Plane nonlinear shear waves in isotropic media are subject only to cubic nonlinearity at leading order and therefore generate only odd harmonics during propagation. Wavefront curvature in shear wave beams breaks the symmetry in the material response and yields quadratic nonlinearity, such that a second harmonic may be generated at second order by a shear wave beam depending on the polarization of the wave field. Recent analyses of quadratic nonlinearity in shear wave beams [Spratt et al., AIP Conf. Proc. 1685, 080007 (2015); Kaufinger et al., Wave Motion 139, 103595 (2025)] have been concerned with second-harmonic generation by a single-frequency primary beam. The inclusion of a second collinear source-frequency beam leads to the generation of sum- and difference-frequency wave fields via quadratic nonlinear interactions between the two source-frequency beams, which corresponds to a shear wave parametric array. Here, closed-form analytical solutions and numerical simulations are presented for a bifrequency collinear source with radial polarization and Gaussian amplitude shading. Examples of the sum- and difference-frequency wave fields are presented using parameters consistent with tissue-like media for applications to ultrasound shear wave elastography. [P.G.K. is supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.] 9:50–10:10 Break

BACKGROUND:Chronic low back pain (cLBP) profoundly impacts quality of life, yet its underlying mechanisms remain poorly understood. Three-dimensional (3D) ultrasound imaging offers valuable insights into cLBP but poses challenges of manual annotation due to large data volume and poor image quality. OBJECTIVES:We aim to develop and validate a novel approach called Cross-Scan Fusion Network (CSFN) for segmenting anatomical tissue layers in 3D ultrasound images. MATERIALS AND METHODS:We analyzed 3D B-mode ultrasound volumes of the lumbar region, with six tissue layers annotated: dermis, superficial fat, superficial fascial membrane, deep fat, deep fascial membrane, and muscle. The dataset included 69 labeled scans from 29 subjects and 30 unlabeled scans from 10 subjects. Labeled scans were split into training (n = 19), validation (n = 10), and independent test (n = 40) sets. For annotation efficiency analysis, 5, 10, 15, and 19 scans in the training set were separately treated as annotated, with the remainder considered unannotated. CSFN leverages a VoxelMorph-style elastic registration network trained with a novel Projected Hausdorff Distance Loss (PHDL) to accurately register anatomical tissue layers across 3D scans. This supports both sample-efficient learning (CSFN-SEL) and semi-supervised learning (CSFN-SSL). In the CSFN-SEL, controlled wrap ratios are applied to pairs of labeled scans to synthesize realistic image-mask pairs, while in the CSFN-SSL, labeled scans are registered onto unlabeled scans to generate high-quality synthesized scans for augmentation. Both real and synthetic data are then combined to train an nnU-Net segmentor, enabling robust segmentation with minimal manual annotations. CSFN was compared to fully-supervised nnU-Net with and without augmentation, and SimCLR (nnU-Net backbone). Model segmentation performance was evaluated using the Dice coefficient, while registration quality was assessed using Dice and Average Symmetric Surface Distance (ASSD). Results were reported as mean ± standard deviation(SD) and compared using paired two-tailed t-tests on class-wise subject averages. Significance was set at 0.05 and adjusted for multiple comparisons. RESULTS:CSFN-SEL consistently outperformed the fully supervised nnU-Net baseline across varying numbers of labeled training samples, improving the mean Dice coefficient from 69.34% to 74.62% (+5.28%, p-value < 0.05/3). CSFN-SSL further improved performance, achieving 79.33% (±1.96%) and 81.14% (±1.43%) with 5 and 19 training samples, respectively. With only five labeled scans, CSFN-SSL delivered a 9.51% performance gain (effect size d = 0.671, p-value < 0.05/3) with minimal annotation. CONCLUSION:CSFN improves segmentation accuracy and robustness even with very few labeled scans, providing an effective and practical solution for advancing cLBP imaging and analysis. CLINICAL RELEVANCE SATEMENT:CSFN enables accurate, automated segmentation of anatomical tissue layers in 3D ultrasound scans with minimal manual annotations, potentially accelerating the clinical evaluation and management of cLBP.

Shear waves are employed in medical ultrasound imaging because they reveal variations in viscoelastic properties of soft tissue. Focused shear waves produced by a longitudinally vibrating piston at several hundred hertz are investigated experimentally in soft tissue phantoms and using an analytical model for shear wave beam generation and propagation. Experiments employed a spherically concave piston shaped to focus the shear wave beam at a depth of 4 cm in a soft tissue phantom. Our initial analytical model was confined to the source plane, with zero displacement surrounding the piston. However, the actual source condition is a traction-free surface surrounding the piston, and the edges of the piston extend 9 mm into the medium. Using shear wave holography, we infer the actual source condition by backpropagation of the displacement field several cm removed from the origin to the plane at the piston edge. We find that the actual source condition for an impulse driving function is dominated by a bipolar edge wave. However, we find that adding a central “bowl wave” inspired by the curvature of the piston further refines the source condition and provides improved accuracy in the near field.

Slow dynamics in natural and man-made rocks such as sandstone, limestone, and concrete is characterized by a reduction in the stiffness due to a large-amplitude vibration. After the vibration ends, the rock stiffness remains reduced but recovers to the original value over the course of hours. Conventional laboratory studies of slow dynamics investigated the material response to narrowband stimuli, e.g., nonlinear resonant spectroscopy or propagation of a tone burst. In 2017, Tom Muir obtained a block of sandstone with a novel and “impactful” approach in mind: investigating slow dynamics due to impulsive stimuli. Tom built an apparatus in which the heaviest hammer he had in his garage impacted one end of a long sandstone bar. Longitudinal motion of the sandstone along its length was measured with a laser vibrometer as the resulting unipolar strain pulse bounced back and forth. Slow dynamics manifested as an initial reduction in the round-trip time of the pulse from one end to the other that slowly recovered with each round trip. Follow-up dynamic acoustoelastic testing revealed that the softening was due almost entirely to the tensile phase of the impulsive deformation. This presentation is a summary of Muir et al. [JASA 147, 1006–1014 (2020)].

Noninvasive liver stiffness assessment using shear wave elastography is often limited by wave attenuation in deep tissue. We introduce and validate a handheld focused shear wave transient elastography (fTE) device with interchangeable concave pistons to generate focused shear waves for enhanced elastography in deep tissues. The device consists of a 3D-printed concave circular piston fit over the face of a phased ultrasound array driven by a mechanical vibrator. Benchtop setup validated shear wave speed (SWS) measurement against ground-truth linear array imaging. Handheld setup assessed measurement repeatability across three piston geometries in tissue-mimicking gelatin phantoms. Supersonic shear wave imaging (SSI) provided independent reference measurements to validate fTE SWS calculations. Shear wave amplitude at 45 mm depth and SWS measurement consistency were assessed. Benchtop validation confirmed that fTE-measured SWS agreed within 10

A time-domain numerical algorithm was presented at the Spring 2011 ASA meeting for simulation of radially polarized shear wave beams in a viscous medium with both quadratic and cubic nonlinearity [Spratt et al., JASA 129, 2679 (2011)]. The present work focuses on harmonic generation in soft elastic media with arbitrary absorption and dispersion, and therefore a frequency-domain numerical algorithm is desired. Such an algorithm was recently developed to model second-harmonic generation due to weak quadratic nonlinearity in soft tissue-like media, motivated originally to confirm analytical perturbation solutions for this field and to include source conditions for which analytical solutions are not available [Kaufinger et al., JASA 157 (2025); doi: 10.1121/10.0037533]. Here, a frequency-domain algorithm is presented with both quadratic and cubic nonlinearity evaluated via convolution of the harmonics. For simplicity only radially polarized (axisymmetric) shear wave beams are considered, which is common in shear wave elastography. Simulations are presented for cases with purely quadratic, purely cubic, and combined nonlinearities to examine how nonlinear and diffraction phenomena affect harmonic generation and waveform distortion in shear wave beams. Simulations will also be presented for parameters relevant to soft tissue. [C.A.C. is supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]

Layer-wise segmentation of three-dimensional (3D) ultrasound for chronic lower back pain (cLBP) requires a large amount of labeled images. To mitigate this burden, we propose a Generative Reinforcement Network (GRN) that integrates a generative adversarial network (GAN) framework with a segmentation model. The generator is coupled to a segmentor via segmentation-aware feedback and regularized by a discriminator. At each iteration, the segmentation loss is back-propagated into the generator to produce easy-to-learn reconstructions that directly reduce downstream segmentation error (reinforcement augmentation, RAug), while adversarial feedback from the discriminator (PatchGAN) encourages realistic reconstructions. We also introduce segmentation-guided enhancement (SGE), where the pre-trained generator enhances input images at inference to improve segmentation. GRN has two variants: GRN-SEL, which uses RAug only, and GRN-SSL, which additionally applies interpolation-consistency training (ICT) on unlabeled data by interpolating generator-reconstructed pairs and enforcing prediction consistency. We evaluate GRN primarily on a fully annotated lumbar back ultrasound dataset (MUSCLE). Two public benchmark datasets (skin lesion, Kvasir) were also used to demonstrate its generalizability. On the MUSCLE dataset, GRN-SEL with SGE reduces labeling efforts by up to 70% while improving the Dice Similarity Coefficient (DSC) by 1.98% compared to the models trained on fully labeled datasets. Across all three datasets and label fractions, GRN consistently outperforms state-of-the-art semi-supervised methods. These results suggest the effectiveness of the GRN framework in optimizing segmentation performance with significantly less labeled data. The source code is publicly available at https://github.com/Francisdadada/GRN.

Conventional time-domain algorithms that solve the augmented Burgers equation describing nonlinear propagation in a relaxing fluid have a high computational cost associated with discretizing thin shocks. The Burgers equation can be expressed using intrinsic coordinates [Hammerton and Crighton, J. Fluid Mech. 252, 585–599 (1993)], in which waveforms remain single valued beyond the point at which waveform steepening renders them multivalued in physical coordinates. Presented here is a fast simulation approach based on intrinsic coordinates with shocks inserted into the multivalued pressure waveform using the equal area rule from weak shock theory, yielding a single-valued waveform in physical coordinates without requiring fine discretization of the shock. A two-stage approach is developed by first solving the modified Burgers equation in intrinsic coordinates out to distances where shocks are no longer expected to be thin. Beyond that distance, the solution is propagated using a time-domain algorithm in physical coordinates without restrictively small discretization in time. The two-stage approach achieves high accuracy and significantly reduced computational cost when compared to time-domain numerical solutions using exclusively physical coordinates. Computational efficiency and accuracy are demonstrated with simulations of N waves propagating in air and shocks with exponential tails in seawater, each involving two relaxation mechanisms.

The elastic response of soft tissues at audio frequencies is closely associated with disease-related changes in tissue microstructure and function. The propagation speed of shear waves in tissue, which is related to the shear modulus, is used to map tissue stiffness noninvasively, for example to assess breast lesion malignancy and liver disease severity. Conventional approaches for shear wave excitation are based on the acoustic radiation force or vibration of a small piston on the skin, both of which generate small-amplitude, diverging shear waves, and are limited in their ability for penetration to the required depths, especially in the assessment of liver stiffness because liver disease is often associated with obesity. Our group conceived and realized experimentally focused shear wave beams, generated by vibration of a concave piston source, which converge toward the measurement region, thereby maintaining high amplitude at the required depths. An overview is presented of recent progress in the application of focused shear wave elastography in the context of fatty liver disease assessment. Recent advances in the prediction of nonlinear effects in shear wave beam propagation will also be discussed. [P.G.K. was supported by the Chester M. McKinney Graduate Fellowship in Acoustics at ARL:UT.]

Chronic myofascial pain (MP) that often appears as chronic lower back pain (cLBP) is a significant public health problem. Lack of reliable quantitative biomarkers makes the diagnosis still challenging in current clinics. This research aims to use 3-D-ultrasound to develop a classifier to quantitatively identify different cLBP cases including those with MP points (trigger or tender points) and without MP points. The hypothesis is from a previous study where reduced shear motion in the thoracolumbar fascia indicates tissue stiffening due to cLBP. We developed an approach using row-column-addressing (RCA) array to record tissue motions during lower back flexion in 3-D, followed by tissue motion tracking and 3-D strain tensor computation. Experimental results of the shear strain tensors were obtained from 81 human back sides including 34 labeled to have MP points (19 are trigger points). Significantly higher mean (p-value = 0.03) and median (p-value = 0.009) of the shear strain were found in cases with MP points. Area under (AUC) the receiver operating characteristic (ROC) curve were around 0.63 either using mean or median to classify cases with or without MP points. The preliminary result demonstrated an encouraging approach to be further developed as a surrogate biomarker to diagnose cLBP.

Myofascial pain (MP) is a leading cause of chronic low back pain, yet its tissue-level drivers remain poorly defined and lack reliable image biomarkers. Existing studies focus predominantly on muscle while neglecting fascia, fat, and other soft tissues that play integral biomechanical roles. We developed an anatomically grounded explainable artificial intelligence (AI) framework, LAYER (Layer-wise Analysis for Yielding Explainable Relevance Tissue), that analyses six tissue layers in three-dimensional (3D) ultrasound and quantifies their contribution to MP prediction. By utilizing the largest multi-model 3D ultrasound cohort consisting of over 4,000 scans, LAYER reveals that non-muscle tissues contribute substantially to pain prediction. In B-mode imaging, the deep fascial membrane (DFM) showed the highest saliency (0.420), while in combined B-mode and shear-wave images, the collective saliency of non-muscle layers (0.316) nearly matches that of muscle (0.317), challenging the conventional muscle-centric paradigm in MP research and potentially affecting the therapy methods. LAYER establishes a quantitative, interpretable framework for linking layer-specific anatomy to pain physiology, uncovering new tissue targets and providing a generalizable approach for explainable analysis of soft-tissue imaging.

Background and Aims: Liver fibrosis assessment using transient elastography (TE) or 2-dimensional shear wave elastography (2DSWE) exhibits high rates of failure and unreliability in patients with obesity. Novel focused shear wave elastography (fSWE) aims to enhance liver stiffness measurement (LSM) in patients with obesity and MASLD by using shear waves that converge toward the LSM region, rather than diverge as in TE and 2DSWE. The aim of the present study was to demonstrate the feasibility of LSM by fSWE, with comparison to TE and 2DSWE, in a pilot cohort of MASLD patients. Methods: We prospectively enrolled 26 adult subjects at a single clinical site. For each subject, LSM was performed using fSWE, TE, and 2DSWE and baseline clinical characteristics were obtained in a single visit. Fibrosis stage was known in 19 subjects who had prior biopsy or LSM by magnetic resonance elastography. Results: LSM was obtained in 15 subjects by fSWE, 26 subjects by TE, and 23 subjects by 2DSWE. The correlation between TE and fSWE was 92% and between TE and 2DSWE was 67%. In the subset of subjects with body mass index >35 kg/m2 (n = 12), LSM by fSWE was obtained in 7 subjects and had correlation of 87% with TE. The area under the receiver operating characteristic curve in detecting advanced fibrosis was 0.92 for fSWE, compared to 0.89 for TE and 0.74 for 2DSWE. Conclusion: A novel elastography technique, fSWE, exhibited high concordance with TE and better diagnostic performance than 2DSWE. If confirmed in larger prospective studies, fSWE may represent a promising screening strategy for patients with coexisting MASLD and obesity.

Recent analyses of second-harmonic generation in a focused shear wave beam, both analytically [Kaufinger et al., Wave Motion 139, 103595 (2025)] and numerically [Kaufinger et al., JASA 157 (2025); doi: 10.1121/10.0037533], have been concerned primarily with radially polarized beams for comparison with corresponding measurements in tissue-mimicking gelatin phantoms [Cormack et al., IEEE TBME 71, 621 (2024)]. A radially polarized fundamental beam yields a second harmonic that also has radial polarization. However, other source polarizations may be considered. We consider the class of affine polarizations, for which the radiated beam polarization is described as a superposition of constant polarization, e.g., linear or elliptical, and first-order stretches and shears, e.g., radial, torsional, or pure shearing motion. An analytical and numerical assessment is conducted for second-harmonic generation in focused shear wave beams in tissue-like media with arbitrary affine source polarization. In general, it is found that the polarization of the second harmonic does not match that of the fundamental beam. Particular attention is devoted to the longitudinal component of the displacement field that may be used for elastography measurements in potential medical applications. [PGK is supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]

Myofascial pain is associated with chronic lower back pain (LBP) and is a global health problem that affects almost all adults at some point in their lives. The myofascial components of chronic LBP, including trigger pain points (TPP) that are characterized by pain radiating from these points to broader areas, are difficult to diagnose due to a lack of reliable imaging biomarkers. Here, we present preliminary measurements of three-dimensional vibration-controlled ultrasound transient elastography to explore changes in muscle stiffness that accompany myofascial TPP. We scanned 16 subjects with identified myofascial TPP and 16 without any pain points. Elastic waves were excited by applying vibrations to the skin surface using a wide bar driven by a 150-Hz tone burst at four specific locations, including the multifidus and erector spinae muscles, bilaterally at the level of L3 and L4 vertebrae. Propagating waves were captured with the 3-D volumetric image using a row-column array transducer (RCA, Vermon RC6gV, 6 MHz). The propagation speed of the traveling wave was calculated throughout the muscle volume using a time-of-flight approach. Preliminary comparisons suggest that propagation speeds may be higher in lower back muscles with TPP, indicating the potential diagnostic value for myofascial components in chronic LBP.

Second-harmonic generation in a focused shear wave beam with Gaussian amplitude shading and radial polarization can be described analytically using a perturbation solution [Kaufinger et al., JASA 155, A350 (2024)]. Recently, focused radially polarized shear wave beams were generated in tissue-mimicking gelatin phantoms with an oscillating concave circular piston [Cormack et al., IEEE TBME 71, 621 (2024)]. To model second-harmonic generation in a focused shear wave beam with source conditions more relevant to the experiments, i.e., without Gaussian amplitude shading, the nonlinear evolution equation is solved numerically by successive approximations in k-space using a fourth-order Runge–Kutta stepping scheme. The linear solution is obtained first, which is then substituted into the quadratic terms to solve for the nonlinearly generated second harmonic. Emphasis is placed on how more realistic source conditions, including super-Gaussian amplitude shading or source conditions estimated from measurements, affect the generation of the second harmonic. Attention is also devoted to the longitudinal displacement field that is calculated locally from the transverse displacement field and the assumption of material incompressibility. [PGK is supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]

Ultrasound-based tests for liver fibrosis such as transient elastography (TE) are attractive due to high accessibility and low cost, but suffer from nondiagnostic test rates of up to 20% in patients with coexisting obesity due to limited penetration to deep livers. Focused shear wave elastography (fSWE), in which a concave vibration source generates converging shear waves for increased signal at the needed depths, was recently introduced to overcome this limitation. In clinical application the focused shear wave must penetrate through the viscous body wall, past the rib cage, and into the liver stiffness measurement (LSM) region. Here, custom simulations are employed to investigate penetration to the LSM region in fSWE. The body wall and liver are modeled as viscoelastic and ribs as perfectly absorbing obstacles, each with stiffness and size based on measurements from a cohort of MASLD patients with obesity. Correlation of fSWE penetration with liver stiffness, liver depth, and intercostal space width is moderately negative, moderately-strongly negative, and strong, respectively. Unfocused shear waves (based on Fibroscan XL) show similar correlations, but with 3.5x lower signal amplitude in the LSM region. Results suggest that liver depth and stiffness do not significantly adversely affect fSWE compared to conventional TE, while intercostal space width may. The custom simulation can be used for optimization of fSWE for clinical application.

Nonlinear shear wave propagation is typically modeled using the slow scale approximation, where it is assumed that nonlinear effects occur over the course of many wavelengths of propagation, i.e., that the nonlinear length z sh is larger than the wavelength λ. However, Catheline et al. [Phys. Rev. Lett. 91, 164301 (2003)] reported shock formation in an initially sinusoidal plane shear wave within one wavelength of propagation from the source in gelatin. Here, we investigate limits of the slow scale approximation for cubically nonlinear plane shear waves by comparing with the exact solution of the nonlinear wave equation. The dimensionless parameter Λ = λ/z sh quantifies the source amplitude limits before the slow scale approximation breaks down. As Λ (amplitude) increases, the slow scale approximation overpredicts phase speed, leading to an underestimation of shock formation distance and overestimation of waveform distortion and harmonic generation. For the case of Catheline et al., Λ = 1.07 and we find an 11% overprediction of the third harmonic amplitude at the shock formation distance. This analysis provides criteria on source amplitude for when the slow scale approximation may be invalid in the modeling of nonlinear shear wave propagation in soft tissues. [Work supported by the ARL:UT McKinney Fellowship in Acoustics.]

Objective: To implement and validate a 3D volume imaging sequence and 3D strain estimation procedure for enhanced biaxial mechanical testing of excised ventricular myocardium. Methods: One specimen of right and one of left ventricular excised porcine myocardium were tested using dualloading protocol quasistatic biaxial mechanical testing. During biaxial testing, volume ultrasound (US) images were acquired using a row-column addressed array probe using a synthetic aperture imaging sequence. Volume US images were used to compute tissue deformation using 3D correlation-based US speckle tracking. US-derived tissue strains were validated against repeated measurements using conventional optical camera imaging of the specimen surface deformation. Results: Speckle tracking yielded high-fidelity maps of tissue deformation in 3D throughout the entire sample volume. US-derived tissue strain is in good agreement with ground-truth camera-derived surface strain measurements (root mean square error is 1.6% strain). Conclusion: The 3D full-thickness strain measurement with US imaging is accurate and can enhance biomechanical insights from biaxial experimentation, especially in large tissues such as porcine and human myocardium where assumptions of plane stress and incompressibility may not apply.