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Real-time simulation of ultrasound images is increasingly important for providing a means of presenting a wide variety of clinical images for the training of ultrasound specialists and technologists. In order to realistically represent the visual effects caused by changes to the transducer position or its focal properties, very rapid transducer field response calculations are needed, typically on the order of a fraction of a second. Currently available methods are severely limited in this regard. Based on the impulse response, a point source/receiver method for accurately calculating the fields produced by ultrasound transducer arrays is proposed and illustrated with realistic B-mode and Doppler spectral display simulations. The results of this method (FAMUS II), which accounts for the attenuation frequency dependence of the propagating medium, are compared with those obtained with Field II both in terms of quality and computational speed. From a clinical simulation perspective, the qualitative differences are small. Because the method is inherently parallelizable, significant gains in computational speed can be achieved. For example, in B-mode imaging using an eight-core CPU, FAMUS II is shown to be more than two orders of magnitude faster than that achieved by Field II. As a result, we believe that this new method represents a significant step toward achieving real-time performance.

Ultrasound simulators relying on impulse response methods are faithful to the mechanisms of image formation from the underlying radio-frequency signals, but as a result tend to be relatively slow. At the other extreme are fast techniques, often motivated by the development of teaching and training simulators, which approximate the image formation processes rather than rigorously modeling the underlying physics. Previously, we have shown that transmit field distributions from linear phased-array transducers can be modeled accurately and efficiently using arrays of point sources. This approach is now extended to point sources/receivers, which allows for simulation of the transmit/receive fields, and thus the physical processes underlying ultrasound image formation. Field distributions and fast-time signals are shown to compare favorably to those obtained using the impulse response method. Doppler spectrogram and B-mode images derived from these signals also show excellent agreement with the results obtained using the impulse response method, but with a computational savings of nearly two orders of magnitude. Because of the inherent simplicity of our Fast and Mechanistic Ultrasound Simulation (FAMUS) approach, CPU parallelization was readily achieved, and further orders of magnitude speed improvements, and thus real-time performance, can be anticipated via extension to modern graphics processing units.

An effective way to generate localized narrowband low-frequency shear waves within tissue noninvasively, is by the modulated radiation force, resulting from the interference of two confocal quasi-CW ultrasound beams of slightly different frequencies. By using approximate viscoelastic Green's functions, investigations of the properties of the propagated shear-field component at the fundamental modulation frequency were previously reported by our group. However, high-amplitude source excitations may be needed to increase the signal-to-noise-ratio for shear-wave detection in tissue. This paper reports a study of the generation and propagation of dynamic radiation force components at harmonics of the modulation frequency for conditions that generally correspond to diagnostic safety standards. We describe the propagation characteristics of the resulting harmonic shear waves and discuss how they depend on the parameters of nonlinearity, focusing gain, and absorption. For conditions of high viscosity (believed to be characteristic of soft tissue) and higher modulation frequencies, the approximate shear wave Green's function is inappropriate. A more exact viscoelastic Green's function is derived in k-space, and using this, it is shown that the lowpass and dispersive effects, associated with a Voigt model of tissue, are more accurately represented. Finally, it is shown how the viscoelastic properties of the propagating medium can be estimated, based on several spectral components of the shearwave spectrum.

Because of their adaptability to the slow-time signal contents, eigen-based filters have shown potential in improving the flow detection performance of color flow images. This paper proposes a new eigen-based filter called the Hankel-SVD filter that is intended to process each slowtime ensemble individually. The new filter is derived using the notion of principal Hankel component analysis, and it achieves clutter suppression by retaining only the principal components whose order is greater than the clutter eigen-space dimension estimated from a frequency based analysis algorithm. To assess its efficacy, the Hankel-SVD filter was first applied to synthetic slow-time data (ensemble size: 10) simulated from two different sets of flow parameters that model: 1) arterial imaging (blood velocity: 0 to 38.5 cm/s, tissue motion: up to 2 mm/s, transmit frequency: 5 MHz, pulse repetition period: 0.4 ms) and 2) deep vessel imaging (blood velocity: 0 to 19.2 cm/s, tissue motion: up to 2 cm/s, transmit frequency: 2 MHz, pulse repetition period: 2.0 ms). In the simulation analysis, the post-filter clutter-to- blood signal ratio (CBR) was computed as a function of blood velocity. Results show that for the same effective stopband size (50 Hz), the Hankel-SVD filter has a narrower transition region in the post-filter CBR curve than that of another type of adaptive filter called the clutter-downmixing filter. The practical efficacy of the proposed filter was tested by application to in vivo color flow data obtained from the human carotid arteries (transmit frequency: 4 MHz, pulse repetition period: 0.333 ms, ensemble size: 10). The resulting power images show that the Hankel-SVD filter can better distinguish between blood and moving-tissue regions (about 9 dB separation in power) than the clutter-downmixing filter and a fixed-rank multi ensemble-based eigen-filter (which showed a 2 to 3 dB separation).

Parametric spectral estimators can potentially be used to obtain flow estimates directly from raw slow-time ensembles whose clutter has not been suppressed. We present a new eigen-based parametric flow estimation method called the matrix pencil, whose principles are based on a matrix form under the same name. The presented method models the slow-time signal as a sum of dominant complex sinusoids in the slow-time ensemble, and it computes the principal Doppler frequencies by using a generalized eigen-value problem-formulation and matrix rank reduction principles. Both fixed rank (rank-one, rank-two) and adaptive-rank matrix pencil flow estimators are proposed, and their potential applicability to color flow signal processing is discussed. For the adaptive-rank estimator, the nominal rank was defined as the minimum eigen-structure rank that yields principal frequency estimates with a spread greater than a prescribed bandwidth. In our initial performance evaluation, the fixed-rank matrix pencil estimators were applied to raw color flow data (transmit frequency: 5 MHz; pulse repetition period: 0.175 ms; ensemble size: 14) acquired from a steady flow phantom (70 cm/s at centerline) that was surrounded by rigid-tissue-mimicking material. These fixed-rank estimators produced velocity maps that are well correlated with the theoretical flow profile (correlation coefficient: 0.964 to 0.975). To facilitate further evaluation, the matrix pencil estimators were applied to synthetic slow-time data (transmit frequency: 5 MHz; pulse repetition period: 1.0 ms; ensemble size: 10) modeling flow scenarios without and with tissue motion (up to 1 cm/s). The bias and root-mean-squared error of the estimators were computed as a function of blood-signal-to-noise ratio and blood velocity. The matrix pencil flow estimators showed that they are comparatively less biased than most of the existing frequency-based flow estimators like the lagone autocorrelator.

A highly localized source of low-frequency shear waves can be created by the modulated radiation force resulting from two intersecting quasi-continuous-wave ultrasound beams of slightly different frequencies. In contrast to most other radiation force-based methods, these shear waves can be narrowband. Consequently, different frequency-dependent effects will not significantly affect their spectrum as they propagate within a viscoelastic medium, thereby enabling the viscoelastic shear properties of the medium to be determined at any given modulation frequency. This can be achieved by tracking the shear wave phase delay and change in amplitude over a specific distance. In this paper we explore the properties of short duration (dynamic) low-frequency shear wave propagation and study how the shear displacement field depends on the excitation conditions. Our investigations make use of the approximate Green's functions for viscoelastic media, and the evolution of such waves is studied in the spatiotemporal domain from a theoretical perspective. Although nonlinearities are included in our confocal source model, just the properties of the fundamental shear component are examined in this paper. We examine how the shear wave propagation is affected by the shear viscosity, the coupling wave, the spatial distribution of the force, the shear speed, and the duration of the modulated wave. A method is proposed for estimating the shear viscosity of a viscoelastic medium. In addition, it is shown how the Voigt model paremeters can be extracted from the frequency-dependent speed and attenuation.

Abstract-Many forms of spinal fusion involve the placement of long screws through the pedicles into the vertebral body. During the procedure, there is substantial risk of damage to vital neural and vascular structures due to the limited visibility of anatomic landmarks and high anatomic variability. As an alternative to current guidance systems, we have investigated the feasibility of performing ultrasound imaging through cancellous bone for the purpose of pedicle screw guidance. Quantitative ultrasonic characterization and A-mode imaging of seven defatted vertebral cancellous bone specimens was performed along the craniocaudal axis in water with unfocused, 1-MHz and 3.5- MHz broadband transducers. The center frequency attenuation increased considerably from 10.5 +/- 4.6 dB/cm at 1 MHz to 24.1 +/- 7.2 dB/cm at 3.5 MHz, while the speed of sound exhibited moderate positive dispersion, increasing from 1489 +/- 4.7 m/s at 1 MHz to 1494 +/- 4.2 m/s at 3.5 MHz. Despite the high attenuation and large specimen thickness (1.0-1.9 cm), A-mode imaging through cancellous bone to detect an aluminum reflector was possible in 83.2% and 70.1% of the cases at 1 MHz and 3.5 MHz, respectively. Specimen boundaries were identifiable with clinically sufficient average accuracy of 1.1 mm and 0.9 mm in the 1 MHz and 3.5 MHz A-mode images, respectively.

In Doppler ultrasound, transit-time broadening arises from the finite scatterer transit time through the sample volume. As a unifying description of this broadening mechanism, a generalized amplitude modulation signal model was developed to collectively account for the transit-time effects of the ultrasound beam geometry and the range gate characteristics. Simulations based on a pulsed linear-array system also were performed to study the broadening extent for different scatterer flow lines. With our signal model and simulation results, some generalized insights were obtained on the characteristics of transit-time broadening. First, as consistent with previous findings, we found that, for scatterers passing though the center of the sample volume, the broadening extent mainly depends on beam-forming characteristics at higher beam-flow angles, but it is more dependent on range gate parameters at smaller angles. Second, for the central flow line, a transition angle exists in which a significant change occurs in the governing parameters of transit-time broadening. Third, for the general case in which scatterers undertake an off-central path through the sample volume, the broadening extent depends on both the beam geometry and the range gate. Bandwidth skewing and further spectral broadening also can be seen for these off-central flow lines.

Diffractionless solutions of the wave equation in the form of X-waves have previously been obtained based on the inviscid form of the wave equation. A new general solution to the cylindrically symmetric wave equation for a medium with classical viscous losses is obtained. Particular solutions called dissipative Arcsin X-waves have been derived from this general solution. The properties of these waves are discussed for both infinite and finite size transducers and for different viscous liquids. To calculate the field produced by a finite transducer diameter, we have derived a dissipative form of the Rayleigh integral.