trans. Blomed. Eng. BME-9, 218-225 (1990); Borup et al., Ultrason. Imaging 14, 69-85 (1992)] the inverse imaging problem has been solved by means of a two-step iterative method. In this paper, a third step is introduced for ultrasound imaging of the breast. In this step, which is based on statistical pattern recognition, classification of tissue types and a priori knowledge of the anatomy of the breast are integrated into the iterative method. Use of this material classification technique results in more rapid convergence to the inverse solution--approximately 40% fewer iterations are required--as well as greater accuracy. In addition, tumors are detected early in the reconstruction process. Results for reconstructions of a simple two-dimensional model of the human breast are presented. These reconstructions are extremely accurate when system noise and variations in tissue parameters are not too great. However, for the algorithm used, degradation of the reconstructions and divergence from the correct solution occur when system noise and variations in parameters exceed threshold values. Even in this case, however, tumors are still identified within a few iterations.

Comparisons of the Rayleigh and K-distribution models using in vivo breast and liver tissue

There is a strong interest in finding out which statistical model is the most appropriate for describing the envelope of the backscattered ultrasonic echoes from different types of tissues. The Rayleigh model is commonly employed, but this requires conditions, such as the presence of large number of randomly located scatterers with fairly uniform cross-sections, that are not always met. However, our research indicates that a model based on the K-distribution may provide a better fit to empirical data over a range of scattering conditions than the standard Rayleigh model. In this study, we looked at the K-distribution as a descriptor of the backscattered envelope of the breast and liver tissues (in vivo). By examining data from various tissue regions, a goodness-of-fit test (a least squares error method) was used to determine whether a Rayleigh or K-distribution model is more appropriate. From a large group of patients and volunteer scans (a total of 72 subjects), the fit between the K-distribution and the data is shown to have a much smaller error than the Rayleigh model.

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.

Phase aberration correction using near-field signal redundancy. I. Principles [Ultrasound medical imaging]

The signal redundancy principle in the near field is analyzed quantitatively. It is found that common midpoint signals are not identical (or redundant) for echoes coming from arbitrary target distributions in the near field. A dynamic near-field correction is proposed to reduce the difference between common midpoint signals for echoes coming from the region of interest. When phase aberrations are present, it is shown that the dynamic correction can generally be done assuming no phase aberration, and the relative time-shift between common midpoint signals can be used to measure phase-aberration profiles. A phase-aberration correction algorithm based on that principle is proposed. In this algorithm, after common midpoint signals are collected they are dynamically corrected for near-field effects and cross-correlated with one another. In a related way, the phase errors are measured from peak positions of these cross-correlation functions. The phase-aberration profile across the array is derived from these measurements. The relationship between the errors in the derived phase aberration profile and the errors in the measured relative time-shift between common midpoint signals is derived. A method for treating the situation of different transmission and reception phase-aberration profiles is also proposed. This algorithm works for general target distributions, iteration is not required, and it can be used in other near-field, pulse-echo, imaging systems.

Finite amplitude distortion-based inhomogeneous pulse echo ultrasonic imaging

Ultrasonic pulse echo imaging in inhomogeneous media suffers from significant lateral and contrast resolution losses due to the defocusing effects of the inhomogeneities. The losses in lateral and contrast resolution are associated with increases in the width of the mainbeam and increases in sidelobe levels, respectively. These two forms of resolution loss represent significant hurdles to improving the clinical utility of biomedical ultrasonic imaging. A number of research efforts are currently under way to investigate the defocusing effects of tissue and to consider corrective measures. All of these efforts assume linear propagation, and base the image-formation process on the reception of the transmitted pulse. A novel pulse echo imaging scheme in which the image is formed using the finite amplitude distortion components of the received pulse is considered here. Alternatively, this could be described as image formation using the nonlinearly-generated higher harmonics. In homogeneous beam propagations, it has been established that the sidelobes of nonlinearly-generated higher harmonics are much lower than their linear counterparts. Computations considered here suggest that this relationship also holds for the case of propagations through abdominal wall and breast wall tissue. These computations also suggest that the lateral resolution limits imposed by abdominal wall and breast wall tissue are slightly smaller for nonlinearly-generated second harmonics than for their linear counterparts. The resulting potential of these higher harmonics to improve image resolution is investigated.

Wavefront amplitude distortion and image sidelobe levels. II. In vivo experiments

For part I, see ibid., vol.40, no.6, p.747-753 (1993). In vivo measurements of the rise of the sidelobe level in a single-source image obtained through the female breast as a function of the distortion of the wavefront amplitude are described. The measured sidelobe levels are the average sidelobe floor (ASF) and the peak sidelobe level (PSL). The ASF is shown to be proportional to the variance of the modulus of the wavefront normalized to the square of its mean value, with a proportionality constant close to the value predicted by theory. The PSL similarly increases linearly. The average ratio of PSL to ASF is 5 (7 dB).

Wavefront amplitude distortion and image sidelobe levels. I. Theory and computer simulations

The quality of an imaging system is degraded by propagation anomalies that distort wavefronts propagating through the medium. Adaptive phase-deaberration algorithms compensate for phase errors in the wavefront. The algorithms suffer, however, when the wavefront is also significantly distorted. A theory which shows that the rise of image background level, which is the average sidelobe floor (ASF), in a single point-like source image is proportional to the amplitude distortion of the wavefront and inversely proportional to the effective number of array elements is derived. From the theory, the tolerance to the amplitude distortion, after the phasefront has been corrected by a deaberration algorithm, can be calculated based on the design requirement of the sidelobe floor for a given array. Computer simulations show good agreement with the theory.