Power spectral strain estimators in elastography

Robust Estimation of Displacement in Real-Time Freehand Ultrasound Strain Imaging

We present a novel and efficient approach for robust estimation of displacement in real-time strain imaging for freehand ultrasound elastography by utilizing pre- and post-deformation ultrasound images. We define a quality factor for image lines and find the line with the highest value of quality factor to serve as the seed line for generating the displacement map. We also develop an analytical framework for coarse-to-fine displacement estimation, obtain an initial estimate of the seed line's displacement with subsample precision, and propagate it to the entire image to obtain a high quality strain image. Our fast strategy for estimating the seed line's displacement enables us to enhance the robustness without sacrificing the speed by identifying a new seed line when the quality falls below a given threshold. This is more efficient than the existing approaches that utilize multiple seed lines to improve robustness. Simulations, phantom experiments, and clinical studies show high signal-to-noise-ratio and contrast-to-noise-ratio values in our method for a wide range of average strain levels (1%-10%). Phantom experiments also demonstrate that our method is robust against corrupt and decorrelated data. Our method is superior to the existing real-time methods as it can produce high-quality strain images for up to 10% average strain levels at the rate of 20 frames/s on conventional CPUs.

Estimation of Strain Elastography from Ultrasound Radio-Frequency Data by Utilizing Analytic Gradient of the Similarity Metric

Most strain imaging techniques follow a pipeline strategy: in the first step, tissue displacement is estimated from radio-frequency (RF) frames, and in the second step, a spatial derivative operation is applied. There are two main issues that arise from this framework. First, the gradient operation amplifies noise, and therefore, smoothing techniques have to be adopted. Second, strain estimation does not exploit the original RF data. It rather relies solely on the noisy displacement field. In this paper, a novel technique is proposed that utilizes both the displacement field and the RF frames to accurately obtain the strain estimates. The normalized cross correlation (NCC) metric between two corresponding windows around the samples of the pre- and post-compressed images is employed to generate a dissimilarity measurement. The derivative of NCC with respect to the strain is analytically derived using the chain rule. This allows an efficient minimization of the dissimilarity metric with respect to the strain using the gradient descent optimization technique. The effectiveness of the proposed method is investigated through simulation data, phantom experiments, and in vivo patient data. The experimental results show that exploiting the information in RF data significantly improves the strain estimates.

Elastography: Imaging the elastic properties of soft tissues with ultrasound

Elastography is a method that can ultimately generate several new kinds of images, called elastograms. As such, all the properties of elastograms are different from the familiar properties of sonograms. While sonograms convey information related to the local acoustic backscatter energy from tissue components, elastograms relate to its local strains, Young's moduli or Poisson's ratios. In general, these elasticity parameters are not directly correlated with sonographic parameters, i.e. elastography conveys new information about internal tissue structure and behavior under load that is not otherwise obtainable. In this paper we summarize our work in the field of elastography over the past decade. We present some relevant background material from the field of biomechanics. We then discuss the basic principles and limitations that are involved in the production of elastograms of biological tissues. Results from biological tissues in vitro and in vivo are shown to demonstrate this point. We conclude with some observations regarding the potential of elastography for medical diagnosis.

Comparison of windowing effects on elastography images: Simulation, phantom and in vivo studies

In this paper, we have evaluated the use of smooth windows for ultrasound elastography. In ultrasound elastography, local tissue strain is estimated using operations such as cross-correlation on local segments of RF data. In this process, local data segments are selected by multiplying the RF data by a rectangular window. Such data truncation causes non-ideal spectral behavior, which can be mitigated by using smooth windows. Accordingly, we hypothesize that the use of smooth windows may improve the elastographic signal-to-noise ratio (SNRe) and contrast-to-noise ratio (CNRe) of strain images. The effects of using smooth windows have not been fully characterized for time-domain strain estimators. Thus, we have compared the elastographic performance of rectangular, Hanning, Gaussian, and Chebyshev windows used in conjunction with cross-correlation based algorithm and adaptive stretching algorithm using finite element method (FEM) simulation, experimental phantom, and in vivo data. Smooth windows are found to improve the SNRe by up to 3.94 for FEM data and by up to 1.76 for phantom data which represent 76% and 60.52% improvements, respectively. CNRe improves by up to 12.23 for FEM simulated data and by up to 4.28 for phantom data which represent 213.07% and 248.2% improvements, respectively. Mean structural similarity (MSSIM) was used for assessing the image perceptual quality and smooth windows improved it by up to 0.22 (85.98% improvement) for simulated data. We have evaluated these parameters at 1-6% applied strains for the experimental phantom and at 1%, 2%, 4%, 6%, 8%, and 12% applied strains for FEM simulation. We observed a maximum deterioration in axial resolution of 0.375 mm (which is on the order of the wavelength, 0.3mm) due to smooth windows. "Salt-and-pepper" noise from false-peak errors has also been reduced. Smooth windows increased the lesion-to-background contrast (by increasing the CNRe by 213.07%) of a low contrast lesion (10-dB). For the in vivo cases, use of smooth windows resulted in better depiction of lesions, which is important for lesion classification. In this work, we have used an ATL Ultramark 9 scanner with an L10-5 (7.5 MHz) probe for the phantom experiment and a Sonix SP500 scanner with an L14-5/38 probe (10 MHz) for in vivo data collection.

Ultrasound Elastography for Estimation of Regional Strain of Multilayered Hydrogels and Tissue-Engineered Cartilage

Tissue-engineered (TE) cartilage constructs tend to develop inhomogeneously, thus, to predict the mechanical performance of the tissue, conventional biomechanical testing, which yields average material properties, is of limited value. Rather, techniques for evaluating regional and depth-dependent properties of TE cartilage, preferably non-destructively, are required. The purpose of this study was to build upon our previous results and to investigate the feasibility of using ultrasound elastography to non-destructively assess the depth-dependent biomechanical characteristics of TE cartilage while in a sterile bioreactor. As a proof-of-concept, and to standardize an assessment protocol, a well-characterized three-layered hydrogel construct was used as a surrogate for TE cartilage, and was studied under controlled incremental compressions. The strain field of the construct predicted by elastography was then validated by comparison with a poroelastic finite-element analysis (FEA). On average, the differences between the strains predicted by elastography and the FEA were within 10%. Subsequently engineered cartilage tissue was evaluated in the same test fixture. Results from these examinations showed internal regions where the local strain was 1-2 orders of magnitude greater than that near the surface. These studies document the feasibility of using ultrasound to evaluate the mechanical behaviors of maturing TE constructs in a sterile environment.

Direct and gradient-based average strain estimation by using weighted nearest neighbor cross-correlation peaks

In this paper, two novel approaches, gradient-based and direct strain estimation techniques, are proposed for high-quality average strain imaging incorporating a cost function maximization. Stiffness typically is a continuous function. Consequently, stiffness of proximal tissues is very close to that of the tissue corresponding to a given data window. Hence, a cost function is defined from exponentially weighted neighboring pre- and post-compression RF echo normalized cross-correlation peaks in the lateral (for displacement estimation) or in both the axial and the lateral (for direct strain estimation) directions. This enforces a controlled continuity in displacement/strain and average displacement/strain is calculated from the corresponding maximized cost function. Axial stress causes lateral shift in the tissue. Therefore, a 1-D post-compression echo segment is selected by incorporating Poisson's ratio. Two stretching factors are considered simultaneously in gradient-based strain estimation that allow imaging the lesions properly. The proposed time-domain gradient-based and direct-strain-estimation-based algorithms demonstrate significantly better performance in terms of elastographic signal-to-noise ratio (SNRe), elastographic contrast-to-noise ratio (CNRe), peak signal-to-noise ratio (PSNR), and mean structural similarity (MSSIM) than the other reported time-domain gradient-based and direct-strain-estimation techniques in finite element modeling (FEM) simulation and phantom experiments. For example, in FEM simulation, it has been found that the proposed direct strain estimation method can improve up to approximately 2.49 to 8.71, 2.2 to 6.63, 1.5 to 5, and 1.59 to 2.45 dB in the SNRe, CNRe, PSNR, and MSSIM compared with the traditional direct strain estimation method, respectively, and the proposed gradient-based algorithm demonstrates 2.99 to 16.26, 18.74 to 23.88, 3 to 9.5, and 0.6 to 5.36 dB improvement in the SNRe, CNRe, PSNR, and MSSIM, respectively, compared with a recently reported time-domain gradient-based technique. The range of improvement as noted above is for low to high applied strains. In addition, the comparative results using the in vivo breast data (including malignant or benign masses) also show that the lesion size is better defined by the proposed gradient-based average strain estimation technique.

Frequency-domain-based strain estimation and high-frame-rate imaging for quasi-static elastography

In freehand elastography, quasi-static tissue compression is applied through the ultrasound probe, and the corresponding axial strain is estimated by calculating the time shift between consecutive echo signals. This calculation typically suffers from a poor signal-to-noise ratio or from the decorrelation between consecutive echoes resulting from an erroneous axial motion impressed by the operator. This paper shows that the quality of elastograms can be improved through the integration of two distinct techniques in the strain estimation procedure. The first technique evaluates the displacement of the tissue by analyzing the phases of the echo signal spectra acquired during compression. The second technique increases the displacement estimation robustness by averaging multiple displacement estimations in a high-frame-rate imaging system, while maintaining the typical elastogram frame-rate. The experimental results, obtained with the Ultrasound Advanced Open Platform (ULA-OP) and a cyst phantom, demonstrate that each of the proposed methods can independently improve the quality of elastograms, and that further improvements are possible through their combination.

A hybrid CPU-GPGPU approach for real-time elastography

Ultrasound elastography is becoming a widely available clinical imaging tool. In recent years, several real- time elastography algorithms have been proposed; however, most of these algorithms achieve real-time frame rates through compromises in elastographic image quality. Cross-correlation- based elastographic techniques are known to provide high- quality elastographic estimates, but they are computationally intense and usually not suitable for real-time clinical applications. Recently, the use of massively parallel general purpose graphics processing units (GPGPUs) for accelerating computationally intense operations in biomedical applications has received great interest. In this study, we investigate the use of the GPGPU to speed up generation of cross-correlation-based elastograms and achieve real-time frame rates while preserving elastographic image quality. We propose and statistically analyze performance of a new hybrid model of computation suitable for elastography applications in which sequential code is executed on the CPU and parallel code is executed on the GPGPU. Our results indicate that the proposed hybrid approach yields optimal results and adequately addresses the trade-off between speed and quality.

Recent results in nonlinear strain and modulus imaging

We report a summary of recent developments and current status of our team's efforts to image and quantify in vivo nonlinear strain and tissue mechanical properties. Our work is guided by a focus on applications to cancer diagnosis and treatment using clinical ultrasound imaging and quasi-static tissue deformations. We review our recent developments in displacement estimation from ultrasound image sequences. We discuss cross correlation approaches, regularized optimization approaches, guided search methods, multiscale methods, and hybrid methods. Current implementations can return results of high accuracy in both axial and lateral directions at several frames per second.We compare several strain estimators. Again we see a benefit from a regularized optimization approach. We then discuss both direct and iterative methods to reconstruct tissue mechanical property distributions from measured strain and displacement fields. We review the formulation, discretization, and algorithmic considerations that come into play when attempting to infer linear and nonlinear elastic properties from strain and displacement measurements. Finally we illustrate our progress with example applications in breast disease diagnosis and tumor ablation monitoring. Our current status shows that we have demonstrated quantitative determination of nonlinear parameters in phantoms and in vivo, in the context of 2D models and data. We look forward to incorporating 3D data from 2D transducer arrays to noninvasively create calibrated 3D quantitative maps of nonlinear elastic properties of breast tissues in vivo.

Filter-based compounded delay estimation with application to strain imaging

Ultrasonic wave interference produces local fluctuations in both the envelope, known as speckle, and phase of echoes. Furthermore, such fluctuations are correlated in space, and subsequent motion estimation from the envelope and/or phase signal produces patterned, correlated errors. Compounding, or combining information from multiple decorrelated looks, reduces such effects. We propose using a filter bank to create multiple looks to produce a compounded motion estimate. In particular, filtering in the lateral direction is shown to preserve delay estimation accuracy in the filtered sub-bands while creating decorrelation between sub-bands at the expense of some lateral resolution. For Gaussian apodization, we explicitly compute the induced signal decorrelation produced by Gabor filters. Furthermore, it is shown that lateral filtering is approximately equivalent to steering, in which filtered sub-bands correspond to signals extracted from shifted sub-apertures. Field II simulation of a point spread function verifies this claim. We use phase zero and its variants as displacement estimators for our compounded result. A simplified deformation model is used to provide computer simulations of deforming an elastic phantom. Simulations demonstrate root mean square error (RMSE) reduction in both displacement and strain of the compounded result over conventional and its laterally blurred versions. Then we apply the methods to experimental data using a commercial elastic phantom, demonstrating an improvement in strain SNR.

Theoretical limitations of the elastic wave equation inversion for tissue elastography

This article examines the theoretical limitations of the local inversion techniques for the measurement of the tissue elasticity. Most of these techniques are based on the estimation of the phase speed or the algebraic inversion of a one-dimensional wave equation. To analyze these techniques, the wave equation in an elastic continuum is revisited. It is proven that in an infinite medium, harmonic shear waves can travel at any phase speed greater than the classically known shear wave speed, mu/rho, by demonstrating this for a special case with cylindrical symmetry. Hence in addition to the mechanical properties of the tissue, the phase speed depends on the geometry of the wave as well. The elastic waves in an infinite cylindrical rod are studied. It is proven that multiple phase speeds can coexist for a harmonic wave at a single frequency. This shows that the phase speed depends not only on the mechanical properties of the tissue but also on its shape. The final conclusion is that the only way to avoid theoretical artifacts in the elastograms obtained by the local inversion techniques is to use the shear wave equation as expressed in the curl of the displacements, i.e., the rotations, for the inversion.

Quasi-Static Ultrasound Elastography

Elastography is a new imaging modality where elastic tissue parameters related to the structural organization of normal and pathological tissues are imaged. Basic principles underlying the quasi-static elastography concept and principles are addressed. The rationale for elastographic imaging is reinforced using data on elastic properties of normal and abnormal soft tissues. The several orders of magnitude difference between the elastic modulus of normal and abnormal tissues which is the primary contrast mechanism in elastographic imaging underlines the probability of success with this imaging modality. Recent advances enabling the clinical practice of elastographic imaging in real-time on clinical ultrasound systems is also discussed.In quasi-static elastography, radiofrequency echo signals acquired before and after a small (about 1%) of applied deformation are correlated to estimate tissue displacements. Local tissue displacement vector estimates between small segments of the pre- and post-deformation signals are estimated and the corresponding strain distribution imaged. Elastographic imaging techniques are based on the hypothesis that soft tissues deform more than stiffer tissue, and these differences can be quantified in images of the tissue strain tensor or the Young's modulus.Clinical applications of quasi-static elastography have mushroomed over the last decade, with the most commonly imaged areas being the breast, prostate, thyroid, cardiac, treatment monitoring of ablation procedures and vascular imaging applications.

Improving IVUS palpography by incorporation of motion compensation based on block matching and optical flow

Intravascular ultrasound (IVUS) strain imaging of the luminal layer in coronary arteries, coined as IVUS palpography, utilizes conventional radio frequency (RF) signals acquired at 2 different levels of a compressional load. The signals are cross-correlated to obtain the microscopic tissue displacements, which can be directly translated into local strain of the vessel wall. However, (apparent) tissue motion and nonuniform deformation of the vessel wall, due to catheter wiggling, reduce signal correlation and result in invalid strain estimates. Implications of probe motion were studied on the tissue-mimicking phantom. The measured circumferential tissue displacement and level of the speckle decorrelation amounted to 12 degrees and 0.58, respectively, for the catheter displacement of 456 microm. To compensate for the motion artifacts in IVUS palpography, a novel method based on the feature-based scale-space optical flow (OF), and classical block matching (BM) algorithm, were employed. The computed OF vector and BM displacement fields quantify the amount of local tissue misalignment in consecutive frames. Subsequently, the extracted circumferential displacements are used to realign the signals before strain computation. Motion compensation reduces the RF signal decorrelation and increases the number of valid strain estimates. The advantage of applying the motion correction in IVUS palpography was demonstrated in a midscale validation study on 14 in vivo pullbacks. Both methods substantially increase the number of valid strain estimates in the partial and compounded palpograms. Mean relative improvement in the number of valid strain estimates with motion compensation in comparison to one without motion compensation amounts to 28% and 14%, respectively. Implementation of motion compensation methods boosts the diagnostic value of IVUS palpography.

Noninvasive vascular ultrasound elastography applied to the characterization of experimental aneurysms and follow-up after endovascular repair

Experimental and simulation studies were conducted to noninvasively characterize abdominal aneurysms with ultrasound (US) elastography before and after endovascular treatment. Twenty three dogs having bilateral aneurysms surgically created on iliac arteries with venous patches were investigated. In a first set of experiments, the feasibility of elastography to differentiate vascular wall elastic properties between the aneurismal neck (healthy region) and the venous patch (pathological region) was evaluated on six dogs. Lower strain values were found in venous patches (p < 0.001). In a second set of experiments, 17 dogs having endovascular repair (EVAR) by stent graft (SG) insertion were examined three months after SG implantation. Angiography, color Doppler US, examination of macroscopic sections and US elastography were used. The value of elastography was validated with the following end points by considering a solid thrombus of a healed aneurysm as a structure with small deformations and a soft thrombus associated with endoleaks as a more deformable tissue: (1) the correlation between the size of healed organized thrombi estimated by elastography and by macroscopic examinations; (2) the correlation between the strain amplitude measured within vessel wall elastograms and the leak size; and (3) agreement on the presence and size of endoleaks as determined by elastography and by combined reference imaging modalities (angiography + Doppler US). Mean surfaces of solid thrombi estimated with elastography were found correlated with those measured on macroscopic sections (r = 0.88, p < 0.001). Quantitative strain values measured within the vessel wall were poorly linked with the leak size (r = 0.12, p = 0.5). However, the qualitative evaluation of leak size in the aneurismal sac was very good, with a Kappa agreement coefficient of 0.79 between elastography and combined reference imaging modalities. In summary, complementing B-scan and color Doppler, noninvasive US elastography was found to be potentially a relevant tool for aneurismal follow-up after EVAR, provided it allows geometrical and mechanical characterizations of the solid thrombus within the aneurismal sac. This elasticity imaging technique might help detecting potential complications during follows-up subsequent to EVAR.

Reduction of influence of variation in center frequencies of RF echoes on estimation of artery-wall strain

Atherosclerotic change of the arterial wall leads to a significant change in its elasticity. For assessment of elasticity, measurement of arterial wall deformation is required. For motion estimation, correlation techniques are widely used, and we have developed a phase-sensitive correlation method, namely, the phased-tracking method, to measure the regional strain of the arterial wall due to the heartbeat. Although phase-sensitive methods using demodulated complex signals require less computation in comparison with methods using the correlation between RF signals or iterative methods, the displacement estimated by such phase-sensitive methods are biased when the center frequency of the RF echo apparently varies. One of the reasons for the apparent change in the center frequency would be the interference of echoes from scatterers within the wall. In the present study, a method was introduced to reduce the influence of variation in the center frequencies of RF echoes on the estimation of the artery-wall strain when using the phase-sensitive correlation technique. The improvement in the strain estimation by the proposed method was validated using a phantom. The error from the theoretical strain profile and the standard deviation in strain estimated by the proposed method were 12.0% and 14.1%, respectively, significantly smaller than those (23.7% and 46.2%) obtained by the conventional phase-sensitive correlation method. Furthermore, in the preliminary in vitro experimental results, the strain distribution of the arterial wall well corresponded with pathology, i.e., the region with calcified tissue showed very small strain, and the region almost homogeneously composed of smooth muscle and collagen showed relatively larger strain and clear strain decay with respect to the radial distance from the lumen.

Evaluating tissue changes with ultrasound during radiofrequency ablation

The purpose of this study was to estimate tissue changes during radiofrequency (RF) ablation by correlating echo frequency shifts and temperature elevations. Experiments were performed on phantoms (tissue mimicking gel) and in-vitro turkey breast. Heating was performed with a modified RF-ablation system. Intermittent RF was applied and the temperature at the electrode tip was continually measured by an embedded thermocouple. Various voltages (10-30V) were applied to achieve a wide range of temperature elevations between 10 and 80 degrees C and ablation sizes between 5 and 27 mm in width. B-mode images and raw data were acquired every 5 s by a modified ultrasound imaging system. The raw data from each line and frame was processed using an algorithm to measure spectral shifts of the echo signals in the power spectrum. The phantom experiments showed positive frequency shifts as the temperature rose, with dependency on the heating rate. A linear relationship (R(2) > 0.96) was found between the RF-applied voltage and the width of the heated area, defined by frequency changes larger than 0.05 MHz. In-vitro experiments showed a correlation (R(2) = 0.84) between the width of the coagulated area and the maximal width of the region with more than 0.12 MHz frequency shifts, but a lower correlation (R(2) = 0.4) between the width of the coagulated area and the temperature elevation. In conclusion, correlation was found between echo frequency shifts and temperature elevations and between echo frequency shifts and the width of the ablated area during intermittent RF ablation. Our results suggest that, with further refinement and validation, ultrasound could be used to measure RF heating and its induced coagulation.

Angular strain estimation method for elastography

In the conventional cross-correlation-based strain estimation, there is a trade-off between the interpolation accuracy and the computational requirement. On the other hand, the autocorrelation-based method does not need interpolation, but it cannot estimate the wide range of displacements for elastography. We have developed a new strain estimator, called the angular strain estimation method, which does not need any interpolation and can estimate strain without restricting the range of displacements. The new method estimates strain utilizing complex correlation between correlated ultrasound signals from pre-and post-compression frames. From simulation and experiments, we found that the angular strain estimation method improves the accuracy and strain image quality compared to the conventional strain estimator using cross correlation with interpolation. Furthermore, it is computationally efficient and can be readily incorporated in ultrasound machines for rea -time elastography.

Direct phase-based strain estimator for ultrasound tissue elasticity imaging

Palpation has been widely used to detect hard tumorous tissues surrounded by softer normal tissues. The goal of ultrasound tissue elasticity imaging is to extract information regarding tissue stiffness that is closely related to pathology. For this tissue elasticity imaging, compression is applied first, and the amount of resulting tissue deformation or strain needs to be estimated. Traditionally, strain estimators aim to accurately derive tissue displacements between pre- and post-compression and compute strain from the displacements. However, the displacement can be as large as a thousand times of strain for typical compression levels used in ultrasound elasticity imaging. Error in displacement estimation leads to a large variance in strain, thus resulting in poor signal to noise ratio for the estimated strain. We have developed a novel strain estimator that directly estimates strain from the phase of temporal and spatial correlation instead of estimating small strain from large displacements. SNRe (signal to noise ratio of elastogram) and CNRe (contrast to noise ratio of elastogram) using the direct strain estimator are at least three times and six times larger than that using conventional displacement-based strain estimators, respectively. These results indicate that the direct strain estimator can significantly improve accuracy and lesion detectability in ultrasound elasticity imaging. In addition, the direct strain estimator is computationally efficient compared to conventional estimators, thus enabling the realtime implementation and clinical use of this new ultrasound imaging mode.

Assessment of myocardial regional strain and strain rate by tissue tracking in B-mode echocardiograms

To date, established ultrasonic methods for myocardial regional deformation recovery are based on the Doppler effect, which has inherent limitations restricting its accuracy and use. The reported time domain methods show in vivo insufficient accuracy. A novel approach is elaborated mimicking the human observer who reaches robust diagnosis upon the B-mode data. In a region-of-interest (ROI), acoustic markers stable for tracking are selected. A weighting index presenting the quality of tracking of each marker is used for spatial polynomial fitting. For the feasibility study, a simple straight ROI was selected, which matches the septum. A thorough proof of concept is provided by comparing with a gold standard method and by applying the method to clinical datasets. The peak systolic longitudinal strains of 12 normals were -15% + -2.3% and, of 12 patients with a light-to-mild dysfunction of the apical-septal segment, they were -9% + -0.8% (p < 0.05). Enhancements of the method using spline fitting are introduced.

Comparison of shift estimation strategies in spectral elastography

This paper compares the performance of various spectral shift estimators for use in spectral elastography, namely, the normalized cross-correlation (NCC), sum squared difference (SSD) and sum absolute difference (SAD). Simulation and experimental results demonstrate that the spectral SSD-based elastographic method exhibits no marked difference in performance compared to the more computationally costly NCC-based approach, which has conventionally been the preferred estimator in spectral elastography. The spectral SAD-based strain estimator, despite being computationally less burdening, failed to exhibit performance comparable to that of the NCC- and SSD-based techniques. Furthermore, though spectral subsample estimation techniques using a cosine-fit interpolation method outperformed that of the parabolic-fit method in terms of both reduced bias errors and standard deviations, the latter was analyzed in this study due to computational simplicity. The role of spectral density was evaluated without and with parabolic-based subsample interpolation. Based on minimizing computational complexity, it is concluded that a (low density) spectral SSD strain estimator coupled with parabolic-based subsample estimation is the preferred choice for spectral elastography.

Analysis of a hybrid spectral strain estimation technique in elastography

Conventional spectral elastographic techniques estimate strain using cross-correlation methods. Despite promising results, decorrelation effects compromise the accuracy of these techniques and, subsequently, the tissue strain estimates. Since tissue compression in the time-domain corresponds to upscaling in the frequency-domain, decorrelation effects become more pronounced as tissue strains increase and are a fundamental concern in spectral cross-correlation elastography. In this paper, a two-stage hybrid spectral elastographic technique is introduced. For the first stage, an approximated spectral scaling factor (i.e. initial strain estimate) is employed to compensate for bandwidth broadening (due to tissue compression) between pre- and post-compression power spectra pairs. The second stage then estimates any residual strain information using spectral cross-correlation methods due to improper scaling factor selection in the first stage. This novel hybrid spectral elastographic technique was compared to both conventional spectral and adaptive temporal elastographic methods in simulation and experimentation. In addition to demonstrating enhancement in performance over the conventional spectral elastographic technique, the hybrid spectral-based method introduced in this paper is shown to outperform the adaptive temporal-based elastographic approach.

Investigation of parametric spectral estimation techniques for elasticity imaging

Several autoregressive (AR) and autoregressive moving average (ARMA) parametric spectral estimators were evaluated for use in tissue strain estimation. Using both 1-D simulations and in vitro phantom experiments, the performance of these parametric spectral strain estimators were compared against both a nonparametric discrete Fourier transform (DFT) spectral strain estimator and a coherent elastographic technique. Parametric spectral estimator model orders were selected based on a modified strain filter approach. This technique illustrated the trade-offs between different signal-processing parameters and a strain estimator performance measure, namely the area under the strain filter (using applied strain dynamic range of 0.1 to 50%). The Yule-Walker AR spectral strain estimator outperformed all other parametric methods evaluated, but failed to outperform the DFT-based approach. Furthermore, both these spectral strain-estimation techniques exhibit an elastographic signal-to-noise ratio (SNR(e)) and strain estimation dynamic range not achievable using conventional elastography without global stretching.

Theoretical derivation of SNR, CNR and spatial resolution for a local adaptive strain estimator for elastography

Conventional techniques in elastography estimate the axial strain as the gradient of the displacement (time-delay) estimates obtained using cross-correlation of pre- and temporally stretched postcompression radiofrequency (RF) A-line segments. The use of a constant stretch factor for stretching the postcompression A-line is not adequate in the presence of heterogeneous targets that are commonly encountered. This led to the development of several adaptive strain estimation techniques in elastography. Yet, a theoretical framework for the image quality of adaptive strain estimation has not been established. In this work, we develop theoretical expressions for the image quality [measured in terms of the signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR) and spatial resolution] of elastograms obtained using an adaptive strain estimator developed by Alam et al. (1998). We show a linear trade-off between the SNR and axial resolution of the strain elastogram with respect to the window length used for strain estimation. The CNR shows a quadratic tradeoff with the axial resolution with respect to the window length. The SNR, CNR and axial resolution are shown to improve with the ultrasonic bandwidth.

Adaptive spectral strain estimators for elastography

In conventional elastography, internal tissue deformations, induced by external compression applied to the tissue surface, are estimated by cross-correlation analysis of echo signals obtained before and after compression. Conventionally, strains are estimated by computing the gradient of estimated displacement. However, gradient-based algorithms are highly susceptible to noise and decorrelation, which could limit their utility. We previously developed strain estimators based on a frequency-domain (spectral) formulation that were shown to be more robust but less precise compared to conventional strain estimators, In this paper, we introduce a novel spectral strain estimator that estimates local strain by maximizing the correlation between the spectra of pre- and postcompression echo signals using iterative frequency-scaling of the latter; we also discuss a variation of this algorithm that may be computationally more efficient but less precise. The adaptive spectral strain estimator combines the advantages of time- and frequency-domain methods and has outperformed conventional estimators in experiments and 2-D finite-element simulations.

Elastographic imaging of thermal lesions in liver in-vivo using diaphragmatic stimuli

Radiofrequency or microwave ablations are interstitial focal ablative therapies that can be used in a percutaneous fashion for treating tumors in the liver, kidney, and prostate. These modalities provide in situ destruction of tumors. We present a method for in-vivo elastographic visualization of the ablated regions in the liver during and after thermal therapy. In-vivo elastographic imaging uses compressions of the liver due to movement of the diaphragm during the respiratory cycle. Elastography of the liver and other abdominal organs has not been attempted previously due to the difficulty in providing controlled compressions. Gating of the data acquisition to the respiratory waveform would provide access to data where the compression increments are similar in both magnitude and direction, thereby enabling reproducible imaging of the thermal lesion or tumor. Comparison of elastograms with gross-pathology of ablated tissue illustrates the correspondence between elastographic image features and pathology. Ultrasound is routinely used to guide the rf ablation procedure, so the same imaging system could be used for elastographic imaging. Since the technique utilizes physiological motion of the diaphragm due to respiration, it may also be employed in the visualization of cancerous tumors in the liver.

A zero-crossing strain estimator for elastography

A novel zero-crossing tracking strain estimator (ZCT) has been developed for elastography. This technique is based on tracking the zero-crossings between the pre- and postcompression A-lines, and does not require global or adaptive A-line stretching. For multicompression elastography, ZCT can be implemented as a tracking scheme, where a temporal track of the zero-crossings between successive radiofrequency (RF) A-lines is obtained, or as an averaging scheme, where a cumulation of the interframe strains is performed, to yield high elastographic signal-to-noise ratio (SNR). Other advantages of the scheme include fast processing and its potential to be implemented in hardware. The limitations of the technique are the need for small compression steps due to lack of robustness when large compression steps (> 3% applied compression) are used. Simulations and experiments were performed to illustrate its utility as an alternative strain-estimation technique. This technique provides lower SNR but higher contrast-to-noise ratio (CNR) than the conventional strain-estimation techniques in elastography.

Elastography: Imaging the elastic properties of soft tissues with ultrasound

Elastography is a method that can ultimately generate several new kinds of images, called elastograms. As such, all the properties of elastograms are different from the familiar properties of sonograms. While sonograms convey information related to the local acoustic backscatter energy from tissue components, elastograms relate to its local strains, Young's moduli or Poisson's ratios. In general, these elasticity parameters are not directly correlated with sonographic parameters, i.e. elastography conveys new information about internal tissue structure and behavior under load that is not otherwise obtainable. In this paper we summarize our work in the field of elastography over the past decade. We present some relevant background material from the field of biomechanics. We then discuss the basic principles and limitations that are involved in the production of elastograms of biological tissues. Results from biological tissues in vitro and in vivo are shown to demonstrate this point. We conclude with some observations regarding the potential of elastography for medical diagnosis.

Analysis of an adaptive strain estimation technique in elastography

Elastography is based on the estimation of strain due to tissue compression or expansion. Conventional elastography involves computing strain as the gradient of the displacement (time-delay) estimates between gated pre- and postcompression signals. Uniform temporal stretching of the postcompression signals has been used to reduce the echo-signal decorrelation noise. However, a uniform stretch of the entire postcompression signal is not optimal in the presence of strain contrast in the tissue and could result in loss of contrast in the elastogram. This has prompted the use of local adaptive stretching techniques. Several adaptive strain estimation techniques using wavelets, local stretching and iterative strain estimation have been proposed. Yet, a quantitative analysis of the improvement in quality of the strain estimates overconventional strain estimation techniques has not been reported. We propose a two-stage adaptive strain estimation technique and perform a quantitative comparison with the conventional strain estimation techniques in elastography. In this technique, initial displacement and strain estimates using global stretching are computed, filtered and then used to locally shift and stretch the postcompression signal. This is followed by a correlation of the shifted and stretched postcompression signal with the precompression signal to estimate the local displacements and hence the local strains. As proof of principle, this adaptive stretching technique was tested using simulated and experimental data.

Estimating the elastographic signal-to-noise ratio using correlation coefficients

In conventional elastography, strain is estimated from the gradient of the displacement (time-delay) estimates. The displacement estimates involve estimating the peak location of the cross-correlation function between matching pre- and post-compression A-lines. Bias errors in estimating the peak location of the cross-correlation function, amplified by the gradient operation on the displacement estimates (needed for the computation of the strain), could result in values of elastographic signal-to-noise ratio (SNR(e)) that exceed the theoretical upper bounds, thereby hindering a consistent interpretation of this parameter. These algorithmic errors have not been accounted for by the theory. We propose the use of the measured correlation coefficients in the theoretical SNR(e) expressions to estimate the SNR(e), rather than computing them directly from the elastograms. This methodology results in values of SNR(e) that are lower than the theoretical upper bounds, thereby avoiding the problems associated with computing SNR(e) directly from the elastograms. Using simulated models of uniformly elastic phantoms, a proof of principle of such an SNR(e) measure is shown.

Ultrasound monitoring of temperature change during radiofrequency ablation: preliminary in-vivo results

Radiofrequency (RF) ablation is an interstitial focal ablative therapy that can be used in a percutaneous fashion and permits in situ destruction of hepatic tumors. However, local tumor recurrence rates after RF ablative therapy are as high as 34% to 55%, which may be due in part to the inability to monitor accurately temperature profiles in the tissue being ablated, and to visualize the subsequent zone of necrosis (thermal lesion) formed. The goal of the work described in this paper was to investigate methods for the real-time and in vivo monitoring of the spatial distribution of heating and temperature elevation to achieve better control of the degree of tissue damage during RF ablation therapy. Temperature estimates are obtained using a cross-correlation algorithm applied to RF ultrasound (US) echo signal data acquired at discrete intervals during heating. These temperature maps were used to display the initial temperature rise and to continuously update a thermal map of the treated region. Temperature monitoring is currently performed using thermosensors on the prongs (tines) of the RF ablation probe. However, monitoring the spatial distribution of heating is necessary to control the degree of tissue damage produced.

Ultrasonic properties of random media under uniaxial loading

Acoustic properties of two types of soft tissue-like media were measured as a function of compressive strain. Samples were subjected to uniaxial strains up to 40% along the axis of the transducer beam. Measurements were analyzed to test a common assumption made when using pulse-echo waveforms to track motion in soft tissues--that local properties of wave propagation and scattering are invariant under deformation. Violations of this assumption have implications for elasticity imaging procedures and could provide new opportunities for identifying the sources of backscatter in biological media such as breast parenchyma. We measured speeds of sound, attenuation coefficients, and echo spectra in compressed phantoms containing randomly positioned scatterers either stiffer or softer than the surrounding gelatin. Only the echo spectra of gel media with soft scatterers varied significantly during compression. Centroids of the echo spectra were found to be shifted to higher frequencies in proportion to the applied strain up to 10%, and increased monotonically up to 40% at a rate depending on the scatterer size. Centroid measurements were accurately modeled by assuming incoherent scattering from oblate spheroids with an eccentricity that increases with strain. While spectral shifts can be accurately modeled, recovery of lost echo coherence does not seem possible. Consequently, spectral variance during compression may ultimately limit the amount of strain that can be applied between two data fields in heterogeneous media such as lipid-filled tissues. It also appears to partially explain why strain images often produce greater echo decorrelation in tissues than in commonly used graphite-gelatin test phantoms.

Direct strain estimation in elastography using spectral cross-correlation

Spectral estimation of tissue strain has been performed previously by using the centroid shift of the power spectrum or by estimating the variation in the mean scatterer spacing in the spectral domain. The centroid shift method illustrates the robustness of the direct, incoherent strain estimator. In this paper, we present a strain estimator that uses spectral cross-correlation of the pre- and postcompression power spectrum. The centroid shift estimator estimates strain from the mean center frequency shift, while the spectral cross-correlation estimates the shift over the entire spectrum. Spectral cross-correlation is shown to be more sensitive to small shifts in the power spectrum and, thus, provides better estimation for smaller strains when compared to the spectral centroid shift. Spectral cross-correlation shares all the advantages gained using the spectral centroid shift, in addition to providing accurate and precise strain estimation for small strains. The variance and noise properties of the spectral strain estimators quantified by their respective strain filters are also presented.

Elastography--the movement begins

The advent of real-time ultrasound in the 1970s, together with a growing interest in tissue characterization, led to a number of investigators using the nature of tissue motion to distinguish healthy from diseased tissue. Our group at the (then) Ultrasonics Institute demonstrated the use of phase methods for detecting very small tissue motions, using natural stimuli. The method could also be applied in the lag (autocorrelation) domain to directly measure the amount of deformation to high accuracy. This method was also applied to measuring the amount of dilatation of blood vessels using both conventional and intravascular ultrasound. A basic limitation of these techniques was the poor spatial resolution, and quasistatic methods soon replaced this method of measuring tissue deformation. However, a new way of assessing the health of tissues had been established.

Spectral estimators in elastography

Like velocity, strain induces a time delay and a time scaling to the received signal. Elastography typically uses time delay techniques to indirectly (i.e. via the displacement estimate) measure tissue strain induced by an applied compression, and considers time scaling as a source of distortion. More recently, we have shown that the time scaling factor can also be spectrally estimated and used as a direct measure of strain. Strain causes a Doppler-like frequency shift and a change in bandwidth of the bandpass power spectrum of the echo signal. Two frequency shift strain estimators are described that have been proven to be more robust but less precise when compared to time delay estimators, both in simulations and experiments. The increased robustness is due to the insensitivity of the spectral techniques to phase decorrelation noise. In this paper we discuss and compare the theoretical and experimental findings obtained with traditional time delay estimators and with the newly proposed spectral methods.

Shear strain estimation and lesion mobility assessment in elastography

Elastography typically measures and images the normal strain component along the insonification/compression axis, i.e., in the axial direction. We have recently shown that, by using interpolation and cross-correlation methods of transversely displaced RF echo segments, it is possible to measure and image displacement and strain transversely to the beam with good precision. This enables the estimation and imaging of all three principal normal strain components. Generally, motion in a direction other than that in which strain is estimated may result in decorrelation noise, severely corrupting the estimates. Therefore, a correction method is applied to correct the displacement and strain estimates for decorrelating motion. In this paper, we show how corrected displacement estimates can also be used to estimate and image the shear strain components. This may allow us to identify regions of decorrelation noise in the normal strain measurement that are due to shear strain. Shear strain estimates provide supplementary information, which can characterize different tissue elements based on their mobility. In the case of breast lesions, low mobility is related to malignancy. Following an in vivo case, we show with 2D simulations how assessment of tumor mobility can be achieved with shear strain estimation.