The purpose of this methods and concepts tutorial is to present the homodyned K-distribution (HKD) statistical modeling of the echo envelope of received radio frequency (RF) signals in the context of medical quantitative ultrasound (QUS) imaging, with the aim of explaining its physical, mathematical, and statistical foundations. Several notions and equations are recalled from previous works on HKD modeling and estimation methods. Proofs of claims are presented in Appendices that can be found in Supplementary Materials. Some descriptions have been completed or refined without modifying the main conclusions on HKD or mixtures of HKDs. Mixtures of HKDs are recalled, as well as other models proposed in previous works, such as the generalized KD (GKD), HKD with additive Gaussian noise (HKDN), and the generalized HKD (GHKD), the latter resorting to the generalized central limit theorem (CLT) in the case where the scattering cross section has infinite variance. This article also presents three innovations on the topic: 1) a revised derivation of the HKD model based on Stein's condition to obtain an explicit rate of convergence of the CLT in the case of weakly dependent terms, corresponding to ultrasound (US) scatterers; 2) HKD imaging under frequency-domain filtering of RF signals, yielding information on second-order statistics of the echo envelope; and 3) quantitative results on the Kolmogorov distance between the HKD and other distributions (Nakagami and Rice distributions, GKD, HKDN, and GHKD) together with the domains insuring validity (i.e., statistical equivalence with a confidence level of 0.05).
In focused ultrasound (FUS) therapy, passive acoustic mapping (PAM) with convex arrays is often employed to monitor the cavitation activity in the human abdomen, given their large acoustic window. However, phase aberration caused by the speed-of-sound (SoS) heterogeneity in the abdominal wall degrades the image quality, leading to inaccurate localization of the cavitation source and, hence, deteriorates the safety and efficacy level of the therapy. In this work, we derive the general solution to the wave equation in SoS heterogeneous media in polar coordinates. With the solution, we propose the real-time heterogeneous helical wave spectrum (HHWS) method to account for SoS heterogeneity in transabdominal PAM with convex arrays. In both the in silico and in vitro experiments mimicking transabdominal PAM imaging of single and multiple microbubble (MB) cavitation source(s) in humans, the results clearly demonstrated the phase aberration-correction capability of the HHWS method with improved image quality and source localization accuracy, compared with the helical wave spectrum (HWS) method for homogeneous media. A parallel implementation of the HHWS method realized a several tens of milliseconds image reconstruction speed for phase-aberration-corrected PAM in a large field of view (FOV). Combined with B-mode imaging, real-time dual-mode monitoring of MB cavitation activity in the heterogeneous medium mimicking the human abdominal wall with a single probe has been realized. These results well demonstrated the potential of the HHWS method for transabdominal PAM with convex arrays, for safe, effective, and controlled cavitation-based FUS therapies.
Cascaded dual-polarity wave (CDW) imaging enhances signal-to-noise ratio (SNR) by transmitting polarity-alternating pulse sequences, followed by decoding to reinforce coherent signals. This study assesses the in vivo feasibility of CDWs for velocity vector imaging (VVI) in the carotid artery, compared to conventional plane waves (cPWs). Two decoding strategies were evaluated: frequency domain decoding of CDW (F-CDW), offering moderate SNR improvement with reduced motion sensitivity, and time-domain decoding of CDW (T-CDW), providing higher SNR gains but larger motion sensitivity. cPW imaging was performed using constant gain (cPWCG), set patient-specific to avoid clipping, and maximum gain (cPW-HG). VVI using CDW and cPW imaging was obtained in 20 carotid arteries, including ten hemodynamic significant stenoses. A comparison was made based on SNR, percentage of reliable velocity estimates, and agreement with conventional pulsed wave Doppler. Results showed improved SNR and reliability using CDW compared to cPW-CG. The median SNR at peak systole increased from 0.9 dB (cPW-CG) to 2.8 dB (F-CDW) and 4.7 dB (T-CDW). T-CDW showed the greatest improvement, even outperforming cPW-HG (SNR = 1.2 dB) based on SNR and reliability. All methods showed similar agreement with pulsed wave Doppler. Although CDW demonstrated clear benefits, its full potential was limited by restricted gain settings to prevent clipping. CDW is particularly promising for imaging deeper-located carotid arteries, where higher gains can be applied to further enhance SNR beyond conventional plane wave techniques.
Imaging of targeted organs, such as the urinary bladder, could be transformative for preventive healthcare and early disease diagnosis when used to assess their real-time function. However, wearable and portable ultrasound (US) imaging systems often face constraints related to power consumption, form factor, cost, and signal resolution, particularly for deep tissues like the bladder. High-accuracy platforms with large channel counts can generate data streams of up to 10 GB/s, posing significant challenges in reducing computational complexity, achieving power efficiency, and maintaining wireless connectivity. Recent advancements in wearable US sensors have demonstrated potential for low-power, unobtrusive solutions but often fail to meet the accuracy and efficiency needed in clinical settings. This work presents an algorithm-centric proof of concept that reconstructs missing US channels through field-programmable gate array (FPGA)-accelerated deep learning, effectively doubling the imaging aperture while halving analog front-end requirements. We developed a lightweight U-Net convolutional neural network (L-UNET) with 222 609 parameters, specifically optimized for sparse-array RF data reconstruction. The network is deployed on a deep learning processing unit (DPU) using mixed quantization-aware training (Mixed-QAT) that selectively applies 8-bit integer precision while preserving two critical layers at 16-bit floating point (FP), achieving mean-squared error (MSE) of 1.48 $\times$ 10 compared to 1.22 $\times$ 10 for 32-bit FP. The FPGA implementation leverages a single-core accelerator, executing inference in 221 ms/frame with deterministic latency suitable for real-time reconstruction. By processing only odd-indexed physical channels and inferring even-indexed channels through the convolutional neural network (CNN), our approach maintains B-mode image quality (peak signal-to-noise ratio (PSNR) >18 dB and structural similarity index (SSIM) > 0.5) while reducing data acquisition complexity. The system achieves 0.918-W average power consumption in a 32-channel configuration, demonstrating that CNNbased sparse-array reconstruction on embedded FPGAs offers a viable path toward fully integrated US monitoring systems.
False-positive indications in breast cancer screening cause pain and anxiety for patients and are a time and cost waste to healthcare systems. New quantitative ultrasound (QUS) scanners aim to measure intrinsic acoustic properties of soft tissues to aid better clinical decision-making. This study details the performance characterization of a novel phase-insensitive ultrasound computed tomography (Q-UCT) scanner, developed at U.K. National Physical Laboratory (NPL), for quantitative acoustic attenuation coefficient mapping of the breast. Scans of multiple commercially sourced anthropomorphic breast phantoms were acquired, with the results being compared to the X-ray computed tomography (XCT) imagery and ground-truth attenuation coefficients obtained from measurements of the constituent phantom materials. The novel system demonstrated the ability to detect the presence of inserts as small as 4 mm in diameter and measure the intrinsic attenuation of larger inserts and host materials with attenuation coefficients ranging from 0.7 to 4.1 dB cm-1 at 3.2 MHz. For the host materials, agreement with the ground-truth values of attenuation lies within the expanded measurement uncertainties of the ground-truth values.
This article presents the design, simulation, fabrication, and characterization of the first "bell plate" microelectromechanical resonators in silicon-oninsulator (SOI) technology. These resonators are actuated by electrostatic force and exhibit a high-quality factor of up to 160 at 180 kHz resonant frequency, resulting in an f × Q product exceeding 28 GHz. Several designs were explored, and all (2, 0)-mode resonators systematically outperformed the first clamped-free mode in terms of Q-factor. This mode was investigated through finite element simulations and experimental measurements and compared to the first clamped-free mode. The resonators were actuated with dc lower than 1 V and ac lower than 250 mV at resonance, and their mechanical motion was measured by laser Doppler vibrometry. Dynamic characterization was performed both in open-loop and closed-loop configurations. The temperature coefficient of frequency (TCF) of the (2, 0)-mode is mainly dominated by the silicon properties, leading to a value equal to -48 ppm/°C. These results demonstrate that MEMS resonators with bell plate geometries are promising for high-Q applications such as sensing and time references.
UltraFlex is an iterative model-based ultrasonic flexible-array shape calibration framework that uses automatic differentiation. This work evaluates array shape calibration model performance while examining multiple image quality metrics: speckle brightness, envelope entropy, coherence factor, lag-one coherence, common-midpoint correlation coefficient (CMCC), and common-midpoint phase error (CMPE). The accuracy of these image quality metrics was evaluated on simulated phantoms using a variety of array shapes. Experimental phantom and in vivo liver datasets were also investigated using transducers with known geometries. While speckle brightness, envelope entropy, and coherence factor enable model convergence under many conditions, lag-one coherence, CMCC, and CMPE enable more accurate element position estimations and improved visual ultrasound image focusing quality. Furthermore, the models based on the CMCC and phase-error quality metrics are the most robust against additive white noise while achieving median mean Euclidean errors (MEEs) of 3.7 μm for simulation, 29.7 μm for phantom, and 69.0 μm for in vivo liver data. These array shape calibration results show promise for future development of experimental flexible- and wearableultrasonic arrays.
Acceleration sensing is widely applied from consumer electronics to inertial navigation. Conventional accelerometers are mainly based on capacitive or optical principles. However, these approaches either suffer from limited sensitivity or face challenges in integration. Therefore, it is imperative to develop novel acceleration sensing systems based on new physical principles. This article explores 2-D phononic crystals (PnCs) for highsensitivity acceleration sensing. It introduces a novel approach where ultrasound is utilized for the first time to sense acceleration through the PnCs structure. Defective PnCs create a resonant cavity that produces sharp transmission peaks within the band gap. Acceleration causes a frequency shift in these peaks. The research employs the plane wave expansion (PWE) method and the finite element method (FEM) to calculate the band structure and transmission spectra of the PnCs. Both numerical and experimental results demonstrate that this approach is suitable for acceleration sensing, with the experiment achieving a sensitivity of 276 Hz/g, a measured bandwidth of 152 Hz, and a theoretical noise estimation of 7.01 ng/√Hz. Moreover, it is expected to reach the order of 105 Hz/g with the microfabrication techniques in the future. This innovative application of PnCs demonstrates significant potential across a range of microelectromechanical system (MEMS) sensors.
Gas vesicles (GVs) are air-filled protein nanostructures (∼85 nm diameter, ∼500 nm length) with the physical property to scatter sound. This new class of contrast agent serves as an acoustic analog to green fluorescent proteins and enables ultrasound imaging of cells that have been genetically labelled with GVs. To date, methods to produce GVs rely on expensive CO ₂ shakers, limiting accessibility and scalability. In this study, we present a cost-effective and scalable protocol to produce GVs using an adapted bubble column photobioreactor design. This production method operates at approximately 10% of the cost of the state-of-the-art, while utilizing off-the-shelf components for broader accessibility and dissemination. We characterized GVs produced with both photobioreactor and shaker-incubator production methods using hydrostatic collapse pressure measurements, hydrodynamic diameter measurements, and ultrasound imaging. Our results demonstrate that GVs produced with both methods exhibit identical physicochemical properties, ensuring intercompatibility. In summary, this new protocol to produce GVs lowers the barrier to producing GVs in research labs, thereby creating the possibility of a broader use of GVs as ultrasound contrast agents and biosensors for a wide array of biomedical applications.
Achieving higher resolution for deeper tissue structures remains a significant challenge in ultrasound (US) imaging due to the inherent limitations of diffraction. Swept synthetic aperture (SSA) techniques, which utilize the motion of a single transducer to effectively increase the imaging aperture, offer a promising solution. Building on SSA, we propose that freehand SSA provides a flexible approach with real-time adaptability to varying patient anatomies. This article introduces the optically tracked SSA (OT-SSA) platform, an approach that integrates external tracking to ensure accurate transducer positioning during freehand sweeps. Key sources of image degradation, such as spatial calibration error, tracking precision, and out-of-plane motion were directly analyzed and addressed within the system. In in vivo quadriceps imaging, OT-SSA reduced average lateral speckle autocorrelation size from 2.33 to 0.49 mm compared to a stationary aperture, demonstrating substantial resolution gains. The results establish OT-SSA as a robust and adaptable approach for high-resolution imaging.
Acoustic metamaterials (AMMs) offer significant promise for ultrasound probe backing layers due to their capacity to enhance acoustic energy dissipation through tailored sub wavelength structures. However, practical implementation remains challenging due to difficulties in reliably reproducing the micrometer-scale features required for MHz-frequency operation and the lack of quality assurance processes linking design intent to fabricated performance. This work presents the evaluation of a 3-D-printed acoustic isolator-type metamaterial (AI-MM) backing designed for MHz operation using a custom aluminum oxide resin. Directional transmission intensity measurements revealed frequency-dependent asymmetry in forward and backward wave propagation (in both experiments and simulations), consistent with passive acoustic isolator behavior. X-ray micro-computed tomography (micro-CT) imaging of AI-MM samples revealed dimensional deviations, apex rounding, and local density variation. Attenuation spectra showed that AI-MM backings consistently outperformed homogeneous controls in both simulation and experiment, with frequency-dependent trends indicating enhanced scattering and viscous losses. A local attenuation peak near 2.6 MHz was within the operational range estimated from the measured geometry (2.22-2.94 MHz), underscoring the importance of linking performance to real-world fabrication. These findings support the potential of AI-MMs as tunable passive components in ultrasound systems and highlight the need for integrated design, fabrication, and validation workflows.
This study presents a high-fill-factor piezoelectric micromachined ultrasonic transducer (PMUT) array fabricated via the cavity silicon-on-insulator (CSOI) process. The center frequency of the PMUT is 4.89 MHz in air and 3.5 MHz in a gel-type couplant, along with a -6-dB photoacoustic (PA) bandwidth of 146%. A miniaturized PA sensing system (4.6 mm × 2.0 mm × 5.2 mm) was developed by integrating the PMUT with a compact vertical-cavity surface-emitting laser (VCSEL). Simulation results reveal critical parameters for optimizing a PA system. The increase in laser excitation energy correspondingly improves the efficiency of PA signal generation, and spatial nonuniformity in optical energy distribution requires algorithmic compensation to prevent signal distortion. The small footprint of the PMUT minimizes phase differences, enabling distortion-free signal detection at close range, while its broad bandwidth ensures high-fidelity signal capture at an optimized center frequency. Guided by these findings, the VCSEL parameters were optimized to a 28-ns pulsewidth and an average output power of 63.6 μW. Comprehensive characterization, including electrical impedance, acoustic response, and PA bandwidth tests, demonstrated the consistency of the PMUT fabrication process, broadband capability, and superiority of the PMUT in close-range sensing. Phantom-based testing showed that the system can acquire multidepth phantom signals, and the cylindrical wave radiation analysis further highlighted the critical role of laser-PMUT spacing in maintaining signal integrity. This feasibility study validates the compact system as a promising platform for portable PA devices under ideal phantom and ex vivo conditions.
The introduction of genetically encoded gas vesicles (GVs), protein nanostructures with the ability to scatter sound, has created the possibility for deep tissue cellular imaging. GVs establish a platform for biomolecular engineering and were successfully repurposed into acoustic reporter genes and acoustic biosensors. Alongside molecular engineering developments, a method called cross amplitude modulation (xAM) has emerged as the gold standard for non-destructive ultrasound imaging of GVs thanks to its sensitivity and specificity in living biological tissues. Here, we present latest xAM theory and imaging principles. Specifically, we report 1) analytical expressions for the X-wave beam width and primary-to-secondary lobes distance; 2) experimental observations of nondiffractive xAM beams; 3) a method to modulate the secondary lobe level of xAM beams; 4) a demonstration of the incoherent nature of the xAM image noise that can be leverage to increase sensitivity through frame averaging, 5) a beamforming formalism to enhance xAM contrast-to-noise ratio without reducing framerate. Ultimately, the rise of the field of Biomolecular Ultrasound will rest on the co-development of genetically encoded probes and dedicated imaging methods such as xAM and its 3D extension, nonlinear sound-sheet microscopy.
This article presents the first fully integrated, highly compact single-element integrated gammaultrasound ( $\gamma $ -US) probe for simultaneous molecular and anatomical imaging. The probe integrates a PZT-5A ultrasound (US) transducer with a Ce:GAGG scintillator and silicon photomultiplier (SiPM), enabling dual-modality detection along the same line-of-sight (LOS). The tungsten-epoxy composite serves dual roles as both the US backing layer and $\gamma $ collimator, making it innovative and significantly reduces size and complexity. Furthermore, a single-channel frequency-based multiplexed circuit enables real-time dual-modality data acquisition (DAQ). The $\gamma $ part of the probe achieves 17.3% energy resolution (FWHM at 122 keV), 80.0 cps/MBq sensitivity, and 2.69 mm spatial resolution at 1 cm distance in air. The US component provides a 36.0% fractional bandwidth (FBW), 5.95 dB signal-to-noise ratio (SNR), 1.32 mm axial resolution, and 4.90 mm lateral resolution at 5 cm depth in water. Finally, a fused B-mode image of a breast phantom validates the probe's imaging capability. This integrated probe design offers a compact, cost-effective solution for handheld medical diagnostics and nondestructive testing (NDT), with minimal performance trade-offs compared to standalone systems.
Transcranial ultrasound localization microscopy (t-ULM) faces significant challenges for broader clinical and research applications, particularly in addressing image quality degradation caused by the skull. Research on nonhuman primate (NHP) models, with their human-like cranial characteristics, offers crucial insights for technical innovations and neuroscience applications of t-ULM. In this study, we developed a systematic pipeline for t-ULM of NHP, incorporating low-frequency diverging wave emission, phase aberration correction, and microbubble (MB) detection equalization. We also explored the contrast agent strategies and imaging plane selection. We achieved an optimal spatial resolution of 93 $\mu $ m in the coronal section and 105 $\mu $ m in the sagittal section at an emission frequency of 2.23 MHz, while both maintaining 5-8-cm penetration depth and 6-cm lateral field of view. We also obtained the hemodynamic mapping with a wide dynamic range up to 40 cm/s at a 1000-Hz compounded frame rate. This work validates the feasibility of t-ULM in the NHP and provides important tools and references for further neuroscience applications of t-ULM.
Recent advancements in next-generation wireless systems have expanded the need for radio frequency front-ends (RFFEs) toward the millimeter-wave (mmWave) range. This work introduces two methods targeting the efficient design of solidly mounted surface acoustic wave (SAW) resonator architectures based on lithium niobate on silicon carbide (LN-on-SiC) heteroacoustic waveguides for mmWave applications. The first method uses a longitudinal SAW (L-SAW) mode in X-cut LN to achieve a high phase velocity of 6500 m/s and a figure of merit (FoM) of 6.53 at 22.42 GHz, enabled by strong acoustic confinement and careful wavelength scaling. The second method presents a novel electrode-guided shear horizontal SAW (EG SH-SAW) mode in Y-cut LN, leveraging electrode design to confine higher order SH modes and mitigate internal stress cancellation. The fabricated EG SH-SAW resonator achieves operation at 23.5 GHz with a coupling coefficient k2 of 1.6% and an FoM of 4.16. Both methods demonstrate resonators successfully scaled toward mmWave range with high Q-factors and open the potential for future solidly mounted frequency-scalable, high-performance acoustic devices in mmWave bands.
Hydrophone spatial resolution and spatial averaging effects are determined by the frequencydependent effective sensitive element diameter deff(f) rather than the geometrical sensitive element diameter dg. The objective of this work was to quantify average deff(f) for needle hydrophones as a function of dg and f. Estimates of effective radii aeff(f) = deff(f)/2 were inferred from directivity measurements from 0.5 to 20 MHz on 16 needle hydrophones with dg = 2ag ranging from 75 to 1000 μm (139 hydrophone/frequency combinations). Effective sensitive element diameter deff(f) exceeded dg by over 100% when λ > 4dg (where λ is the wavelength). For kag > 0.75 (where k = 2π/λ), deff(f) was consistent with the "rigid piston" (RP) theory, reinforcing a previous report from our laboratories. However, for kag < 0.75, deff(f) showed noticeable deviations from RP theory and fell between predictions from RP theory and predictions for an unbaffled (UB) circular piston. Examples: 1) for a needle hydrophone with dg = 75 μm at 1 MHz (kag = 0.16), the data imply that average deff = 505 μm, and 2) for a needle hydrophone with dg = 400 μm at 500 kHz (common parameters for human transcranial neuromodulation; kag = 0.42), the data imply that average deff = 1215 μm.
Passive acoustic mapping (PAM) is a powerful and widely used method of imaging cavitation activity. However, the presence of a container around a cavitating sample in experiments performed in vitro can introduce significant aberrations into recorded cavitation noise and resulting PAM images. These artifacts may lead to energy being incorrectly estimated or mapped to the wrong place, preventing accurate correlation between cavitation and bioeffects. In this work, we quantify these acoustic effects for six common types of sample containers using an acoustic reciprocity experiment, then use the results to inform the design of a new container with improved acoustic transparency. Existing vessels were found to introduce up to 13-dB broadband insertion loss and change the location and spread of energy in PAM images by up to 1 mm and 25%, respectively. The new container caused up to 1.4-dB insertion loss (the lowest of any container tested) and introduced no significant phase aberration, source location error, or change in energy spread to the PAM images. Testing the new container with real cavitation noise produced very similar insertion loss figures of up to 1.6 dB. These results highlight deficiencies in existing sample containers for the purposes of quantifying cavitation activity with PAM, which is increasingly desired as cavitation matures as a therapy. The guidelines for acoustic transparency developed here may assist researchers in avoiding container aberrations and enable accurate measurement of cavitation energy in future studies.
The ability of ultrasound imaging to deliver real-time visualization of tissue structures and surgical instruments can provide essential benefits in guiding medical interventions. In spinal cord injury research, small animal models are commonly used, but their size restricts the applicability of many standard ultrasound systems. Capacitive Micromachined Ultrasonic Transducers (CMUTs) offer advantages over traditional piezoelectric transducers, including a smaller form factor, high design flexibility, and improved acoustic performance. CMUT structures made of polymers (polyCMUTs) can be produced cost-effectively and quickly, while potentially offering flexible, biocompatible transducers for next-generation ultrasound systems. This study introduces the first polyCMUT probe designed for imaging spinal cords in rats. A compact 11 MHz, 64 channel probe with a 12.9 x 6.5 mm small tip was developed through a three-stage fabrication process, combining in-house manufactured polyCMUT arrays with electronics, integrated in a research imaging system. Performance evaluation included electrical impedance measurements, acoustic characterization, and in-vitro and ex-vivo imaging. Quality analysis validated the stability of the fabrication process, demonstrating high yield and minimal variability, with a standard deviation in resonance frequency of less than 1%. The probe successfully visualized key anatomical structures like the central canal as well as real-time imaging of needle insertion into tissue. However, distinguishing between gray and white matter remained challenging due to limitations in frequency and bandwidth. This study demonstrates the potential of the polyCMUT technology for developing tailored ultrasound solutions. Future work will focus on optimizing high-frequency performance and advancing toward in-vivo applications to provide meaningful tools in spinal cord injury research and therapeutic interventions.
