Shear Modulus Imaging Research Articles

Shear complex modulus imaging utilizing frequency combination in the least mean square/algebraic Helmholtz inversion

Shear complex modulus imaging utilizing frequency combination in the least mean square/algebraic Helmholtz inversion

Model-Based Quantitative Elasticity Reconstruction Using ADMM.

We introduce two model-based iterative methods to obtain shear modulus images of tissue using magnetic resonance elastography. The first method jointly finds the displacement field that best fits tissue displacement data and the corresponding shear modulus. The displacement satisfies a viscoelastic wave equation constraint, discretized using the finite element method. Sparsifying regularization terms in both shear modulus and displacement are used in the cost function minimized for the best fit. The second method extends the first method for multifrequency tissue displacement data. The formulated problems are bi-convex. Their solution can be obtained iteratively by using the alternating direction method of multipliers. Sparsifying regularizations and the wave equation constraint filter out sensor noise and compressional waves. Our methods do not require bandpass filtering as a preprocessing step and converge fast irrespective of the initialization. We evaluate our new methods in multiple in silico and phantom experiments, with comparisons with existing methods, and we show improvements in contrast to noise and signal-to-noise ratios. Results from an in vivo liver imaging study show elastograms with mean elasticity comparable to other values reported in the literature.

Two-dimensional complex shear modulus imaging of soft tissues by integration of Algebraic Helmoltz Inversion and LMS filter into dealing with noisy data: a simulation study.

Elasticity and viscosity of soft tissues can be obtained from the complex shear modulus imaging (CSMI). CSMI is often used not only to investigate the structure of tissues but also to detect tumors in tissues. One of the most popular ways to categorize the methods used in CSMI is into quasi-static and dynamic methods. In the dynamic method, a force excitation is used to create the shear wave propagation, and the particle velocities are measured to extract their amplitude and phase at spatial locations. These parameters are then employed to directly or indirectly estimate the Complex Shear Modulus (CSM) represented by elasticity and viscosity. Algebraic Helmholtz Inversion (AHI) algorithm provides the direct estimation of CSM using the Finite Difference Time Domain (FDTD) technique. The limitation of this method, however, is that the noise generated from measuring the particle velocity strongly degrades the accuracy of the estimation. To overcome this problem, we proposed in this paper an adaptive AHI (AAHI) algorithm that offers a good performance in CSMI with a mean error of 2.06%.

Improving three-dimensional mechanical imaging of breast lesions with principal component analysis.

Elastography has emerged as a new tool for detecting and diagnosing many types of diseases including breast cancer. To date, most clinical applications of elastography have utilized two-dimensional strain images. The goal of this paper is to present a new quasi-static elastography technique that yields shear modulus images in three dimensions. An automated breast volume scanner was used to acquire ultrasound images of the breast as it was gently compressed. Cross-correlation between successive images was used to determine the displacement within the tissue. The resulting displacement field was filtered of all but compressive motion through principal component analysis. This displacement field was used to infer spatial distribution of shear modulus by solving a 3D elastic inverse problem. Three dimensional shear modulus images of benign breast lesions for two subjects were generated using the techniques described above. It was found that the lesions were visualized more clearly in images generated using the displacement data de-noised through the use of principal components. We have presented experimental and algorithmic techniques that lead to three-dimensional imaging of shear modulus using quasi-static elastography. This work demonstrates feasibility of this approach, and lays the foundation for images of other, more informative, mechanical parameters.

VISCOELASTIC MODULUS RECONSTRUCTION USING TIME HARMONIC VIBRATIONS

This paper presents a new iterative reconstruction method to provide high-resolution images of shear modulus and viscosity via the internal measurement of displacement fields in tissues. To solve the inverse problem, we compute the Frechet derivatives of the least-squares discrepancy functional with respect to the shear modulus and shear viscosity. The proposed iterative reconstruction method using this Fr´echet derivative does not require any differentiation of the displacement data for the full isotropic linearly viscoelastic model, whereas the standard algebraic inversion method requires at least double differentiation. Because the minimization problem is ill-posed and highly nonlinear, this adjoint-based optimization method needs a very well-matched initial guess. We find a good initial guess. For a well-matched initial guess, numerical experiments show that the proposed method considerably improves the quality of the reconstructed viscoelastic images.

On the use of local speckle field as a correction factor for shear modulus estimates based on multiple-track-locations methods

Acoustic-radiation-force impulse (ARFI) imaging for characterization of shear modulus of biological tissues employs either multiple-track-locations (MTL) methods or single-track-location (STL) methods. MTL estimates of shear modulus at different depths suffer from more variability compared to those of STL estimates. Our studies have shown a significant correlation between bias in shear-wave arrival time estimates and local speckle field lateral statistics. We propose using the local speckle field as a surrogate for the unknown bias apparent in MTL shear-wave speed estimates. This local speckle field is determined using a “swept-receive acquisition” that is produced by holding the transmit beam fixed while laterally translating the receive aperture. Application of various lateral weighting functions to the swept-receive image results in an approximate compensation to the tracking bias. In this study, we implement our technique on simulation and experimental data from gelatin phantoms. Additionally, the effect of varying transmit-receive aperture f/# on the accuracy of our compensation method is investigated in simulation. Finally, the quality of compensated MTL shear modulus images are quantified and compared to those of the uncompensated MTL and of STL methods in matched tissue mimicking phantom experiments.

A survey of ultrasound elastography approaches to percutaneous ablation monitoring.

Percutaneous thermal ablation has been widely used as a minimally invasive treatment for tumors. Treatment monitoring is essential for preventing complications while ensuring treatment efficacy. Mechanical testing measurements on tissue reveal that tissue stiffness increases with temperature and ablation duration. Different types of imaging methods can be used to monitor ablation procedures, including temperature or thermal strain imaging, strain imaging, modulus imaging, and shear modulus imaging. Ultrasound elastography demonstrates the potential to become the primary imaging modality for monitoring percutaneous ablation. This review briefly presented the state-of-the-art ultrasound elastography approaches for monitoring radiofrequency ablation and microwave ablation. These techniques were divided into four groups: quasi-static elastography, acoustic radiation force elastography, sonoelastography, and applicator motion elastography. Their advantages and limitations were compared and discussed. Future developments were proposed with respect to heat-induced bubbles, tissue inhomogeneities, respiratory motion, three-dimensional monitoring, multi-parametric monitoring, real-time monitoring, experimental data center for percutaneous ablation, and microwave ablation monitoring.

Shear modulus imaging by direct visualization of propagating shear waves with phase-sensitive optical coherence tomography

We propose an integrated method combining low-frequency mechanics with optical imaging to map the shear modulus within the biological tissue. Induced shear wave propagating in tissue is tracked in space and time using phase-sensitive optical coherence tomography (PhS-OCT). Local estimates of the shear-wave speed obtained from tracking results can image the local shear modulus. A PhS-OCT system remotely records depth-resolved, dynamic mechanical waves at an equivalent frame rate of ∼47 kHz with the high spatial resolution. The proposed method was validated by examining tissue-mimicking phantoms made of agar and light scattering material. Results demonstrate that the shear wave imaging can accurately map the elastic moduli of these phantoms.

탄성 영상법 개발을 위한 유연성 높은 초음파 시스템의 구현

Recently, several ultrasound imaging techniques for tissue characterization have been developed. Among them, ultrasound elastography is regarded as the most promising modality and has been rapidly developed. One of ultrasound elastography techniques is shear modulus imaging. Normal and cancerous tissues show big difference of shear moduli and they have good image contrast. However shear wave elastography requires more complicated hardware and more computations for image reconstruction algorithm. Therefore new efficient techniques are being developed. In this paper, we have developed a very flexible ultrasound system for elastography experiments. The developed system has capabilities to acquire ultrasound RF data of all channels and generate arbitrary ultrasound pulse sequences. It has a huge amount of memories for RF data acquisition and a simple and flexible pulse generator. We have verified the performance of the system showing conventional B-mode images and preliminary results of elastography. The developed system will be used to verify our own reconstruction algorithm and to develop more efficient elastography techniques.

A Simulation study on iterative shear velocity image reconstruction for ultrasound transient elastography

Purpose Ultrasound transient elastography takes images of shear modulus that is strongly associated with pathological and physiological states of biological tissues. Propagating shear wave velocity in the tissue is related to its shear modulus. In this paper, we propose an iterative shear velocity image reconstruction method for ultrasound transient elastography which is robust to the noise and fast in computation.

3-D FDTD simulation of shear waves for evaluation of complex modulus imaging

The Navier equation describing shear wave propagation in 3-D viscoelastic media is solved numerically with a finite differences time domain (FDTD) method. Solutions are formed in terms of transverse scatterer velocity waves and then verified via comparison to measured wave fields in heterogeneous hydrogel phantoms. The numerical algorithm is used as a tool to study the effects on complex shear modulus estimation from wave propagation in heterogeneous viscoelastic media. We used an algebraic Helmholtz inversion (AHI) technique to solve for the complex shear modulus from simulated and experimental velocity data acquired in 2-D and 3-D. Although 3-D velocity estimates are required in general, there are object geometries for which 2-D inversions provide accurate estimations of the material properties. Through simulations and experiments, we explored artifacts generated in elastic and dynamic-viscous shear modulus images related to the shear wavelength and average viscosity.

A hybrid one-step inversion method for shear modulus imaging using time-harmonic vibrations

We propose a hybrid inversion method for imaging the shear modulus μ in tissue-like subjects using internal measurement of the displacement u induced by an external low-frequency mechanical vibrations made on the boundary of the subject. The proposed method is designed to provide high-resolution imaging in a heterogeneous subject, with no need for an iterative procedure, and deal with the intrinsically noisy displacement data. We recover the shear modulus μ by decomposing it into two components: one is for capturing the main feature of μ using a relatively noise-insensitive inversion method, and the other is to correct the residual caused by the quantity ∇μ × ∇u. Numerical simulations show that the proposed method significantly improves reconstructions without requiring boundary conditions.

Calculating tissue shear modulus and pressure by 2D log-elastographic methods

Shear modulus imaging, often called elastography, enables detection and characterization of tissue abnormalities. In this paper the data are two displacement components obtained from successive MR or ultrasound data sets acquired while the tissue is excited mechanically. A 2D plane strain elastic model is assumed to govern the 2D displacement, u. The shear modulus, μ, is unknown and whether or not the first Lamé parameter, λ, is known the pressure p = λ∇ ⋅ u which is present in the plane strain model cannot be measured and is unreliably computed from measured data and can be shown to be an order one quantity in the units kPa. So here we present a 2D log-elastographic inverse algorithm that (1) simultaneously reconstructs the shear modulus, μ, and p, which together satisfy a first-order partial differential equation system, with the goal of imaging μ; (2) controls potential exponential growth in the numerical error and (3) reliably reconstructs the quantity p in the inverse algorithm as compared to the same quantity computed with a forward algorithm. This work generalizes the log-elastographic algorithm in Lin et al (2009 Inverse Problems 25) which uses one displacement component, is derived assuming that the component satisfies the wave equation and is tested on synthetic data computed with the wave equation model. The 2D log-elastographic algorithm is tested on 2D synthetic data and 2D in vivo data from Mayo Clinic. We also exhibit examples to show that the 2D log-elastographic algorithm improves the quality of the recovered images as compared to the log-elastographic and direct inversion algorithms.

Shear Modulus Imaging with Spatially-Modulated Ultrasound Radiation Force

The application of Spatially-Modulated Ultrasound Radiation Force (SMURF) to shear modulus imaging is demonstrated in tissue-mimicking phantoms and porcine liver. Scanning and data acquisition was performed with a Siemens Antares ultrasound scanner and VF7-3 linear array operating at 4.21 MHz. Modulus estimates in uniform phantoms of Zerdine with shear moduli of 5.1 and 12.4 kPa exhibited standard deviations within 6% of the mean value. Zerdine spheres 1 cm in diameter (nominally 2.7, 4.7 and 15 kPa) in a 8 kPa (nominal) background are clearly resolved. Cross sectional images of a soft conical inclusion in a gelatin-based phantom indicate a spatial resolution of approximately 2.5 mm. Images of the shear modulus of an ex-vivo sample of porcine liver tissue show an average value of 3 kPa. A stifflesion induced with 0.5 mL of 10% glutaraldehyde is clearly visible as a region of shear modulus in excess of 10 kPa. A modulus gradient associated with the diffusion of the glutaraldehyde is visible. Two pulse sequences were examined, differing only in the timing of the beams used to generate the shear waves. Details of the beam sequences and subsequent signal processing are presented.

Shear Modulus Decomposition Algorithm in Magnetic Resonance Elastography

Magnetic resonance elastography (MRE) is an imaging modality capable of visualizing the elastic properties of an object using magnetic resonance imaging (MRI) measurements of transverse acoustic strain waves induced in the object by a harmonically oscillating mechanical vibration. Various algorithms have been designed to determine the mechanical properties of the object under the assumptions of linear elasticity, isotropic and local homogeneity. One of the challenging problems in MRE is to reduce the noise effects and to maintain contrast in the reconstructed shear modulus images. In this paper, we propose a new algorithm designed to reduce the degree of noise amplification in the reconstructed shear modulus images without the assumption of local homogeneity. Investigating the relation between the measured displacement data and the stress wave vector, the proposed algorithm uses an iterative reconstruction formula based on a decomposition of the stress wave vector. Numerical simulation experiments and real experiments with agarose gel phantoms and human liver data demonstrate that the proposed algorithm is more robust to noise compared to standard inversion algorithms and stably determines the shear modulus.

Ultrasound estimation of breast tissue biomechanical properties using a similarity-based non-linear optimization approach

The in vivo estimation of tissue elasticity parameters is important for realistic tissue deformation modelling and diagnosis tasks such as cancer mass detection and characterization. Elastography (strain imaging) provides non-quantitative information about tissue stiffness and is becoming well established clinically. Acoustic radiation force imaging, supersonic shear wave imaging and (Young's) modulus imaging are all evolving as quantitative methods. This paper concerns the latter. The established approach to Young's modulus reconstruction involves solving the so-called inverse elasticity problem of recovering elastic parameters by comparing the displacement field from the measurements and the theoretical tissue deformation modelling. In this paper, a new modulus imaging pathway is proposed in which the inverse problem of elasticity reconstruction has been converted into a global optimization problem involving an image similarity measure. This approach is applied to ultrasound images and the tissue elasticity distribution is recovered by adaptively adding new regions based on the local mismatch of the images using a multiscaled split-and-merge approach. For this experimental evaluation of the performance of the proposed method, first synthetic images are used with different Gaussian noise levels. The reconstructed elasticity shows good agreement with the ground-truth. A comparison of the proposed method with a conventional displacement-based method is made using a gelatine phantom. The results using both methods agree remarkably well with the theoretical prediction. A further in vivo study on 19 breast cancer masses was performed. The present method estimated an elasticity contrast of 6.41 ± 0.98 between cancerous tissue and normal tissue, which is consistent with values reported elsewhere in the literature.

Shear modulus imaging with 2-D transient elastography.

In previous works, we have shown that time-resolved 2-D transient elastography is a promising technique for characterizing the elasticity of soft tissues. It involves the measurement of the displacements induced by the propagation of low frequency (LF) pulsed shear waves in biological tissues. In this paper, we present a novel apparatus that contains a LF vibrating device surrounding a linear array of 128 ultrasonic transducers that performs ultrafast ultrasonic imaging (up to 10,000 frames/s) and that is able to follow in real time the propagation of a LF shear wave in the human body. The vibrating device is made of two rods, fixed to electromagnetic vibrators, that produce in the ultrasonic image area a large amplitude shear wave. The geometry has been chosen both to enhance the sensitivity and to create a quasi linear shear wave front in the imaging plane. An inversion algorithm is used to recover the shear modulus map from the spatio-temporal data, and the first experimental results obtained from tissue-equivalent materials are presented.

Imaging the permeability structure within the near-surface sediments by acoustic crosswell tomography

The geotechnical structures of permeability, porosity and shear strength within the near-surface sediments of Tokyo area are imaged by analytically inverting the acoustic wave velocity and attenuation fields. The acoustic velocity and attenuation fields were previously measured by a Pseudo Random Binary Sequence (PRBS)-based crosswell acoustic tomography device. A quadratic equation of permeability derived from the Biot theory is used for the permeability inversion of the measured acoustic velocity–attenuation fields. The porosity and shear modulus images are also extracted from the velocity and attenuation fields using the newly derived quadratic dispersion equation and an empirical shear modulus–porosity–depth of burial relation. The acoustically measured images of permeability, porosity and shear modulus are favorably compared with the engineering tests performed on the cores and boreholes.

超音波盃計測に基づく絹織ずり弾性定数イメージング法の有効性

For various soft tissues (e.g., breast, liver, etc.), we are developing the ultrasonic strain measurement-based shear modulus reconstruction/imaging technique. To clarify the limitation of this technique as the diagnostic tool, together with improving the technique we are collecting clinical shear modulus images. Furthermore, we are applying the technique as the monitoring technique for the effectiveness of chemical therapy (e.g., anticancer drug, ethanol) and thermal therapy (e.g., rf electromagnetic wave, HIFU, etc.). Here, we showed shear modulus images obtained in quasi-real time. Using the conventional Work Station, the quantitative images were obtained on ten seconds order. In particular, by exhibiting the superiority of the shear modulus imaging compared with the simultaneous B-mode imaging, we delineated the effectiveness of the technique as the clinical visualization technique for diagnosis and therapy. For instance, shear modulus value of in vivo human breast carcinoma was significantly high (typical value : 6.33×106 N/m2). Shear modulus images were also obtained on in vivo human liver tissues. On the in vitro calf liver, shear modulus value of electromagnetic wave-induced thermal lesion became about five times higher after cooling down. We believe that this technique is currently available, and yet in the near future this technique will allow the combined diagnosis/therapy system for opening up a novel clinical style.

Imaging the permeability structure within near-surface sediments by acoustic crosswell tomography

Permeability structure within near-surface sediments is imaged by analytically inverting the measured fields of acoustic wave velocity and attenuation. The acoustic velocity and attenuation fields at 1000 Hz were previously measured by a pseudorandom binary sequence (PRBS) based crosswell acoustic tomography device [T. Yamamoto, J. Acoust. Soc. Am. 98, 2235–2248 (1995)]. A quadratic equation of permeability derived from the Biot theory is used for the permeability imaging. The porosity and shear modulus images are also extracted from the velocity and attenuation fields using the newly derived quadratic dispersion equation and an empirical shear modulus porosity depth of burial relation. The acoustically measured images of permeability, porosity, and shear modulus are favorably compared with the engineering tests performed on the cores and boreholes.