Frequency-sum beamforming for passive cavitation imaging

Generalized frequency-sum beamforming for low frequencies

For direction-of-arrival (DOA) estimation in the low-frequency range, we improve spatial resolution using generalized frequency-sum (gFS) beamforming with the Qth order frequency-sum autoproduct. The order Q does not exceed the maximum value, determined by the criteria that the sum of frequencies used to create the autoproduct must be less than the array's spatial Nyquist frequency. Unlike other high-resolution beamformers, gFS maintains stable performance even with a single snapshot and is unaffected by the coherence of steering vectors. Rigorous analysis using the multinomial expansion has shown the inapplicability of gFS to multi-DOA scenarios. Simulation and experimental results support that the method is a practical alternative for low-frequency single-DOA estimation with limited data.

Simultaneous High-Frame-Rate Acoustic Plane-Wave and Optical Imaging of Intracranial Cavitation in Polyacrylamide Brain Phantoms during Blunt Force Impact

Blunt and blast impacts occur in civilian and military personnel, resulting in traumatic brain injuries necessitating a complete understanding of damage mechanisms and protective equipment design. However, the inability to monitor in vivo brain deformation and potential harmful cavitation events during collisions limits the investigation of injury mechanisms. To study the cavitation potential, we developed a full-scale human head phantom with features that allow a direct optical and acoustic observation at high frame rates during blunt impacts. The phantom consists of a transparent polyacrylamide material sealed with fluid in a 3D-printed skull where windows are integrated for data acquisition. The model has similar mechanical properties to brain tissue and includes simplified yet key anatomical features. Optical imaging indicated reproducible cavitation events above a threshold impact energy and localized cavitation to the fluid of the central sulcus, which appeared as high-intensity regions in acoustic images. An acoustic spectral analysis detected cavitation as harmonic and broadband signals that were mapped onto a reconstructed acoustic frame. Small bubbles trapped during phantom fabrication resulted in cavitation artifacts, which remain the largest challenge of the study. Ultimately, acoustic imaging demonstrated the potential to be a stand-alone tool, allowing observations at depth, where optical techniques are limited.

Passive acoustic mapping with absolute time-of-flight information and delay-multiply-sum beamforming

BACKGROUND

Passive acoustic mapping (PAM) is showing increasing application potential in monitoring ultrasound therapy by spatially resolving cavitation activity. PAM with the relative time-of-flight information leads to poor axial resolution when implemented with ultrasound diagnostic transducers. Through utilizing the absolute time-of-flight information preserved by the transmit-receive synchronization and applying the common delay-sum (DS) beamforming algorithm, PAM axial resolution can be greatly improved in the short-pulse excitation scenario, as with active ultrasound imaging. However, PAM with the absolute time-of-flight information (referred as AtPAM) suffers from low imaging resolution and weak interference suppression when the DS algorithm is applied.

PURPOSE

This study aims to propose an enhanced AtPAM algorithm based on delay-multiply-sum (DMS) beamforming, to address the shortcomings of the DS-based AtPAM algorithm.

METHODS

In DMS beamforming, the element signals delayed by the absolute time delays are first processed with a signed square-root operation and then multiplied in pairs and finally summed, the resulting beamformed output is further band-pass filtered. The performances of DS- and DMS-based AtPAMs are compared by experiments, in which an ultrasound diagnostic transducer (a linear array) is employed to passively sense the wire signals generated by an unfocused ultrasound transducer and the cavitation signals generated by a focused therapeutic ultrasound transducer in a flow phantom. The AtPAM image quality is assessed by main-lobe width (MLW), intensity valley value (IVV), area of pixels (AOP), signal-to-interference ratio (SIR), and signal-to-noise ratio (SNR).

RESULTS

The single-wire experimental results show that compared to the DS algorithm, the DMS algorithm leads to an enhanced AtPAM image with a decreased transverse MLW of 0.15 mm and an improved SIR and SNR of 31.50 and 18.77 dB. For the four-wire images, the transverse (axial) IVV is decreased by 18.37 dB (13.11 dB) and the SIR (the SNR) is increased by 26.13 dB (18.47 dB) when using the DMS algorithm. The cavitation activity is better highlighted by DMS-based AtPAM, which decreases the AOP by 0.81 mm² (-10-dB level) and 4.43 mm² (-20-dB level) and increases the SIR and SNR by 20.14 and 10.48 dB respectively. The pixel distributions of AtPAM images of both wires and cavitation activity also indicate a better suppression of the DMS algorithm in sidelobe and noise.

CONCLUSIONS

The experimental results illustrate that the DMS algorithm can improve the image quality of AtPAM compared to the DS algorithm. DMS-based AtPAM is beneficial for detecting cavitation activity during short-pulse ultrasound exposure with high resolution, and further for monitoring short-pulse ultrasound therapy.

Time-Resolved Passive Cavitation Mapping Using the Transient Angular Spectrum Approach

Passive cavitation mapping (PCM), which generates images using bubble acoustic emission signals, has been increasingly used for monitoring and guiding focused ultrasound surgery (FUS). PCM can be used as an adjunct to magnetic resonance imaging to provide crucial information on the safety and efficacy of FUS. The most widely used algorithm for PCM is delay-and-sum (DAS). One of the major limitations of DAS is its suboptimal computational efficiency. Although frequency-domain DAS can partially resolve this issue, such an algorithm is not suitable for imaging the evolution of bubble activity in real time and for cases in which cavitation events occur asynchronously. This study investigates a transient angular spectrum (AS) approach for PCM. The working principle of this approach is to backpropagate the received signal to the domain of interest and reconstruct the spatial-temporal wavefield encoded with the bubble location and collapse time. The transient AS approach is validated using an in silico model and water bath experiments. It is found that the transient AS approach yields similar results to DAS, but it is one order of magnitude faster. The results obtained by this study suggest that the transient AS approach is promising for fast and accurate PCM.

Use of the Cross-Spectral Density Matrix for Enhanced Passive Ultrasound Imaging of Cavitation

Passive ultrasound imaging is of great interest for cavitation monitoring. Spatiotemporal monitoring of cavitation bubbles in therapeutic applications is possible using an ultrasound imaging probe to passively receive the acoustic signals from the bubbles. Fourier-domain (FD) beamformers have been proposed to process the signals received into maps of the spatial localization of cavitation activity, with reduced computing times with respect to the time-domain approach, and to take advantage of frequency selectivity for cavitation regime characterization. The approaches proposed have been mainly nonadaptive, and these have suffered from low resolution and contrast, due to the many reconstruction artifacts. Inspired by the array-processing literature and in the context of passive ultrasound imaging of cavitation, we propose here a robust estimation of the second-order statistics of data through spatial covariance matrices in the FD or cross-spectral density matrices (CSMs). The benefits of such formalism are illustrated using advanced reconstruction algorithms, such as the robust Capon beamformer, the Pisarenko class beamformer, and the multiple signal classification approach. Through both simulations and experiments in a water tank, we demonstrate that enhanced localization of cavitation activity (i.e., improved resolution and contrast with respect to nonadaptive approaches) is compatible with the rapid and frequency-selective approaches of the FD. Robust estimation of the CSM and the derived adaptive beamformers paves the way to the development of powerful passive ultrasound imaging tools.

Assessment of Collaborative Robot (Cobot)-Assisted Histotripsy for Venous Clot Ablation

OBJECTIVE

The application of bubble-based ablation with the focus ultrasound therapy histotripsy is gaining traction for the treatment of venous thrombosis, among other pathologies. For extensive clot burden, the histotripsy source must be translated to ensure uniform bubble activity throughout the vascular obstruction. The purpose of this study was to evaluate the targeting accuracy of a histotripsy system comprised of a focused source, ultrasound image guidance, and a collaborative robot (cobot) positioner. The system was designed with a primary emphasis for treating deep vein thrombosis.

METHODS

Studies to test treatment planning and targeting bubble activity with the histotripsy-cobot system were conducted in an in vitro clot model. A tissue-mimicking phantom was also targeted with the system, and the predicted and actual areas of liquefaction were compared to gauge the spatial accuracy of ablation.

RESULTS

The system provided submillimeter accuracy for both tracking along an intended path (within 0.6 mm of a model vessel) and targeting bubble activity within the venous clot model (0.7 mm from the center of the clot). Good correlation was observed between the planned and actual liquefaction locations in the tissue phantom, with an average Dice similarity coefficient of 77.8%, and average Hausdorff distance of 1.6 mm.

CONCLUSION

Cobots provide an effective means to apply histotripsy pulses over a treatment volume, with the ablation precision contingent on the quality of image guidance.

SIGNIFICANCE

Overall, these results demonstrate cobots can be used to guide histotripsy ablation for targets that extend beyond the natural focus of the transducer.

Dual-Array Passive Acoustic Mapping for Cavitation Imaging With Enhanced 2-D Resolution

Passive acoustic mapping (PAM) techniques have been developed for the purposes of detecting, localizing, and quantifying cavitation activity during therapeutic ultrasound procedures. Implementation with conventional diagnostic ultrasound arrays has allowed planar mapping of bubble acoustic emissions to be overlaid with B-mode anatomical images, with a variety of beamforming approaches providing enhanced resolution at the cost of extended computation times. However, no passive signal processing techniques implemented to date have overcome the fundamental physical limitation of the conventional diagnostic array aperture that results in point spread functions with axial/lateral beamwidth ratios of nearly an order of magnitude. To mitigate this problem, the use of a pair of orthogonally oriented diagnostic arrays was recently proposed, with potential benefits arising from the substantially expanded range of observation angles. This article presents experiments and simulations intended to demonstrate the performance and limitations of the dual-array system concept. The key finding of this study is that source pair resolution of better than 1 mm is now possible in both dimensions of the imaging plane using a pair of 7.5-MHz center frequency conventional arrays at a distance of 7.6cm. With an eye toward accelerating computations for real-time applications, channel count reductions of up to a factor of eight induce negligible performance losses. Modest sensitivities to sound speed and relative array position uncertainties were identified, but if these can be kept on the order of 1% and 1 mm, respectively, then the proposed methods offer the potential for a step improvement in cavitation monitoring capability.

Doppler Passive Acoustic Mapping

In therapeutic ultrasound using microbubbles, it is essential to drive the microbubbles into the correct type of activity and the correct location to produce the desired biological response. Although passive acoustic mapping (PAM) is capable of locating where microbubble activities are generated, it is well known that microbubbles rapidly move within the ultrasound beam. We propose a technique that can image microbubble movement by estimating their velocities within the focal volume. Microbubbles embedded within a wall-less channel of a tissue-mimicking material were sonicated using 1-MHz focused ultrasound. The acoustic emissions generated by the microbubbles were captured with a linear array (L7-4). PAM with robust Capon beamforming was used to localize the microbubble acoustic emissions. We spectrally analyzed the time trace of each position and isolated the higher harmonics. Microbubble velocity maps were constructed from the position-dependent Doppler shifts at different time points during sonication. Microbubbles moved primarily away from the transducer at velocities on the order of 1 m/s due to primary acoustic radiation forces, producing a time-dependent velocity distribution. We detected microbubble motion both away and toward the receiving array, revealing the influence of acoustic radiation forces and fluid motion due to the ultrasound exposure. High-speed optical images confirmed the acoustically measured microbubble velocities. Doppler PAM enables passive estimation of microbubble motion and may be useful in therapeutic applications, such as drug delivery across the blood-brain barrier, sonoporation, sonothrombolysis, and drug release.

Experimental study of airfoil-rotor interaction noise by wavelet beamforming

A wavelet-based beamforming method is performed in this investigation to analyze moving acoustic sources in the time-frequency domain, which is of scientific significance and practical importance. The particular problem considered here is the interaction noise from an airfoil and the downstream rotor in the presence of a moving flow, which could find realistic applications in next-generation underwater and aviation systems. A realistic experimental setup is prepared with a rotating blade and the airfoil in an anechoic wind tunnel. The results show that the wavelet-based beamforming method is very suitable for unsteady sound source imaging, which would be able to strengthen the time-frequency analysis capability of acoustic imaging tests and, consequently, possibly leads to deepened physical insights of various transient and moving systems in underwater and aerospace systems.

Spatiotemporal Assessment of the Cellular Safety of Cavitation-Based Therapies by Passive Acoustic Mapping

Many useful therapeutic bio-effects can be generated using ultrasound-induced cavitation. However, cavitation is also capable of causing unwanted cellular and vascular damage, which should be monitored to ensure treatment safety. In this work, the unique opportunity provided by passive acoustic mapping (PAM) to quantify cavitation dose across an entire volume of interest during therapy is utilised to provide setup-independent measures of spatially localised cavitation dose. This spatiotemporally quantifiable cavitation dose is then related to the level of cellular damage generated. The cavitation-mediated destruction of equine red blood cells mixed with one of two types of cavitation nuclei at a variety of concentrations is investigated. The blood is placed within a 0.5-MHz ultrasound field and exposed to a range of peak rarefactional pressures up to 2 MPa, with 50 to 50,000 cycle pulses maintaining a 5% duty cycle. Two co-planar linear arrays at 90° to each other are used to generate 400-µm-resolution frequency domain robust capon beamforming PAM maps, which are then used to generate estimates of cavitation dose. A relationship between this cavitation dose and the levels of haemolysis generated was found which was comparable regardless of the applied acoustic pressure, pulse length, cavitation agent type or concentration used. PAM was then used to monitor cellular damage in multiple locations within a tissue phantom simultaneously, with the damage-cavitation dose relationship being similar for the two experimental models tested. These results lay the groundwork for this method to be applied to other measures of safety, allowing for improved ultrasound monitoring of cavitation-based therapies.

Correlation Between Brain Tissue Damage and Inertial Cavitation Dose Quantified Using Passive Cavitation Imaging

Focused ultrasound (FUS)-induced cavitation-mediated brain therapies have become emerging therapeutic modalities for neurologic diseases. Cavitation monitoring is essential to ensure the safety of all cavitation-mediated therapeutic techniques as inertial cavitation can be associated with tissue damage. The objective of this study was to reveal the correlation between the inertial cavitation dose, quantified by passive cavitation imaging (PCI), and brain tissue histologic-level damage induced by FUS in combination with microbubbles. An ultrasound image-guided FUS system consisting of a single-element FUS transducer (1.5 MHz) and a co-axially aligned 128-element linear ultrasound imaging array was used to perform FUS treatment of mice. Mice were sonicated by FUS with different peak negative pressures (0.5 MPa, 1.1 MPa, 4.0 MPa and 6.5 MPa) in the presence of systemically injected microbubbles. The acoustic emissions from the FUS-activated microbubbles were passively detected by the imaging array. The pre-beamformed channel data were acquired and processed offline using the frequency-domain delay, sum and integration algorithm to generate inertial cavitation maps. All the mice were sacrificed after the FUS treatment, and their brains were harvested and processed for hematoxylin and eosin staining. The obtained inertial cavitation maps revealed the dynamic changes of microbubble behaviors during FUS treatment at different pressure levels. It was found that the inertial cavitation dose quantified based on PCI had a linear correlation with the scale of histologic-level tissue damage. Findings from this study suggested that PCI can be used to predict histologic-level tissue damage associated with the FUS-induced cavitation.

Delay multiply and sum beamforming method applied to enhance linear-array passive acoustic mapping of ultrasound cavitation

PURPOSE

Passive acoustic mapping (PAM) has been proposed as a means of monitoring ultrasound therapy, particularly nonthermal cavitation-mediated applications. In PAM, the most common beamforming algorithm is a delay, sum, and integrate (DSAI) approach. However, using DSAI leads to low-quality images for the case where a narrow-aperture receiving array such as a standard B-mode linear array is used. This study aims to propose an enhanced linear-array PAM algorithm based on delay, multiply, sum, and integrate (DMSAI).

METHODS

In the proposed algorithm, before summation, the delayed signals are combinatorially coupled and multiplied, which means that the beamformed output of the proposed algorithm is the spatial coherence of received acoustic emissions. We tested the performance of the proposed DMSAI using both simulated and experimental data and compared it with DSAI. The reconstructed cavitation images were evaluated quantitatively by using source location errors between the two algorithms, full width at half maximum (FWHM), size of point spread function (A₅₀ area), signal-to-noise ratio (SNR), and computational time.

RESULTS

The results of simulations and experiments for single cavitation source show that, by introducing DMSAI, the FWHM and the A₅₀ area are reduced and the SNR is improved compared with those obtained by DSAI. The simulation results for two symmetric or nonsymmetric cavitation sources and multiple cavitation sources show that DMSAI can significantly reduce the A₅₀ area and improve the SNR, therefore improving the detectability of multiple cavitation sources.

CONCLUSIONS

The results indicate that the proposed DMSAI algorithm outperforms the conventionally used DSAI algorithm. This work may have the potential of providing an appropriate method for ultrasound therapy monitoring.

Frequency-difference beamforming in the presence of strong random scattering

Frequency-difference beamforming [Abadi, Song, and Dowling (2012). J. Acoust. Soc. Am. 132, 3018-3029] is a nonlinear, out-of-band signal processing technique used to beamform non-zero bandwidth signals at below-band frequencies. This is accomplished with the frequency-difference autoproduct AP(Δω)=P(ω₂)P^*(ω₁), a quadratic product of complex field amplitudes that mimics a genuine field at the difference frequency, Δω=ω₂-ω₁. For frequency-difference beamforming, AP(Δω) replaces the in-band complex field in the conventional beamforming algorithm. Here, the near-field performance of frequency-difference beamforming is evaluated in the presence of 1 to 30 high-contrast spherical scatterers with radius a placed between, and in the plane defined by the source and a 12-element linear receiving array with element spacing d. Based on the center frequency wave number, k, of the 150-200 kHz frequency sweep source signal, the scatterers are large, ka ≈ 15; the array is sparse, kd = 37; and the average source-to-receiver distance is up to 4.3 mean-free-path lengths. Beamforming results from simulations and experiments show that in-band beamforming loses peak-to-sidelobe ratio and fails to reliably locate the source as the scatterer count increases. Using the same signals, frequency-difference beamforming with difference frequencies from 5 to 25 kHz localizes sources reliably with higher peak-to-side-lobe ratios, though with reduced resolution.

Passive cavitation mapping using dual apodization with cross-correlation in ultrasound therapy monitoring

Recently, passive acoustic mapping (PAM) has been successfully applied for dynamic monitoring of ultrasound therapy by beamforming acoustic emissions of cavitation activity during ultrasound exposure. The most widely used PAM algorithm in the literature is time exposure acoustics (TEA), which is a standard delay, sum, and integrate algorithm. However, it results in large point spread function (PSF) and serious imaging artifacts for the case where a narrow-aperture receiving array such as a standard B-mode linear array is used, therefore degrading the quality of cavitation image. To address these challenges, in this paper, we proposed a novel PAM algorithm namely dual apodization with cross-correlation (DAX)-based TEA, in which DAX was originally used as a reconstruction algorithm in medical ultrasound imaging. In the proposed algorithm, two sets of signals were beamformed by two receive apodization functions with alternating elements enabled, and the cross-correlation coefficient of the two signals served as a weighting factor that would be multiplied to the sum of the two signals. The performance of the proposed algorithm was tested on simulated channel data obtained using a multi-bubble model, and experiments were also performed in an in vitro vessel phantom with flowing microbubbles as cavitation nuclei. The reconstructed cavitation images were evaluated quantitatively using established quality metrics including full width at half maximum (FWHM), A_-6dB area, and signal-to-noise ratio (SNR). The results suggested that the proposed algorithm significantly outperformed the conventionally used TEA algorithm. This work may have the potential of providing a useful tool for highly accurate localization of cavitation activity during ultrasound therapy.