Jahan Tavakkoli

Nakagami imaging for detecting thermal lesions induced by high-intensity focused ultrasound in tissue.

High-intensity focused ultrasound induces focalized tissue coagulation by increasing the tissue temperature in a tight focal region. Several methods have been proposed to monitor high-intensity focused ultrasound–induced thermal lesions. Currently, ultrasound imaging techniques that are clinically used for monitoring high-intensity focused ultrasound treatment are standard pulse–echo B-mode ultrasound imaging, ultrasound temperature estimation, and elastography-based methods. On the contrary, the efficacy of two-dimensional Nakagami parametric imaging based on the distribution of the ultrasound backscattered signals to quantify properties of soft tissue has recently been evaluated. In this study, ultrasound radio frequency echo signals from ex vivo tissue samples were acquired before and after high-intensity focused ultrasound exposures and then their Nakagami parameter and scaling parameter of Nakagami distribution were estimated. These parameters were used to detect high-intensity focused ultrasound–induced thermal lesions. Also, the effects of changing the acoustic power of the high-intensity focused ultrasound transducer on the Nakagami parameters were studied. The results obtained suggest that the Nakagami distribution’s scaling and Nakagami parameters can effectively be used to detect high-intensity focused ultrasound–induced thermal lesions in tissue ex vivo. These parameters can also be used to understand the degree of change in tissue caused by high-intensity focused ultrasound exposures, which could be interpreted as a measure of degree of variability in scatterer concentration in various parts of the high-intensity focused ultrasound lesion.

A new algorithm for time-delay estimation in ultrasonic echo signals [Correspondence]

Time-delay estimation determines the relative displacement between two ultrasound echo signals. In this paper, we propose a new time-delay estimation algorithm which uses only the sign function to obtain the corresponding timedelay estimate. The performance of the proposed algorithm was compared with two established algorithms, i.e., normalized cross-correlation (NCC) and sum of squared differences (SSD), using metrics such as statistical analysis and computational time. All simulated ultrasound echo signals were generated using ultrasound simulation software. The results indicated that overall, the proposed algorithm had similar accuracy and precision compared with the NCC and SSD algorithms; however, the computational time of the proposed algorithm was about 70% less than NCC and SSD, which showed a significant improvement.

Estimating dynamic changes of tissue attenuation coefficient during high-intensity focused ultrasound treatment

BackgroundThis study investigated the dynamic changes of tissue attenuation coefficients before, during, and after high-intensity focused ultrasound (HIFU) treatment at different total acoustic powers (TAP) in ex vivo porcine muscle tissue. It further assessed the reliability of employing changes in tissue attenuation coefficient parameters as potential indicators of tissue thermal damage.MethodsTwo-dimensional pulse-echo radio frequency (RF) data were acquired before, during, and after HIFU exposure to estimate changes in least squares attenuation coefficient slope (Δβ) and attenuation coefficient intercept (Δα0). Using the acquired RF data, Δβ and Δα0 images, along with conventional B-mode ultrasound images, were constructed. The dynamic changes of Δβ and Δα0, averaged in the region of interest, were correlated with B-mode images obtained during the HIFU treatment process.ResultsAt a HIFU exposure duration of 40 s and various HIFU intensities (737–1,068 W/cm2), Δβ and Δα0 increased rapidly to values in the ranges 1.5–2.5 dB/(MHz.cm) and 4–5 dB/cm, respectively. This rapid increase was accompanied with the appearance of bubble clouds in the B-mode images. Bubble activities appeared as strong hyperechoic regions in the B-mode images and caused fluctuations in the estimated Δβ and Δα0 values. After the treatment, Δβ and Δα0 values gradually decreased, accompanied by fade-out of hyperechoic spots in the B-mode images. At 10 min after the treatment, they reached values in ranges 0.75–1 dB/(MHz.cm) and 1–1.5 dB/cm, respectively, and remained stable within those ranges. At a long HIFU exposure duration of around 10 min and low HIFU intensity (117 W/cm2), Δβ and Δα0 gradually increased to values of 2.2 dB/(MHz.cm) and 2.2 dB/cm, respectively. This increase was not accompanied with the appearance of bubble clouds in the B-mode images. After HIFU treatment, Δβ and Δα0 gradually decreased to values of 1.8 dB/(MHz.cm) and 1.5 dB/cm, respectively, and remained stable at those values.ConclusionsΔβ and Δα0 estimations were both potentially reliable indicators of tissue thermal damage. In addition, Δβ and Δα0 images both had significantly higher contrast-to-speckle ratios compared to the conventional B-mode images and outperformed the B-mode images in detecting HIFU thermal lesions at all investigated TAPs and exposure durations.

Unmitigated numerical solution to the diffraction term in the parabolic nonlinear ultrasound wave equation

Various numerical algorithms have been developed to solve the Khokhlov-Kuznetsov-Zabolotskaya (KZK) parabolic nonlinear wave equation. In this work, a generalized time-domain numerical algorithm is proposed to solve the diffraction term of the KZK equation. This algorithm solves the transverse Laplacian operator of the KZK equation in three-dimensional (3D) Cartesian coordinates using a finite-difference method based on the five-point implicit backward finite difference and the five-point Crank-Nicolson finite difference discretization techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term. In addition, a new empirical algorithm based on the LU decomposition technique is proposed to solve the system of linear equations obtained from this discretization. The proposed empirical algorithm improves the calculation speed and memory usage, while the order of computational complexity remains linear in calculation of the diffraction term in the KZK equation. For evaluating the accuracy of the proposed algorithm, two previously published algorithms are used as comparison references: the conventional 2D Texas code and its generalization for 3D geometries. The results show that the accuracy/efficiency performance of the proposed algorithm is comparable with the established time-domain methods.

A novel numerical solution to the diffraction term in the KZK nonlinear wave equation

Nonlinear ultrasound modeling is finding an increasing number of applications in both medical and industrial areas where due to high pressure amplitudes the effects of nonlinear propagation are no longer negligible. Taking nonlinear effects into account makes the ultrasound beam analysis more accurate in these applications. One of the most widely used nonlinear models for propagation of 3D diffractive sound beams in dissipative media is the KZK (Khokhlov, Kuznetsov, Zabolotskaya) parabolic nonlinear wave equation. Various numerical algorithms have been developed to solve the KZK equation. Generally, these algorithms fall into one of three main categories: frequency domain, time domain and combined time-frequency domain. The intrinsic parabolic approximation in the KZK equation imposes a limiting accuracy on the solution to the diffraction term of the KZK equation, particularly for field points in near field or in far off-axis regions. In this work we developed a novel generalized time domain numerical algorithm to solve the diffraction term of the KZK equation. The algorithm solves the Laplacian operator of the KZK equation in 3D Cartesian coordinates using a novel finite difference technique. This leads to a more accurate solution to the diffraction term in the KZK equation without compromising calculational efficiency. The outcome is a new numerical algorithm to solve the KZK equation with higher accuracy and increased efficiency compared to current algorithms.

Performance study of a new time-delay estimation algorithm in ultrasonic echo signals and ultrasound elastography.

Time-delay estimation has countless applications in ultrasound medical imaging. Previously, we proposed a new time-delay estimation algorithm, which was based on the summation of the sign function to compute the time-delay estimate (Shaswary et al., 2015). We reported that the proposed algorithm performs similar to normalized cross-correlation (NCC) and sum squared differences (SSD) algorithms, even though it was significantly more computationally efficient. In this paper, we study the performance of the proposed algorithm using statistical analysis and image quality analysis in ultrasound elastography imaging. Field II simulation software was used for generation of ultrasound radio frequency (RF) echo signals for statistical analysis, and a clinical ultrasound scanner (Sonix® RP scanner, Ultrasonix Medical Corp., Richmond, BC, Canada) was used to scan a commercial ultrasound elastography tissue-mimicking phantom for image quality analysis. The statistical analysis results confirmed that, in overall, the proposed algorithm has similar performance compared to NCC and SSD algorithms. The image quality analysis results indicated that the proposed algorithm produces strain images with marginally higher signal-to-noise and contrast-to-noise ratios compared to NCC and SSD algorithms.

Temperature dependence of acoustic harmonics generated by nonlinear ultrasound beam propagation in ex vivo tissue and tissue-mimicking phantoms

Abstract Purpose: Hyperthermia is a cancer treatment technique that could be delivered as a stand-alone modality or in conjunction with chemotherapy or radiation therapy. Noninvasive and real-time temperature monitoring of the heated tissue improves the efficacy and safety of the treatment. A temperature-sensitive acoustic parameter is required for ultrasound-based thermometry. In this paper the amplitude and the energy of the acoustic harmonics of the ultrasound backscattered signal are proposed as suitable parameters for noninvasive ultrasound thermometry. Materials and methods: A commercial high frequency ultrasound imaging system was used to generate and detect acoustic harmonics in tissue-mimicking gel phantoms and ex vivo bovine muscle tissues. The pressure amplitude and the energy content of the backscattered fundamental frequency (p1 and E1), the second (p2 and E2) and the third (p3 and E3) harmonics were detected in pulse-echo mode. Temperature was increased from 26° to 46 °C uniformly through both samples. The amplitude and the energy content of the harmonics and their ratio were measured and analysed as a function of temperature. Results: The average p1, p2 and p3 increased by 69%, 100% and 283%, respectively as the temperature was elevated from 26° to 46 °C in tissue samples. In the same experiment the average E1, E2 and E3 increased by 163%, 281% and 2257%, respectively. A similar trend was observed in tissue-mimicking gel phantoms. Conclusions: The findings suggest that the harmonics generated due to nonlinear ultrasound beam propagation are highly sensitive to temperature and could potentially be used for noninvasive ultrasound tissue thermometry.

An Acoustic backscatter-based method for estimating attenuation towards monitoring lesion formation in high intensity focused ultrasound

This work investigated the transient characteristics of tissue attenuation coefficient before, during and after HIFU treatment at different total acoustic powers (TAP) in ex-vivo porcine muscle tissues. Dynamic changes of attenuation coefficient parameters were correlated with conventional B-mode ultrasound images over the whole HIFU treatment process. Two-dimensional pulse-echo radiofrequency (RF) data were acquired to estimate the changes of least squares attenuation coefficient slope (▵β) and attenuation coefficient intercept (▵α0) averaged in the region of interest, and to construct ▵β, ▵α0, and B-mode images simultaneously. During HIFU treatment, bubble activities were visible as strong hyperechoic regions in the B-mode images, causing fluctuations in ▵β and ▵α0 during treatment. ▵β and ▵α0 increased with the appearance of bubble clouds in the B-mode images to values in the range of 1.5-2.5 [dB/(MHz.cm)] and 4-5 [dB/cm], respectively. After the treatment, ▵β and ▵α0 gradually decreased, accompanied b...

Technical Note: Bone mineral density measurements of strontium-rich trabecular bone-mimicking phantoms using quantitative ultrasound

PURPOSE Bone quantity, as determined by the current gold standard, dual energy X-ray absorptiometry (DXA), through measured areal bone mineral density (aBMD), is subject to positive biases if bone strontium levels are high. This is of particular concern for populations administered strontium-based compounds for the treatment of osteoporosis. This study investigated the dependence of bone mineral density (BMD) determinations, and associated ultrasound-determined indices, obtained by quantitative ultrasound (QUS), on bone strontium content using a new generation of trabecular bone-mimicking phantoms. METHODS A new generation of bone-mimicking phantoms, consisting of hydroxyapatite (HA) and gelatin, was developed. Castor oil layers were included in these phantoms to create a multilayer bone-mimicking phantom. These phantoms were prepared using a bone mineral fraction consisting of varying strontium concentrations in the range of 0-2.5% mol/mol as strontium-substituted HA. The effect of varying bone strontium content on determined quality indices was evaluated based on determined speed of sound (SOS), broadband ultrasound attenuation (BUA) and determined quantitative ultrasound index (QUI) for phantoms with varying BMD values and varying strontium concentration using two QUS systems: a clinical Sahara® system and an in-house research system with two identical transducers with center frequency of 1 MHz. The two QUS systems were also compared through a Bland-Altman analysis. RESULTS Both the clinical system and the research QUS systems showed a strong dependency between BMD and BUA, indicating a potential for QUS to be used as a means of estimating BMD (p = 0.001). SOS was found to have no correlation to BMD (p = 0.546). There was no correlation observed between BUA and increasing bone strontium concentrations for the research (p = 0.749) and clinical (p = 0.609) QUS systems. Similarly, no dependency was observed between the SOS and bone strontium levels up to 2.5 mol/mol [Sr/(Sr+Ca)]% for the research (p = 0.862) and clinical (p = 0.481) QUS systems. No effect on the QUI values was observed with changing strontium levels with either research (p = 0.939) or clinical QUS systems (p = 0.931). A Bland-Altman analysis showed that there was a clear offset in determined QUI values for both systems but they are in agreement with one another. CONCLUSIONS Bone quality can be assessed through the use of QUS while increasing bone strontium concentration was found to have no effect on QUS-determined quality indices. This study concludes that QUS can potentially be used for the determination of bone quality without introducing biases due to bone strontium levels as is known to be the case with DXA determined aBMD.

Temperature dependence of acoustic harmonics generated by nonlinear ultrasound wave propagation in water at various frequencies

Ultrasound-based thermometry requires a temperature-sensitive acoustic parameter that can be used to estimate the temperature by tracking changes in that parameter during heating. The objective of this study is to investigate the temperature dependence of acoustic harmonics generated by nonlinear ultrasound wave propagation in water at various pulse transmit frequencies from 1 to 20 MHz. Simulations were conducted using an expanded form of the Khokhlov-Zabolotskaya-Kuznetsov nonlinear acoustic wave propagation model in which temperature dependence of the medium parameters was included. Measurements were performed using single-element transducers at two different transmit frequencies of 3.3 and 13 MHz which are within the range of frequencies simulated. The acoustic pressure signals were measured by a calibrated needle hydrophone along the axes of the transducers. The water temperature was uniformly increased from 26 °C to 46 °C in increments of 5 °C. The results show that the temperature dependence of the harmonic generation is different at various frequencies which is due to the interplay between the mechanisms of absorption, nonlinearity, and focusing gain. At the transmit frequencies of 1 and 3.3 MHz, the harmonic amplitudes decrease with increasing the temperature, while the opposite temperature dependence is observed at 13 and 20 MHz.