Local Phase Velocity Based Imaging: A New Technique Used for Ultrasound Shear Wave Elastography

Deep Learning With Physics-Embedded Neural Network for Full Waveform Ultrasonic Brain Imaging

The convenience, safety, and affordability of ultrasound imaging make it a vital non-invasive diagnostic technique for examining soft tissues. However, significant differences in acoustic impedance between the skull and soft tissues hinder the successful application of traditional ultrasound for brain imaging. In this study, we propose a physics-embedded neural network with deep learning based full waveform inversion (PEN-FWI), which can achieve reliable quantitative imaging of brain tissues. The network consists of two fundamental components: forward convolutional neural network (FCNN) and inversion sub-neural network (ISNN). The FCNN explores the nonlinear mapping relationship between the brain model and the wavefield, replacing the tedious wavefield calculation process based on the finite difference method. The ISNN implements the mapping from the wavefield to the model. PEN-FWI includes three iterative steps, each embedding the F CNN into the ISNN, ultimately achieving tomography from wavefield to brain models. Simulation and laboratory tests indicate that PEN-FWI can produce high-quality imaging of the skull and soft tissues, even starting from a homogeneous water model. PEN-FWI can achieve excellent imaging of clot models with constant uniform distribution of velocity, randomly Gaussian distribution of velocity, and irregularly shaped randomly distributed velocity. Robust differentiation can also be achieved for brain slices of various tissues and skulls, resulting in high-quality imaging. The imaging time for a horizontal cross-sectional imag e of the brain is only 1.13 seconds. This algorithm can effectively promote ultrasound-based brain tomography and provide feasible solutions in other fields.

Ultrasound Shear Elastography With Expanded Bandwidth (USEWEB): A Novel Method for 2D Shear Phase Velocity Imaging of Soft Tissues

Ultrasound shear wave elastography (SWE) is a noninvasive approach for evaluating mechanical properties of soft tissues. In SWE either group velocity measured in the time-domain or phase velocity measured in the frequency-domain can be reported. Frequency-domain methods have the advantage over time-domain methods in providing a response for a specific frequency, while time-domain methods average the wave velocity over the entire frequency band. Current frequency-domain approaches struggle to reconstruct SWE images over full frequency bandwidth. This is especially important in the case of viscoelastic tissues, where tissue viscoelasticity is often studied by analyzing the shear wave phase velocity dispersion. For characterizing cancerous lesions, it has been shown that considerable biases can occur with group velocity-based measurements. However, using phase velocities at higher frequencies can provide more accurate evaluations. In this paper, we propose a new method called Ultrasound Shear Elastography with Expanded Bandwidth (USEWEB) used for two-dimensional (2D) shear wave phase velocity imaging. We tested the USEWEB method on data from homogeneous tissue-mimicking liver fibrosis phantoms, custom-made viscoelastic phantom measurements, phantoms with cylindrical inclusions experiments, and in vivo renal transplants scanned with a clinical scanner. We compared results from the USEWEB method with a Local Phase Velocity Imaging (LPVI) approach over a wide frequency range, i.e., up to 200-2000 Hz. Tests carried out revealed that the USEWEB approach provides 2D phase velocity images with a coefficient of variation below 5% over a wider frequency band for smaller processing window size in comparison to LPVI, especially in viscoelastic materials. In addition, USEWEB can produce correct phase velocity images for much higher frequencies, up to 1800 Hz, compared to LPVI, which can be used to characterize viscoelastic materials and elastic inclusions.

Ultrasound Shear Wave Propagation Modeling in General Tissue-Like Viscoelastic Materials

OBJECTIVE

This study aims to present an approach for the simulation of ultrasound elastic waves propagation in a diverse range of heterogeneous tissue-like viscoelastic materials, including, but not limited to, Kelvin-Voigt, Zener, Maxwell, Burger's, and Maxwell-Wiechert models, while also allowing for modeling highly viscous fluids.

METHODS

Ultrasound shear wave elastography (SWE) serves as a cost-effective modality for noninvasive, quantitative assessment of soft tissue viscoelastic mechanical properties. To explore tissue viscoelasticity, measuring the shear wave phase velocity in the frequency domain is a common method. In this paper, we employ modeling and numerical simulations to enhance the development of SWE methods. The study employs the staggered grid finite difference (SGFD) method along with recursive calculations of convolution integrals pertinent to linear viscoelastic models.

RESULTS

The presented numerical method demonstrates its capability to simulate the propagation of ultrasound elastic waves, both longitudinal and shear, across a broad spectrum of tissue-like viscoelastic heterogeneous materials. The approach successfully accommodates various viscoelastic models without requiring additional modifications in the numerical model, thus enabling a comprehensive exploration of different viscoelastic behaviors commonly observed in diverse tissue types.

CONCLUSION

The developed combination of the SGFD method and recursive calculation of convolution integrals presents a novel and versatile approach in modeling linear viscoelastic tissue-like materials for SWE applications. This method eliminates the need for model-specific adaptations in numerical simulations, thereby offering flexibility for exploring and understanding diverse viscoelastic behaviors inherent in different heterogeneous tissue types, contributing significantly to the advancement of ultrasound SWE for diagnostic purposes.

Evaluation of Robustness of S-Transform Based Phase Velocity Estimation in Viscoelastic Phantoms and Renal Transplants

Ultrasound shear wave elastography (SWE) methods are being used to differentiate healthy versus diseased tissue on the basis of their viscoelastic mechanical properties. Tissue viscoelasticity is often studied by analyzing shear wave phase velocity dispersion curves, which is the variation of phase velocity with frequency or wavelength. Recently, a unique approach using a generalized Stockwell transformation (GST-SFK) was proposed for the calculation of dispersion curves in viscoelastic media over expanded frequency band. In this work, the method's robustness was evaluated on data from five custom-made viscoelastic tissue-mimicking phantoms and sixty in vivo renal transplants. For each phantom, 15 shear wave motion data acquisitions were taken, while 10-13 acquisitions were acquired for renal transplants measured in the renal cortex. For each data-set mean and standard deviation (SD) of estimated phase velocity dispersion curves were studied. In addition, the viscoelastic parameters of the Zener model were examined, which were preceded by a convergence analysis. For viscoelastic phantoms scanned with a research ultrasound scanner, and for the in vivo renal transplants scanned with a clinical scanner, the decisive advantage of the GST-SFK method over the standard two-dimensional Fourier transform (2D-FT) method was shown. The GST-SFK method provided dispersion curve estimates with lower SD over a wider frequency band in comparison to the 2D-FT method. These advantages are relevant to the analysis of the mechanical properties of tissues in clinical practice to discriminate healthy from diseased tissue.

Feasibility of Phase Velocity Imaging Using Multi Frequency Oscillation-Shear Wave Elastography

OBJECTIVE

To assess viscoelasticity, a pathologically relevant biomarker, shear wave elastography (SWE) generally uses phase velocity (PV) dispersion relationship generated via pulsed acoustic radiation force (ARF) excitation pulse. In this study, a multi-frequency oscillation (MFO)- excitation pulse with higher weight to higher frequencies is proposed to generate PV images via the generation of motion with energy concentrated at the target frequencies in contrast to the broadband frequency motion generated in pulsed SWE (PSWE).

METHODS

The feasibility of MFO-SWE to generate PV images at 100 to 1000 Hz in steps of 100 Hz was investigated by imaging 6 and 70 kPa inclusions with 6.5 and 10.4 mm diameter and ex vivo bovine liver with and without the presence of an aberration layer and chicken muscle ex vivo, and 4T1 mouse breast tumor, in vivo with comparisons to PSWE.

RESULTS

MFO-SWE-derived CNR was statistically higher than PSWE for 6 kPa (both with and without aberration) and 70 kPa (with aberration) inclusions and derived SNR of the liver was statistically higher than PSWE at higher frequency (600-1000 Hz). Quantitatively, at 600-1000 Hz, MFO-SWE improved CNR of inclusions (without and with) aberration on an average by (8.2 and 156)% and of the tumor by 122%, respectively, and improved SNR of the liver (without and with) aberration by (20.2 and 51.5)% and of chicken muscle by 72%, respectively compared to the PSWE.

CONCLUSIONS AND SIGNIFICANCE

These results indicate the advantages of MFO-SWE to improve PV estimation at higher frequencies which could improve viscoelasticity quantification and feature delineation.

On the Role of Coherent Plane Wave Compounding in Shear Wave Elasticity Imaging: The Convolution Effect and Its Implications

OBJECTIVE

The clinical applicability of shear wave elasticity imaging (SWEI) has been confounded by its appreciable inter-system variability and unsatisfactory sensitivity. While SWEI relies on plane wave imaging (PWI) to achieve real-time rendering, it has been rarely noticed that PWI can affect SWEI's performance. This work is aimed at demonstrating that the use of coherent plane wave compounding (CPWC) can be a factor causing SWEI's underperformance.

METHODS

We presented a model to formally describe the slow-time behavior of CPWC in motion tracking. This model reveals that CPWC introduces temporal convolution on the observed motion, making the motion sampling process a low-pass filter (LPF). For validation, shear waves were produced in a phantom in the same way but sampled via PWI using different compounding numbers (CN) and pulse repetition frequencies (PRF), with the obtained signals compared with the inferences drawn from our model. Similar experiments were performed to reconstruct two small targets in the phantom in order to appraise the impact of CPWC on SWEI's sensitivity.

DISCUSSION

The validation experiment shows that the measurements match well with the model inferences, which verifies the LPF nature of CPWC. The phantom study also shows that either increasing CN or decreasing PRF can cause the loss of high-frequency motion information, leading to blurred target delineation by SWEI.

CONCLUSION

The convolution effect can help understand the variability of SWEI. Researchers should beware this effect when working on SWEI standardization. Clinicians using SWEI should also be cautious because this effect makes it harder to identify small lesions.

Two-Dimensional Damage Localization Using a Piezoelectric Smart Aggregate Approach-Implementation on Arbitrary Shaped Concrete Plates

This paper presents the application of a hybrid approach for damage localization in concrete plates of arbitrary geometric shapes and a constant thickness. The hybrid algorithm utilizes fast discrete wavelet transformation, energy approach and time of flight criteria for the purpose of the localization of single- and multi-damage problems inside or on the periphery of concrete plates. A brief theoretical background of the hybrid method as well as numerical procedures for modeling the piezoelectric smart aggregate and ultrasonic wave propagation are presented. Experimental and numerical verification of the damage localization were performed on square samples/models with one or two damages and with 16 positions of piezoelectric smart actuator/sensor aggregates. After the verification of the hybrid method, a numerical simulation was performed on models with one or two damages for plates of arbitrary geometric shapes. Based on the obtained results, it was concluded that the proposed method can be applied to damage localization in concrete plates of arbitrary geometric shapes. The presented method and numerical procedure can be further used in research through varying the geometry, number and position of damages as well as the number and position of piezoelectric smart aggregates.

A Miniature Dual-Fiber Probe for Quantitative Optical Coherence Elastography

OBJECTIVE

Optical coherence elastography (OCE) allows for high resolution analysis of elastic tissue properties. However, due to the limited penetration of light into tissue, miniature probes are required to reach structures inside the body, e.g., vessel walls. Shear wave elastography relates shear wave velocities to quantitative estimates of elasticity. Generally, this is achieved by measuring the runtime of waves between two or multiple points. For miniature probes, optical fibers have been integrated and the runtime between the point of excitation and a single measurement point has been considered. This approach requires precise temporal synchronization and spatial calibration between excitation and imaging.

METHODS

We present a miniaturized dual-fiber OCE probe of 1 mm diameter allowing for robust shear wave elastography. Shear wave velocity is estimated between two optics and hence independent of wave propagation between excitation and imaging. We quantify the wave propagation by evaluating either a single or two measurement points. Particularly, we compare both approaches to ultrasound elastography.

RESULTS

Our experimental results demonstrate that quantification of local tissue elasticities is feasible. For homogeneous soft tissue phantoms, we obtain mean deviations of 0.15 ms-1 and 0.02 ms-1 for single-fiber and dual-fiber OCE, respectively. In inhomogeneous phantoms, we measure mean deviations of up to 0.54 ms-1 and 0.03 ms-1 for single-fiber and dual-fiber OCE, respectively.

CONCLUSION

We present a dual-fiber OCE approach that is much more robust in inhomogeneous tissues. Moreover, we demonstrate the feasibility of elasticity quantification in ex-vivo coronary arteries.

SIGNIFICANCE

This study introduces an approach for robust elasticity quantification from within the tissue.

Cross-Image Dependency Modeling for Breast Ultrasound Segmentation

We present a novel deep network (namely BUSSeg) equipped with both within- and cross-image long-range dependency modeling for automated lesions segmentation from breast ultrasound images, which is a quite daunting task due to (1) the large variation of breast lesions, (2) the ambiguous lesion boundaries, and (3) the existence of speckle noise and artifacts in ultrasound images. Our work is motivated by the fact that most existing methods only focus on modeling the within-image dependencies while neglecting the cross-image dependencies, which are essential for this task under limited training data and noise. We first propose a novel cross-image dependency module (CDM) with a cross-image contextual modeling scheme and a cross-image dependency loss (CDL) to capture more consistent feature expression and alleviate noise interference. Compared with existing cross-image methods, the proposed CDM has two merits. First, we utilize more complete spatial features instead of commonly used discrete pixel vectors to capture the semantic dependencies between images, mitigating the negative effects of speckle noise and making the acquired features more representative. Second, the proposed CDM includes both intra- and inter-class contextual modeling rather than just extracting homogeneous contextual dependencies. Furthermore, we develop a parallel bi-encoder architecture (PBA) to tame a Transformer and a convolutional neural network to enhance BUSSeg's capability in capturing within-image long-range dependencies and hence offer richer features for CDM. We conducted extensive experiments on two representative public breast ultrasound datasets, and the results demonstrate that the proposed BUSSeg consistently outperforms state-of-the-art approaches in most metrics.

Evaluating Variability of Commercial Liver Fibrosis Elastography Phantoms

OBJECTIVE

Liver fibrosis has been found to increase the mechanical stiffness of the liver. To mimic different stages of liver fibrosis, commercially available phantoms (Model 039, CIRS, Inc.) have been produced for clinical quality assurance and research purposes. The purpose of this study was to investigate the mechanical property variability of the phantoms in two lots of CIRS Model 039 phantoms.

METHODS

Each lot consisted of phantoms of four stiffness types, and there were 8-10 phantoms of each type. Shear wave elastography measurements were conducted on each phantom at 10 different angles. Group velocity measurements and phase velocity curves were calculated for every SWE acquisition. Multilevel functional principal component analysis (MFPCA) was performed on phase velocity data, which decomposes each phase velocity curve into the sum of eigenfunctions of two levels. The variance of the component scores of levels 1 and 2 were used to represent inter-phantom and intra-phantom variability, respectively. The 95% confidence intervals of phase velocity in a phantom type were calculated to reflect curve variability.

DISCUSSION

The standard deviations of the group velocity for phantoms of any type were less than 0.04 and 0.02 m/s for lots 1 and 2, respectively. For both lots, in every type, the phase velocity curves of most individual phantoms fall within the 95% confidence interval.

CONCLUSION

MFPCA is an effective tool for analyzing the inter- and intra-phantom variability of phase velocity curves. Given the known variability of a fully tested lot, estimation of the variability of a new lot can be performed with a reduced number of phantoms tested.

Optical force estimation for interactions between tool and soft tissues

Robotic assistance in minimally invasive surgery offers numerous advantages for both patient and surgeon. However, the lack of force feedback in robotic surgery is a major limitation, and accurately estimating tool-tissue interaction forces remains a challenge. Image-based force estimation offers a promising solution without the need to integrate sensors into surgical tools. In this indirect approach, interaction forces are derived from the observed deformation, with learning-based methods improving accuracy and real-time capability. However, the relationship between deformation and force is determined by the stiffness of the tissue. Consequently, both deformation and local tissue properties must be observed for an approach applicable to heterogeneous tissue. In this work, we use optical coherence tomography, which can combine the detection of tissue deformation with shear wave elastography in a single modality. We present a multi-input deep learning network for processing of local elasticity estimates and volumetric image data. Our results demonstrate that accounting for elastic properties is critical for accurate image-based force estimation across different tissue types and properties. Joint processing of local elasticity information yields the best performance throughout our phantom study. Furthermore, we test our approach on soft tissue samples that were not present during training and show that generalization to other tissue properties is possible.

A New Estimation Scheme for Improving the Performance of Shear Wave Elasticity Imaging

Shear wave velocity (SWV) reconstruction based on time-of-flight (TOF) is widely adopted to realize shear wave elasticity imaging (SWEI). It typically breaks down the reconstruction of a SWV image into many kernels and treats them independently. We hypothesized that information exchange among kernels improves the performance of SWEI. Therefore, we propose the approach of iterative re-weighted least squares based on inter-kernel communication (IKC-IRLS). We also hypothesized that time-to-peak (TTP) is superior to cross-correlation (CC) in visualizing small targets because TTP uses higher shear wave frequencies than CC. To examine the hypotheses, IKC-IRLS was combined with TTP data and compared with four established methods. The five methods were tested by imaging several small-size stiff targets (2.5, 4.0 and 6.4 mm in diameter) using different kernel sizes in the simulation and real experiments. The results indicate that the IKC-IRLS approach can mitigate speckle noise and is robust to TTP outliers. Consequently, the proposed method achieves the highest contrast-to-noise ratio and the lowest mean absolute percentage error of target in almost all tested cases.

Imaging of Single Transducer-Harmonic Motion Imaging-Derived Displacements at Several Oscillation Frequencies Simultaneously

Mapping of mechanical properties, dependent on the frequency of motion, is relevant in diagnosis, monitoring treatment response, or intra-operative surgical resection planning. While shear wave speeds at different frequencies have been described elsewhere, the effect of frequency on the "on-axis" acoustic radiation force (ARF)-induced displacement has not been previously investigated. Instead of generating single transducer-harmonic motion imaging (ST-HMI)-derived peak-to-peak displacement (P2PD) image at a particular frequency, a novel multi-frequency excitation pulse is proposed to generate P2PD images at 100-1000 Hz simultaneously. The performance of the proposed excitation pulse is compared with the ARFI by imaging 16 different inclusions (Young's moduli of 6, 9, 36, 70 kPa and diameters of 1.6, 2.5, 6.5, and 10.4 mm) embedded in an 18 kPa background. Depending on inclusion size and stiffness, the maximum CNR and contrast were achieved at different frequencies and were always higher than ARFI. The frequency, at which maximum CNR and contrast were achieved, increased with stiffness for fixed inclusion's size and decreased with size for fixed stiffness. In vivo feasibility is tested by imaging a 4T1 breast cancer mouse tumor on Day 6, 12, and 19 post-injection of tumor cells. Similar to phantoms, the CNR of ST-HMI images was higher than ARFI and increased with frequency for the tumor on Day 6. Besides, P2PD at 100-1000 Hz indicated that the tumor became stiffer with respect to the neighboring non-cancerous tissue over time. These results indicate the importance of using a multi-frequency excitation pulse to simultaneously generate displacement at multiple frequencies to better delineate inclusions or tumors.

The influence of acoustic radiation force beam shape and location on wave spectral content for arterial dispersion ultrasound vibrometry

Objective. Arterial dispersion ultrasound vibrometry (ADUV) relies on the use of guided waves in arterial geometries for shear wave elastography measurements. Both the generation of waves through the use of acoustic radiation force (ARF) and the techniques employed to infer the speed of the resulting wave motion affect the spectral content and accuracy of the measurement. In particular, the effects of the shape and location of the ARF beam in ADUV have not been widely studied. In this work, we investigated how such variations of the ARF beam affect the induced motion and the measurements in the dispersive modes that are excited. Approach. The study includes an experimental evaluation on an arterial phantom and an in vivo validation of the observed trends, observing the two walls of the waveguide, simultaneously, when subjected to variations in the ARF beam extension (F/N) and focus location. Main results. Relying on the theory of guided waves in cylindrical shells, the shape of the beam controls the selection and nature of the induced modes, while the location affects the measured dispersion curves (i.e. variation of phase velocity with frequency or wavenumber, multiple modes) across the waveguide walls. Significance. This investigation is important to understand the spectral content variations in ADUV measurements and to maximize inversion accuracy by tuning the ARF beam settings in clinical applications.

A Non-invasive Method to Estimate the Stress-Strain Curve of Soft Tissue Using Ultrasound Elastography

Ultrasound elastography performed under small strain conditions has been intensively studied. However, small deformations may be not sufficiently large to differentiate some abnormal tissues. By combining quasi-static and shear wave elastography, we developed a non-invasive method to estimate the localized stress- strain curve of materials. This method exerts progressive multistep uniaxial compression on the materials, and shear wave measurements were performed at every compression step. This method estimates the 2-D displacements between steps via a 2-D region growing motion tracking method and accumulates these displacements to obtain the large material displacements with respect to the initial configuration. At each step, the shear modulus and stress were calculated according to linear elastic theory. The proposed method was tested on custom-made tissue-mimicking phantoms. Mechanical compression testing was conducted on the samples made of the same material as the phantoms and taken as the reference. The stress-strain curves for the same material from the proposed method and from mechanical testing are in good agreement. The root mean square error (RMSE) and area percentage error (APE) of the stress-strain curve between ultrasound measurement and mechanical testing for soft materials ranged from 0.18 to 0.26 kPa and from 5.6% to 7.8%, respectively. The RMSE and APE for stiff materials ranged from 0.56 to 1.17 kPa and 8.0% to 17.9%. Therefore, our method was able to provide good estimates of the stress-strain curve for tissue-mimicking materials.

Imaging the Local Nonlinear Viscoelastic Properties of Soft Tissues: Initial Validation and Expected Benefits

Imaging tissue mechanical properties has shown promise in noninvasive assessment of numerous pathologies. Researchers have successfully measured many linear tissue mechanical properties in laboratory and clinical settings. Currently, multiple complex mechanical effects such as frequency-dependence, anisotropy, and nonlinearity are being investigated separately. However, a concurrent assessment of these complex effects may enable more complete characterization of tissue biomechanics and offer improved diagnostic sensitivity. In this work, we report for the first time a method to map the frequency-dependent nonlinear parameters of soft tissues on a local scale. We recently developed a nonlinear elastography model that combines strain measurements from arbitrary tissue compression with radiation-force-based broadband shear wave speed (WS) measurements. Here, we extended this model to incorporate local measurements of frequency-dependent shear modulus. This combined approach provides a local frequency-dependent nonlinear parameter that can be obtained with arbitrary, clinically realizable tissue compression. Initial assessments using simulations and phantoms validate the accuracy of this approach. We also observed improved contrast in nonlinearity parameter at higher frequencies. Results from ex-vivo liver experiments show 32, 25, 34, and 38 dB higher contrast in elastograms than traditional linear elasticity, elastic nonlinearity, viscosity, and strain imaging methods, respectively. A lesion, artificially created by injection of glutaraldehyde into a liver specimen, showed a 59% increase in the frequency-dependent nonlinear parameter and a 17% increase in contrast ratio.

Evaluation of Robustness of Local Phase Velocity Imaging in Homogenous Tissue-Mimicking Phantoms

Shear wave elastography (SWE) is a method of evaluating mechanical properties of soft tissues. Most current implementations of SWE report the group velocity for shear wave velocity, which assumes an elastic, isotropic, homogenous and incompressible tissue. Local phase velocity imaging (LPVI) is a novel method of phase velocity reconstruction that allows for accurate evaluation of shear wave velocity at specified frequencies. This method's robustness was evaluated in 11 elastic and 8 viscoelastic phantoms using linear and curvilinear arrays. We acquired data with acoustic radiation force push beams with different focal depths and F-numbers and reconstructed phase velocity images over a wide range of frequencies. Regardless of phantom, push beam focal depth and reconstruction frequency, an F-number around 3.0 was found to produce the largest usable area in the phase velocity reconstructions. For elastic phantoms scanned with a linear array, the optimal focal depth, frequency range and maximum region of interest (ROI) were 20-30 mm, 100-400 Hz and 2.70 cm², respectively. For viscoelastic phantoms scanned with a linear array, the optimal focal depth, frequency and maximum ROI were 20-30 mm, 100-300 Hz and 1.54 cm², respectively. For the curvilinear array in the same phantoms, optimal focal depth, frequency range and maximum ROIs were 45-60 mm, 100-400 and 100-300 Hz and 1.54 cm², respectively. In further work, LPVI reconstructions from inclusion phantoms will be evaluated to simulate non-homogeneous tissues. Additionally, LPVI will be evaluated in larger-volume phantoms to account for wave reflection from the containers when using the curvilinear array.

Reconstruction of shear wave speed in tissue-mimicking phantoms from aliased pulse-echo imaging of high-frequency wavefields

Quantitative elasticity estimation in medical and industrial applications may benefit from advancements in reconstruction of shear wave speed with enhanced resolution. Here, shear wave speed is reconstructed from pulse-echo ultrasound imaging of elastic waves induced by high-frequency (>400 Hz), time-harmonic mechanical excitation. Particle displacement in shear wavefields is mapped from measured interframe phase differences with compensation for timing of multiple scan lines, then processed by spatial Fourier analysis to estimate the predominant wave speed and analyzed by algebraic wavefield inversion to reconstruct wave speed maps. Reconstructions of shear wave speed from simulated wavefields illustrate the accuracy and spatial resolution available with both methods, as functions of signal-to-noise ratio and sizes of windows used for Fourier analysis or wavefield smoothing. The methods are applied to shear wavefields with frequencies up to six times the Nyquist rate, thus extending the frequency range measurable by a given imaging system. Wave speed measurements in tissue-mimicking phantoms are compared with supersonic shear imaging and mechanical tensile testing, demonstrating feasibility of the wavefield measurement and wave speed reconstruction methods employed.

Acoustic Radiation Force: A Review of Four Mechanisms for Biomedical Applications

Radiation force is a universal phenomenon in any wave motion where the wave energy produces a static or transient force on the propagation medium. The theory of acoustic radiation force (ARF) dates back to the early 19th century. In recent years, there has been an increasing interest in the biomedical applications of ARF. Following a brief history of ARF, this article describes a concise theory of ARF under four physical mechanisms of radiation force generation in tissue-like media. These mechanisms are primarily based on the dissipation of acoustic energy of propagating waves, the reflection of the incident wave, gradients of the compressional wave speeds, and the spatial variations of energy density in standing acoustic waves. Examples describing some of the practical applications of ARF under each mechanism are presented. This article concludes with a discussion on selected ideas for potential future applications of ARF in biomedicine.

Domain Knowledge Powered Deep Learning for Breast Cancer Diagnosis Based on Contrast-Enhanced Ultrasound Videos

In recent years, deep learning has been widely used in breast cancer diagnosis, and many high-performance models have emerged. However, most of the existing deep learning models are mainly based on static breast ultrasound (US) images. In actual diagnostic process, contrast-enhanced ultrasound (CEUS) is a commonly used technique by radiologists. Compared with static breast US images, CEUS videos can provide more detailed blood supply information of tumors, and therefore can help radiologists make a more accurate diagnosis. In this paper, we propose a novel diagnosis model based on CEUS videos. The backbone of the model is a 3D convolutional neural network. More specifically, we notice that radiologists generally follow two specific patterns when browsing CEUS videos. One pattern is that they focus on specific time slots, and the other is that they pay attention to the differences between the CEUS frames and the corresponding US images. To incorporate these two patterns into our deep learning model, we design a domain-knowledge-guided temporal attention module and a channel attention module. We validate our model on our Breast-CEUS dataset composed of 221 cases. The result shows that our model can achieve a sensitivity of 97.2% and an accuracy of 86.3%. In particular, the incorporation of domain knowledge leads to a 3.5% improvement in sensitivity and a 6.0% improvement in specificity. Finally, we also prove the validity of two domain knowledge modules in the 3D convolutional neural network (C3D) and the 3D ResNet (R3D).

Plane wave elastography: a frequency-domain ultrasound shear wave elastography approach

In this paper, we propose plane wave elastography (PWE), a novel ultrasound shear wave elastography (SWE) approach. Currently, commercial methods for SWE rely on directional filtering based on the prior knowledge of the wave propagation direction, to remove complicated wave patterns formed due to reflection and refraction. The result is a set of decomposed directional waves that are separately analyzed to construct shear modulus fields that are then combined through compounding. Instead, PWE relies on a rigorous representation of the wave propagation using the frequency-domain scalar wave equation to automatically select appropriate propagation directions and simultaneously reconstruct shear modulus fields. Specifically, assuming a homogeneous, isotropic, incompressible, linear-elastic medium, we represent the solution of the wave equation using a linear combination of plane waves propagating in arbitrary directions. Given this closed-form solution, we formulate the SWE problem as a nonlinear least-squares optimization problem which can be solved very efficiently. Through numerous phantom studies, we show that PWE can handle complicated waveforms without prior filtering and is competitive with state-of-the-art that requires prior filtering based on the knowledge of propagation directions.

Phase Velocity Estimation With Expanded Bandwidth in Viscoelastic Phantoms and Tissues

Ultrasound shear wave elastography (SWE) is a technique used to measure mechanical properties to evaluate healthy and pathological soft tissues. SWE typically employs an acoustic radiation force (ARF) to generate laterally propagating shear waves that are tracked in the spatiotemporal domains, and algorithms are used to estimate the wave velocity. The tissue viscoelasticity is often examined through analyzing the shear wave phase velocity dispersion curves, which is the variation of phase velocity with frequency or wavelength. A number of available methods to estimate dispersion exist, which can differ in resolution and variance. Moreover, most of these techniques reconstruct dispersion curves for a limited frequency band. In this work, we propose a novel method used for dispersion curve calculation. Our unique approach uses a generalized Stockwell transformation combined with a slant frequency-wavenumber analysis (GST-SFK). We tested the GST-SFK method on numerical phantom data generated using a finite-difference-based method in tissue-mimicking viscoelastic media. In addition, we evaluated the method on numerical shear wave motion data with different amounts of white Gaussian noise added. Additionally, we performed tests on data from custom-made tissue-mimicking viscoelastic phantom experiments, ex vivo porcine liver measurements, and in vivo liver tissue experiments. We compared results from our method with two other techniques used for estimating shear wave phase velocity: the two-dimensional Fourier transform (2D-FT) and the eigenvector (EV) method. Tests carried out revealed that the GST-SFK method provides dispersion curve estimates with lower errors over a wider frequency band in comparison to the 2D-FT and EV methods. In addition, the GST-SFK provides expanded bandwidth by a factor of two or more to be used for phase velocity estimation, which is meaningful for a tissue dispersion analysis in vivo.

Feasibility of Harmonic Motion Imaging Using a Single Transducer: In Vivo Imaging of Breast Cancer in a Mouse Model and Human Subjects

Harmonic motion imaging (HMI) interrogates the mechanical properties of tissues by simultaneously generating and tracking harmonic oscillation using focused ultrasound and imaging transducers, respectively. Instead of using two transducers, the objective of this work is to develop a single transducer HMI (ST-HMI) to both generate and track harmonic motion at "on-axis" to the force for facilitating data acquisition. In ST-HMI, the amplitude-modulated force was generated by modulating excitation pulse duration and tracking of motion was performed by transmitting tracking pulses interleaved between excitation pulses. The feasibility of ST-HMI was performed by imaging two elastic phantoms with three inclusions (N = 6) and comparing it with acoustic radiation force impulse (ARFI) imaging, in vivo longitudinal monitoring of 4T1, orthotropic breast cancer mice (N = 4), and patients (N = 3) with breast masses in vivo. Six inclusions with Young's moduli of 8, 10, 15, 20, 40, and 60 kPa were embedded in a 5 kPa background. The ST-HMI-derived peak-to-peak displacement (P2PD) successfully detected all inclusions with [Formula: see text] of the linear regression between the P2PD ratio of background to inclusion versus Young's moduli ratio of inclusion to background. The contrasts of 10 and 15 kPa inclusions were higher in ST-HMI than ARFI-derived images. In the mouse study, the median P2PD ratio of tumor to non-cancerous tissues was 3.0, 5.1, 6.1, and 7.7 at 1, 2, 3, and 4 weeks post-injection of the tumor cells, respectively. In the clinical study, ST-HMI detected breast masses including fibroadenoma, pseudo angiomatous stromal hyperplasia, and invasive ductal carcinoma with a P2PD ratio of 1.37, 1.61, and 1.78, respectively. These results indicate that ST-HMI can assess the mechanical properties of tissues via generation and tracking of harmonic motion "on-axis" to the ARF. This study is the first step towards translating ST-HMI in clinics.

Viscoelastic parameter estimation using simulated shear wave motion and convolutional neural networks

Ultrasound shear wave elastography (SWE) techniques have been very useful for the analysis of tissue rheological properties, but there are still obstacles for robust evaluation of viscoelastic tissue properties. In this proof-of-concept study, we investigate whether convolutional neural networks (CNN) are capable of retrieving the elasticity and viscosity parameters from simulated shear wave motion images. Staggered-grid finite difference simulations based on a Kelvin-Voigt rheological model were used to generate data for this study. The wave motion datasets were created using Kelvin-Voigt shear elasticity values ranging from 1 to 25 kPa, shear viscosities ranging from 0 to 10 Pa⋅s, and two different push profiles using f-numbers of 1 and 2. The CNN architectures, optimized using mean squared error loss, were then trained to retrieve a specific viscoelastic parameter. Both elasticity and viscosity values were successfully retrieved, with regression R² values above 0.99 when correlating the estimated mechanical properties versus the true mechanical properties. The CNN performance was also compared to estimation of shear elasticity and viscosity from fitting dispersion curves estimated from two-dimensional Fourier transform analysis. The results demonstrated that the CNN models were robust to noise, vertical position and partially to f-number. The architecture was proven to be robust to multiple push profiles if trained properly. The CNN results showed higher accuracy over the full viscoelastic parameter range compared to the Fourier-based analysis. The overall results showed the CNNs' potential to be an alternative to complex mathematical analyses such as Fourier analysis and dispersion curve estimation used currently for shear wave viscoelastic parameter estimation.

Spectral interferometric depth-resolved photoacoustic viscoelasticity imaging

Viscoelasticity is closely related to the physiological characteristics of biological tissues. In this Letter, we propose a novel spectral interferometric depth-resolved photoacoustic viscoelasticity imaging (SID-PAVEI) method, to the best of our knowledge for the first time, which breaks the plight of surface viscoelasticity imaging and achieves an internal visible microscale SID-PAVEI in a noncontact fashion. In this work, we employ a high-sensitive and depth-resolved spectral domain low coherence interferometry (SDLCI) to remotely track photoacoustic-induced strain response of absorbers in situ. By decoupling the phase and amplitude of the photoacoustic-encoded spectral interference signal, the SID-PAVEI and scattering structure imaging (SSI) can be obtained simultaneously. Depth-resolved performance of the SID-PAVEI and the SSI in one scan were demonstrated by imaging biological tissues. The method opens new perspectives for three-dimensional microscale viscoelasticity imaging and provides a great potential in multi-parametric characterizing pathological information.

Local Phase Velocity Based Imaging of Viscoelastic Phantoms and Tissues

Assessment of soft tissue elasticity and viscosity is of interest in several clinical applications. In this study, we present the feasibility of the local phase velocity based imaging (LPVI) method to create images of phase velocity and viscoelastic parameters in viscoelastic tissue-mimicking materials and soft tissues. In viscoelastic materials, it is necessary to utilize wave-mode isolation using a narrow bandpass filter combined with a directional filter in order to robustly reconstruct phase velocity images with LPVI in viscoelastic media over a wide range of frequencies. A pair of sequential focused acoustic radiation force push beams, focused once on the left-hand side and once on the right-hand side of the probe, was used to produce broadband propagating shear waves. The local shear wave phase velocity is then recovered in the frequency domain for multiple frequencies, for both acquired data sets. Then, a 2-D shear wave velocity map is reconstructed by combining maps from two separate acquisitions. By testing the method on simulated data sets and performing in vitro phantom and in vivo liver tissue experiments, we show the ability of the proposed technique to generate shear wave phase velocity maps at various frequencies in viscoelastic materials. Moreover, a nonlinear least-squares problem is solved in order to locally estimate elasticity and viscosity parameters. The LPVI method with added directional and wavenumber filters can produce phase velocity images, which can be used to characterize the viscoelastic materials.

Shear Wave Velocity Estimation Using the Real-Time Curve Tracing Method in Ultrasound Elastography

The estimation of shear wave velocity is very important in ultrasonic shear wave elasticity imaging (SWEI). Since the stability and accuracy of ultrasonic testing equipment have been greatly improved, in order to further improve the accuracy of shear wave velocity estimation and increase the quality of shear wave elasticity maps, we propose a novel real-time curve tracing (RTCT) technique to accurately reconstruct the motion trace of shear wave fronts. Based on the curve fitting of each frame shear wave, the propagation velocity of two-dimensional shear waves can be estimated. In this paper, shear wave velocity estimation and shear wave image reconstruction are implemented for homogeneous regions and stiff spherical inclusion regions with different elasticity, respectively. The experimental result shows that the proposed shear wave velocity estimation method based on the real-time curve tracing method has advantages in accuracy and anti-noise performance. Moreover, by eliminating artifacts of shear wave videos, the velocity map acquired can restore the shape of inclusions better. The real-time curve tracing method can provide a new idea for the estimation of shear wave velocity and elastic parameters.

DSWE-Net: A deep learning approach for shear wave elastography and lesion segmentation using single push acoustic radiation force

Ultrasound-based non-invasive elasticity imaging modalities have received significant consideration for tissue characterization over the last few years. Though substantial advances have been made, the conventional Shear Wave Elastography (SWE) methods still suffer from poor image quality in regions far from the push location, particularly those which rely on single focused ultrasound push beam to generate shear waves. In this study, we propose DSWE-Net, a novel deep learning-based approach that is able to construct Young's modulus maps from ultrasonically tracked tissue velocity data resulting from a single acoustic radiation force (ARF) push. The proposed network employs a 3D convolutional encoder, followed by a recurrent block consisting of several Convolutional Long Short-Term Memory (ConvLSTM) layers to extract high-level spatio-temporal features from different time-frames of the input velocity data. Finally, a pair of coupled 2D convolutional decoder blocks reconstructs the modulus image and additionally performs inclusion segmentation by generating a binary mask. We also propose a multi-task learning loss function for end-to-end training of the network with 1260 data samples obtained from a simulation environment which include both bi-level and multi-level phantom structures. The performance of the proposed network is evaluated on 140 synthetic test data and the results are compared both qualitatively and quantitatively with that of the current state of the art method, Local Phase Velocity Based Imaging (LPVI). With an average SSIM of 0.90, RMSE of 0.10 and 20.69 dB PSNR, DSWE-Net performs much better on the imaging task compared to LPVI. Our method also achieves an average IoU score of 0.81 for the segmentation task which makes it suitable for localizing inclusions as well. In this initial study, we also show that our method gains an overall improvement of 0.09 in SSIM, 4.81 dB in PSNR, 2.02 dB in CNR, and 0.09 in RMSE over LPVI on a completely unseen set of CIRS tissue mimicking phantom data. This proves its better generalization capability and shows its potential for use in real-world clinical practice.

Three-dimensional shear wave elastography on conventional ultrasound scanners with external vibration

Two-dimensional (2D) ultrasound shear wave elastography (SWE) has been widely used for soft tissue properties assessment. Given that shear waves propagate in three dimensions (3D), extending SWE from 2D to 3D is important for comprehensive and accurate stiffness measurement. However, implementation of 3D SWE on a conventional ultrasound scanner is challenging due to the low volume rate (tens of Hertz) associated with limited parallel receive capability of the scanner's hardware beamformer. Therefore, we developed an external mechanical vibration-based 3D SWE technique allowing robust 3D shear wave tracking and speed reconstruction for conventional scanners. The aliased shear wave signal detected with a sub-Nyquist sampling frequency was corrected by leveraging the cyclic nature of the sinusoidal shear wave generated by the external vibrator. Shear wave signals from different sub-volumes were aligned in temporal direction to correct time delays from sequential pulse-echo events, followed by 3D speed reconstruction using a 3D local frequency estimation algorithm. The technique was validated on liver fibrosis phantoms with different stiffness, showing good correlation (r = 0.99, p < 0.001) with values measured from a state-of-the-art SWE system (GE LOGIQ E9). The phantoms with different stiffnesses can be well-differentiated regardless of the external vibrator position, indicating the feasibility of the 3D SWE with regard to different shear wave propagation scenarios. Finally, shear wave speed calculated by the 3D method correlated well with magnetic resonance elastography performed on human liver (r = 0.93, p = 0.02), demonstrating the in vivo feasibility. The proposed technique relies on low volume rate imaging and can be implemented on the widely available clinical ultrasound scanners, facilitating its clinical translation to improve liver fibrosis evaluation.

Fast Randomized Singular Value Decomposition-Based Clutter Filtering for Shear Wave Imaging

The mechanical properties of soft tissues can be quantitatively characterized through the estimation of shear wave velocity (SWV) using various motion estimation methods, such as the commonly used block matching (BM) methods. However, such methods suffer from slow computational speed and many tunable parameters. In order to solve these problems, Butterworth filter-based clutter filter wave imaging (BW-CFWI) is recently proposed to detect the mechanical wave propagation by highlighting the tissue velocity induced by mechanical wave, without using any motion estimation methods. In this study, in order to improve the SWV estimation performance of the clutter filter wave imaging (CFWI) method, we propose singular value decomposition (SVD)-based clutter filter for CFWI (SVD-CFWI) and further accelerate it using a randomized SVD (rSVD)-based clutter filter (rSVD-CFWI). Homogeneous phantoms with different Young's moduli are used to investigate the influences of the cutoff order of singular value and iteration time on the performance of SWV estimation. An elasticity phantom with stepped cylindrical inclusions is tested for comparison of rSVD-CFWI, SVD-CFWI, BW-CFWI, and normalized cross-correlation (NCC)-based BM (NCC-BM). The performances of the proposed methods are also evaluated on data acquired from the bicipital muscle in vivo. The results of phantom experiments show that rSVD-CFWI and SVD-CFWI reconstruct SWV maps with improved shape of the inclusions. For the softest inclusion with a diameter of 10.40 mm, the contrast-to-noise ratios (CNRs) between the inclusions and background obtained with rSVD-CFWI (3.78 dB) and SVD-CFWI (3.71 dB) are higher than those obtained with BW-CFWI (0.55 dB) and NCC-BM (0.70 dB). For the stiffest inclusion with a diameter of 10.40 mm, higher CNRs are also achieved by rSVD-CFWI (5.68 dB) and SVD-CFWI (5.07 dB) than by BW-CFWI (2.92 dB) and NCC-BM (2.36 dB). In the in-vivo experiments, more homogeneous SWV maps and smaller standard deviations of SWVs are obtained with rSVD-CFWI and SVD-CFWI than with BW-CFWI and NCC-BM. Besides, RSVD-CFWI has lower computational complexity than SVD-CFWI and NCC-BM and has lower memory space requirement than SVD-CFWI. The computational speed of rSVD-CFWI is comparable to that of BW-CFWI and over 10 times higher than that of SVD-CFWI. Therefore, RSVD-CFWI is demonstrated to be a competitive tool for fast shear wave imaging.

Four-dimensional (4D) phase velocity optical coherence elastography in heterogeneous materials and biological tissue

The variations of mechanical properties in soft tissues are biomarkers used for clinical diagnosis and disease monitoring. Optical coherence elastography (OCE) has been extensively developed to investigate mechanical properties of various biological tissues. These methods are generally based on time-domain data and measure the time-of-flight of the localized shear wave propagations to estimate the group velocity. However, there is considerable information that can be obtained from examining the mechanical properties such as wave propagation velocities at different frequencies. Here we propose a method to evaluate phase velocity, wave velocity at various frequencies, in four-dimensional space (x, y, z, f), called 4D-OCE phase velocity. The method enables local estimates of the phase velocity of propagating mechanical waves in a medium. We acquired and analyzed data with this method from a homogeneous reference phantom, a heterogeneous phantom material with four different excitation cases, and ex vivo porcine kidney tissue. The 3D-OCE group velocity was also estimated to compare with 4D-OCE phase velocity. Moreover, we performed numerical simulation of wave propagations to illustrate the boundary behavior of the propagating waves. The proposed 4D-OCE phase velocity is capable of providing further information in OCE to better understand the spatial variation of mechanical properties of various biological tissues with respect to frequency.

Single-Cell Photoacoustic Microrheology

Rheological properties, such as elasticity and viscosity, are fundamental biomechanical parameters that are related to the function and pathological status of cells and tissues. In this paper, an innovative photoacoustic microrheology (PAMR), which utilized the time and phase characteristics of photoacoustic (PA) response, was proposed to extract elastic modulus and viscosity. The feasibility and accuracy of the method were validated by tissue-mimicking agar-gelatin phantoms with various viscoelasticity values. PAMR realized single cell elasticity and viscosity mappings on the adipocyte and myocyte with micrometer scale. In clinical samples, normal blood cells and iron deficiency anemia cells were successfully distinguished due to their various rheological properties. This method expands the scope of conventional PA imaging and opens new possibilities for developing microrheological technology, prefiguring great clinical potential for interrogating mechanocellular properties.

Fast Local Phase Velocity-Based Imaging: Shear Wave Particle Velocity and Displacement Motion Study

Fast and precise noninvasive evaluation of tissue mechanical properties is of high importance in ultrasound shear wave elastography. In this study, we present an updated, faster version of the local phase velocity-based imaging (LPVI) method used to create images of local phase velocity in soft tissues. The updated LPVI implementation uses 1-D Fourier transforms in spatial dimensions separately in comparison to its original implementation. A directional filter is applied upon the shear wave field to extract the left-to-right (LR) and right-to-left (RL) propagating shear waves. A local shear wave phase velocity map is recovered based on both LR and RL waves. Finally, a 2-D shear wave velocity map is reconstructed by combining the LR and RL phase velocity maps. LPVI performance for shear wave displacement and velocity-wave motion data is examined. A study of LPVI used for only one data acquisition with multiple focused ultrasound push beams is presented. The lesion placement with respect to the pushes and whether two sequential pushes provided different results from two simultaneous radiation force pushes was investigated. The addition of white Gaussian noise to the wave motion data was also tested to examine the LPVI method's performance. Robust and accurate shear wave phase velocity maps are reconstructed using the proposed LPVI method using numerical tissue-mimicking phantoms with inclusions. Results from the numerical phantom study showed that the reconstructed, asymmetric inclusions, for various axial locations, are better preserved for shear wave particle velocity signals compared with particle displacement motion data.

Two-Point Frequency Shift Method for Shear Wave Attenuation Measurement

Ultrasound shear wave elastography (SWE) is an increasingly used noninvasive modality for quantitative evaluation of tissue mechanical properties. SWE typically uses an acoustic radiation force to produce laterally propagating shear waves that are tracked in the spatial and temporal domains, in order to obtain the wave velocity. One of the ways to study the viscoelasticity is through studying the shear wave phase velocity dispersion curves. Shear wave attenuation can be also characterized in viscoelastic tissues with methods that use multiple lateral data samples. In this article, we present an alternative method for measuring the shear wave attenuation without using a rheological model two-point frequency shift (2P-FS). The technique uses information related to the amplitude spectra FS of shear waves measured at only two lateral locations. The theoretical basis for the 2P-FS is derived and validated. We examined how the first signal position and the distance between the two locations affect the shear wave attenuation estimation in the 2P-FS method. We tested this new method on digital phantom data created using the local interaction simulation approach (LISA) in viscoelastic media. Moreover, we tested data acquired from custom-made tissue-mimicking viscoelastic phantom experiments and ex vivo porcine liver measurements. We compared results from the 2P-FS method with the other two techniques used for assessing a shear wave attenuation: the FS-based method and the attenuation-measuring ultrasound shear wave elastography (AMUSE) technique. In addition, we evaluated the 2P-FS algorithm with different levels of added white Gaussian noise to the shear wave particle velocity using numerical phantoms. Tests conducted showed that the 2P-FS method gives robust results based on only two measurements and can be used to measure attenuation of viscoelastic soft tissues.

Two Point Method For Robust Shear Wave Phase Velocity Dispersion Estimation of Viscoelastic Materials

Ultrasound shear wave elastography (SWE) is an imaging modality used for noninvasive, quantitative evaluation of tissue mechanical properties. SWE uses an acoustic radiation force to produce laterally propagating shear waves that can be tracked in spatial and temporal domains in order to obtain the wave velocity. One of the ways to study the viscoelasticity is through examining the shear wave velocity dispersion curves. In this paper, we present an alternative method to two-dimensional Fourier transform (2D-FT). Our unique approach (2P-CWT) considers shear wave propagation measured in two lateral locations only and uses wavelet transformation analysis. We used the complex Morlet wavelet function as the mother wavelet to filter two shear waves at different locations. We examined how the first signal position and the distance between the two locations affect the shear wave velocity dispersion estimation in 2P-CWT. We tested this new method on a digital phantom data created using the local interaction simulation approach (LISA) in viscoelastic media with and without added white Gaussian noise to the wave motion. Moreover, we tested data acquired from custom made tissue mimicking viscoelastic phantom experiments and ex vivo porcine liver measurements. We compared results from 2P-CWT with the 2D-FT technique. 2P-CWT provided dispersion curves estimation with lower errors over a wider frequency band in comparison to 2D-FT. Tests conducted showed that the two-point technique gives results with better accuracy in simulation results and can be used to measure phase velocity of viscoelastic materials.