Precision estimation and imaging of normal and shear components of the 3D strain tensor in elastography

Analytical Estimation of Out-of-plane Strain in Ultrasound Elastography to Improve Axial and Lateral Displacement Fields. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2020;2020:2055-2058. [PMID: 33018409 DOI: 10.1109/embc44109.2020.9176086] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Many types of cancers are associated with changes in tissue mechanical properties. This has led to the development of elastography as a clinically viable method where tissue mechanical properties are mapped and visualized for cancer detection and staging. In quasi-static ultrasound elastography, a mechanical stimulation is applied to the tissue using ultrasound probe. Using ultrasound radiofrequency (RF) data acquired before and after the stimulation, the tissue displacement field can be estimated. Elasticity image reconstruction algorithms use this displacement data to generate images of the tissue elasticity properties. The accuracy of the generated elasticity images depends highly on the accuracy of the tissue displacement estimation. Tissue incompressibility can be used as a constraint to improve the estimation of axial and, more importantly, the lateral displacements in 2D ultrasound elastography. Especially in clinical applications, this requires accurate estimation of the out-of-plane strain. Here, we propose a method for providing an accurate estimate of the out-of-plane strain which is incorporated in the incompressibility equation to improve the axial and lateral displacements estimation before elastography image reconstruction. The method was validated using in silico and tissue mimicking phantom studies, leading to significant improvement in the estimated displacement.

Accelerating 3-D GPU-based Motion Tracking for Ultrasound Strain Elastography Using Sum-Tables: Analysis and Initial Results

Now, with the availability of 3-D ultrasound data, a lot of research efforts are being devoted to developing 3-D ultrasound strain elastography (USE) systems. Because 3-D motion tracking, a core component in any 3-D USE system, is computationally intensive, a lot of efforts are under way to accelerate 3-D motion tracking. In the literature, the concept of Sum-Table has been used in a serial computing environment to reduce the burden of computing signal correlation, which is the single most computationally intensive component in 3-D motion tracking. In this study, parallel programming using graphics processing units (GPU) is used in conjunction with the concept of Sum-Table to improve the computational efficiency of 3-D motion tracking. To our knowledge, sum-tables have not been used in a GPU environment for 3-D motion tracking. Our main objective here is to investigate the feasibility of using sum-table-based normalized correlation coefficient (ST-NCC) method for the above-mentioned GPU-accelerated 3-D USE. More specifically, two different implementations of ST-NCC methods proposed by Lewis et al. and Luo-Konofagou are compared against each other. During the performance comparison, the conventional method for calculating the normalized correlation coefficient (NCC) was used as the baseline. All three methods were implemented using compute unified device architecture (CUDA; Version 9.0, Nvidia Inc., CA, USA) and tested on a professional GeForce GTX TITAN X card (Nvidia Inc., CA, USA). Using 3-D ultrasound data acquired during a tissue-mimicking phantom experiment, both displacement tracking accuracy and computational efficiency were evaluated for the above-mentioned three different methods. Based on data investigated, we found that under the GPU platform, Lou-Konofaguo method can still improve the computational efficiency (17–46%), as compared to the classic NCC method implemented into the same GPU platform. However, the Lewis method does not improve the computational efficiency in some configuration or improves the computational efficiency at a lower rate (7–23%) under the GPU parallel computing environment. Comparable displacement tracking accuracy was obtained by both methods.

A Fast Peak-Searching Algorithm for Ultrasonic Elastography

Tissue axial strain estimation with ultrasound elastography has become a hot field in recent years. However, for keypoints tracking-based elastography algorithms, locating extrema in multimodal ultrasonic radiofrequency signals is still a challenging problem. In this paper, a new method is proposed to locate the local maxima and minima of the RF signals directly without derivation operation. This algorithm can accurately locate extrema even if disturbed peaks resulting from different noise exist. Furthermore, the new algorithm can speed up approximately 79% of the implementation process as compared with the standard cross-correlation method on the same computing platform. In addition, the elastographic signal-to-noise ratio and the contrast-to-noise ratio are also significantly improved with this new method.

A GPU-Accelerated 3-D Coupled Subsample Estimation Algorithm for Volumetric Breast Strain Elastography

Our primary objective of this paper was to extend a previously published 2-D coupled subsample tracking algorithm for 3-D speckle tracking in the framework of ultrasound breast strain elastography. In order to overcome heavy computational cost, we investigated the use of a graphic processing unit (GPU) to accelerate the 3-D coupled subsample speckle tracking method. The performance of the proposed GPU implementation was tested using a tissue-mimicking phantom and in vivo breast ultrasound data. The performance of this 3-D subsample tracking algorithm was compared with the conventional 3-D quadratic subsample estimation algorithm. On the basis of these evaluations, we concluded that the GPU implementation of this 3-D subsample estimation algorithm can provide high-quality strain data (i.e., high correlation between the predeformation and the motion-compensated postdeformation radio frequency echo data and high contrast-to-noise ratio strain images), as compared with the conventional 3-D quadratic subsample algorithm. Using the GPU implementation of the 3-D speckle tracking algorithm, volumetric strain data can be achieved relatively fast (approximately 20 s per volume [2.5 cm ×2.5 cm ×2.5 cm]).

3D Myocardial Elastography In Vivo

Strain evaluation is of major interest in clinical cardiology as it can quantify the cardiac function. Myocardial elastography, a radio-frequency (RF)-based cross-correlation method, has been developed to evaluate the local strain distribution in the heart in vivo. However, inhomogeneities such as RF ablation lesions or infarction require a three-dimensional approach to be measured accurately. In addition, acquisitions at high volume rate are essential to evaluate the cardiac strain in three dimensions. Conventional focused transmit schemes using 2D matrix arrays, trade off sufficient volume rate for beam density or sector size to image rapid moving structure such as the heart, which lowers accuracy and precision in the strain estimation. In this study, we developed 3D myocardial elastography at high volume rates using diverging wave transmits to evaluate the local axial strain distribution in three dimensions in three open-chest canines before and after radio-frequency ablation. Acquisitions were performed with a 2.5 MHz 2D matrix array fully programmable used to emit 2000 diverging waves at 2000 volumes/s. Incremental displacements and strains enabled the visualization of rapid events during the QRS complex along with the different phases of the cardiac cycle in entire volumes. Cumulative displacement and strain volumes depict high contrast between non-ablated and ablated myocardium at the lesion location, mapping the tissue coagulation. 3D myocardial strain elastography could thus become an important technique to measure the regional strain distribution in three dimensions in humans.

3D Quasi-Static Ultrasound Elastography With Plane Wave In Vivo

In biological tissue, an increase in elasticity is often a marker of abnormalities. Techniques such as quasi-static ultrasound elastography have been developed to assess the strain distribution in soft tissues in two dimensions using a quasi-static compression. However, as abnormalities can exhibit very heterogeneous shapes, a three dimensional approach would be necessary to accurately measure their volume and remove operator dependency. Acquisition of volumes at high rates is also critical to performing real-time imaging with a simple freehand compression. In this study, we developed for the first time a 3D quasi-static ultrasound elastography method with plane waves that estimates axial strain distribution in vivo in entire volumes at high volume rate. Acquisitions were performed with a 2D matrix array probe of 2.5 MHz frequency and 256 elements. Plane waves were emitted at a volume rate of 100 volumes/s during a continuous motorized and freehand compression. 3D B-mode volumes and 3D cumulative axial strain volumes were successfully estimated in inclusion phantoms and in ex vivo canine liver before and after a high intensity focused ultrasound ablation. We also demonstrated the in vivo feasibility of the method using freehand compression on the calf muscle of a human volunteer and were able to retrieve 3D axial strain volume at a high volume rate depicting the differences in stiffness of the two muscles which compose the calf muscle. 3D ultrasound quasi-static elastography with plane waves could become an important technique for the imaging of the elasticity in human bodies in three dimensions using simple freehand scanning.

Recovering vector displacement estimates in quasistatic elastography using sparse relaxation of the momentum equation

We consider the problem of estimating the 2D vector displacement field in a heterogeneous elastic solid deforming under plane stress conditions. The problem is motivated by applications in quasistatic elastography. From precise and accurate measurements of one component of the 2D vector displacement field and very limited information of the second component, the method reconstructs the second component quite accurately. No a priori knowledge of the heterogeneous distribution of material properties is required. This method relies on using a special form of the momentum equations to filter ultrasound displacement measurements to produce more precise estimates. We verify the method with applications to simulated displacement data. We validate the method with applications to displacement data measured from a tissue mimicking phantom, and in-vivo data; significant improvements are noticed in the filtered displacements recovered from all the tests. In verification studies, error in lateral displacement estimates decreased from about 50% to about 2%, and strain error decreased from more than 250% to below 2%.

Assessing the accuracy and reproducibility of modality independent elastography in a murine model of breast cancer

Cancer progression has been linked to mechanics. Therefore, there has been recent interest in developing noninvasive imaging tools for cancer assessment that are sensitive to changes in tissue mechanical properties. We have developed one such method, modality independent elastography (MIE), that estimates the relative elastic properties of tissue by fitting anatomical image volumes acquired before and after the application of compression to biomechanical models. The aim of this study was to assess the accuracy and reproducibility of the method using phantoms and a murine breast cancer model. Magnetic resonance imaging data were acquired, and the MIE method was used to estimate relative volumetric stiffness. Accuracy was assessed using phantom data by comparing to gold-standard mechanical testing of elasticity ratios. Validation error was [Formula: see text]. Reproducibility analysis was performed on animal data, and within-subject coefficients of variation ranged from 2 to 13% at the bulk level and 32% at the voxel level. To our knowledge, this is the first study to assess the reproducibility of an elasticity imaging metric in a preclinical cancer model. Our results suggest that the MIE method can reproducibly generate accurate estimates of the relative mechanical stiffness and provide guidance on the degree of change needed in order to declare biological changes rather than experimental error in future therapeutic studies.

Approaches to accommodate noisy data in the direct solution of inverse problems in incompressible plane-strain elasticity

We apply the adjoint weighted equation method (AWE) to the direct solution of inverse problems of incompressible plane strain elasticity. We show that based on untreated noisy displacements, the reconstruction of the shear modulus can be very poor. We link this poor performance to loss of coercivity of the weak form when treating problems with discontinuous coefficients. We demonstrate that by smoothing the displacements and appending a regularization term to the AWE formulation, a dramatic improvement in the reconstruction can be achieved. With these improvements, the advantages of the AWE method as a direct solution approach can be extended to a wider range of problems.

Analysis of 2-D motion tracking in ultrasound with dual transducers

We study displacement and strain measurement error of dual transducers (two linear arrays, aligned orthogonally and coplanar). Displacements along the beam of each transducer are used to obtain measurements in two-dimensions. Simulations (5MHz) and experiments (10MHz) are compared to measurements with a single linear array, with and without angular compounding. Translation simulations demonstrate factors of 1.07 larger and 8.0 smaller biases in the axial and lateral directions respectively, for dual transducers compared to angular compounding. As the angle between dual transducers decreases from 90° to 40°, for 1% compression simulations, the lateral RMS error ranges from 2.1 to 3.9μm compared to 9μm with angular compounding. Simulation of dual transducer misalignment of 1mm and 2° result in errors of less than 9μm. Experiments demonstrate factors of 3.0 and 5.2 lower biases for dual transducers in the axial and lateral directions respectively compared to angular compounding.

Medical ultrasound: imaging of soft tissue strain and elasticity

After X-radiography, ultrasound is now the most common of all the medical imaging technologies. For millennia, manual palpation has been used to assist in diagnosis, but it is subjective and restricted to larger and more superficial structures. Following an introduction to the subject of elasticity, the elasticity of biological soft tissues is discussed and published data are presented. The basic physical principles of pulse-echo and Doppler ultrasonic techniques are explained. The history of ultrasonic imaging of soft tissue strain and elasticity is summarized, together with a brief critique of previously published reviews. The relevant techniques-low-frequency vibration, step, freehand and physiological displacement, and radiation force (displacement, impulse, shear wave and acoustic emission)-are described. Tissue-mimicking materials are indispensible for the assessment of these techniques and their characteristics are reported. Emerging clinical applications in breast disease, cardiology, dermatology, gastroenterology, gynaecology, minimally invasive surgery, musculoskeletal studies, radiotherapy, tissue engineering, urology and vascular disease are critically discussed. It is concluded that ultrasonic imaging of soft tissue strain and elasticity is now sufficiently well developed to have clinical utility. The potential for further research is examined and it is anticipated that the technology will become a powerful mainstream investigative tool.

Three-dimensional cardiac strain imaging in healthy children using RF-data

In this study, a new radio-frequency (RF)-based, three-dimensional (3-D) strain imaging technique is introduced and applied to 3-D full volume ultrasound data of the heart of healthy children. Continuing advances in performance of transducers for 3-D ultrasound imaging have boosted research on 3-D strain imaging. In general, speckle tracking techniques are used for strain imaging. RF-based strain imaging has the potential to yield better performance than speckle- based methods because of the availability of phase information but such a system output is commercially not available. Furthermore, the relatively low frame rate of 3-D ultrasound data has limited broad application of RF-based cardiac strain imaging. In this study, the previously reported two-dimensional (2-D) strain methodology was extended to the third dimension. Three-dimensional RF-data were acquired in 13 healthy children, in the age range of 6-15 years, at a relatively low frame rate of 38-51 Hz. A 3-D, free-shape, coarse-to-fine displacement and strain estimation algorithm was applied to the RF-data. The heart was segmented using 3-D ellipsoid fitting. Strain was estimated in the radial (R), circumferential (C) and longitudinal directions (L). Our preliminary results reveal the applicability of the 3-D strain estimation technique on full volume 3-D RF-data. The technique enabled 3-D strain imaging of all three strain components. The average strains for all children were in the lateral wall R = 37 ± 10% (infero-lateral) and R = 32% ± 10% (antero-lateral), C = -9% ± 4% (antero-lateral) and C = -9% ± 4% (infero-lateral), L = -18% ± 6 % (antero-lateral) and L = -15% ± 4% (infero-lateral). In the septum, strains were found to be R = 24% ± 10% (antero-septal) and R = 13% ± 5% (infero-septal), C = -13% ± 5% (antero-septal) and -13% ± 5% (infero-septal) and L = -13% ± 3% (antero-septal) and L = -16% ± 5% (infero-septal). Strain in the anterior and inferior walls seemed underestimated, probably caused by the low (in-plane) resolution and poor image quality. The field-of-view as well as image quality were not always sufficient to image the entire left ventricle. It is concluded that 3-D strain imaging using RF-data is feasible, but validation with other modalities and with conventional 3-D speckle tracking techniques will be necessary.

Correlation based 3-D segmentation of the left ventricle in pediatric echocardiographic images using radio-frequency data

Clinical diagnosis of heart disease might be substantially supported by automated segmentation of the endocardial surface in three-dimensional (3-D) echographic images. Because of the poor echogenicity contrast between blood and myocardial tissue in some regions and the inherent speckle noise, automated analysis of these images is challenging. A priori knowledge on the shape of the heart cannot always be relied on, e.g., in children with congenital heart disease, segmentation should be based on the echo features solely. The objective of this study was to investigate the merit of using temporal cross-correlation of radio-frequency (RF) data for automated segmentation of 3-D echocardiographic images. Maximum temporal cross-correlation (MCC) values were determined locally from the RF-data using an iterative 3-D technique. MCC values as well as a combination of MCC values and adaptive filtered, demodulated RF-data were used as an additional, external force in a deformable model approach to segment the endocardial surface and were tested against manually segmented surfaces. Results on 3-D full volume images (Philips, iE33) of 10 healthy children demonstrate that MCC values derived from the RF signal yield a useful parameter to distinguish between blood and myocardium in regions with low echogenicity contrast and incorporation of MCC improves the segmentation results significantly. Further investigation of the MCC over the whole cardiac cycle is required to exploit the full benefit of it for automated segmentation.

Alignment and calibration of dual ultrasound transducers using a wedge phantom

We present a novel method of aligning two orthogonal ultrasound transducers into a coincident scan plane. A wedge phantom design provides visual feedback to the user to facilitate alignment. Calibration provides the transformation from one transducer to the other as well as a measure of the residual error in alignment. Mean alignment error is shown to be under 1° in the rotation axes and 1 mm in translation after repeated manual alignments. The repeatability of wedge based calibration has similar results compared with N-fiducial based calibration. The accuracy of the calibration for mapping points from one transducer to the other is found to have a mean error of 1.6 mm. The dual transducer system is well suited to imaging anatomy such as the breast and may be used for spatial compounding for improving B-mode images and motion estimation compounding for improving elastography results.

A high-frame-rate ultrasound system for the study of tissue motions

In this article, a technique for measuring fast periodic motion is proposed. The sequencing used in this technique is similar to the one used in conventional color Doppler systems. However, a phase correction algorithm is introduced which compensates for the acquisition delays. Criteria for the types of motion which could be detected correctly by the system are developed and presented. Effective frame rates of several hundred hertz to a few kilohertz have been achieved with the system. Applications of the system in tissue elastography are presented together with experimental results from tissue mimicking phantoms.

Volumetric elasticity imaging with a 2-D CMUT array

This article reports the use of a two-dimensional (2-D) capacitive micro-machined ultrasound transducer (CMUT) to acquire radio-frequency (RF) echo data from relatively large volumes of a simple ultrasound phantom to compare three-dimensional (3-D) elasticity imaging methods. Typical 2-D motion tracking for elasticity image formation was compared with three different methods of 3-D motion tracking, with sum-squared difference (SSD) used as the similarity measure. Differences among the algorithms were the degree to which they tracked elevational motion: not at all (2-D search), planar search, combination of multiple planes and plane independent guided search. The cross-correlation between the predeformation and motion-compensated postdeformation RF echo fields was used to quantify motion tracking accuracy. The lesion contrast-to-noise ratio was used to quantify image quality. Tracking accuracy and strain image quality generally improved with increased tracking sophistication. When used as input for a 3-D modulus reconstruction, high quality 3-D displacement estimates yielded accurate and low noise modulus reconstruction.

A 2D strain estimator with numerical optimization method for soft-tissue elastography

Elastography is a bioelasticity-based imaging modality which has been proved to be a potential evaluation tool to detect the tissue abnormalities. Conventional method for elastography is to estimate the displacement based on cross-correlation technique firstly, then strain profile is calculated as the gradient of the displacement. The main problem of this method arises from the fact that the cross-correlation between pre- and post-compression signals will be decreased because of the signal's compression-to-deformation. It may constrain the estimation of the displacement. Numerical optimization, as an efficient tool to estimate the non-rigid deformation in image registration, has its potential to achieve the elastogram. This paper incorporates the idea of image registration into elastography and proposes a radio frequency (RF) signal registration strain estimator based on the minimization of a cost function using numerical optimization method with Powell algorithm (NOMPA). To evaluate the proposed scheme, the simulation data with a hard inclusion embedded in the homogeneous background is produced for analysis. NOMPA can obtain the displacement profiles and strain profiles simultaneously. When compared with the cross-correlation based method, NOMPA presents better signal-to-noise ratio (SNR, 32.6+/-1.5 dB vs. 23.8+/-1.1 dB) and contrast-to-noise ratio (CNR, 28.8+/-1.8 dB vs. 21.7+/-0.9 dB) in axial normal strain estimation. The in vitro experiment of porcine liver with ethanol-induced lesion is also studied. The statistic results of SNR and CNR indicate that strain profiles by NOMPA performs better anti-noise and target detectability than that by cross-correlation based method. Though NOMPA carry a heavier computational burden than cross-correlation based method, it may be an useful method to obtain 2D strains in elastography.

Theoretical limitations of the elastic wave equation inversion for tissue elastography

This article examines the theoretical limitations of the local inversion techniques for the measurement of the tissue elasticity. Most of these techniques are based on the estimation of the phase speed or the algebraic inversion of a one-dimensional wave equation. To analyze these techniques, the wave equation in an elastic continuum is revisited. It is proven that in an infinite medium, harmonic shear waves can travel at any phase speed greater than the classically known shear wave speed, mu/rho, by demonstrating this for a special case with cylindrical symmetry. Hence in addition to the mechanical properties of the tissue, the phase speed depends on the geometry of the wave as well. The elastic waves in an infinite cylindrical rod are studied. It is proven that multiple phase speeds can coexist for a harmonic wave at a single frequency. This shows that the phase speed depends not only on the mechanical properties of the tissue but also on its shape. The final conclusion is that the only way to avoid theoretical artifacts in the elastograms obtained by the local inversion techniques is to use the shear wave equation as expressed in the curl of the displacements, i.e., the rotations, for the inversion.

Effects of various parameters on lateral displacement estimation in ultrasound elastography

Complementary to axial, lateral displacement and strain can provide important information on the biological soft tissues. In this paper, the effects of key parameters (i.e., lateral displacement, pitch, beamwidth, beam overlap and interpolation) on lateral displacement estimation were investigated, in simulations and homogeneous phantom experiments, using lateral rigid motion only to study its fundamentals separately from the effects of axial motion and 2-D deformation on lateral displacement estimation. The performance of the lateral motion estimator was evaluated by measuring its associated bias, jitter and correlation coefficient. Simulation results showed that the bias and jitter of the lateral displacement estimation and correlation coefficient of RF signals undergo periodic variations depending on the lateral displacement, with a period equal to the pitch. The performance of the lateral estimation was improved when a smaller pitch or a larger beamwidth, was used. The effect of the pitch on the lateral estimation on lateral displacement estimation was found to be greater than the beamwidth effect. Therefore, a smaller pitch is preferred when the beam overlap remains the same. The use of cubic spline, instead of linear interpolation, increases the correlation coefficient, and decreases the jitter, with the trade-off of increased bias. The results of the phantom experiments were shown in good agreement with the simulation findings, including the periodic variation of the performance with lateral displacement and effects of pitch, beamwidth and interpolation method on lateral displacement estimation. In conclusion, smaller pitch, wider beamwidth and spline interpolation were shown to be key in reducing the jitter error in the lateral displacement estimation.

Performance evaluation of methods for two-dimensional displacement and strain estimation using ultrasound radio frequency data

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

Orthopedic interface tissue engineering for the biological fixation of soft tissue grafts

Interface tissue engineering is a promising new strategy aimed at the regeneration of tissue interfaces and ultimately enabling the biological fixation of soft tissue grafts used in orthopedic repair and sports medicine. Many ligaments and tendons with direct insertions into subchondral bone exhibit a complex enthesis consisting of several distinct yet continuous regions of soft tissue, noncalcified fibrocartilage, calcified fibrocartilage, and bone. Regeneration of this multi-tissue interface will be critical for functional graft integration and improving long-term clinical outcome. This review highlights current knowledge of the structure-function relationship at the interface, the mechanism of interface regeneration, and the strategic biomimicry implemented in stratified scaffold design for interface tissue engineering and multi-tissue regeneration. Potential challenges and future directions in this emerging field are also discussed. It is anticipated that interface tissue engineering will lead to the design of a new generation of integrative fixation devices for soft tissue repair, and it will be instrumental for the development of integrated musculoskeletal tissue systems with biomimetic complexity and functionality.

Correlation analysis of three-dimensional strain imaging using ultrasound two-dimensional array transducers

Two-dimensional (2D) transducer arrays represent a promising solution for implementing real time three-dimensional (3D) ultrasound elastography. 2D arrays enable electronic steering and focusing of ultrasound beams throughout a 3D volume along with improved slice thickness performance when compared to one-dimensional (1D) transducer arrays. Therefore, signal decorrelation caused by tissue motion in the elevational (out-of-plane) direction needs to be considered. In this paper, a closed form expression is derived for the correlation coefficient between pre- and postdeformation ultrasonic radio frequency signals. Signal decorrelation due to 3D motion of scatterers within the ultrasonic beam has been considered. Computer simulations are performed to corroborate the theoretical results. Strain images of a spherical inclusion phantom generated using 1D and 2D array transducers are obtained using a frequency domain simulation model. Quantitative image quality parameters, such as the signal-to-noise and contrast-to-noise ratios obtained using 1D, 2D, and 3D motion tracking algorithms, are compared to evaluate the performance with the 3D strain imaging system. The effect of the aperture size for 2D arrays and other factors that affect signal decorrelation are also discussed.

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.

High-frame rate, full-view myocardial elastography with automated contour tracking in murine left ventricles in vivo

Myocardial elastography is a novel method for noninvasively assessing regional myocardial function, with the advantages of high resolution and high precision. The purpose in this paper was to isolate the left ventricle from other structures for better displacement and strain visualization. Using a high-resolution (30 MHz) ultrasound system and a retrospective electrocardiogram (ECG)-gating technique, an extremely high frame rate (up to 8 kHz) was previously shown achievable for full-view (12-mm times 12-mm) myocardial elastography in the murine left ventricle. In vivo experiments were performed in anesthetized normal and infarcted mice [one day after left anterior descending (LAD) coronary artery ligation]. Radio frequency (RF) signals of the left ventricle (LV) in the long-axis view and the associated ECG were simultaneously acquired, with the ECG allowing gating of the RF signals. Incremental axial displacement of the myocardium was estimated using a one-dimensional (1-D) cross-correlation function. The cumulative displacement and strain then were calculated from the incremental displacement. In this paper, after manual selection of 40-50 points along the endo-and epicardial borders in the first frame of the cine-loop, myocardial contour was automatically tracked across the entire LV throughout a full cardiac cycle, which correctly determined the region of interest (ROI) for better interpretation. The cine-loop of the cumulative displacement and strain in one cardiac cycle, in both the normal and infarcted cases, showed that motion and deformation in the infarcted myocardium were significantly reduced, and that the infarcted region underwent thinning, rather than thickening, during systole. High precision of the displacement estimation, due to high frequency (30 MHz) and high frame rate (up to 8 kHz) available with this system, allowed for automated tracking of a manually-initialized myocardial contour over an entire cardiac cycle. High frame rate, full-view myocardial elastography with automated contour tracking could provide regional strain information of the LV throughout an entire cardiac cycle, and characterize normal as well as detect abnormal myocardial function, such as an infarction. The method of automated contour tracking can further enhance the capability of the elastographic technique with minimal user intervention while providing accurate functional information for the detection of disease throughout the entire cardiac cycle.

Theoretical quality assessment of myocardial elastography with in vivo validation

Myocardial elastography (ME), a radio frequency (RF)-based speckle tracking technique with one-dimensional (1-D) cross correlation and novel recorrelation methods in a 2-D search was proposed to estimate and fully image 2-D transmural deformation field and to detect abnormal cardiac function. A theoretical framework was first developed in order to evaluate the performance of 2-D myocardial elastography based on a previously developed 3-D finite-element model of the canine left ventricle. A normal (control) and an ischemic (left-circumflex, LCx) model, which more completely represented myocardial deformation than a kinematic model, were considered. A 2-D convolutional image formation model was first used to generate RF signals for quality assessment of ME in the normal and ischemic cases. A 3-D image formation model was further developed to investigate the effect of the out-of-plane motion on the 2-D, in-plane motion estimation. Both orthogonal, in-plane displacement components (i.e., lateral and axial) between consecutive RF frames were iteratively estimated. All the estimated incremental 2-D displacements from end-diastole (ED) to end-systole (ES) were then accumulated to acquire the cumulative 2-D displacements, which were further used to calculate the cumulative 2-D systolic finite strains. Furthermore, the cumulative systolic radial and circumferential strains, which were angle- and frame-rate independent, were obtained from the 2-D finite-strain components and imaged in full view to detect the ischemic region. We also explored the theoretical understanding of the limitations of our technique for the accurate depiction of disease and validated it in vivo against tagged magnetic resonance imaging (tMRI) in the case of a normal human myocardium in a 2-D short-axis (SA) echocardiographic view. The theoretical framework succeeded in demonstrating that the 2-D myocardial elastography technique was a reliable tool for the complete estimation and depiction of the in-plane myocardial deformation field as well as for accurate identification of pathological mechanical function using established finite-element, left-ventricular canine models. In a preliminary study, the 2-D myocardial elastography was shown capable of imaging myocardial deformation comparable to equivalent tMRI estimates in a clinical setting.

Myocardial elastography at both high temporal and spatial resolution for the detection of infarcts

Myocardial elastography is a novel method for noninvasively assessing regional myocardial function, with the advantages of high spatial and temporal resolution and high signal-to-noise ratio (SNR). In this paper, in-vivo experiments were performed in anesthetized normal and infarcted mice (one day after left anterior descending coronary artery [LAD] ligation) using a high-resolution (30 MHz) ultrasound system (Vevo 770, VisualSonics Inc., Toronto, ON, Canada). Radiofrequency (RF) signals of the left ventricle (LV) in longitudinal (long-axis) view and the associated electrocardiogram (ECG) were simultaneously acquired. Using a retrospective ECG gating technique, 2-D full field-of-view RF frames were acquired at an extremely high frame rate (8 kHz) that resulted in high-quality incremental displacement and strain estimation of the myocardium. The incremental results were further accumulated to obtain the cumulative displacements and strains. Two-dimensional and M-mode displacement images and strain images (elastograms), as well as displacement and strain profiles as a function of time, were compared between normal and infarcted mice. Incremental results clearly depicted cardiac events including LV contraction, LV relaxation and isovolumetric phases in both normal and infarcted mice, and also evidently indicated reduced motion and deformation in the infarcted myocardium. The elastograms indicated that the infarcted regions underwent thinning during systole rather than thickening, as in the normal case. The cumulative elastograms were found to have higher elastographic SNR (SNR(e)) than the incremental elastograms (e.g., 10.6 vs. 4.7 in a normal myocardium, and 6.0 vs. 2.4 in an infarcted myocardium). Finally, preliminary statistical results from nine normal (m = 9) and seven infarcted (n = 7) mice indicated the capability of the cumulative strain in differentiating infracted from normal myocardia. In conclusion, myocardial elastography could provide regional strain information at simultaneously high temporal (>/=0.125 ms) and spatial ( approximately 55 microm) resolution as well as high precision ( approximately 0.05 microm displacement). This technique was thus capable of accurately characterizing normal myocardial function throughout an entire cardiac cycle, at the same high resolution, and detecting and localizing myocardial infarction in vivo.

Shear wave speed recovery using moving interference patterns obtained in sonoelastography experiments

Two new experiments were created to characterize the elasticity of soft tissue using sonoelastography. In both experiments the spectral variance image displayed on a GE LOGIC 700 ultrasound machine shows a moving interference pattern that travels at a very small fraction of the shear wave speed. The goal of this paper is to devise and test algorithms to calculate the speed of the moving interference pattern using the arrival times of these same patterns. A geometric optics expansion is used to obtain Eikonal equations relating the moving interference pattern arrival times to the moving interference pattern speed and then to the shear wave speed. A cross-correlation procedure is employed to find the arrival times; and an inverse Eikonal solver called the level curve method computes the speed of the interference pattern. The algorithm is tested on data from a phantom experiment performed at the University of Rochester Center for Biomedical Ultrasound.

Experimental three dimensional strain estimation from ultrasonic sectorial data

Most of the studies devoted to elastography are focused on the estimation of the axial component of the strain. However when subjected to any load, whatever the direction, soft biological media deform in the three spatial dimensions. The aim of our work is to build a three dimensional strain mapping from data acquired with a 3D clinical sectorial probe. The estimation of radial strain is based on the estimation of local scaling factors. A method of cross-correlation of interpolated signals between adjacent radiofrequency lines was used to estimate the angular displacement and strain. For the sectorial strain estimation, the same displacement estimation technique has been implemented. The method has been tested on experimental data acquired on calibrated phantoms and compared to simulation.

Elastographic imaging of strain distribution in the anterior cruciate ligament and at the ligament-bone insertions

The anterior cruciate ligament (ACL) functions as a mechanical stabilizer in the tibiofemoral joint, and is the most commonly injured knee ligament. To improve the clinical outcome of tendon grafts used for ACL reconstructions, our long-term goal is to promote graft-bone integration via the regeneration of the native ligament-bone interface. An understanding of strain distribution at this interface is crucial for functional scaffold design and clinical evaluation. Experimental determination, however, has been difficult due to the small length scale of the insertion sites. This study utilizes ultrasound elastography to characterize the response of the ACL and ACL-bone interface under tension. Specifically, bovine tibiofemoral joints were mounted on a material testing system and loaded in tension while radiofrequency (RF) data were acquired at 5 MHz. Axial strain elastograms between RF frames and a reference frame were generated using crosscorrelation and recorrelation techniques. Elastographic analyses revealed that when the joint was loaded in tension, complex strains with both compressive and tensile components occurred at the tibial insertion, with higher strains found at the insertion sites. In addition, the displacement was greatest at the ACL proper and decreased in value gradually from ligament to bone, likely a reflection of the matrix organization at the ligament-bone interface. Our results indicate that elastography is a novel method that can be readily used to characterize the mechanical properties of the ACL and its insertions into bone.

Correlation analysis of the beam angle dependence for elastography

Signal decorrelation is a major source of error in the displacements estimated using correlation techniques for elastographic imaging. Previous papers have addressed the variation in the correlation coefficient as a function of the applied compression for a finite window size and an insonification angle of zero degrees. The recent use of angular beam-steered radio-frequency echo signals for spatial angular compounding and shear strain estimation have demonstrated the need for understanding signal decorrelation artifacts for data acquired at different beam angles. In this paper, we provide both numerical and closed form theoretical solutions of the correlation between pre- and post-compression radio-frequency echo signals acquired at a specified beam angle. The expression for the correlation coefficient obtained is a function of the beam angle and the applied compression for a finite duration window. Accuracy of the theoretical results is verified using tissue-mimicking phantom experiments on a uniformly elastic phantom using beam-steered data acquisitions on a linear array transducer. The theory predicts a faster decorrelation with changes in the beam or insonification angle for longer radio-frequency echo signal segments and at deeper locations in the medium. Theoretical results provide useful information for improving angular compounding and shear strain estimation techniques for elastography.

3-D correlation-based speckle tracking

Widely-used 1-D/2-D speckle tracking techniques in elasticity imaging often experience significant speckle decorrelation in applications involving large elevational motion (i.e., out of plane motion). The problem is more pronounced for cardiac strain rate imaging (SRI) since it is very difficult to confine cardiac motion to a single image plane. Here, we present a 3-D correlation-based speckle tracking algorithm. Conceptually, 3-D speckle tracking is just an extension of 2-D phase-sensitive correlation-based speckle tracking. However, due to its high computational cost, optimization schemes, such as dynamic programming, decimation and two-path processing, are introduced to reduce the computational burden. To evaluate the proposed approach, a 3-D bar phantom under uniaxial compression was simulated for benchmark tests. A more sophisticated 3-D simulation of the left ventricle of the heart was also made to test the applicability of 3-D speckle tracking in cardiac SRI. Results from both simulations clearly demonstrated the feasibility of 3-D correlation-based speckle tracking. With the ability to follow 3-D speckle in 3-D space, 3-D speckle tracking outperforms lower-dimensional speckle tracking by minimizing decorrelation caused by pure elevational translation. In other words, 3-D tracking can push toward solely deformation-limited, decorrelation-optimized speckle tracking. Hardware implementation of the proposed 3-D speckle tracking algorithm using field programmable gate arrays (FPGA) is also discussed.