Tradeoffs in elastographic imaging

This paper presents the tradeoffs in elastographic imaging. Elastography is viewed as a new imaging modality and presented in terms of three fundamental concepts that constitute the basis for the elastographic imaging process. These are the tissue elastic deformation process, the statistical analysis of strain estimation and the image characterization. The first concept involves the use of the contrast transfer efficiency (CTE) that describes the mapping of a distribution of local tissue elastic moduli into a distribution of local longitudinal tissue strains. The second concept defines the elastographic system and the relationship between ultrasonic and signal processing parameters. This process is described in terms of a stochastic framework (the strain filter) that provides upper and practical performance bounds and their dependence on the various system parameters. Finally, the output image, the elastogram, is characterized by its image parameters, such as signal-to-noise ratio, contrast-to-noise ratio, dynamic range and resolution. Finite-element simulations are used to generate examples of elastograms that are confirmed by the theoretical prediction tools.     

Performance Evaluation of Methods for Two-Dimensional Displacement and Strain Estimation Using Ultrasound Radio Frequency Data

In elastography, several methods for 2-D strain imaging have been introduced, based on both raw frequency (RF) data and speckle-tracking. Although the precision and lesion detectability of axial strain imaging in terms of elastographic signal-to-noise ratio (SNRe) and elastographic contrast-to-noise ratio (CNRe) have been reported extensively, analysis of lateral precision is still lacking. In this paper, the performance of different 2-D correlation RF- and envelope-based strain estimation methods was evaluated using simulation data and phantom experiments. Besides window size and interpolation methods for subsample displacement estimation, the influence of recorrelation techniques was examined. Precision and contrast of the measured displacements and strains were assessed using the difference between modeled and measured displacements, SNRe and CNRe. In general, a 2-D coarse-to-fine displacement estimation method is favored, using envelope data for window sizes exceeding the theoretical upper bound for strain estimation. Using 2-D windows of RF data resulted in better displacement estimates for both the axial and lateral direction than 1-D RF-based or envelope-based techniques. Obtaining subsample lateral displacement estimates by fitting a predefined shape through the cross-correlation function (CCF) yielded results similar to those obtained with up-sampling of RF data in the lateral direction. Using a CCF model was favored because of the decreased computation time. Local aligning and stretching of the windows (recorrelation) resulted in an increase of 2–17 and 6–7 dB in SNRe for axial and lateral strain estimates, respectively, over a range of strains (0.5 to 5.0%). For a simulated inhomogeneous phantom (2.0% applied strain), the measured axial and lateral SNRes were 29.2 and 20.2 dB, whereas the CNRes were 50.2 dB and 31.5 dB, respectively. For the experimental data, lower SNRe (axial: 28.5 dB; lateral: 17.5 dB) and CNRe (axial: 39.3 dB; lateral: 31 dB) were found. In conclusion, a coarse-to-fine approach is favored using RF data on a fine scale. The use of 2D parabolic interpolation is favored to obtain subsample displacement estimates. Recorrelation techniques, such as local aligning and stretching, increase SNRe and CNRe in both directions. (E-mail: r.lopata@cukz.umcn.nl)     

Performance of Two Dimensional Displacement and Strain Estimation Techniques Using a Phased Array Transducer

The goal of this study was to investigate the applicability of conventional 2-D displacement and strain imaging techniques to phased array radiofrequency (RF) data. Furthermore, the possible advantages of aligning and stretching techniques for the reduction of decorrelation artefacts was examined. Data from both realistic simulations and phantoms were used in this study. Recently, the used processing concepts were successfully applied to linear array data. However, their applicability to sector scan data is not trivial because of the polar grid. Homogeneous and inhomogeneous tissue phantoms were simulated at a range of strains (0 to 5%) using Field II^©. The inhomogeneous phantom, a commonly used tumor/lesion model, was also constructed using gelatin/agar solutions. A coarse-to-fine displacement algorithm was applied, using aligning and stretching to enhance re-correlation. Vertical and horizontal strains were reconstructed from the axial and lateral displacements. Results revealed that the error on displacement estimates was lower when using 2-D data windows rather than 1-D windows. For regions at large depths and large insonification angles, the allowed lateral window size was limited. Still, 1-D windows resulted in larger errors. The re-correlation techniques resulted in a significant increase in the elastographic signal-to-noise ratio (SNRe) and elastographic contrast-to-noise ratio (CNRe) of the vertical and horizontal strain components. An increase of the SNRe of 5–20 dB was observed over a range of strains (0.5 to 5.0%). In the inhomogeneous phantom, a vertical SNRe of 27.7 dB and a horizontal SNRe of 16.7 dB were measured in the background. The vertical and horizontal CNRe were 35 dB and 23.1 dB, respectively. For the experimental data, lower SNRe (vertical: 19.1 dB; horizontal: 11.4 dB) and CNRe (vertical: 33.3 dB; horizontal: 12.5 dB) were found. In conclusion, 2-D window matching of sector scan data is feasible and outperforms 1-D window matching. Furthermore, the use of re-correlation techniques enhances both precision and contrast of strain images. (E-mail: r.lopata@cukz.umcn.nl)     

The effects of digitization on the elastographic signal-to-noise ratio

In elastography, the tissue under investigation is compressed and the resulting strain is estimated from the gradient of the displacement (time-delay) estimates. The displacements are typically estimated by cross-correlating the radiofrequency (RF) ultrasound signals of the pre- and postcompressed tissue. One of the parameters used to quantify the resulting quality of the elastogram is the elastographic signal-to-noise ratio (SNR(e)). For a uniformly elastic target (a single elastic modulus), the dependence of the SNR(e) on the applied strain has a bandpass characteristic that has been termed the strain filter. Theoretical expressions for the upper bound on the strain filter were developed earlier. Yet, simulated as well as experimental strain filters derived from uniformly elastic phantoms deviate from these upper bounds. The failure to achieve the upper bounds could be partially attributed to the fact that, in both simulations and experiments, the RF signals used to compute the TDEs are sampled and quantized. Using simulated models of uniformly elastic phantoms, a study of the dependence of the strain filter on the quantization and sampling rates was performed. The results indicated that the strain filter improves with both the sampling rate and the quantization, as expected. A theoretical analysis was done to incorporate quantization as a derating factor to the strain filter.     

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.     

Performance Optimization in Elastography: Multicompression with Temporal Stretching

A general theoretical framework known as the strain filter has been previously used to evaluate the performance in elastography. The strain filter describes the relationship among the resolution, dynamic range, sensitivity and elastographic SNR (SNR_e), and may be plotted as a graph of the upper bound of the SNR_evs. the strain experienced by the tissue, for a desired elastographic axial resolution as determined by the data window length. The ideal strain filter has an infinitely high, flat all-pass characteristic shape in thestrain domain, which means that all local tissue strains are displayed in the elastogram with infinite SNR_e; it also means that the strain dynamic range in the elastogram is infinite as well. Practical strain filters obtained using a single tissue compression have abandpasscharacteristic shape in the strain domain, where the −3 dB width of this bandpass characteristic may be defined as the elastographic dynamic range. In this paper, we present an optimal technique for stretching multicompression elastography, practiced by selecting the optimum incremental applied strain using the strain filter. Two techniques, temporal stretching and multicompression elastography, are combined in this paper to improve elastogram quality. Stretching multicompression elastography using the optimal applied strain increment alters the shape of the strain filter from its bandpass characteristic to a more desirable high-emphasis filter. The dynamic range of optimal stretching multicompression elastography is limited only by tissue nonlinearities. This optimal applied strain increment minimizes signal decorrelation and achieves the maximum achievable elastographic SNR_e.     

三维多回波聚合梯度回波序列在腰骶丛成像中的初步应用

目的  探讨3D多回波聚合梯度回波序列（3D GEMEC）在腰骶丛神经成像中的应用价值。方法  回顾性分析2022年8~9月六安市人民医院以腰腿疼为主诉的32例住院患者的影像学资料,男15例,女17例,年龄28~78（60.1±15.8）岁。在不同1.5T平台上分别完成腰骶丛3D GEMEC序列和三维T2加权快速梯度回波（3D T2 FFE）序列,比较两种序列腰骶丛神经的信噪比、对比噪声比和主观显示效果。结果  3D GEMEC序列腰骶丛神经的信噪比、对比噪声比以及主观显示效果与3D T2 FFE序列的差异均无统计学意义（P=0.250、0.146、0.083）。结论  3D GEMEC序列可以清晰地显示腰骶丛神经的解剖结构并抑制背景信号,在腰骶丛神经病变的诊断方面具有一定的临床应用前景。     

The nonstationary strain filter in elastography: Part II. Lateral and elevational decorrelation

The nonstationary evolution of the strain filter due to lateral and elevational motion of the tissue scatterers across the ultrasound beam is analyzed for the 1-D cross-correlation-based strain estimator. The effective correlation coefficient that includes the contributions due to lateral and elevational signal decorrelation is used to derate the upper bound of the signal-to-noise ratio in the elastogram (SNR_e) predicted by the ideal strain filter. In the case of an elastically homogeneous target, if the transducer is on the axis of symmetry of such target in the elevational direction, the motion of the scatterers out the imaging plane is minimized. In addition, the ultrasound beam along the elevational direction is broader, allowing scatterers to stay longer within the beam during tissue compression. Under these conditions, lateral signal decorrelation becomes the primary contributor to the nonstationary behavior of the strain filter. Both the elastographic SNR_e and the dynamic range are reduced, with an increase in lateral decorrelation. Finite element simulations and phantom experiments are presented in this paper to corroborate the theoretical strain filter. The nonstationary behavior of the strain filter is reduced by confining the tissue in the lateral direction (minimizing motion of tissue scatterers), thereby improving the quality of the elastogram.     

Echo-Computed Tomography Strain Imaging of Healthy and Diseased Carotid Specimens

To improve our understanding of the mechanical behavior of human atherosclerotic plaque tissue, fully 3-D geometrical, morphological and dynamical information is essential. For this purpose, four-dimensional (3-D+t) strain imaging using an ultrasound tomography approach (echo-computed tomography) was performed in carotid arteries in vitro. The method was applied to a carotid phantom (CPh), a porcine carotid artery (PC) and human carotid atherosclerotic plaque samples (HC, n = 5). Each sample was subjected to an intraluminal pressure, after which 2-D longitudinal ultrasound images were obtained for 36 angles along the circumferential direction. Local deformations were estimated using a 2-D strain algorithm, and 3-D radial strain data were reconstructed. At systole, median luminal strains of 15% (CPh) and 18% (PC) were found, which is in agreement with the stiffness of the material and applied pressure pulse. The elastographic signal-to-noise ratio was consistent in all directions and ranged from 16 to 36 dB. Furthermore, realistic but more complex strain patterns were found for the HC, with 99th percentile systolic strain values ranging from 0.1% to 18%.     

On the signal-to-noise ratio of a synthetic aperture ultrasound imaging method

Conventional synthetic aperture ultrasound imaging requires wide angular response of the probe which presumes the use of a narrow transducer element. As a result the signal-to-noise ratio and the contrast resolution become poor. The problem can be overcome by using a multielement subarray and making the beam narrower. This study shows that the signal-to-noise ratio can be improved by > 15 dB compared to the conventional synthetic aperture approach and still preserve excellent spatial resolution. Assuming equal driving voltage, the performance is only about 6 dB worse than with a phased array system at its transmit and receive focus. This difference can be easily compensated if equal transmission power is employed.     

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.     

Optimal imaging with adaptive mesh refinement in electrical impedance tomography

In non-linear electrical impedance tomography the goodness of fit of the trial images is assessed by the well-established statistical chi2 criterion applied to the measured and predicted datasets. Further selection from the range of images that fit the data is effected by imposing an explicit constraint on the form of the image, such as the minimization of the image gradients. In particular, the logarithm of the image gradients is chosen so that conductive and resistive deviations are treated in the same way. In this paper we introduce the idea of adaptive mesh refinement to the 2D problem so that the local scale of the mesh is always matched to the scale of the image structures. This improves the reconstruction resolution so that the image constraint adopted dominates and is not perturbed by the mesh discretization. The avoidance of unnecessary mesh elements optimizes the speed of reconstruction without degrading the resulting images. Starting with a mesh scale length of the order of the electrode separation it is shown that, for data obtained at presently achievable signal-to-noise ratios of 60 to 80 dB, one or two refinement stages are sufficient to generate high quality images.     

An Angular Compounding Technique Using Displacement Projection for Noninvasive Ultrasound Strain Imaging of Vessel Cross-Sections

Strain is considered to be a useful indicator of atherosclerotic plaque vulnerability. This study introduces an alternative for a recently introduced strain imaging method that combined beam steered ultrasound acquisitions to construct radial strain images of transverse cross-sections of superficial arteries. In that study, axial strains were projected in the radial direction. Using the alternative method introduced in this study, axial displacements are projected radially, followed by a least squares estimation of radial strains. This enables the use of a larger projection angle. Consequently, fewer acquisitions at smaller beam steering angles are required to construct radial strain images. Simulated and experimentally obtained radio-frequency data of radially expanding vessel phantoms were used to compare the two methods. Using only three beam steering angles (–30°, 0° and 30°), the new method outperformed the older method that used seven different angles and up to 45° of beam steering: the root mean squared error was reduced by 38% and the elastographic signal- and contrast-to-noise ratios increased by 1.8 dB and 4.9 dB, respectively. The new method was also superior for homogeneous and heterogeneous phantoms with eccentric lumens. To conclude, an improved noninvasive method was developed for radial strain imaging in transverse cross-sections of superficial arteries. (E-mail: r.hansen@cukz.umcn.nl)     

Poroelastography: imaging the poroelastic properties of tissues.

In the field of elastography, biological tissues are conveniently assumed to be purely elastic solids. However, several tissues, including brain, cartilage and edematous soft tissues, have long been known to be poroelastic. The objective of this study is to show the feasibility of imaging the poroelastic properties of tissue-like materials. A poroelastic material is a material saturated with fluid that flows relative to a deforming solid matrix. In this paper, we describe a method for estimating the poroelastic attributes of tissues. It has been analytically shown that during stress relaxation of a poroelastic material (i.e., sustained application of a constant applied strain over time), the lateral-to-axial strain ratio decreases exponentially with time toward the Poisson's ratio of the solid matrix. The time constant of this variation depends on the elastic modulus of the solid matrix, its permeability and its dimension along the direction of fluid flow. Recently, we described an elastographic method that can be used to map axial and lateral tissue strains. In this study, we use the same method in a stress relaxation case to measure the time-dependent lateral-to-axial strain ratio in poroelastic materials. The resulting time-sequenced images (poroelastograms) depict the spatial distribution of the fluid within the solid at each time instant, and help to differentiate poroelastic materials of distinct Poisson's ratios and permeabilities of the solid matrix. Results are shown from finite-element simulations.     

Spatial resolution in optical coherence elastography of bounded media

Dynamic optical coherence elastography (OCE) tracks mechanical wave propagation in the subsurface region of tissue to image its shear modulus. For bulk shear waves, the lateral resolution of the reconstructed modulus map (i.e., elastographic resolution) can approach that of optical coherence tomography (OCT), typically a few tens of microns. Here we perform comprehensive numerical simulations and acoustic micro-tapping OCE experiments to show that for the typical situation of guided wave propagation in bounded media, such as cornea, the elastographic resolution cannot reach the OCT resolution and is mainly defined by the thickness of the bounded tissue layer. We considered the excitation of both broadband and quasi-harmonic guided waves in a bounded, isotropic medium. Leveraging the properties of broadband pulses, a robust method for modulus reconstruction with minimum artifacts at interfaces is demonstrated. In contrast, tissue bounding creates large instabilities in the phase of harmonic waves, leading to serious artifacts in modulus reconstructions.     

A quantitative comparison of modulus images obtained using nanoindentation with strain elastograms

Tissue stiffness is generally known to be associated with pathologic changes. Ultrasound (US) elastography, on the other hand, is capable of imaging tissue strain, which may or may not be well-correlated with tissue stiffness. Hence, a quantitative comparison between the elastographic tissue strain images and the corresponding tissue modulus images needed to be performed to evaluate the usefulness of elastography in imaging tissue stiffnesss properties. Simulations were performed to demonstrate and quantify the similarities between modulus images and strain elastograms. This was followed by comparing nanoindenter-based modulus images with strain elastograms of thin slices of tissue-mimicking phantoms. Finally, some beef slices, canine prostates, ovine kidneys and breast cancers grown in mice were used to demonstrate the qualitative correspondence between modulus images and strain elastograms. The simulations and the experiments indicated that it is feasible to perform quantitative comparisons between strain images (using elastography) and modulus images on certain tissue structures and geometries. A good quantitative correspondence (correlation values of greater than 0.8) between structures in the modulus and strain images could be obtained at scales equal to or larger than 20 Qlambda (where Q is the quality factor defined as the ratio of the center frequency over the band width and lambda is the wavelength of the US system) modulus contrasts larger than 5, applied strains between 0.5% and 3% and window lengths for computing strain elastograms between 3 Qlambda and 5 Qlambda. The gelatin-phantom experiments showed lower values of correlation (values around 0.5) than with theory and simulations. The decrease in correlation was attributed to the presence of measurement noise in both strain elastography and modulus imaging, an increase of dimensionality of the problem (from 2-D to 3-D), local anisotropy, heterogeneity and nonstationarity. Experiments on real tissue slices showed further decrease in the correlation to around 0.3, possibly due to additional confounding factors such as time-dependent mechanical properties and geometrical distortions in the tissue during imaging. The work presented in this paper demonstrates that there is an intrinsic relationship between strain elastograms and the actual distribution of soft tissue elastic moduli, and bodes well for continued work in the area of elastography.     

Nonlinear stress-strain relationships in tissue and their effect on the contrast-to-noise ratio in elastograms

The practice of elastography is generally limited to small applied compressions (typically 1%), under the assumption of a linear stress-strain relationship in biological tissue. However, the recent reports of larger applied compressions and precompression levels to increase the strain contrast violate the above assumption. The nonlinear stress-strain relationships in different breast tissue types significantly alter the contrast in elastography, especially for large applied compression. The moduli of normal fibrous and glandular breast tissue (along with cancerous lesions) are strain-dependent, with tissue stiffness increasing with applied compression. In this paper, we illustrate that the strain-dependence of the modulus has a significant impact on the elastographic contrast and on the contrast-to-noise ratio, and may even cause a reversal of the contrast in certain situations. This paper also emphasizes the effect of the precompression strain level on the strain contrast.     

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.     

Evaluating thin compression paddles for mammographically compatible ultrasound

We are developing a combined digital mammography/3D ultrasound system to improve detection and/or characterization of breast lesions. Ultrasound scanning through a mammographic paddle could significantly reduce signal level, degrade beam focusing and create reverberations. Thus, appropriate paddle choice is essential for accurate sonographic lesion detection and assessment with this system. In this study, we characterized ultrasound image quality through paddles of varying materials (lexan, polyurethane, TPX, mylar) and thicknesses (0.25 to 2.5 mm). Analytical experiments focused on lexan and TPX, which preliminary results demonstrated were most competitive. Spatial and contrast resolution, side-lobe and range lobe levels, contrast and signal strength were compared with no-paddle images. When the beamforming of the system was corrected to account for imaging through the paddle, the TPX 2.5 mm paddle performed the best. Test objects imaged through this paddle demonstrated < or = 15% reduction in spatial resolution, < or = 7.5 dB signal loss, < or = 3 dB contrast loss and range lobe levels > or = 35 dB below signal maximum over 4 cm. TPX paddles <2.5 mm could also be used with this system, depending on imaging goals. In 10 human subjects with cysts, small CNR losses were observed but were determined to be statistically insignificant. Radiologists concluded that 75% of cysts in through-paddle scans were at least as detectable as in their corresponding direct-contact scans.