Breast tumor classification using axial shear strain elastography: a feasibility study.

Recently, the feasibility of visualizing the characteristics of bonding at an inclusion-background boundary using axial-shear strain elastography was demonstrated. In this paper, we report a feasibility study on the utility of the axial-shear strain elastograms in the classification of in vivo breast tumor as being benign or malignant. The study was performed using data sets obtained from 15 benign and 15 malignant cases that were biopsy proven. A total of three independent observers were trained, and their services were utilized for the study. A total of 9 cases were used as training set and the remaining cases were used as testing set. The feature from the axial-shear strain elastogram, namely, the area of the axial-shear region, was extracted by the observers. The observers also outlined the tumor area on the corresponding sonogram, which was used to normalize the area of the axial-shear strain region. There are several observations that can be drawn from the results. First, the result indicates that the observers consistently ( approximately 82% of the cases) noticed the characteristic pattern of the axial-shear strain distribution data as predicted in the previous simulation studies, i.e. alternating regions of positive and negative axial-shear strain values around the tumor-background interface. Second, the analysis of the result suggests that in approximately 57% of the cases in which the observers did not visualize tumor in the sonogram, the elastograms helped them to locate the tumor. Finally, the analysis of the result suggests that for the discriminant feature value of 0.46, the number of unnecessary biopsies could be reduced by 56.3% without compromising on sensitivity and on negative predictive value (NPV). Based on the results in this study, feature values greater than 0.75 appear to be indicative of malignancy, while values less than 0.46 to be indicative of benignity. Feature values between 0.46 and 0.75 may result in an overlap between benign and malignant cases.

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.

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.

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.

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.

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.

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.

Effect of lesion boundary conditions on axial strain elastograms: a parametric study.

Ultrasound elastography produces strain images of compliant tissues under quasi-static compression. When a material is compressed, there are several parameters that affect the stress-distribution and, hence, the strain distribution in the material. The state of bonding of an inclusion to the background material is a critical parameter. Heretofore, in the field of elastography, the inclusion was considered to be firmly bonded to the background material and analytical solutions were derived for the elasticity problem involving simple geometries like circular inclusion (for two dimensional [2D]) and spherical inclusion (three dimensional [3D]). Under these conditions, simple analytical expressions relating the strain contrast to the modulus contrast were derived. However, it is known that the state of bonding of some tumors to their surrounding tissues depends on the type of the lesion. For example, benign lesions of the breast are known to be loosely bonded to the surrounding tissue, while malignant breast lesions are firmly bonded. In this study, we perform a parametric study using finite element modeling (FEM) to investigate the validity of the analytical expression relating the strain contrast to the modulus contrast, when the state of bonding at the inclusion/background interface spans a large dynamic range. The results suggest that estimated modulus contrast using the analytical expression is sensitive to the region-of-interest within the inclusion that is considered in the computation of the strain contrast. By considering the inclusion region lying along the axis of lateral symmetry instead of whole region of the inclusion, the estimated modulus contrast (obtained using the analytical expression present in the literature) can be computed to within a systematic error of 10% of the actual modulus contrast. Additional estimation errors are expected to accrue in experimental and in vivo conditions.

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.

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.

Enhancing the performance of model-based elastography by incorporating additional a priori information in the modulus image reconstruction process.

Model-based elastography is fraught with problems owing to the ill-posed nature of the inverse elasticity problem. To overcome this limitation, we have recently developed a novel inversion scheme that incorporates a priori information concerning the mechanical properties of the underlying tissue structures, and the variance incurred during displacement estimation in the modulus image reconstruction process. The information was procured by employing standard strain imaging methodology, and introduced in the reconstruction process through the generalized Tikhonov approach. In this paper, we report the results of experiments conducted on gelatin phantoms to evaluate the performance of modulus elastograms computed with the generalized Tikhonov (GTK) estimation criterion relative to those computed by employing the un-weighted least-squares estimation criterion, the weighted least-squares estimation criterion and the standard Tikhonov method (i.e., the generalized Tikhonov method with no modulus prior). The results indicate that modulus elastograms computed with the generalized Tikhonov approach had superior elastographic contrast discrimination and contrast recovery. In addition, image reconstruction was more resilient to structural decorrelation noise when additional constraints were imposed on the reconstruction process through the GTK method.

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.

Design and Testing of a Single-Element Ultrasound Viscoelastography System for Point-of-Care Edema Quantification.

Management of fluid overload in patients with end-stage renal disease represents a unique challenge to clinical practice because of the lack of accurate and objective measurement methods. Currently, peripheral edema is subjectively assessed by palpation of the patient's extremities, ostensibly a qualitative indication of tissue viscoelastic properties. New robust quantitative estimates of tissue fluid content would allow clinicians to better guide treatment, minimizing reactive treatment decision making. Ultrasound viscoelastography (UVE) can be used to estimate strain in viscoelastic tissue, deriving material properties that can help guide treatment. We are developing and testing a simple, low-cost UVE system using a single-element imaging transducer that is simpler and less computationally demanding than array-based systems. This benchtop validation study tested the feasibility of using the UVE system by measuring the mechanical properties of a tissue-mimicking material under large strains. We generated depth-dependent creep curves and viscoelastic parameter maps of time constants and elastic moduli for the Kelvin model of viscoelasticity. During testing, the UVE system performed well, with mean UVE-measured strain matching standard mechanical testing with maximum absolute errors ≤4%. Motion tracking revealed high correlation and signal-to-noise ratios, indicating that the system is reliable.

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.

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.

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.

In vivo elastographic investigation of ethanol-induced hepatic lesions.

Ethanol-induced hepatic lesions were investigated in swine for in vivo use as a strain imaging animal model. Lesions (n = 25) were induced by injecting ethanol (doses 0.33 to 2.0 mL) directly into the surgically exposed liver at depths of 12, 15 or 25 mm. Lesions were imaged with a modified HDI 1000 scanner (Philips Medical Systems, Bothell, WA, USA). The elastograms (n = 91) characterized lesions as being areas harder than the surrounding soft hepatic tissue. Elastographic lesion sizes and the corresponding injected ethanol dose used to induce the lesions were shown to be statistically significant (r(2) = 0.22; p = 0.029) using a linear regression analysis. Additionally, lesion depth was shown to be statistically insignificant (r(2) < 0.12; p > 0.10) when regressed against elastographic lesion size. An analysis of elastographic and gross pathology lesion sizes indicated no correlation (r(2) < 0.01; p = 0.973). Subsequently, lesion types were sorted by size and regression lines were computed from quasilinear regions of the corresponding run charts. Trend lines indicate a four-to-three size relationship between the selected elastographic and pathology lesion sizes. Comparison of elastogram lesion sizes from two independent observers using a paired t-test resulted in no statistically significant difference (p = 0.14). In conclusion, ethanol-induced hepatic lesions in swine is a suitable animal model for evaluation of strain-based imaging systems, due to the ease of generation and repeatability.

Dynamic measurement of internal solid displacement in articular cartilage using ultrasound backscatter.

Mechanics of articular cartilage can be represented using poroelastic theories where fluid and solid displacements are viscously coupled to create a time-dependent spatially heterogeneous behavior. In recent models of this tissue, finite element methods have been used to predict tissue deformation as a function of time for adult articular cartilage bearing a characteristic depth-dependent structure and composition. However, current experimental methods are limited in providing verification of these predictions. The current study presents an apparatus for imaging the radial displacement profile of cartilage in unconfined compression using an ultrasound technique called elastography. We acquired ultrasound A-scans across the lateral diameter of full-thickness cartilage disks containing a thin layer of underlying bone, during axial compression. Elastography was then applied to correlate temporally sequential A-scans to estimate the solid radial displacement profile in articular cartilage while it undergoes compression and stress-relaxation. Both time-dependent and depth-dependent solid radial displacement profiles were obtained with a precision better than 0.2 micro The results generally agree with predictions of poroelastic models, demonstrating lateral expansion with an effective Poisson's ratio just after completion of the compression phase of the mechanical tests reaching values from 0.18 to 0.4 (depending on compression speed), followed by contraction to lower values. A more restricted movement was observed at both the articular surface and near to the subchondral bone than at regions midway between these two locations.

Axial resolution in elastography.

The limits and trade-offs of the axial resolution in elastography were investigated using a controlled simulation study. The axial resolution in elastography was estimated as the distance between the full widths at half-maximum of the strain profiles of two equally stiff lesions embedded in a softer homogeneous background. The results show that the upper bound of the axial resolution in elastography is controlled by the physical wave parameters of the ultrasound (US) system used to acquire the data (transducer center frequency and band- width). However, an inappropriate choice of the parameters used to process the US data (cross-correlation window length and shift between consecutive windows) may compromise the best resolution attainable. The measured elastographic axial resolution was found to be on the order of the ultrasonic wavelength.