Analysis of an adaptive strain estimation technique in elastography

A novel filter for accurate estimation of fluid pressure and fluid velocity using poroelastography

Fluid pressure and fluid velocity carry important information for cancer diagnosis, prognosis and treatment. Recent work has demonstrated that estimation of these parameters is theoretically possible using ultrasound poroelastography. However, accurate estimation of these parameters requires high quality axial and lateral strain estimates from noisy ultrasound radio frequency (RF) data. In this paper, we propose a filtering technique combining two efficient filters for removal of noise from strain images, i.e., Kalman and nonlinear complex diffusion filters (NCDF). Our proposed filter is based on a novel noise model, which takes into consideration both additive and amplitude modulation noise in the estimated strains. Using finite element and ultrasound simulations, we demonstrate that the proposed filtering technique can significantly improve image quality of lateral strain elastograms along with fluid pressure and velocity elastograms. Technical feasibility of the proposed method on an in vivo set of data is also demonstrated. Our results show that the CNRe of the lateral strain, fluid pressure and fluid velocity as estimated using the proposed technique is higher by at least 10.9%, 51.3% and 334.4% when compared to the results obtained using a Kalman filter only, by at least 8.9%, 27.6% and 219.5% when compared to the results obtained using a NCDF only and by at least 152.3%, 1278% and 742% when compared to the results obtained using a median filter only for all SNRs considered in this study.

Improvement of Lesion Detection by Complete Angular Compound Ultrasonic Elastography

Quasi-static ultrasound elastography is an emerging diagnostic imaging modality for determining the stiffness of pathologically changed soft tissues, which do not show significant differences in acoustic impedance for B-mode imaging. Although some methods were applied to improve the signal-to-noise ratio (SNRe) and contrast-to-noise ratio (CNRe) of the constructed elastogram, nonuniform strain distribution at the internal boundary of a hard inclusion, even with the uniform displacement on the surface, is an inherent mechanical effect and results in distortion at the detected lesion boundary. To overcome such stress concentrations, a new elastographic modality was proposed, where the elastograms from different angles throughout 360° were compounded. The strain field and subsequent ultrasound images were calculated using the finite element method (FEM) and Field II, respectively, from which the elastograms were constructed. The performance of complete angular compound elastography with varied interval angles, lesion sizes, and ratios of Young's moduli of the lesion to the background was simulated and compared with that of conventional axial strain elastography. It is found that viewing the lesion from only about 10 angles (interval of 36°) would significantly improve the image quality of elastogram (increasing SNRe by at least 13% and CNRe by at least 5.8 dB), reduce the lesion distortion in the lateral direction, and enhance the sensitivity, resolution, and accuracy of lesion detection. A preliminary phantom study showed similar improvements. Altogether, complete angular compound elastography improves the elastogram quality and reduces the mechanical effects in lesion detection.

Real-time tissue elastography for the detection of vulnerable carotid plaques in patients undergoing endarterectomy: a pilot study

We examined the utility of ultrasonic real-time tissue elastography (RTE) and conventional B-mode ultrasound (US) in the detection of vulnerable carotid atherosclerotic plaques. This prospective study comprised 19 patients scheduled for carotid endarterectomy. Results obtained from pre-operative RTE and B-mode US and post-operative pathology were compared. RTE encoded low, average and high deformability as blue, green and red, respectively. Tissue hardness was scored on a 5-point scale, and relative strains were calculated. The relative strain was 1.12 ± 0.14 for fibrous plaques (n = 4), 0.28 ± 0.07 for atherosclerotic plaques (n = 5), 0.47 ± 0.31 for intraplaque hemorrhage/thrombosis (n = 5) and 0.98 ± 1.04 for complex plaques (n = 5). The sensitivity, specificity and accuracy of detection of vulnerable plaques were 25%, 100% and 84.2% for B-mode US, 50%, 100% and 89.4% for RTE and 62.5%, 100% and 94.7% for the combination. Ultrasonic RTE is a potential candidate for a non-invasive and effective approach to identify vulnerable atherosclerotic plaques in the carotid artery.

Non-invasive evaluation of liver cirrhosis using ultrasound

Ultrasound (US) is essential in both assessment of the potentially cirrhotic liver and surveillance of selected patients with chronic hepatitis as liver biopsy can be misleading or inaccurate in up to 25% of cases. Various techniques are already in routine use, such as grey-scale imaging, Doppler US, and contrast-enhanced US (CEUS), while newer techniques such as elastography and hepatic vein transit time (HVTT) have the potential to exclude patients without significant fibrosis or cirrhosis; however, they are operator dependent and require specific software. Grey-scale imaging may demonstrate changes, such as volume redistribution, capsule nodularity, parenchymal nodularity, and echotexture changes. The Doppler findings in the hepatic and portal veins, hepatic artery, and varices allow assessment of liver cirrhosis. However, the operator needs to be aware of limitations of these techniques. Low mechanical index CEUS plays an important role in the assessment of complications of cirrhosis, such as hepatocellular carcinoma and portal vein thrombus. Optimized US technique is crucial for accurate diagnosis of the cirrhotic liver and its complications.

Analysis of correlation coefficient filtering in elasticity imaging

Correlation-based speckle tracking methods are commonly used in elasticity imaging to estimate displacements. In the presence of local strain, a larger window size results in larger displacement error. To reduce tracking error, we proposed a short correlation window followed by a correlation coefficient filter. Although simulation and experimental results demonstrated the efficacy of the method, it was not clear why correlation coefficient filtering reduces tracking error since tracking error increases if normalization before filtering is not applied. In this paper, we analyzed tracking errors by estimating phase variances of the cross-correlation function and the correlation coefficient at the true time lag based on statistical properties of these functions' real and imaginary parts. The role of normalization is clarified by identifying the effect of the cross-correlation function's amplitude fluctuation on the function's imaginary part. Furthermore, we present analytic forms for predicting axial displacement error as a function of strain, system parameters (signal-to-noise ratio, center frequency, and signal and noise bandwidths), and tracking parameters (window and filter sizes) for cases with and without normalization before filtering. Simulation results correspond to theory well for both noise-free cases and general cases with an empirical correction term included for strains up to 4%.

On the differences between two-dimensional and three-dimensional simulations for assessing elastographic image quality: a simulation study

In this work, we introduced an elastographic simulation framework, which estimates upper bounds on elastographic image quality by accounting for three-dimensional (3D) tissue motion and the 3D nature of the ultrasound beam. For the boundary conditions and the range of applied strains considered in this study, it was observed that for applied strains smaller than 0.7%, fast two-dimensional (2D) simulations and 3D simulations predicted similar upper bounds on elastographic signal-to-noise (SNR(e)) and contrast-to-noise ratios (CNR(e)); however, for applied strains greater than 0.7%, the predictions by 2D simulations grossly overestimated the achievable results when compared with upper bound results from 3D simulations. It was also found that linear increments in the elevational-to-lateral beamwidth ratio (beam ratio) resulted in nonlinear degradation in the achievable upper bounds on elastographic signal-to-noise ratio. For the modulus contrast ratio of ten between the target and the background, the peak difference in the prediction of contrast-to-noise by 2D and 3D simulations was approximately 10 dB, whereas, for modulus contrast ratio of 1.5, the peak difference increased to approximately 30 dB. No significant difference was observed between the spatial resolution predicted by 2D and 3D simulations; however, increase in beam ratio resulted in decrease in target detectability, especially at lower modulus contrast ratios.

Displacement vector measurement using instantaneous ultrasound signal phase - multidimensional autocorrelation and doppler methods

Two new methods of measuring a multidimensional displacement vector using an instantaneous ultrasound signal phase are described, i.e., the multidimensional autocorrelation method (MAM) and multidimensional Doppler method (MDM). A high measurement accuracy is achieved by combining either method with the lateral Gaussian envelope cosine modulation method (LGECMM) or multidirectional synthetic aperture method (MDSAM). Measurement accuracy is evaluated using simulated noisy echo data. Both methods yield accurate measurements comparable to that of our previously developed cross-spectrum phase gradient method (MCSPGM); however, they require less computational time (the order, MDM < MAM approximate, equals MCSPGM) and would provide realtime measurements. Moreover, comparisons of LGECMM and MDSAM performed by geometrical evaluations clarifies that LGECMM has potentials to yield more accurate measurements with less computational time. Both MAM and MDM can be applied to the measurement of tissue strain, blood flow, sonar data, and other target motions.

The feasibility of using poroelastographic techniques for distinguishing between normal and lymphedematous tissues in vivo

Lymphedema is a common condition involving an abnormal accumulation of lymphatic fluid in the interstitial space that causes swelling, most often in the arm(s) and leg(s). Lymphedema is a significant lifelong concern that can be congenital or develop following cancer treatment or cancer metastasis. Common methods of evaluation of lymphedema are mostly qualitative making it difficult to reliably assess the severity of the disease, a key factor in choosing the appropriate treatment. In this paper, we investigate the feasibility of using novel elastographic techniques to differentiate between lymphedematous and normal tissues. This study represents the first step of a larger study aimed at investigating the combined use of elastographic and sonographic techniques for the detection and staging of lymphedema. In this preliminary study, poroelastographic images were generated from the leg (8) and arm (4) subcutis of five normal volunteers and seven volunteers having lymphedema, and the results were compared using statistical analyses. The preliminary results reported in this paper suggest that it may be feasible to perform poroelastography in different lymphedematous tissues in vivo and that poroelastography techniques may be of help in differentiating between normal and lymphedematous tissues.

Estimation of displacement location for enhanced strain imaging

Ultrasonic strain imaging usually begins with displacement estimates computed using finite-length sections of RF ultrasound signals. Amplitude variations in the ultrasound are known to perturb the location at which the displacement estimate is valid. If this goes uncorrected, it is a significant source of estimation noise, which is amplified when displacement fields are converted into strain images. We present a study of this effect based on theoretical analysis and practical experiments. A correction method based on the analysis is tested on phase zero and correlation coefficient strain imaging, and compared to the amplitude compression techniques of earlier studies. We also test adaptive strain estimation to provide a benchmark, but the performance of our new method matches or surpasses this benchmark under normal scanning conditions. Furthermore, the new correction is suitable for real time applications owing to its extreme computational simplicity.

3D prostate elastography: algorithm, simulations and experiments

A multi-resolution hybrid strain estimator is presented. The estimator is locally initialized by the B-mode tracking stage. Nonlinear and linear stretching regimes are applied in successive RF tracking stages for refining the estimated axial and lateral displacements. A staggering operator is used to derive the strain images from the reconstructed axial displacements. Simulations and experiments, conducted at a center frequency of 12 MHz, 40% fractional bandwidth, on a 128 element transducer with 0.2 mm pitch, with elastographic window length of 2 mm and overlap of 90%, demonstrate a 3-6 dB improvement in the elastographic contrast-to-noise ratio over the results obtained using conventional multi-stage stretching based strain estimators. The average image cross-correlation coefficient obtained using the proposed algorithm was improved by 6-8%. 3D elastographic simulations conducted to study the performance of a 3D elastographic imaging framework predict achievable axial and lateral resolutions of approximately five and ten wavelengths, respectively. A close correspondence between inclusions reconstructed from experimental elastograms and the known physical shape of actual 3D inclusions demonstrates the potential application of 3D elastography for identifying and classifying the detected lesions (invisible in sonograms) on the basis of their shape.

The feasibility of estimating and imaging the mechanical behavior of poroelastic materials using axial strain elastography

In this paper, we have investigated the feasibility of imaging the mechanical behavior of poroelastic materials using axial strain elastography. Cylindrical samples obtained from poroelastic materials having different elastic and permeability properties were subjected to a constant compression force (a classical creep experiment), during which poroelastographic data were acquired. For comparison, we also tested a few gelatin phantoms and non-homogeneous poroelastic phantoms constructed by combining different poroelastic materials. From the acquired data, we generated time-dependent sequences of axial strain elastograms and effective Poisson's ratio elastograms, which were then used for generating axial strain and effective Poisson's ratio time-constant elastograms. Thereafter, the various poroelastographic images were analyzed to evaluate the presence of statistically significant differences among the two types of poroelastic samples and for image quality analysis. The results of this study demonstrate that it is technically feasible to use axial strain elastography to distinguish among homogeneous poroelastic materials characterized by different elastic and permeability properties. They also show that the use of axial strain elastography instead of effective Poisson's ratio elastography results in objectively higher quality poroelastograms of the temporal behavior of the poroelastic materials under loading. However, the use of effective Poisson's ratio elastography may in any case be required to verify that the temporal changes occurring in the axial strains of the homogeneous poroelastic samples are also accompanied by temporal changes of the effective Poisson's ratios and are therefore due to poroelastic behavior.

Visualization of bonding at an inclusion boundary using axial-shear strain elastography: a feasibility study

Ultrasound elastography produces strain images of compliant tissues under quasi-static compression. In axial-shear strain elastography, the local axial-shear strain resulting from application of quasi-static axial compression to an inhomogeneous material is imaged. The overall hypothesis of this work is that the pattern of axial-shear strain distribution around the inclusion/background interface is completely determined by the bonding at the interface after normalization for inclusion size and applied strain levels, and that it is feasible to extract certain features from the axial-shear strain elastograms to quantify this pattern. The mechanical model used in this study consisted of a single stiff circular inclusion embedded in a homogeneous softer background. First, we performed a parametric study using finite-element analysis (FEA) (no ultrasound involved) to identify possible features that quantify the pattern of axial-shear strain distribution around an inclusion/background interface. Next, the ability to extract these features from axial-shear strain elastograms, estimated from simulated pre- and post-compression noisy RF data, was investigated. Further, the feasibility of extracting these features from in vivo breast data of benign and malignant tumors was also investigated. It is shown using the FEA study that the pattern of axial-shear strain distribution is determined by the degree of bonding at the inclusion/background interface. The results suggest the feasibility of using normalized features that capture the region of positive and negative axial-shear strain area to quantify the pattern of the axial-shear strain distribution. The simulation results showed that it was feasible to extract the features, as identified in the FEA study, from axial-shear strain elastograms. However, an effort must be made to obtain axial-shear strain elastograms with the highest signal-to-noise ratio (SNR(asse)) possible, without compromising the resolution. The in vivo results demonstrated the feasibility of producing and extracting features from the axial-shear strain elastograms from breast data. Furthermore, the in vivo axial-shear strain elastograms suggest an additional feature not identified in the simulations that may potentially be used for distinguishing benign from malignant tumors-the proximity of the axial-shear strain regions to the inclusion/background interface identified in the sonogram.

Real-time elastography for noninvasive assessment of liver fibrosis in chronic viral hepatitis

OBJECTIVE

Recently, transient elastography (FibroScan) has been introduced for noninvasive staging of liver fibrosis. Here, we investigated a novel approach for noninvasive assessment of liver fibrosis using sonography-based real-time elastography, which can be performed with conventional ultrasound probes during a routine sonography examination.

MATERIALS AND METHODS

Real-time elastography was performed in 79 patients with chronic viral hepatitis and known fibrosis stage and in 20 healthy volunteers. A specially developed program was used for quantification of tissue elasticity. Stepwise logistic regression analysis was performed to define an elasticity score using variables with high reproducibility in a preceding analysis of data from 16 different patients. In addition, aspartate transaminase-to-platelet ratio index (APRI) and routine laboratory values were included in the analysis.

RESULTS

The Spearman's correlation coefficient between the elasticity scores obtained using real-time elastography and the histologic fibrosis stage was 0.48, which is highly significant (p < 0.001). The diagnostic accuracy expressed as areas under receiver operating characteristic (ROC) curves were 0.75 for the diagnosis of significant fibrosis (fibrosis stage according to METAVIR scoring system [F] > or = F2), 0.73 for severe fibrosis (F > or = F3), and 0.69 for cirrhosis. For a combined elasticity-laboratory score, the areas under the ROC curves were 0.93, 0.95, and 0.91, respectively.

DISCUSSION

Real-time elastography is a new and promising sonography-based noninvasive method for the assessment of liver fibrosis in patients with chronic viral hepatitis.

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.

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

Poroelastography is a novel elastographic technique for imaging the time variation of the mechanical behaviour of poroelastic materials. Poroelastograms are generated as a series of time-sequenced effective Poisson's ratio (EPR) elastograms, obtained from the imaged material under sustained compression. In the companion report (Righetti et al 2007 Phys. Med. Biol. 52 1303), we investigated image quality of EPR elastography starting from a theoretical analysis of the performance limitations of axial strain elastography and lateral strain elastography. In this report, we extend this analysis to poroelastography. The theoretical analysis reported in these two companion papers allows understanding the performance limitations of these novel techniques and identifying the fundamental parameters that control their signal-to-noise ratio, contrast-to-noise ratio and resolution. The results of these studies also indicate that EPR elastograms and poroelastograms of reasonable image quality can be generated in practical applications that may be of clinical interest provided that advanced elastographic techniques in combination with other commonly employed imaging methods to increase signal-to-noise and contrast-to-noise ratios are used.

Improvement of elastographic displacement estimation using a two-step cross-correlation method

The cross-correlation algorithm used to compute the local strain components for elastographic imaging requires a minimum radio-frequency data segment length of around 10 wavelengths to obtain accurate and precise strain estimates with a reasonable signal-to-noise ratio. Shorter radio-frequency data segments generally introduce increased estimation errors as the information content in the data segment reduces. However, shorter data segments and increased overlaps are essential to improve the axial resolution in the strain image. In this paper, we propose a two-step cross-correlation technique that enables the use of window lengths on the order of a single wavelength to provide displacement and strain estimates with similar noise properties as those obtained with a 10 wavelength window. The first processing step utilizes a window length on the order of 10 wavelengths to obtain coarse displacement estimates between the pre- and post-compression radio frequency data frames. This coarse displacement is then interpolated and utilized as the initial guess-estimate for the second cross-correlation processing step using the smaller window. This step utilizes a single wavelength window to improve the axial resolution in strain estimation, without significantly compromising the noise properties of the image. Simulation and experimental results show that the signal-to-noise and contrast-to-noise ratio estimates improve significantly at the smaller window lengths with the two-step processing when compared with the use of a similar sized window in the currently utilized single window method.

Signal-to-noise ratio, contrast-to-noise ratio and their trade-offs with resolution in axial-shear strain elastography

In axial-shear strain elastography, the local axial-shear strain resulting from the application of quasi-static axial compression to an inhomogeneous material is imaged. In this paper, we investigated the image quality of the axial-shear strain estimates in terms of the signal-to-noise ratio (SNR(asse)) and contrast-to-noise ratio (CNR(asse)) using simulations and experiments. Specifically, we investigated the influence of the system parameters (beamwidth, transducer element pitch and bandwidth), signal processing parameters (correlation window length and axial window shift) and mechanical parameters (Young's modulus contrast, applied axial strain) on the SNR(asse) and CNR(asse). The results of the study show that the CNR(asse) (SNR(asse)) is maximum for axial-shear strain values in the range of 0.005-0.03. For the inclusion/background modulus contrast range considered in this study (<10), the CNR(asse) (SNR(asse)) is maximum for applied axial compressive strain values in the range of 0.005%-0.03%. This suggests that the RF data acquired during axial elastography can be used to obtain axial-shear strain elastograms, since this range is typically used in axial elastography as well. The CNR(asse) (SNR(asse)) remains almost constant with an increase in the beamwidth while it increases as the pitch increases. As expected, the axial shift had only a weak influence on the CNR(asse) (SNR(asse)) of the axial-shear strain estimates. We observed that the differential estimates of the axial-shear strain involve a trade-off between the CNR(asse) (SNR(asse)) and the spatial resolution only with respect to pitch and not with respect to signal processing parameters. Simulation studies were performed to confirm such an observation. The results demonstrate a trade-off between CNR(asse) and the resolution with respect to pitch.

OCT-based elastography for large and small deformations

We present two approaches to speckle tracking for optical coherence tomography (OCT)-based elastography, one appropriate for small speckle motions and the other for large, rapid speckle motions. Both approaches have certain advantages over traditional cross-correlation based motion algorithms. We apply our algorithms to quantifying the strain response of a mechanically inhomogeneous, bi-layered polyvinyl alcohol tissue phantom that is subjected to either small or large dynamic compressive forces while being imaged with a spectral domain OCT system. In both the small and large deformation scenarios, the algorithms performed well, clearly identifying the two mechanically disparate regions of the phantom. The stiffness ratio between the two regions was estimated to be the same for the two scenarios and both estimates agreed with the expected stiffness ratio based on earlier mechanical testing. No single numerical approach is appropriate for all cases and the experimental conditions dictate the proper choice of speckle shift algorithm for OCT-based elastography studies.

Imaging the mechanical stiffness of skin lesions by in vivo acousto-optical elastography

Optical elastography is an imaging modality that relies on variations in the local mechanical properties of biological tissues as the contrast mechanism for image formation. Skin lesions, such as melanomas and other invasive conditions, are known to alter the arrangement of collagen fibers in the skin and thus should lead to alterations in local skin mechanical properties. We report on an acousto-optical elastography (AOE) imaging modality for quantifying the mechanical behavior of skin lesions. The method relies upon stimulating the tissue with a low frequency acoustic force and imaging the resulting strains in the tissue by means of quantifying the magnitude of the dynamic shift in a back-reflected laser speckle pattern from the skin. The magnitude of the shift reflects the local stiffness of the tissue. We demonstrate AOE on a tissue-mimicking phantom, an in vivo mouse melanoma lesion and two types of in vivo human melanocytic nevi. The skin lesions we examined were found to have distinct mechanical properties that appear to correlate with the varying degrees of dermal involvement of the lesions.

Resolution of axial shear strain elastography

The technique of mapping the local axial component of the shear strain due to quasi-static axial compression is defined as axial shear strain elastography. In this paper, the spatial resolution of axial shear strain elastography is investigated through simulations, using an elastically stiff cylindrical lesion embedded in a homogeneously softer background. Resolution was defined as the smallest size of the inclusion for which the strain value at the inclusion/background interface was greater than the average of the axial shear strain values at the interface and inside the inclusion. The resolution was measured from the axial shear strain profile oriented at 45 degrees to the axis of beam propagation, due to the absence of axial shear strain along the normal directions. The effects of the ultrasound system parameters such as bandwidth, beamwidth and transducer element pitch along with signal processing parameters such as correlation window length (W) and axial shift (DeltaW) on the estimated resolution were investigated. The results show that the resolution (at 45 degrees orientation) is determined by the bandwidth and the beamwidth. However, the upper bound on the resolution is limited by the larger of the beamwidth and the window length, which is scaled inversely to the bandwidth. The results also show that the resolution is proportional to the pitch and not significantly affected by the axial window shift.

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.

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.

A new method for generating poroelastograms in noisy environments

Poroelastography has been recently introduced as a new elastographic technique that may be used to describe the spatial and temporal behavior of poroelastic materials. The experimental methodology proposed thus far for phantoms and tissues in vitro requires the acquisition of a precompression rf frame, the application of a unit step strain compression to the sample and the acquisition of subsequent post-compression frames from the material. Elastograms and poroelastograms are generated by cross-correlating the sequentially-acquired postcompression frames with the reference precompression frame. The application of poroelastography to tissues in vivo must address the echo decorrelation problems that are encountered due to uncontrolled tissue motion, which may become significant shortly after the acquisition of the precompression frame. In this paper, we investigate the feasibility of performing poroelastography experiments using an alternative experimental scheme. In the proposed experimental methodology, the reference precompression frame is continuously moved while the time interval between the frames that are correlated is kept short. This allows long data acquisition times with simultaneous minimization of the decorrelation due to undesired tissue motion in vivo. We validated this new method using both a step and a ramp compression functions. We performed poroelastographic simulations and experiments in phantoms and in tissues in vivo. The results were compared to those obtained using the traditional acquisition methodology. This study shows that the two methods yield similar results in vitro and suggests that the new method may be more robust to decorrelation noise in applications in vivo.

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.

Comparative evaluation of strain-based and model-based modulus elastography

Elastography based on strain imaging currently endures mechanical artefacts and limited contrast transfer efficiency. Solving the inverse elasticity problem (IEP) should obviate these difficulties; however, this approach to elastography is often fraught with problems because of the ill-posed nature of the IEP. The aim of the present study was to determine how the quality of modulus elastograms computed by solving the IEP compared with those produced using standard strain imaging methodology. Strain-based modulus elastograms (i.e., modulus elastograms computed by simply inverting strain elastograms based on the assumption of stress uniformity) and model-based modulus elastograms (i.e., modulus elastograms computed by solving the IEP) were computed from a common cohort of simulated and gelatin-based phantoms that contained inclusions of varying size and modulus contrast. The ensuing elastograms were evaluated by employing the contrast-to-noise ratio (CNR(e)) and the contrast transfer efficiency (CTE(e)) performance metrics. The results demonstrated that, at a fixed spatial resolution, the CNR(e) of strain-based modulus elastograms was statistically equivalent to those computed by solving the IEP. At low modulus contrast, the CTE(e) of both elastographic imaging approaches was comparable; however, at high modulus, the CTE(e) of model-based modulus elastograms was superior.

A method for generating permeability elastograms and Poisson's ratio time-constant elastograms

The feasibility of imaging the permeability and Poisson's ratio time-constant of porous media was investigated. The study involved the following steps. First, poroelastograms were generated from porous tofu phantoms under sustained compression. The sample materials used for the experiments were previously characterized through independent mechanical measurements. Second, corresponding Poisson's ratio time-constant elastograms were generated by calculating and displaying the decay time-constants of the local Poisson's ratios over the time interval in which the poroelastograms were acquired. Finally, for homogeneous samples, permeability elastograms were generated using the poroelastograms in combination with a previously proposed biphasic theoretical model, under very specific conditions. A comparison between the results obtained using poroelastography and those obtained through independent mechanical measurements suggests that poroelastography may be used for imaging the local time-dependent behavior of poroelastic media.

An experimental characterization of elastographic spatial resolution: analysis of the trade-offs between spatial resolution and contrast-to-noise ratio

An experimental study of the spatial resolution in elastography was conducted. Models that involved two cylindrical inclusions arranged as a wedge were used to characterize the axial and lateral resolution of the axial strain elastograms. A study of the dependence of the spatial resolution on several factors such as the algorithmic parameters, the applied strain and the modulus contrast was performed. The axial resolution was found to show a linear dependence with respect to the algorithmic parameters, namely the window length and the window shift used for strain estimation. The lateral resolution showed a weak dependence on the algorithmic parameters. A weak dependence of the spatial resolution on factors such as the modulus contrast and the applied strain was found. The trade-offs between the spatial resolution and the elastographic contrast-to-noise ratio (CNR(e)) were then analyzed. A nonlinear trade-off between the CNR(e) and the axial and lateral resolution was shown for conventional strain estimation techniques, with the CNR(e) improving at a more than linear rate with respect to a linear degradation in the resolution. This study provided an experimental framework for characterizing the spatial resolution in elastography and facilitating a comparison of the CNR(e) with spatial resolution.

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.

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.

Comparing elastographic strain images with modulus images obtained using nanoindentation: preliminary results using phantoms and tissue samples

Conventional elastography involves quasistatic mechanical compression (external or internal) of the tissue under ultrasonic insonification to obtain radiofrequency (RF) A-lines before and after compression. Cross-correlation of the pre- and postcompression A-lines results in displacement images with axial gradients that produce the strain images (strain elastograms). Though the strain elastograms show structural similarities to the modulus images, they are not related in a simple way to the modulus images because the strains depend on both modulus and geometry of the materials being deformed. Therefore, a quantification of the similarities between the strain and modulus images may enhance the interpretation confidence of strain elastograms in depicting tissue structure. To demonstrate similarities between modulus images and strain elastograms, a feasibility study of using nanoindentation to obtain modulus images of thin slices of tissue and tissue-mimicking phantoms (agar-gelatin mixtures) was performed first, with encouraging results. This was followed by a comparison of modulus images and strain elastograms obtained from the same sample slices. The experimental results indicated that, under certain experimental conditions, it is feasible to perform quantitative comparisons between strain images (using elastography) and modulus images. A good visual, as well as quantitative, correspondence between structures in the modulus and strain images could be obtained at a 3-mm scale.

The feasibility of using elastography for imaging the Poisson's ratio in porous media

The feasibility of using elastography for experimentally estimating and imaging the Poisson's ratio of porous media under drained and undrained conditions was investigated. Using standard elastographic procedures, static and time-sequenced poroelastograms (strain ratio images) of homogeneous cylindrical gelatin and commercially available tofu samples were generated under sustained applied axial strain. The experimental data show similar trends to those that were observed in finite-elements simulations, and to those that were calculated from classical theoretical models proposed for biphasic materials with similar mechanical properties. To demonstrate the applicability of elastography to monitor time-dependent changes in nonhomogeneous porous structures as well, preliminary time-sequenced poroelastograms were obtained from two-layer porous phantoms and porcine muscle samples in vitro. The results suggest that elastography may have significant potential for quantitatively mapping the time-dependent mechanical behavior of poroelastic media, which is related to the dynamics of fluid flow and to the elasticity and permeability parameters of the media.

Realtime-Elastographie

It is well known that some diseases, such as cancer, lead to a change of tissue hardness (i.e. the so-called elasticity modulus). The reconstruction of tissue elasticity provides the sonographer with important additional information which can be applied for the diagnosis of these diseases. Elasticity imaging has recently attracted attention as a technique which directly reveals the physical property of tissue and enables us to determine the change of tissue hardness caused by diseases. The elasticity modulus, i.e. the tissue elasticity distribution can be calculated from the strain and the stress of the examined structures. While the strain field can be estimated from the RF signals returned from tissue structures before and after compression, it is impossible to measure the stress field directly within the tissue. Another problem is that the compression of harder tissue structures is often followed by a lateral displacement of these structures. It is nearly impossible to represent the volume of this sideslip with conventional 2D methods but its calculation is indispensable for an accurate determination of the tissue elasticity of the examined structures. To overcome these problems, we propose the so-called Extended CA-method (Extended Combined Autocorrelation Method) which allows the reconstruction of the tissue elasticity of the examined structures on the basis of the 3-dimensional finite element model. The new technique enables a highly accurate estimation of the tissue elasticity distribution and the adequate compensation of sideslips. The realtime elasticity imaging described in this article, can easily be performed with the SonoElastography module that can be integrated into the platform of the HITACHI EUB-8500 system. Like colour Doppler examinations, tissue elasticity imaging can easily be performed with conventional ultrasound probes and does not require additional instruments (e.g. for measuring pressure or vibrations). The calculation of tissue elasticity distribution is performed in realtime and the examination results are represented in colour over the conventional B-mode image. The results of the simulations and phantom experiments performed verify that with the information obtained by the new realtime elasticity imaging method, lesions can be detected and represented more rapidly and with higher accuracy than with conventional methods based on the 2D Model, and that even lesions invisible on B-mode images can be detected.

Elastography imaging of small animal oncology models: a feasibility study

To test the feasibility of applying ultrasonic elastography on small animal oncology models, experiments were performed in vitro and in situ on murine mammary lesions induced exogenously by tumor cell line 66.3. In vitro studies involved three 1-week-old excised tumors embedded in a phantom block with ultrasonic properties similar to those of soft biologic tissues. In situ studies involved five mice whose bodies were embedded in pure gelatin blocks. The data were acquired from the blocks with a clinical scanner modified to have an automated compressor assembly and processed to construct the elastograms at various imaging planes within each block. The results were analyzed both qualitatively and quantitatively to assess the merits of the elastographic imaging and its limitations for in vivo serial studies of tumors in small animal oncology models.

Visualisation of HIFU lesions using elastography of the human prostate in vivo: preliminary results

An imaging system was developed for prostate elastography in vivo using a transrectal ultrasound (US) probe to guide high-intensity focused US (HIFU) therapy of prostate cancer. Uniform compression was applied using a balloon, while a sector image was acquired. Strain was calculated from the gradient of the displacements obtained from the ultrasonic signal using the cross-correlation technique. Elastograms were acquired on a total of 31 patients undergoing HIFU therapy for localised prostate cancer. For two patients, only part of the prostate was treated and posttherapy magnetic resonance imaging (MRI) confirmed the size and position of the HIFU lesions seen in the elastograms as low strain areas, with a strain contrast ratio between 1.6 and 3.2. The whole prostate was treated for the next 29 patients. After treatment, the whole prostate appeared to be stiff in the elastograms and a 40% to 60% (mean 50%) decrease in average strain was observed when compared to strains measured before HIFU application. Tumours identified by biopsies and sonograms could occasionally be seen in the preoperative elastograms. Decorrelation effects occurred mainly because of low sonographic signal-to-noise ratio (SNR) and of out-of-plane motion induced by respiration.

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.

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.

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.

Elastographic imaging using staggered strain estimates

Conventional techniques in elastography estimate strain as the gradient of the displacement estimates obtained through crosscorrelation of pre- and postcompression rf A-lines. In these techniques, the displacements are estimated over overlapping windows and the strains are estimated as the gradient of the displacement estimates over adjacent windows. The large amount ofnoise at high window overlaps may result in poor quality elastograms, thus restricting the applicability of conventional strain estimation techniques to low window overlaps, which, in turn, results in a small number of pixels in the image. To overcome this restriction, we propose a multistep strain estimation technique. It computes the first elastogram using nonoverlapped windows. In the next step, the data windows are shifted by a small distance (small fraction of window size) and another elastogram is produced. This is repeated until the cumulative shift equals/exceeds the window size and all the elastograms are staggered to produce the final elastogram. Simulations and experiments were performed using this technique to demonstrate significant improvement in the elastographic signal-to-noise ratio (SNRe) and the contrast-to-noise ratio (CNRe) at high window overlaps over conventional strain estimation techniques, without noticeable loss of spatial resolution. This technique might be suitable for reducing the algorithmic noise in the elastograms at high window overlaps.