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.     

Experimental corroboration of the nonstationary strain estimation errors in elastography

The nonstationary variation in the noise performance of the cross-correlation-based strain estimator due to frequency-dependent attenuation and lateral and elevational signal decorrelation have been addressed theoretically in recent papers using the strain-filter approach. In this paper, we present the experimental verification and corroboration of the nonstationary effects on the strain estimation results. The accuracy and precision of the strain estimate deteriorates with lateral position in the elastogram, due to the lateral motion of tissue scatterers, and with depth, due to frequency-dependent attenuation. The results illustrate that the best strain-estimation noise performance is obtained in the focal zone of the transducer and around the axis of symmetry of the phantom. (E-mail: tvarghese@facstaff.wisc.edu)     

Experimental verification of the correlation behavior of analytic ultrasound radiofrequency signals received from moving structures

Conventional pulsed ultrasound systems are only able to detect motion along the ultrasound beam (i.e., axial motion). If the angle between the actual motion direction and the ultrasound beam is known, then the magnitude of the actual motion can be derived. This technique can be applied for laminar blood-flow measurements in straight vessels, but for tissue motion it is inadequate because the local tissue motion direction is unknown and may be position-dependent. Assessment of both the axial motion and the lateral motion (i.e., in the direction perpendicular to the ultrasound beam) makes angle-independent assessment of the magnitude of the actual motion feasible. Information about the axial and lateral motion is available in a set of radiofrequency (RF) signals obtained along the same line of observation (M-mode). The experiments described in the present paper show that axial and lateral motion can be estimated from the shape of the envelope of the 2-D (spatial and temporal) correlation function of analytic M-mode RF signals. Furthermore, it is demonstrated that the shape is also affected by the Band width of the received RF signals, signal-to–noise ratio, and local amplitude and phase characteristics of the ultrasound beam.     

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.     

Subsample interpolation strategies for sensorless freehand 3D ultrasound

Freehand 3D ultrasound can be acquired without a position sensor by deducing the elevational probe motion from the interframe speckle decorrelation. However, a freehand scan involves lateral and axial, as well as elevational, probe motion. The lateral sampling is determined by the A-line separation and is relatively sparse: lateral motion tracking therefore requires subsample interpolation. In this paper, we investigate the resilience of lateral interpolation techniques to simultaneous lateral and elevational probe motion. We propose a novel interpolation strategy and, through a series of in vitro experiments, compare its performance with that of established alternatives. The new technique is shown to be superior, limiting interpolation errors to around 5% of the length of the freehand reconstruction. (E-mail: rjh80@eng.cam.ac.uk)     

Modeling of the correlation of analytic ultrasound radiofrequency signals for angle-independent motion detection

Conventional pulsed ultrasound systems are able to assess motion of scatterers in the direction of the ultrasound beam, i.e., axial motion, by determining the lag at which the maximum correlation occurs between consecutively-received radiofrequency (rf) signals. The accuracy, resolution, and processing time of this technique is improved by making use of a model for the correlation of rf signals. All previously-described correlation models only include axial motion, but it is common knowledge that lateral motion, i.e., motion in the plane perpendicular to the beam axis, reduces the correlation of rf signals in time. In the present paper, a model for the correlation of analytic rf signals in depth and time is derived and verified. It also includes, aside of some signal and transducer parameters, both axial and lateral motion. The influence of lateral motion on the correlation of (analytic) rf signals is strongly related to local phase and amplitude characteristics of the ultrasound beam. It is shown how the correlation model, making use of an ultrasound transducer with a circular beam shape, can be applied to estimate, independent of angle, the magnitude of the actual motion. Furthermore, it is shown that the model can be applied to estimate the local signal-to-noise ratio and rf bandwidth.     

On the Advantages of Imaging the Axial-Shear Strain Component of the Total Shear Strain in Breast Tumors

Axial-shear strain elastography was described recently as a method to visualize the state of bonding at an inclusion boundary. Although total shear strain elastography was initially proposed for this purpose, it did not evolve beyond the initial reported finite element model (FEM) and simulation studies. One of the major reasons for this was the practical limitation in estimating the tissue motion perpendicular (lateral) to the ultrasound (US) beam as accurately as the motion along the US beam (axial). Nevertheless, there has been a sustained effort in developing methods to improve the lateral motion tracking accuracy and thereby obtain better quality total shear strain elastogram (TSSE). We hypothesize that in some cases, even if good quality TSSE becomes possible, it may still be advantageous to utilize only the axial-shear strain (one of the components of the total shear strain) elastogram (ASSE). Specifically, we show through FEM and corroborating tissue-mimicking gelatin phantom experiments that the unique “fill-in” discriminant feature that was introduced recently for asymmetric breast lesion classification is depicted only in the ASSE and not in the TSSE. Note that the presence or conspicuous absence of this feature in ASSE was shown to characterize asymmetric inclusions' boundaries as either loosely-bonded or firmly-bonded to the surrounding, respectively. This might be an important observation because the literature suggests that benign breast lesions tend to be loosely-bonded, while malignant tumors are usually firmly-bonded. The results from the current study demonstrate that the use of shear strain lesion “fill-in” as a discriminant feature in the differentiation between asymmetric malignant and benign breast lesions is only possible when using the ASSEs and not the TSSEs.     

Sensorless freehand 3D ultrasound in real tissue: speckle decorrelation without fully developed speckle

It has previously been demonstrated that freehand 3D ultrasound can be acquired without a position sensor by measuring the elevational speckle decorrelation from frame to frame. However, this requires that the B-scans contain significant amounts of fully developed speckle. In this paper, we show that this condition is rarely satisfied in scans of real tissue, which instead exhibit fairly ubiquitous coherent scattering. By examining the axial and lateral correlation functions, we propose an heuristic technique to quantify the amount of coherency at each point in the B-scans. This leads to an adapted elevational decorrelation scheme which allows for the coherent scattering. Using the adapted scheme, we demonstrate markedly improved reconstructions of animal tissue in vitro.     

Theoretical bounds on the estimation of transverse displacement, transverse strain and Poisson's ratio in elastography

The Cramér-Rao Lower Bounds (CRLB) are derived for the displacement and strain estimation in directions orthogonal to the ultrasonic beam axis, using a previously-described recorrelation method of axial, lateral and elevational motion estimation. We also compare it to the lateral tracking method that involves the sole use of the axial signal in the transverse direction. Our theoretical results, verified with simulations and phantom experiments, show that elastography is capable of measuring axial and transverse strain at up to 10% axially applied compression. Finally, we predict the performance of the estimation of the Poisson's ratio using decoupled axial and lateral estimates that result from the recorrelation method.     

Elastographic image quality vs. tissue motion in vivo

Elastography is a noninvasive method of imaging tissue elasticity using standard ultrasound equipment. In conventional elastography, axial strain elastograms are generated by cross-correlating pre- and postcompression digitized radio frequency (RF) echo frames acquired from the tissue before and after a small uniaxial compression, respectively. The time elapsed between the pre- and the postcompression frames is referred to as the interframe interval. For in vivo elastography, the interframe interval is critical because uncontrolled physiologic motion such as heartbeat, muscle motion, respiration and blood flow introduce interframe decorrelation that reduces the quality of elastograms. To obtain a measure of this decorrelation, in vivo experimental data (from human livers and thyroids) at various interframe intervals were obtained from 20 healthy subjects. To further examine the effect of the different interframe intervals on the elastographic image quality, the experimental data were also used in combination with elastographic simulation data. The deterioration of elastographic image quality was objectively evaluated by computing the area under the strain filter (SF) at a given resolution. The experimental results of this study demonstrate a statistical exponential behavior of the temporal decay of the echo signal cross-correlation amplitudes from the in vivo tissues due to uncontrollable motion. The results also indicate that the dynamic range and height of the SF are reduced at increased interframe intervals, suggesting that good objective image quality may be achieved provided only that a high frame rate is maintained in elastographic applications.     

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.     

Tissue motion and elevational speckle decorrelation in freehand 3D ultrasound

3D positioning is essential for quantitative volume analysis in 3D ultrasound. Particularly for freehand scanning without an external positioning device, such information must be estimated by analyzing the original 2D images prior to 3D reconstruction. Previous work on freehand 3D positioning has focused on elevational displacement estimation using speckle decorrelation for linear scans. However, the effects of other types of motion have been ignored. Given that all types of motion potentially introduce speckle decorrelation, the accuracy of the elevational displacement estimation is likely to be diminished by the presence of motions of other types. In the present study, simulations were performed to probe the effects of various motions on elevational displacement estimation. In particular, the effects of rotational motions on image correlation are investigated in detail. It is found that these motions significantly affect the estimation results and thus should be taken into account when reconstructing the 3D image. In addition, speckle variations also affect the estimation even when only elevational motion is present. Finally, full motion analysis in freehand scanning may not be possible by only using speckle correlation analysis unless speckle variations can be reduced and the correlation distribution under complex motion can be obtained.     

Angle-independent motion measurement by correlation of ultrasound signals assessed with a single circular-shaped transducer

In medicine, pulsed ultrasound is a widespread noninvasive technique that measures motion in the direction of the ultrasound beam, i.e., axial motion. The magnitude of the actual motion can be determined only if the angle between the ultrasound beam and the direction of motion (transducer-to-motion angle) is known. For blood flow measurements, current pulsed ultrasound systems assume this angle to be equal to the angle between the ultrasound beam and the longitudinal direction of the vessel, as can be estimated from a two-dimensional brightness-mode (B-mode) image that is obtained prior to the blood flow measurement. For tissue motion measurements, current pulsed ultrasound systems are mostly unable to determine the transducer-to-motion angle. Recently, a model has been derived for the correlation of(analytic) radiofrequency (rf) signals, assessed with a circular-shaped ultrasound transducer along the same line of observation. In the present paper, this model is used to derive estimators, requiring only the calculation of a few correlation coefficients, for the motion components (axial, lateral and actual) and for some of the signal parameters (center frequency, bandwidth and signal-to-noise ratio) of the assessed rf signals. The transducer-to-motion angle can be derived from the estimated motion components. For the evaluation of the estimators, rf signals were acquired with a motion-controlled experimental arrangement. The results of the evaluation study show that the transducer-to-motion angle can be estimated with a mean standard deviation of less than 2 degrees.     

Ultrasound-Based Estimation of Fibre-Directional Strain: A Simulation Study

Left ventricular (LV) strains are typically represented with respect to the imaging axes. Contraction within the myocardium occurs along myofibres, which vary in orientation. Therefore, a mismatch exists between the direction in which strain is calculated and that in which contraction occurs. In this study, ultrasound-based fibre orientation and 3-D strain estimation were combined to calculate the fibre-directional strain. Three-dimensional ultrasound volumes were created by simulating simple geometrical phantoms and a phantom based on a finite-element (FE) model of LV mechanics. Fibre-like structures were embedded within tissue-mimicking scatterers. Strains were applied to the numerical phantom, whereas the FE phantom was deformed based on the LV model. Fibre orientation was accurately estimated for both phantoms. There was poor agreement in axial and elevational strains (root mean square error = 29.9% and 12.3%), but good agreement in lateral and fibre-directional strains (root mean square error = 6.4% and 5.9% respectively), which aligned in the midwall. Simplifications to reduce computational complexity caused poor axial and elevational strain estimation. However, calculation of fibre-directional strain from single-modality ultrasound volumes was successful. Further studies, in ex vivo setups because of the fundamental limitations of currently available transducers, are needed to verify real-world performance of the method.     

Ultrasonic temperature imaging for guiding focused ultrasound surgery: effect of angle between imaging beam and therapy beam

Ultrasonic temperature imaging is a promising technique for guiding focused ultrasound surgery (FUS). The FUS system is run at an initial, nonablative intensity and a diagnostic transducer images the heat-induced echo strain, which is proportional to the temperature rise. The echo strain image portrays an elliptical "hot spot" corresponding to the focal region of the therapy transducer. It is anticipated that such images will be used to predict the location of the thermal lesion that would be produced at an ablative intensity. We demonstrated in vitro that heat-induced echo strain images can visualize a spatial peak temperature rise of <2 degrees C (starting at room temperature). However, the imaging beam was perpendicular to the treatment beam in these experiments, whereas the most convenient approach in vivo would be to mount the imaging probe within the housing of the therapy transducer such that the two beams are coaxial. A previous simulation experiment predicted that echo strain images would be noisier for the coaxial configuration because sharp lateral gradients in axial displacement cause increased RF signal decorrelation within the beam width. The aim of the current study was to verify this prediction in vitro. We found, that for a temperature rise of approximately 4 degrees C, the mean contrast-to-noise ratio for coaxial and perpendicular echo strain images was 0.37 (+/-0.24) and 2.00 (+/-0.72) respectively. Furthermore, the decorrelation noise seen in the coaxial images obscured the posterior axial border of the hot spot. We conclude that the coaxial configuration will be useful for localizing the hot spot in the lateral direction. However, it may not be able to depict the axial extent of the hot spot or to portray a parameter that is directly related to temperature rise.     

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.     

Ultrasonic axial strain measurement for lateral tissue deformation

An axial strain measurement technique and a one-dimensional (1D) shear modulus reconstruction technique were developed previously by using the multidimensional radio-frequency (RF) echo phase matching method and an axial strain ratio, respectively. In this study, these techniques have been applied using a conventional ultrasound (US) imaging system with the constraint that the tissue deforms predominantly in the lateral direction, orthogonal to the ultrasound beam axis. Conventionally, axial strain measurement and axial strain ratio are used when the tissue deforms predominantly in the axial direction by extracorporeally applied pressure or vibration. In any case, an axial strain can be accurately measured using the multidimensional RF-echo phase matching method; such a measurement will be useful and will enable a simple reconstruction in a lateral deformation case. The usefulness of these techniques is demonstrated by agar phantom experiments; several problems related to their use in cases such as accuracy, bias error and detectability of inhomogeneity (contrast-to-noise ratio) are addressed. These techniques will be effective for deep regions-of-interest (ROIs) such as liver tissues, which are inaccessible from the body surface and normally deformed by heart motion or pulsation. Moreover, such techniques will enable the evaluation of the elasticity of various tissues under normal motion such as the arm and leg muscles during exercise.     

Learning to estimate out-of-plane motion in ultrasound imagery of real tissue

In freehand 3D ultrasound (US), the relative positions and orientations of the 2D US images are usually obtained from a position tracking device, at the expense of clinical convenience. As an alternative or complement to this approach, transducer motion can be inferred from image content, using image registration techniques to recover in-plane motion and speckle decorrelation to recover out-of-plane motion. One difficulty with the speckle decorrelation approach is that for real tissues, the rate of speckle decorrelation is not only transducer dependent, but also medium dependent. This paper proposes a novel method for estimating the elevational correlation length of US signals in such media by learning its relationship to in-plane image statistics from a pool of synthetic US imagery generated from virtual phantoms of varied micro-structure. Learning takes place within a sparse Gaussian process regression framework. In experiments with synthetic US imagery and real imagery of animal tissue, the approach is shown to generalise well across transducer and medium changes, with performance better than a method based on speckle classification and comparable to our implementation of the heuristic state-of-the-art method. The proposed approach better lends itself to improvement through the creation of more realistic training sets.     

Estimating tissue strain from signal decorrelation using the correlation coefficient

A simple relationship between the correlation coefficient and the applied strain, applicable only at low strains, is presented in this article. This relationship is derived for a Gaussian modulated cosine point spread function. The performance of the strain estimator is analyzed using a theoretical expression for the correlation coefficient along with simulation and experimental results. Both the theoretical and simulation results diverge from the ideal relationship between the strain and the correlation coefficient as the applied strain is increased. Simulation results illustrate that the strain estimate obtained using the correlation coefficient is a biased estimate with a large variability. Experimental results, however, illustrate that strain estimation using the 1-D correlation coefficient estimate is applicable only at high signal-to-noise ratios in the radiofrequency signal and in the absence of lateral and elevational signal decorrelation.     

Lateral resolution in elastography

The factors that control the lateral resolution in elastography were investigated using a simulation study. The lateral resolution was estimated from the simulated axial strain elastograms as the smallest measurable distance between two equally stiff lesions embedded in a homogeneously softer background. The lesions were symmetrically positioned lateral to the center of the target, at the focus of the transducer. Ultrasound (US) systems with different transducer frequencies, bandwidths and f-numbers were simulated. The effects of the ultrasonic parameters, the lateral spacing between adjacent echo signals, the cross-correlation window length, the lesion/background elastic contrast and the lateral motion of scatterers on the estimated lateral resolution were investigated. The results show that the lateral resolution in elastography is proportional to the beam width of the US system used to acquire the data, and is on the same order as the sonographic lateral resolution.