Regularization-Based 2D Strain Tensor Imaging in Quasi-Static Ultrasound Elastography SAGE Publications.

Accurately estimating all strain components in quasi-static ultrasound elastography is crucial for the full analysis of biological media. In this study, 2D strain tensor imaging was investigated, focusing on the use of a regularization method to improve strain images. This method enforces the tissue property of (quasi-) incompressibility, while penalizing strong field variations, to smooth the displacement fields and reduce the noise in the strain components. The performance of the method was assessed with numerical simulations, phantoms, and in vivo breast tissues. For all the media examined, the results showed a significant improvement in both lateral displacement and strain, while axial fields were only slightly modified by the regularization. The introduction of penalty terms allowed us to obtain shear strain and rotation elastograms where the patterns around the inclusions/lesions were clearly visible. In phantom cases, the findings were consistent with the results obtained from the modeling of the experiments. Finally, the easier detectability of the inclusions/lesions in the final lateral strain images was associated with higher elastographic contrast-to-noise ratios (CNRs), with values in the range of [0.54-9.57] versus [0.08-0.38] before regularization.

Reconstructing the Spatial Distribution of the Relative Shear Modulus in Quasi-static Ultrasound Elastography: Plane Stress Analysis.

Quasi-static ultrasound elastography (QSUE) is an imaging technique that mainly provides axial strain maps of tissues when the latter are subjected to compression. In this article, a method for reconstructing the relative shear modulus distribution within a linear elastic and isotropic medium, in QSUE, is introduced. More specifically, the plane stress inverse problem is considered. The proposed method is based on the variational formulation of the equilibrium equations and on the choice of adapted discretization spaces, and only requires displacement fields in the analyzed media to be determined. Results from plane stress and 3-D numerical simulations, as well as from phantom experiments, showed that the method is able to reconstruct the different regions within a medium, with shear modulus contrasts that unambiguously reveal whether inclusions are stiffer or softer than the surrounding material. More specifically, for the plane stress simulations, inclusion-to-background modulus ratios were found to be very accurately estimated, with an error lower than 3%. For the 3-D simulations, for which the plane stress conditions are no longer satisfied, these ratios were, as expected, less accurate, with an error that remained lower than 10% for two of the three cases analyzed but was around 34% for the last case. Concerning the phantom experiments, a comparison with a shear wave elastography technique from a clinical ultrasound scanner was also made. Overall, the inclusion-to-background shear modulus ratios obtained with our approach were found to be closer to those given by the phantom manufacturer than the ratios provided by the clinical system.

On the potential of ultrasound elastography for pressure ulcer early detection.

PURPOSE: Pressure ulcers are areas of soft tissue breakdown induced by a sustained mechanical stress that damages the skin and underlying tissues. They represent a considerable burden to the society in terms of health care and cost. Yet, techniques for prevention and detection of pressure ulcers still remain very limited. In this article, the authors investigated the potential of ultrasound elastography for pressure ulcer early detection. Elastography is an imaging technique providing local information on biological tissue mechanical properties. It is relevant for pressure ulcer detection as this pathology is associated with a gradual stiffening of damaged tissues, beginning in the deeper tissues and progressing toward the skin surface. METHODS: A 2D ultrasound elastography method was proposed and its ability in terms of pressure ulcer detection was validated through numerical simulations and physical acquisitions on pressure ulcer mimicking phantoms. In vivo experiments on a rat model are also reported. A maintained pressure was applied on the animal thigh, with a view to generate a pressure ulcer, and ultrasound data were acquired and processed before and after application of this pressure. RESULTS: Numerical simulations demonstrated that a pressure ulcer can theoretically be detected at a very early stage with ultrasound elastography. Even when the ulcer region was characterized by a low stiffening (ratio of 1.8 relative to normal tissues), the corresponding elastogram clearly underlined the pathological area. This observation was confirmed by the results obtained on a physical phantom mimicking a pressure ulcer at an early stage. Computed elastograms showed strain differences between areas mimicking healthy and pathological tissues. Results corresponding to in vivo experiments revealed a difference in the way tissues behaved before and after the pressure was applied on the animal thigh, which strongly suggests the presence of a pathological area. CONCLUSIONS: Experiments demonstrated that ultrasound elastography is a promising technique for pressure ulcer detection, especially at an early stage of the pathology, when the disease is still visually undetectable. In the absence of any gold standard method, this is also a first step toward the development of a quantitative technique.

2D tissue strain tensor imaging in quasi-static ultrasound elastography.

Accurately estimating all strain components in quasi-static ultrasound elastography is crucial for the full analysis of biological media. In this paper, 2D strain tensor imaging is investigated, using a partial differential equation (PDE)-based regularization method. More specifically, this method employs the tissue property of incompressibility to smooth the displacement fields and reduce the noise in the strain components. The performance of the method is assessed with phantoms and in vivo breast tissues. For all the media examined, the results showed a significant improvement in both lateral displacement and strain but also, to a lesser extent, in the shear strain. Moreover, axial displacement and strain were only slightly modified by the regularization, as expected. Finally, the easier detectability of the inclusion/lesion in the final lateral strain images is associated with higher elastographic contrast-to-noise ratios (CNRs), with values in the range [0.68 - 9.40] vs [0.09 - 0.38] before regularization.

Reconstructing the shear modulus contrast of linear elastic and isotropic media in quasi-static ultrasound elastography.

This study focuses on the reconstruction of the shear modulus contrast in linear elastic and isotropic media, in quasi-static ultrasound elastography. The method proposed is based on the variational formulation of the equilibrium equations and on the choice of adapted discretization spaces to estimate the parameters of interest. Experimental results obtained with CIRS phantoms are presented, for which regions with different mechanical properties can be clearly identified in the stiffness contrast maps. Elastic modulus images collected with a shear-wave elastography technique from a clinical ultrasound scanner (Aixplorer) are also provided for comparison. Results show very similar values for the modulus ratios determined by the two elastography approaches.

Investigation of PVA cryogel Young's modulus stability with time, controlled by a simple reliable technique.

We describe a quasistatic method for mechanical characterization of tissue-mimicking material used in elastography. We demonstrate that it is possible to assess the elasticity modulus with a reasonable reproducibility using simple and easy tools and methods. Possessing a simple relevant technique with evaluated relative error to assess Young's modulus of these phantoms could deeply improve the quality of the research in the field of elastography. The method was tested and validated with four samples of polyvinyl alcohol (PVA) cryogel with different elasticity values corresponding to those of stiffer soft biological tissues. Young's moduli, varying from 70 to 180 kPa depending on the number of freeze-thaw cycles (two to five), were measured within strict measurement conditions and found to have a reproducibility varying from 4% to 8%. Relative error, estimated as the ratio between observed and reference values, varied from 16% to 32%. Besides, measurement stability over 4 months was evaluated. The method demonstrated good feasibility and acceptable reproducibility for mechanically characterizing and controlled over time phantoms used for validating new potential ultrasound imaging techniques in the field of elastography. Nevertheless, in this study, investigation was performed on gel possessing young's modulus values ranging from 80 to 215 kPa. Some tissue values of Young'modulus were reported to be lower, ranging from 0.6 to 28 kPa as liver or glandular values. Consequently, further validation of this static method for mechanical characterization of phantom gels should be performed using softer PVA cryogel.

2-D locally regularized tissue strain estimation from radio-frequency ultrasound images: theoretical developments and results on experimental data.

In this paper, a 2-D locally regularized strain estimation method for imaging deformation of soft biological tissues from radio-frequency (RF) ultrasound (US) data is introduced. Contrary to most 2-D techniques that model the compression-induced local displacement as a 2-D shift, our algorithm also considers a local scaling factor in the axial direction. This direction-dependent model of tissue motion and deformation is induced by the highly anisotropic resolution of RF US images. Optimal parameters are computed through the constrained maximization of a similarity criterion defined as the normalized correlation coefficient. Its value at the solution is then used as an indicator of estimation reliability, the probability of correct estimation increasing with the correlation value. In case of correlation loss, the estimation integrates an additional constraint, imposing local continuity within displacement and strain fields. Using local scaling factors and regularization increase the method's robustness with regard to decorrelation noise, resulting in a wider range of precise measurements. Results on simulated US data from a mechanically homogeneous medium subjected to successive uniaxial loadings demonstrate that our method is theoretically able to accurately estimate strains up to 17%. Experimental strain images of phantom and cut specimens of bovine liver clearly show the harder inclusions.

Constant gradient elastography with optimal control RF pulses.

This article presents a new motion encoding strategy to perform magnetic resonance elastography (MRE). Instead of using standard motion encoding gradients, a tailored RF pulse is designed to simultaneously perform selective excitation and motion encoding in presence of a constant gradient. The RF pulse is designed with a numerical optimal control algorithm, in order to obtain a magnetization phase distribution that depends on the displacement characteristics inside each voxel. As a consequence, no post-excitation encoding gradients are required. This offers numerous advantages, such as reducing eddy current artifacts, and relaxing the constraint on the gradients maximum switch rate. It also allows to perform MRE with ultra-short TE acquisition schemes, which limits T2 decay and optimizes signal-to-noise ratio. The pulse design strategy is developed and analytically analyzed to clarify the encoding mechanism. Finally, simulations, phantom and ex vivo experiments show that phase-to-noise ratios are improved when compared to standard MRE encoding strategies.

On the potential of the lagrangian estimator for endovascular ultrasound elastography: in vivo human coronary artery study.

Diagnosis and prognosis of coronary artery atherosclerosis evolution currently rely on plaque morphology and vessel stenosis degree. Such information can accurately be assessed with intravascular ultrasound (IVUS) imaging. A severe complication of coronary artery atherosclerosis is thrombosis, a consequence of plaque rupture or fissure, which might lead to myocardial infarction and sudden ischemic death. Plaque rupture is a complicated mechanical process, correlated with the plaque morphology, composition, mechanical properties and with the blood pressure. Extracting information on the plaque local mechanical properties may reveal relevant features about plaque vulnerability. Accordingly, endovascular elastography (EVE) was introduced to complement IVUS for investigating coronary artery diseases. In this article, in vivo elastographic data are reported for three patients (patient 1, patient 2 and patient 3) who were diagnosed with severe coronary artery stenoses. Time-sequence radio-frequency (RF) data were acquired, in the minutes preceding angioplasty, using an ultrasound scanner working with a 30 MHz mechanical rotating single-element transducer. The elastograms of the radial strain and radial shear distributions within the vessel wall were computed from pairs of successive RF images using the Lagrangian estimator (LE). A hard atherosclerotic plaque (low radial strain and shear) was identified in patient 1. High radial strain and shear values in the plaque areas for patient 2 and patient 3 suggested the presence of lipid cores (soft materials), known to be prone-to-rupture sites when located close to the lumen. To conclude, EVE allowing radial strain and shear images is an improvement over existing EVE methods that may assist IVUS in preoperative vessel lesion assessments and in endovascular therapy planning.

Radiofrequency ultrasound data acquisition with a 640-element array transducer for strain imaging: Experimental results with phantoms and biological tissue samples.

This paper presents ultrasound elastography results obtained with a 640-element array transducer we have recently developed. This probe allows the acquisition of series of three adjacent imaging planes over time and therefore makes possible the computation of 2-D elastograms, with consideration of out-of-plane motion. In this study, elastography experiments were conducted on phantoms and bovine tissue samples, and compression was manually applied to the media via the hand-held ultrasound transducer. The results obtained with the proposed data acquisition and 3-D processing are presented and compared to those from a classical 2-D approach.

Specific Ultrasound Data Acquisition for Tissue Motion and Strain Estimation: Initial Results.

Ultrasound applications such as elastography can benefit from 3-D data acquisition and processing. In this article, we describe a specific ultrasound probe, designed to acquire series of three adjacent imaging planes over time. This data acquisition makes it possible to consider the out-of-plane motion that can occur at the central plane during medium scanning, and is proposed with the aim of improving the results of strain imaging. In this first study, experiments were conducted on phantoms, and controlled axial and elevational displacements were applied to the probe using a motorized system. Radiofrequency ultrasound data were acquired at a 40-MHz sampling frequency with an Ultrasonix ultrasound scanner, and processed using a 3-D motion estimation method. For each of the 2-D regions of interest of the central plane in pre-compression data, a 3-D search was run to determine its corresponding version in post-compression data, with this search taking into account the region-of-interest deformation model chosen. The results obtained with the proposed ultrasound data acquisition and strain estimation were compared with results from a classic approach and illustrate the improvement produced by considering the medium's local displacements in elevation, with notably an increase in the mean correlation coefficients achieved.

Active control of the spatial MRI phase distribution with optimal control theory.

This paper investigates the use of Optimal Control (OC) theory to design Radio-Frequency (RF) pulses that actively control the spatial distribution of the MRI magnetization phase. The RF pulses are generated through the application of the Pontryagin Maximum Principle and optimized so that the resulting transverse magnetization reproduces various non-trivial and spatial phase patterns. Two different phase patterns are defined and the resulting optimal pulses are tested both numerically with the ODIN MRI simulator and experimentally with an agar gel phantom on a 4.7T small-animal MR scanner. Phase images obtained in simulations and experiments are both consistent with the defined phase patterns. A practical application of phase control with OC-designed pulses is also presented, with the generation of RF pulses adapted for a Magnetic Resonance Elastography experiment. This study demonstrates the possibility to use OC-designed RF pulses to encode information in the magnetization phase and could have applications in MRI sequences using phase images.

On the potential of the Lagrangian speckle model estimator to characterize atherosclerotic plaques in endovascular elastography: in vitro experiments using an excised human carotid artery.

Endovascular ultrasound (US) elastography (EVE) was introduced to supplement endovascular US echograms in the assessment of vessel lesions and for endovascular therapy planning. Indeed, changes in the vascular tissue stiffness are characteristic of vessel wall pathologies and EVE appears as a very appropriate imaging technique to outline the elastic properties of vessel walls. Recently, a model-based approach was proposed to assess tissue motion in EVE. It specifically consists of a nonlinear minimization algorithm that was adapted to speckle motion estimation. Regarding the theoretical framework, such an approach considers the speckle as a material property; this assumption then led to the derivation of the optical flow equations, which were suitably combined with the Lagrangian speckle model estimator to provide the full 2-D polar strain tensor. In this study, the proposed algorithm was validated in vitro using a fresh excised human carotid artery. The experimental setup consisted of a cardiovascular imaging system (CVIS) US scanner, working with a 30-MHz mechanical rotating single-element transducer, a digital oscilloscope and a pressuring system. A sequence of radiofrequency (RF) images was collected while incrementally adjusting the intraluminal static pressure steps. The results showed the potential of this 2-D algorithm to characterize and to distinguish an atherosclerotic plaque from the normal vascular tissue. Namely, the geometry as well as some mechanical characteristics of the detected plaque were in good agreement with histology. The results also suggested that there might exist a range of intraluminal pressures for which plaque detectability is optimal.

Fully automatic luminal contour segmentation in intracoronary ultrasound imaging--a statistical approach.

In this paper, a fully automatic method for luminal contour segmentation in intracoronary ultrasound imaging is introduced. Its principle is based on a contour with a priori properties that evolves according to the statistics of the ultrasound texture brightness, which is generally Rayleigh distributed. The main interest of the technique is its fully automatic character. This is insured by an initial contour that is not set by the user, like in classical snake-based algorithms, but estimated and, thus, adapted to each image. Its estimation combines two pieces of information extracted from the a posteriori probability function of the contour position: the function maximum location (or maximum a posteriori estimator) and the first zero-crossing of its derivative. Then, starting from the initial contour, a region of interest is automatically selected and the process iterated until the contour evolution can be ignored. In vivo coronary images from 15 patients, acquired with the 20-MHz central frequency Jomed Invision ultrasound scanner, were segmented with the developed method. Automatic contours were compared to those manually drawn by two physicians in terms of mean absolute difference. The results demonstrate that the error between automatic contours and the average of manual ones is of small amplitude, and only very slightly higher (0.099 +/- 0.032 mm) than the interexpert error (0.097 +/- 0.027 mm).

Characterization of PVA cryogel for intravascular ultrasound elasticity imaging.

The present study characterizes the mechanical properties of polyvinyl alcohol (PVA) cryogel in order to show its utility for intravascular elastography. PVA cryogel becomes harder with an increasing number of freeze-thaw cycles, and Young's modulus and Poisson's ratio are measured for seven samples. Mechanical tests were performed on cylindrical samples with a pressure column and on a hollow cylinder with the calculation of an intravascular elastogram. An image of the Young's modulus was obtained from the elastogram using cylinder geometry properties. Results show the mechanical similitude of PVA cryogel with the biological tissues present in arteries. A good agreement between Young's modulus obtained from pressure column and from elastogram was also observed.

In Vivo response to compression of 35 breast lesions observed with a two-dimensional locally regularized strain estimation method.

The objective of this study was to assess the in vivo performance of our 2-D locally regularized strain estimation method with 35 breast lesions, mainly cysts, fibroadenomas and carcinomas. The specific 2-D deformation model used, as well as the method's adaptability, led to an algorithm that is able to track tissue motion from radiofrequency ultrasound images acquired in clinical conditions. Particular attention was paid to strain estimation reliability, implying analysis of the mean normalized correlation coefficient maps. For all lesions examined, the results indicated that strain image interpretation, as well as its comparison with B-mode data, should take into account the information provided by the mean normalized correlation coefficient map. Different trends were observed in the tissue response to compression. In particular, carcinomas appeared larger in strain images than in B-mode images, resulting in a mean strain/B-mode lesion area ratio of 2.59 ± 1.36. In comparison, the same ratio was assessed as 1.04 ± 0.26 for fibroadenomas. These results are in agreement with those of previous studies, and confirm the interest of a more thorough consideration of size difference as one parameter discriminating between malignant and benign lesions.

3D estimation of soft biological tissue deformation from radio-frequency ultrasound volume acquisitions.

The current research and development of 2D (matrix-shaped) transducer arrays to acquire 3D ultrasound data sets provides new insights into medical ultrasound applications and in particular into elastography. Until very recently, tissue strain estimation techniques commonly used in elastography were mainly 1D or 2D methods. In this paper, a 3D technique estimating biological soft tissue deformation under load from ultrasound radiofrequency volume acquisitions is introduced. This method locally computes axial strains, while considering lateral and elevational motions. Optimal deformation parameters are estimated as those maximizing a similarity criterion, defined as the normalized correlation coefficient, between an initial region and its deformed version, when the latter is compensated for according to these parameters. The performance of our algorithm was assessed with numerical data reproducing the configuration of breast cancer, as well as a physical phantom mimicking a pressure ulcer. Simulation results show that the estimated strain fields are very close to the theoretical values, perfectly discriminating between the harder lesion and the surrounding medium. Experimental strain images of the physical phantom demonstrated the different structures of the medium, even though they are not all detectable on the ultrasound scans. Finally, both simulated and experimental results demonstrate the ability of our algorithm to provide good-quality elastograms, even in the conditions of significant out-of-plane motion.

Locally regularized strain field estimation for freehand elastography.

This paper focuses on strain estimation methods in ultrasound elastography. We recently developed a 2D locally regularized strain estimation algorithm, whose performance was assessed with simulations and experimental data, but in the case of a well controlled medium deformation. In this study, we investigate the robustness of our algorithm to image tissue deformation during freehand scanning. Results on an elastography dedicated phantom and biological tissue ex vivo demonstrate the ability of our algorithm to provide good-quality strain maps, even in more complex loading conditions.

3D ultrasound elastography for early detection of lesions. evaluation on a pressure ulcer mimicking phantom.

A pressure ulcer is a damaged tissue area induced by an unrelieved pressure compressing the tissue during a prolonged period of immobility. The lack of information and studies on the development of this pathology makes its prevention difficult. However, it is both acknowledged that lesions initiate in the deep muscular tissues before they expand to the skin, and that lesions are harder than healthy tissues. Elastography is therefore an interesting tool for an early detection of the pathology. A 3D strain estimation algorithm is presented and evaluated on a PVA-cryogel phantom, mimicking a pressure ulcer at an early stage.