Strain Estimation In Elastography Research Articles

A two-step optical flow method for strain estimation in elastography: Simulation and phantom study

Optical flow (OF) method has been used in ultrasound elastography to estimate the strain distribution in tissues. However the bias of strain estimation by OF has previously been shown to be close to 20%. The objective in this paper is to improve the performance of OF-based strain estimation, a two-step OF method with a local warping technique is proposed in this paper. The local warping technique effectively decreases the decorrelation of the signals, and hence improves the performance of strain estimation. Simulations on both homogeneous and heterogeneous models with different strains are performed. Experiments on a heterogeneous tissue-mimicking phantom are also carried out. Simulation results of the homogeneous model show that the two-step OF method reduces the bias of strain estimation from 23.77% to 1.65%, and reduces the standard deviation of strain estimation from 2.9×10−3 to 0.47×10−3. Simulation results of the heterogeneous model shows that the signals-to-noise ratio (SNRe) of strain estimation is improved by 2.1 and 5.3dB in the inclusion and background, respectively, and the contrast-to-noise ratio (CNRe) is improved by 6.8dB. Finally, results of phantom experiments show that, by using the proposed method, the SNRe is increased by 4.0dB and 8.9dB in the inclusion and background, respectively, while the CNRe is increased by 13.1dB. The proposed two-step OF method is thus demonstrated capable of improving the performance of strain estimation in OF-based elastography.

Wavelet de-noising of strain estimates in elastography at high overlap

Object High overlap of data window is essential to improve axial resolution in elastogaphy.However, correlated errors in displacement estimates increase dramatically with the increase of the overlap, and generate the so-called artifacts. This paper presents a wavelet shrinkage de-noising in strain estimates to reduce the worm artifacts at high overlap. Methods Each of axial strain A-lines was decomposed using discrete wavelet transformation up to 3 levels. The high frequency components of every levels of wavelet coefficients were quantified by using soft threshold function according to different adaptive thresholds. Then the discrete wavelet reconstruction were performed to produce a wavelet shrinkage denoised strain line. Results The simulation results illustrated that the presented technique could efficiently denoise worm artifacts and enhance the elastogram performance indices such as elastographic SNRe and CNRe. Elastogram obtained by wavelet denoising had the closest correspondence with ideal strain image. In addition, the results also demonstrated that wavelet shrinkage de-noising applied in strain estimates could obtain better image quality parameters than that apphed in displacement estimates. The elastic phantom experiments also showed the similar elastogram performance improvement. Conclusion Wavelet shrinkage de-noising can efficiently denoise the worm artifacts noise of elastogram and improve the performance indices of elastogram while maintaining the high axial resolution. Key words: Ultrasound; Elastography; Strain; De-noising; Wavelet transform; Axial resolution; Worm artifacts

Novel Spline-Based Approach for Robust Strain Estimation in Elastography

Robust strain estimation is important in elastography. However, a high signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) are sometimes attained by sacrificing resolution. We propose a least-squares-based smoothing-spline strain estimator that can produce elastograms with high SNR and CNR without significant loss of resolution. The proposed method improves strain-estimation quality by deemphasing displacements with lower correlation in computing strains. Results from finite-element simulation and phantom-experiment data demonstrate that the described strain estimator provides good SNR and CNR without degrading resolution.

Assessing image quality in effective Poisson's ratio elastography and poroelastography: I

The quality of strain estimates in elastography is typically quantified by several quality factors such as the elastographic signal-to-noise ratio, the elastographic contrast-to-noise ratio and the spatial axial and lateral resolutions. While theoretical and simulation works have led to established upper bounds of these image quality factors in axial strain elastography, the performance limitations of lateral strain elastography, effective Poisson's ratio elastography and poroelastography are still not well understood. In this paper, we investigate the theoretical upper bounds of image quality of effective Poisson's ratio elastography starting from an analysis of the performance limitations of axial strain and lateral strain elastography. In the companion paper, we extend our investigation to the theoretical upper bounds of image quality of poroelastography. In both these papers, we also analyse the application of techniques that can be used to improve the performance of these poroelastographic techniques under various experimental conditions.

A novel and robust method for rapid strain estimation in elastography.

In elastography, change in signal shape from tissue deformation and nonaxial tissue motion reduce correlation between the pre- and postcompression echo signals. Appropriate global temporal stretching of postcompression signals can reduce the decorrelation. Adaptive stretching performs a search for the stretch factor that maximizes the correlation between the pre- and postcompression echo signal segments at each data window location. Adaptive stretching is robust but computation intensive. In contrast, global stretching is fast but performs well only in areas where local strains are close to the applied strain. We developed a method that strikes a balance between the speed of global stretching and the performance of adaptive stretching. In this method, several strain maps are computed by performing global stretching with a range of different stretch factors. The area in each computed strain image with strain values closely corresponding to the uniform stretch factor will contain 'good quality' strain estimates. To produce a single elastogram at the end, we identify the strain map with the maximum correlation at each location and the strain value in that strain map at that location is chosen for the combined map. Results from data generated by finite-element simulation and phantom experiments demonstrate that the described strain estimator is significantly less susceptible to signal degradation than conventional strain estimators.

Correction for simultaneous catheter eccentricity and tilt in intravascular elastography.

Intravascular elastography can provide significant new information about the elastic properties of vascular tissue and plaque, useful for the diagnosis of disease and appropriate selection of interventional methods. Knowledge of the plaque composition, vulnerability and its elastic properties can assist the clinician in selecting appropriate interventional techniques. However, several noise sources have to be addressed to obtain quality intravascular elastograms. Misalignment of the vessel lumen and the ultrasound beam can produce erroneous strain estimates in elastography. Errors in the strain estimate are introduced due to the eccentricity and tilt of the intravascular transducer within the vessel lumen. Previous work in this area has provided theoretical expressions for the correction of eccentricity and tilt errors when they occur independent of each other. However, under most imaging conditions, both eccentricity and tilt errors are simultaneously present. In this paper, we extend the theoretical correction factor by accounting for the influence of both of these errors occurring simultaneously in the positioning of the catheter within the vessel lumen.

Trade-offs between the axial resolution and the signal-to-noise ratio in elastography

Elastography involves tracking the ultrasonic A-mode signals before and after mechanical compression of tissue to form a computed image of the local strains undergone by various tissue components. The quality of the strain estimates in elastography is typically quantified using factors such as the elastographic SNR ( SNR e ), contrast-to-noise ratio ( CNR e ), and the spatial resolution. These quality factors depend on the mechanical parameters (such as the applied strain and the boundary conditions), the acoustic parameters (such as the sonographic SNR, the center frequency, and the bandwidth), and the signal-processing parameters (such as the window length and the window separation). Theoretical developments in elastography have established functional relationships between the SNR e and CNR e and these parameters. Similarly, simulations have established empirical relationships between the axial resolution and the acoustic and signal-processing parameters. We find that a trade-off exists between the achievable SNR e ( CNR e ) and the axial resolution in elastography and that the trade-off occurs only with respect to the signal-processing parameters. Theoretical work on the spatial resolution accompanied with simulations and experiments were used to confirm such an observation. The trade-off between the SNR e ( CNR e ) and the resolution was found to be nonlinear, with large improvements in the SNR e being possible at the expense of small reductions in the axial resolution. All the quality factors improve with the acoustic parameters, which suggests the preferred use of transducers with high absolute bandwidths and center frequencies. (E-mail: Jonathan.Ophir@uth.tmc.edu)

Variable uniform stretching for strain estimation in elastography

Variable uniform stretching for strain estimation in elastography

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.

Elastographic imaging

Elastographic imaging

Error analysis in acoustic elastography. I. Displacement estimation.

Correlation between acoustic echo signals obtained before and after application of an external compressional force provides information about the internal deformation of an elastic medium. In this paper, the variance for displacement estimated from an echo data segment and the covariance between two windowed segments that may overlap are derived. The signal and noise spectra are Gaussian and independent. The dependence of the displacement variance on input signal-to-noise ratio (SNRi), time-bandwidth product W, fractional bandwidth Y-1, and the rate of displacement variation with depth a is investigated. The relationship between a and the other experimental parameters is crucial for understanding how signal decorrelation affects displacement error. The expression for displacement variance reduces to the Cramer-Rao lower bound result when a = 0 and W > > 1 for both bandpass and base-band signals. When a not equal to 0 displacement variance increases, and there is an optimal window length at W = square root of 20/a square root of 1 + Y2 for which the displacement variance is minimum. Narrow-band signals produce larger errors than broadband signals for long observation windows when a not equal to 0 and just the opposite when a = 0. Errors are greatest for displacements estimated from the envelope of narrow-band signals. Finally, a general expression for the minimum displacement variance for arbitrary signal and noise spectra is derived as a function of the experimental parameters. These results form a framework for analyzing strain estimates in elastography, the subject of a companion paper.

Error analysis in acoustic elastography. II. Strain estimation and SNR analysis.

Accurate displacement estimates are required to obtain high-quality strain estimates in elastography. In this paper the strain variance is derived from the statistical properties of the displacement field to define a point signal-to-noise ratio for elastography (SNR0). Displacements caused by compressional forces applied along the axis of the transducer beam are modeled by scaling and shifting the axial reflectivity profile of the tissue. The strain variance is given as a function of essential experimental parameters, such as the amount of tissue compression, echo waveform window length, and the amount of window overlap. SNR0 is defined in terms of applied compression and strain variance and normalized by the input signal-to-noise ratio (SNRi) for echo signals, to formulate the performance metric SNR0/SNRi. This quantity characterizes the noise properties, dynamic range, and sensitivity of strain images based on the spatial resolution requirements. The results indicate that low noise, high sensitivity, and limited dynamic range strain images are obtained for high-frequency bandpass signals when the applied strain is small. For large strains, however, one strategy for low-noise strain imaging employs base-band signals to obtain images with large dynamic range but limited peak sensitivity and noise figure. A better strategy includes companding, which eliminates the average strain in the echo signal before cross-correlation to reduce the dynamic range requirement and increase peak sensitivity for strain estimates.

The nonstationary strain filter in elastography: Part I. Frequency dependent attenuation

The accuracy and precision of the strain estimates in elastography depend on a myriad number of factors. A clear understanding of the various factors (noise sources) that plague strain estimation is essential to obtain quality elastograms. The nonstationary variation in the performance of the strain filter due to frequency-dependent attenuation and lateral and elevational signal decorrelation are analyzed in this and the companion paper for the cross-correlation-based strain estimator. In this paper, we focus on the role of frequency-dependent attenuation in the performance of the strain estimator. The reduction in the signal-to-noise ratio ( SNR s ) in the RF signal, and the center frequency and bandwidth downshift with frequency-dependent attenuation are incorporated into the strain filter formulation. Both linear and nonlinear frequency dependence of attenuation are theoretically analyzed. Monte-Carlo simulations are used to corroborate the theoretically predicted results. Experimental results illustrate the deterioration in the precision of the strain estimates with depth in a uniformly elastic phantom. Theoretical, simulation and experimental results indicate the importance of high SNR s values in the RF signals, because the strain estimation sensitivity, elastographic SNR e and dynamic range deteriorate rapidly with a decrease in the SNR s . In addition, a shift in the strain filter toward higher strains is observed at large depths in tissue due to the center frequency downshift.

Theoretical bounds on strain estimation in elastography

Elastography is a technique for the estimation of tissue elasticity that is based on the estimation of strain. Tissue strain can be estimated by finite difference computations of echo time-delay. Echo time-delays are obtained by cross-correlation processing of pre- and post-compression echo signals. Errors in strain estimation can be expressed in terms of the errors in time delay estimation for given echo-signal characteristics. The smallest time delay estimation error is given by the Cramer-Rao Lower Bound (CRLB), which can be achieved when operating under the small error condition. Based on the CRLB, we obtain an expression for the lower bound for the strain estimation error (LBSE). The LBSE equation is derived under the assumption that the post-compression echo signal can be reconstructed to the original shape of the echo signal before compression. The theoretical bound given by the LBSE may or may not be achievable in practice, depending on the compliance with the requirements for echo signal reconstruction. In an example, the obtained LBSE shows that there is potential for significant reduction of the current level of noise in elastograms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>