Urban, Matthew W.

When applied to compressional waves, the Caputo time-fractional wave equation describes power law attenuation in soft tissue. However, when applied to shear waves, the Caputo wave equation produces some unexpected behavior. To demonstrate examples of the time-domain waveforms generated by this fractional calculus model, the Caputo wave equation is numerically evaluated for multiple orders of the time-fractional derivative between 0 and 1, for an extended range of values for the relaxation time, and for a fixed value of the shear wave speed extracted from ex vivo pig liver. The computed waveforms are then compared to the measured shear wave particle velocities obtained from ex vivo pig liver. These comparisons reveal that the full-width at half maximum (FWHM) of the positive component of the main shear wave particle velocity waveform measured in pig liver is at least an order of magnitude greater than the FWHM obtained from the Caputo wave equation for all parameter combinations evaluated. These preliminary results indicate that the Caputo wave equation produces time-domain waveforms that are inconsistent with measured shear wave data in pig liver and that further efforts are required to establish more effective fractional calculus models for shear waves in soft tissue.

Ultrasound shear wave elastography (SWE) is a useful technique for non-invasive tissue assessment. For effective quantitative analysis the employment of physical models is necessary for rheological parameter estimation, such as the Kelvin-Voigt (KV) model. From SWE data, the frequency response can be calculated, and the shear wave velocity dispersion can be fit, yielding the shear elasticity and shear viscosity, μ1 and μ2, respectively. In this study, a parametric evaluation is performed using staggered-grid finite-difference simulations of materials with μ1 = 1–25 kPa (increment: 1 kPa) and μ2 = 0–10 Pa s (increment: 0.5 Pa s), with an acoustic radiation force push of f-number equal to 2. The novel Stockwell transform combined with a slant frequency-wavenumber analysis (GST-SFK) was compared with the two-dimensional Fourier transform for dispersion curve estimation over a variety of frequency ranges. Regardless of dispersion curve estimation technique, the accuracy of estimating μ1 is confounded for μ2 values above 5 Pa s. It was found that KV fitting benefits from wider frequency ranges (up to 1kHz), with lower μ1 and μ2 estimation errors. The GST-SFK was the best dispersion curve calculation technique, yet the KV fitting process was found to be unreliable for parameter estimation in highly viscous media.

Time-domain estimates of the shear wave speed are obtained by performing cross-correlations or by evaluating the time-to-peak for two laterally separated shear wave particle velocity waveforms, where the distance divided by the propagation time yields an approximate value for the shear wave speed. Challenges associated with these time-domain estimation approaches include increasing errors as the shear viscosity increases and the absence of an estimated value for the shear viscosity parameter which is responsible for the rapid attenuation of shear waves in soft tissue. To obtain a time-domain estimate of the shear viscosity that also provides an estimate for the shear wave speed, a nonlinear least squares estimation approach is applied to three-dimensional (3D) shear wave particle velocities computed for a shear elasticity of 1.5 kPa, shear viscosities of 1, 2, 3, and 4 Pa.s, and a realistic simulated 3D acoustic radiation force excitation. The results show cross-correlations tend to over-estimate the value of the shear wave speed, the nonlinear least squares approach tends to under-estimate the value of the shear wave speed, and the nonlinear least square approach produces more accurate estimates as the shear viscosity increases. Two-dimensional maps of each estimated parameter are also shown.

Shear Wave Elastography (SWE) involves estimating mechanical properties through inversion, i.e., matching measured and simulated propagation characteristics of shear waves in the tissue. The accuracy of the estimated properties depends significantly on the specific characteristics/responses that are being matched. These could range from simple group velocity to dispersion curves and to full-wave response (particle velocity measurements). Using specific applications of arterial, liver, and tumor elstography, we illustrate that effective SWE is performed by resorting to an inversion approach, or combination of inversion approaches, guided by the underlying physics. To this end, we present inversion approaches ranging from matching dispersion characteristics to matching full waveform responses and provide rationale for choosing the appropriate technique(s) depending on the problem at hand.

Arterial stiffness is a predictor of cardiovascular diseases, the leading causes of death worldwide. Ultrasound-based methods that measure arterial wave propagation have promise for evaluating local stiffness in vivo. However, geometric properties of arteries cause dispersion, invalidating typical assumptions underlying the relationship between shear modulus G and group velocity cg, which clinical implementations of ultrasound shear wave elastography do not consider. Here, we examine the dependence of these estimates on geometry and evaluate alternative approaches. Wave motion in the proximal wall of an artery after application of focused acoustic radiation force is simulated with a semi-analytical finite element (SAFE) model, and cg is estimated using a time-to-peak algorithm to determine G with several methods. First, the value of G a clinical scanner would report is calculated assuming a bulk medium. Second, a pulse wave velocity (PWV)-based G estimate is calculated by taking cg = PWV and applying the Moens–Korteweg equation. Third, we develop an interpolation-based method to provide a corrected G estimate using data generated by the SAFE model. Simulation results show severe geometry-dependent bias with the bulk method, which is partially ameliorated with the PWV method and substantially improved with the interpolation approach. Results are validated using arterial phantoms.

Applications, such as shear wave elastography and Doppler imaging, require high frame rates. Plane wave compounding (PWC) is widely used for these applications. Comb detection was proposed to combine the high frame rate of PWC and the high signal quality of focused beam scanning. Comb detection transmits multiple focused beams simultaneously to increase the frame rate. These comb beams are scanned laterally to cover the whole region-of-interest. The simultaneous multiple transmission of focused beams causes crosstalk between neighboring beams. Transmit crosstalk is related to the pressure field of transmit beams, and receive crosstalk is determined by the beam profile of receive beamforming. In this study, we varied f-number (F/N) and apodization window and measured their effects on crosstalk based on the pressure field and an arterial wall simulation using Field II. For transmit design, transmit apodization with a Hamming window significantly reduced crosstalk compared to a rectangular window and transmit F/N had little impact on the crosstalk. Regarding receive beamforming, a Hamming window led to lower crosstalk than the rectangular window and F/N from 1 to 5 suppressed crosstalk to below 30 dB. The effects of crosstalk in shear wave motion data from phantom experiments were also analyzed. Comb detection showed less motion artifact than PWC in phantom experiments.

Synthetic aperture (SA) acquisition allows for focusing at all points in ultrasound images during reconstruction. Both delay-and-sum (DAS) and delay-multiply-and-sum (DMAS) have been used to reconstruct SA images. An integral part of both algorithms is the aperture size used to define the beam shape with the f-number. Although f-number variation has been studied in DAS reconstruction, there has not been a systematic study on this topic for DMAS reconstruction in SA imaging. In this work, we evaluated the effects of f-number in DMAS reconstruction using an imaging phantom (CIRS 040GSE). We reconstructed DAS and DMAS images of hyperechoic, hypoechoic, and anechoic contrast targets, as well as point targets, while varying the transmit and receive f-numbers between 0 and 7 in 0.2 increments. Generalized contrast-to-noise ratio (gCNR) was measured for contrast targets. The full width at half maximum (FWHM) was evaluated using point targets. When imaging contrast targets, the DAS and DMAS algorithms responded very differently when varying the f-numbers. DMAS produced higher gCNR values with low transmit f-numbers and high receive f-numbers, while DAS produced higher gCNR values with high transmit and receive f-numbers. When evaluating FWHM, the optimal receive f-number was close to 1 for both algorithms.

AbstractBackgroundApplicator conspicuity in ultrasound‐guided brachytherapy procedures is commonly impaired by imaging artifacts or non‐ideal imaging geometry, which can slow down applicator position digitization and increase the geometric uncertainty of the delivered dose distribution.PurposeThe purpose of this study was to improve the conspicuity of high‐dose rate (HDR) brachytherapy needles under B‐mode ultrasound imaging by applying an echogenic surface coating. Our hypothesis was that an echogenic coating would reduce artifacts and improve needle visualization within regions of signal degradation.MethodsIn this study, 17‐gauge, 25‐cm long titanium HDR brachytherapy needles were coated with acoustically reflective microspheres over a 2.5 cm region starting from the needle tip. Three coating thicknesses (27 μm, 40 μm, 64 μm) were compared against an uncoated control needle. The coated and uncoated needles were imaged using B‐mode ultrasound in a tissue‐equivalent prostate phantom and in a cadaverous male pelvis using a transrectal probe. Needle conspicuity was assessed under multiple conditions: a single needle implant, an implant with multiple needles between the probe and the needle of interest, and an angled needle implant. All images were assessed qualitatively for needle conspicuity and the presence of artifacts and quantitatively using grey‐scale image intensity values.ResultsThe 64 μm echogenic coating reduced the magnitude of reverberation artifacts by 31 ± 14% and comet tail artifacts by 40%–70%. The echogenic coating also improved needle contrast, measured by the relative differences in signal intensity compared with the adjacent environment, when needles were angled up to 30° with respect to the transducer probe in the cadaver. The improvements in conspicuity and artifact reduction increased with increasing coating thickness. The performance of the needles coated with the 64 μm thickness was qualitatively superior and yielded high‐contrast, well‐circumscribed signals in the cadaverous male pelvis, even under situations where a needle was acoustically shadowed by multiple other needles.ConclusionsAn echogenic surface coating reduced imaging artifacts and improved needle conspicuity under realistic clinical conditions for ultrasound‐based prostate or gynecological brachytherapy. The improved conspicuity has the potential to improve the efficiency of needle placement and the accuracy of needle position digitization during brachytherapy procedures.