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.
