Quantitative three-dimensional elasticity imaging from quasi-static deformation: a phantom study

[Reconstruction of elasticity modulus distribution base on semi-supervised neural network]

Accurate reconstruction of tissue elasticity modulus distribution has always been an important challenge in ultrasound elastography. Considering that existing deep learning-based supervised reconstruction methods only use simulated displacement data with random noise in training, which cannot fully provide the complexity and diversity brought by in-vivo ultrasound data, this study introduces the use of displacement data obtained by tracking in-vivo ultrasound radio frequency signals (i.e., real displacement data) during training, employing a semi-supervised approach to enhance the prediction accuracy of the model. Experimental results indicate that in phantom experiments, the semi-supervised model augmented with real displacement data provides more accurate predictions, with mean absolute errors and mean relative errors both around 3%, while the corresponding data for the fully supervised model are around 5%. When processing real displacement data, the area of prediction error of semi-supervised model was less than that of fully supervised model. The findings of this study confirm the effectiveness and practicality of the proposed approach, providing new insights for the application of deep learning methods in the reconstruction of elastic distribution from in-vivo ultrasound data.

Predicting stress and interstitial fluid pressure in tumors based on biphasic theory

The uncontrolled proliferation of cancer cells causes the growth of the tumor mass. Consequently, the normal surrounding tissue exerts a compressive force on the tumor mass to oppose its expansion. These stresses directly promote tumor metastasis and invasion and affect drug delivery. In the past, the mechanical behavior of solid tumors has been extensively studied using linear elastic and nonlinear hyperelastic constitutive models. In this study, we develop a two-dimensional biomechanical model based on the biphasic assumption of the solid matrix and fluid phase of the tissues. Heterogeneous vasculature and nonuniform blood perfusion are also investigated by incorporating in the model a necrotic core and a well-vascularized zone. The findings of our study demonstrate a significant difference between the linear and nonlinear tissue responses to stress, while the interstitial fluid pressure (IFP) distribution is found to be independent of the constitutive model. The proposed biphasic model may be useful for elasticity imaging techniques aiming at predicting stress and IFP in tumors.

Impingement in Insertional Achilles Tendinopathy Occurs Across a Larger Range of Ankle Angles and Is Associated With Increased Tendon Thickness

BACKGROUND

Insertional Achilles tendinopathy (IAT) is characterized by tendon degeneration and thickening near the tendon-bone insertion.¹¹ Calcaneal impingement is believed to contribute to the pathogenesis of IAT.⁵ However, it is unclear how increased tendon thickness in individuals with IAT influences impingement. This study aimed to compare Achilles tendon impingement in individuals with and without IAT.

METHODS

Eight healthy adults and 12 adults with clinically diagnosed symptomatic IAT performed a passive flexion exercise during which ankle flexion angle, anterior-posterior (A-P) thickness, and an ultrasonographic image sequence of the Achilles tendon insertion were acquired. The angle of ankle plantarflexion at which the calcaneus first impinges the Achilles tendon, defined as the impingement onset angle, was identified by (1) a anonymized observer (visual inspection method) and (2) a computational image deformation-based approach (curvature method).

RESULTS

Although the 2 methods provided different impingement onset angles, the measurements were strongly correlated (R² = 0.751, P < .05). The impingement onset angle and the thickness of the Achilles tendon insertion were greater in subjects with clinically diagnosed IAT (P = .0048, P = .0047). Furthermore, impingement onset angle proved to have a moderate correlation with anterior-posterior thickness (R² = 0.454, P < .05).

CONCLUSION

Our findings demonstrated that increased tendon thickness in IAT patients is associated with larger impingement onset angles, raising the range of ankle angles over which the tendon is exposed to impingement.

CLINICAL RELEVANCE

Increased susceptibility to impingement may exacerbate or perpetuate the pathology, highlighting the need for clinical strategies to reduce impingement in IAT patients.

Ultrasound strain mapping of the mouse Achilles tendon during passive dorsiflexion

Immediately prior to inserting into bone, many healthy tendons experience impingement from nearby bony structures. However, super-physiological levels of impingement are implicated in insertional tendinopathies. Unfortunately, the mechanisms underlying the connection between impingement and tendon pathology remain poorly understood, in part due to the shortage of well-characterized animal models of impingement at clinically relevant sites. As a first step towards developing a model of excessive tendon impingement, the objective of this study was to characterize the mechanical strain environment in the mouse Achilles tendon insertion under passive dorsiflexion and confirm that - like humans - mice experience impingement of the tendon insertion from the calcaneus (heel bone) in dorsiflexed ankle positions. Based on previous work in humans, we hypothesized that during dorsiflexion, the mouse Achilles tendon insertion would experience high levels of transverse compressive strain due to calcaneal impingement. A custom-built loading platform was used to apply passive dorsiflexion, while an ultrasound transducer positioned over the Achilles tendon captured radiofrequency images. A non-rigid image registration algorithm was then used to map the transverse compressive strain based on the acquired ultrasound image sequences. Our results demonstrate that during passive dorsiflexion, transverse compressive strains were produced throughout the Achilles tendon, with significantly larger strain magnitudes at the tendon insertion than at the midsubstance. Furthermore, there was increasing transverse compressive strain observed within the Achilles tendon as a function of increasing dorsiflexion angle. This study enhances our understanding of the unique mechanical loading environment of the Achilles tendon under physiologically relevant conditions.

Non-invasive imaging of Young's modulus and Poisson's ratio in cancers in vivo

Alterations of Young's modulus (YM) and Poisson's ratio (PR) in biological tissues are often early indicators of the onset of pathological conditions. Knowledge of these parameters has been proven to be of great clinical significance for the diagnosis, prognosis and treatment of cancers. Currently, however, there are no non-invasive modalities that can be used to image and quantify these parameters in vivo without assuming incompressibility of the tissue, an assumption that is rarely justified in human tissues. In this paper, we developed a new method to simultaneously reconstruct YM and PR of a tumor and of its surrounding tissues based on the assumptions of axisymmetry and ellipsoidal-shape inclusion. This new, non-invasive method allows the generation of high spatial resolution YM and PR maps from axial and lateral strain data obtained via ultrasound elastography. The method was validated using finite element (FE) simulations and controlled experiments performed on phantoms with known mechanical properties. The clinical feasibility of the developed method was demonstrated in an orthotopic mouse model of breast cancer. Our results demonstrate that the proposed technique can estimate the YM and PR of spherical inclusions with accuracy higher than 99% and with accuracy higher than 90% in inclusions of different geometries and under various clinically relevant boundary conditions.

Physics-guided machine learning for 3-D quantitative quasi-static elasticity imaging

We present a 3D extension of the Autoprogressive Method (AutoP) for quantitative quasi-static ultrasonic elastography (QUSE) based on sparse sampling of force-displacement measurements. Compared to current model-based inverse methods, our approach requires neither geometric nor constitutive model assumptions. We build upon our previous report for 2D QUSE and demonstrate the feasibility of recovering the 3D linear-elastic material property distribution of gelatin phantoms under compressive loads. Measurements of boundary geometry, applied surface forces, and axial displacements enter into AutoP where a Cartesian neural network constitutive model (CaNNCM) interacts with finite element analyses to learn physically consistent material properties with no prior constitutive model assumption. We introduce a new regularization term uniquely suited to AutoP that improves the ability of CaNNCMs to extract information about spatial stress distributions from measurement data. Results of our study demonstrate that acquiring multiple sets of force-displacement measurements by moving the US probe to different locations on the phantom surface not only provides AutoP with the necessary information for a CaNNCM to learn the 3D material property distribution, but may significantly improve the accuracy of the Young's modulus estimates. Furthermore, we investigate the trade-offs of decreasing the contact area between the US transducer and phantom surface in an effort to increase sensitivity to surface force variations without additional instrumentation. Each of these modifications improves the ability of CaNNCMs trained in AutoP to learn the spatial distribution of Young's modulus from force-displacement measurements.

Estimation of Vascular Permeability in Irregularly Shaped Cancers Using Ultrasound Poroelastography

OBJECTIVE

Vascular permeability (VP) is a mechanical parameter which plays an important role in cancer initiation, metastasis, and progression. To date, there are only a few non-invasive methods that can be used to image VP in solid tumors. Most of these methods require the use of contrast agents and are expensive, limiting widespread use.

METHODS

In this paper, we propose a new method to image VP in tumors, which is based on the use of ultrasound poroelastography. Estimation of VP by poroelastography requires knowledge of the Young's modulus (YM), Poisson's ratio (PR), and strain time constant (TC) in the tumors. In our method, we find the ellipse which best fits the tumor (regardless of its shape) using an eigen-system-based fitting technique and estimate the YM and PR using Eshelby's elliptic inclusion formulation. A Fourier method is used to estimate the axial strain TC, which does not require any initial guess and is highly robust to noise.

RESULTS

It is demonstrated that the proposed method can estimate VP in irregularly shaped tumors with an accuracy of above [Formula: see text] using ultrasound simulation data with signal-to-noise ratio of 20 dB or higher. In vivo feasibility of the proposed technique is demonstrated in an orthotopic mouse model of breast cancer.

CONCLUSION

The proposed imaging method can provide accurate and localized estimation of VP in cancers non-invasively and cost-effectively.

SIGNIFICANCE

Accurate and non-invasive assessment of VP can have a significant impact on diagnosis, prognosis, and treatment of cancers.

Imaging the Vocal Folds: A Feasibility Study on Strain Imaging and Elastography of Porcine Vocal Folds

Vocal folds are an essential part of human voice production. The biomechanical properties are a good indicator for pathological changes. In particular, as an oscillation system, changes in the biomechanical properties have an impact on the vibration behavior. Subsequently, those changes could lead to voice-related disturbances. However, no existing examination combines biomechanical properties and spatial imaging. Therefore, we propose an image registration-based approach, using ultrasound in order to gain this information synchronously. We used a quasi-static load to compress the tissue and measured the displacement by image registration. The strain distribution was directly calculated from the displacement field, whereas the elastic properties were estimated by a finite element model. In order to show the feasibility and reliability of the algorithm, we tested it on gelatin phantoms. Further, by examining ex vivo porcine vocal folds, we were able to show the practicability of the approach. We displayed the strain distribution in the tissue and the elastic properties of the vocal folds. The results were superimposed on the corresponding ultrasound images. The findings are promising and show the feasibility of the suggested approach. Possible applications are in improved diagnosis of voice disorders, by measuring the biomechanical properties of the vocal folds with ultrasound. The transducer will be placed on the vocal folds of the anesthetized patient, and the elastic properties will be measured. Further, the understanding of the vocal folds’ biomechanics and the voice forming process could benefit from it.

Soft metamaterials with dynamic viscoelastic functionality tuned by pre-deformation

The small amplitude dynamic response of materials can be tuned by employing inhomogeneous materials capable of large deformation. However, soft materials generally exhibit viscoelastic behaviour, i.e. loss and frequency-dependent effective properties. This is the case for inhomogeneous materials even in the homogenization limit when propagating wavelengths are much longer than phase lengthscales, since soft materials can possess long relaxation times. These media, possessing rich frequency-dependent behaviour over a wide range of low frequencies, can be termed metamaterials in modern terminology. The sub-class that are periodic are frequently termed soft phononic crystals although their strong dynamic behaviour usually depends on wavelengths being of the same order as the microstructure. In this paper we describe how the effective loss and storage moduli associated with longitudinal waves in thin inhomogeneous rods are tuned by pre-stress. Phases are assumed to be quasi-linearly viscoelastic, thus exhibiting time-deformation separability in their constitutive response. We illustrate however that the effective incremental response of the inhomogeneous medium does not exhibit time-deformation separability. For a range of nonlinear materials it is shown that there is strong coupling between the frequency of the small amplitude longitudinal wave and initial large deformation. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and applied mathematics'.

Electromagnetic tracking-based freehand 3D quasi-static elastography with 1D linear array: a phantom study

Recent developments in hardware and scanning protocols have advanced conventional 2D quasi-static elastography to 3D level, which provides an intuitive visualization of lesions. A 2D linear array or scanning mechanism is typically required for 3D quasi-static elastography, requiring expensive and specifically designed hardware. In this study, we propose a novel method based on a commercial electromagnetic tracking system for freehand 3D quasi-static elastography with 1D linear array. Phantom experiments are performed to validate the feasibility of the proposed method. During data acquisition, the probe contacts the surface of an elasticity phantom and moves in the elevational direction, while applying sinusoidal-like axial compression to the phantom. For each frame of ultrasound data, the 3D coordinates and orientations of the probe are obtained from an electromagnetic tracking system. A correlation-based algorithm is adopted to obtain a series of axial strain images. Volumetric strain data are reconstructed by using the recorded 3D coordinates and orientations of the probe corresponding to each strain image. The diameters of inclusions are then obtained from the slice plots of the volumetric strain data. The volumes of inclusions are estimated from the isosurface plots. The experimental result shows that the volume estimation of the inclusions has good accuracy, with errors within 2%, while the diameters of the inclusions estimated from three orthogonal planes have larger errors up to 18%. In conclusion, the present framework would promise a reliable and effective solution for freehand 3D quasi-static elastography with 1D linear array.

Improving three-dimensional mechanical imaging of breast lesions with principal component analysis

PURPOSE

Elastography has emerged as a new tool for detecting and diagnosing many types of diseases including breast cancer. To date, most clinical applications of elastography have utilized two-dimensional strain images. The goal of this paper is to present a new quasi-static elastography technique that yields shear modulus images in three dimensions.

METHODS

An automated breast volume scanner was used to acquire ultrasound images of the breast as it was gently compressed. Cross-correlation between successive images was used to determine the displacement within the tissue. The resulting displacement field was filtered of all but compressive motion through principal component analysis. This displacement field was used to infer spatial distribution of shear modulus by solving a 3D elastic inverse problem.

RESULTS

Three dimensional shear modulus images of benign breast lesions for two subjects were generated using the techniques described above. It was found that the lesions were visualized more clearly in images generated using the displacement data de-noised through the use of principal components.

CONCLUSIONS

We have presented experimental and algorithmic techniques that lead to three-dimensional imaging of shear modulus using quasi-static elastography. This work demonstrates feasibility of this approach, and lays the foundation for images of other, more informative, mechanical parameters.

Mechanics Based Tomography: A Preliminary Feasibility Study

We present a non-destructive approach to sense inclusion objects embedded in a solid medium remotely from force sensors applied to the medium and boundary displacements that could be measured via a digital image correlation system using a set of cameras. We provide a rationale and strategy to uniquely identify the heterogeneous sample composition based on stiffness (here, shear modulus) maps. The feasibility of this inversion scheme is tested with simulated experiments that could have clinical relevance in diagnostic imaging (e.g., tumor detection) or could be applied to engineering materials. No assumptions are made on the shape or stiffness quantity of the inclusions. We observe that the novel inversion method using solely boundary displacements and force measurements performs well in recovering the heterogeneous material/tissue composition that consists of one and two stiff inclusions embedded in a softer background material. Furthermore, the target shear modulus value for the stiffer inclusion region is underestimated and the inclusion size is overestimated when incomplete boundary displacements on some part of the boundary are utilized. For displacements measured on the entire boundary, the shear modulus reconstruction improves significantly. Additionally, we observe that with increasing number of displacement data sets utilized in solving the inverse problem, the quality of the mapped shear moduli improves. We also analyze the sensitivity of the shear modulus maps on the noise level varied between 0.1% and 5% white Gaussian noise in the boundary displacements, force and corresponding displacement indentation. Finally, a sensitivity analysis of the recovered shear moduli to the depth, stiffness and the shape of the stiff inclusion is performed. We conclude that this approach has potential as a novel imaging modality and refer to it as Mechanics Based Tomography (MBT).

Spatial distribution of airway wall displacements during breathing and bronchoconstriction measured by ultrasound elastography using finite element image registration

With every breath, the airways within the lungs are strained. This periodic stretching is thought to play an important role in determining airway caliber in health and disease. Particularly, deep breaths can mitigate excessive airway narrowing in healthy subjects, but this beneficial effect is absent in asthmatics, perhaps due to an inability to stretch the airway smooth muscle (ASM) embedded within an airway wall. The heterogeneous composition throughout an airway wall likely modulates the strain felt by the ASM but the magnitude of ASM strain is difficult to measure directly. In this study, we optimized a finite element image registration method to measure the spatial distribution of displacements and strains throughout an airway wall during pressure inflation within the physiological breathing range before and after induced narrowing with acetylcholine (ACh). The method was shown to be repeatable, and displacements estimated from different image sequences of the same deformation agreed to within 5.3μm (0.77%). We found the magnitude and spatial distribution of displacements were radially and longitudinally heterogeneous. The region in the middle layer of the airway experienced the largest radial strain due to a transmural pressure (Ptm) increase simulating tidal breathing and a deep inspiration (DI), while the region containing the ASM (i.e., closest to the lumen) strained least. During induced narrowing with ACh, we observed temporal longitudinal heterogeneity of the airway wall. After constriction, the displacements and strain are much smaller than the relaxed airway and the pattern of strains changed, suggesting the airway stiffened heterogeneously.

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%.

Development of array piezoelectric fingers towards in vivo breast tumor detection

We have investigated the development of a handheld 4 × 1 piezoelectric finger (PEF) array breast tumor detector system towards in vivo patient testing, particularly, on how the duration of the DC applied voltage, the depression depth of the handheld unit, and breast density affect the PEF detection sensitivity on 40 patients. The tests were blinded and carried out in four phases: with DC voltage durations 5, 3, 2, to 0.8 s corresponding to scanning a quadrant, a half, a whole breast, and both breasts within 30 min, respectively. The results showed that PEF detection sensitivity was unaffected by shortening the applied voltage duration from 5 to 0.8 s nor was it affected by increasing the depression depth from 2 to 6 mm. Over the 40 patients, PEF detected 46 of the 48 lesions (46/48)-with the smallest lesion detected being 5 mm in size. Of 28 patients (some have more than one lesion) with mammography records, PEF detected 31/33 of all lesions (94%) and 14/15 of malignant lesions (93%), while mammography detected 30/33 of all lesions (91%) and 12/15 of malignant lesions (80%), indicating that PEF could detect malignant lesions not detectable by mammography without significantly increasing false positives. PEF's detection sensitivity is also shown to be independent of breast density, suggesting that PEF could be a potential tool for detecting breast cancer in young women and women with dense breasts.

Development of a Wireless and Near Real-Time 3D Ultrasound Strain Imaging System

Ultrasound elastography is an important medical imaging tool for characterization of lesions. In this paper, we present a wireless and near real-time 3D ultrasound strain imaging system. It uses a 3D translating device to control a commercial linear ultrasound transducer to collect pre-compression and post-compression radio-frequency (RF) echo signal frames. The RF frames are wirelessly transferred to a high-performance server via a local area network (LAN). A dynamic programming strain estimation algorithm is implemented with the compute unified device architecture (CUDA) on the graphic processing unit (GPU) in the server to calculate the strain image after receiving a pre-compression RF frame and a post-compression RF frame at the same position. Each strain image is inserted into a strain volume which can be rendered in near real-time. We take full advantage of the translating device to precisely control the probe movement and compression. The GPU-based parallel computing techniques are designed to reduce the computation time. Phantom and in vivo experimental results demonstrate that our system can generate strain volumes with good quality and display an incrementally reconstructed volume image in near real-time.

Application of Eshelby's Solution to Elastography for Diagnosis of Breast Cancer

Eshelby's solution is the analytical method that can derive the elastic field within and around an ellipsoidal inclusion embedded in a matrix. Since breast tumor can be regarded as an elastic inclusion with different elastic properties from those of surrounding matrix when the deformation is small, we applied Eshelby's solution to predict the stress and strain fields in the breast containing a suspicious lesion. The results were used to investigate the effectiveness of strain ratio (SR) from elastography in representing modulus ratio (MR) that may be the meaningful indicator of the malignancy of the lesion. This study showed that SR significantly underestimates MR and is varied with the shape and the modulus of the lesion. Based on the results from Eshelby's solution and finite element analysis (FEA), we proposed a surface regression model as a polynomial function that can predict the MR of the lesion to the matrix. The model has been applied to gelatin-based phantoms and clinical ultrasound images of human breasts containing different types of lesions. The results suggest the potential of the proposed method to improve the diagnostic performance of breast cancer using elastography.

Ultrasound strain mapping of Achilles tendon compressive strain patterns during dorsiflexion

Heel lifts are commonly prescribed to patients with Achilles tendinopathy, yet little is known about the effect on tendon compressive strain. The purposes of the current study were to (1) develop a valid and reliable ultrasound elastography technique and algorithm to measure compressive strain of human Achilles tendon in vivo, (2) examine the effects of ankle dorsiflexion (lowering via controlled removal of a heel lift and partial squat) on compressive strain of the Achilles tendon insertion and (3) examine the relative compressive strain between the deep and superficial regions of the Achilles tendon insertion. All tasks started in a position equivalent to standing with a 30mm heel lift. An ultrasound transducer positioned over the Achilles tendon insertion was used to capture radiofrequency images. A non-rigid image registration-based algorithm was used to estimate compressive strain of the tendon, which was divided into 2 regions (superficial, deep). The bland-Altman test and intraclass correlation coefficient were used to test validity and reliability. One-way repeated measures ANOVA was used to compare compressive strain between regions and across tasks. Compressive strain was accurately and reliably (ICC>0.75) quantified. There was greater compressive strain during the combined task of lowering and partial squat compared to the lowering (P=.001) and partial squat (P<.001) tasks separately. There was greater compressive strain in the deep region of the tendon compared to the superficial for all tasks (P=.001). While these findings need to be examined in a pathological population, heel lifts may reduce tendon compressive strain during daily activities.

Visualizing the stress distribution within vascular tissues using intravascular ultrasound elastography: a preliminary investigation

A methodology for computing the stress distribution of vascular tissue using finite element-based, intravascular ultrasound (IVUS) reconstruction elastography is described. This information could help cardiologists detect life-threatening atherosclerotic plaques and predict their propensity to rupture. The calculation of vessel stresses requires the measurement of strain from the ultrasound images, a calibrating pressure measurement and additional model assumptions. In this work, we conducted simulation studies to investigate the effect of varying the model assumptions, specifically Poisson's ratio and the outer boundary conditions, on the resulting stress fields. In both simulation and phantom studies, we created vessel geometries with two fibrous cap thicknesses to determine if we could detect a difference in peak stress (spatially) between the two. The results revealed that (i) Poisson's ratios had negligible impact on the accuracy of stress elastograms, (ii) the outer boundary condition assumption had the greatest effect on the resulting modulus and stress distributions and (iii) in simulation and in phantom experiments, our stress imaging technique was able to detect an increased peak stress for the vessel geometry with the smaller cap thickness. This work is a first step toward understanding and creating a robust stress measurement technique for evaluating atherosclerotic plaques using IVUS elastography.

Algorithms for quantitative quasi-static elasticity imaging using force data

Quasi-static elasticity imaging can improve diagnosis and detection of diseases that affect the mechanical behavior of tissue. In this methodology, images of the shear modulus of the tissue are reconstructed from the measured displacement field. This is accomplished by seeking the spatial distribution of mechanical properties that minimizes the difference between the predicted and the measured displacement fields, where the former is required to satisfy a finite element approximation to the equations of equilibrium. In the absence of force data, the shear modulus is determined only up to a multiplicative constant. In this manuscript, we address the problem of calibrating quantitative elastic modulus reconstructions created from measurements of quasi-static deformations. We present two methods that utilize the knowledge of the applied force on a portion of the boundary. The first involves rescaling the shear modulus of the original minimization problem to best match the measured force data. This approach is easily implemented but neglects the spatial distribution of tractions. The second involves adding a force-matching term to the original minimization problem and a change of variables wherein we seek the log of the shear modulus. We present numerical results that demonstrate the usefulness of both methods.

A regularization-free elasticity reconstruction method for ultrasound elastography with freehand scan

BACKGROUND

In ultrasound elastography, reconstruction of tissue elasticity (e.g., Young's modulus) requires regularization and known information of forces and/or displacements on tissue boundaries. In practice, it is challenging to choose an appropriate regularization parameter; and the boundary conditions are difficult to obtain in vivo. The purpose of this study is to develop a more applicable algorithm that does not need any regularization or boundary force/displacement information.

METHODS

The proposed method adopts the bicubic B-spline as the tissue motion model to estimate the displacement fields. Then the estimated displacements are input to the finite element inversion scheme to reconstruct the Young's modulus of each element. In the inversion, a modulus boundary condition is used instead of force/displacement boundary conditions. Simulation and experiments on tissue-mimicking phantoms are carried out to test the proposed method.

RESULTS

The simulation results demonstrate that Young's modulus reconstruction of the proposed method has a relative error of -3.43 ± 0.43% and root-squared-mean error of 16.94 ± 0.25%. The phantom experimental results show that the target hardening artifacts in the strain images are significantly reduced in the Young's modulus images. In both simulation and phantom studies, the size and position of inclusions can be accurately depicted in the modulus images.

CONCLUSIONS

The proposed method can reconstruct tissue Young's modulus distribution with a high accuracy. It can reduce the artifacts shown in the strain image and correctly delineate the locations and sizes of inclusions. Unlike most modulus reconstruction methods, it does not need any regularization during the inversion procedure. Furthermore, it does not need to measure the boundary conditions of displacement or force. Thus this method can be used with a freehand scan, which facilitates its usage in the clinic.

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.

Noninvasive vascular displacement estimation for relative elastic modulus reconstruction in transversal imaging planes

Atherosclerotic plaque rupture can initiate stroke or myocardial infarction. Lipid-rich plaques with thin fibrous caps have a higher risk to rupture than fibrotic plaques. Elastic moduli differ for lipid-rich and fibrous tissue and can be reconstructed using tissue displacements estimated from intravascular ultrasound radiofrequency (RF) data acquisitions. This study investigated if modulus reconstruction is possible for noninvasive RF acquisitions of vessels in transverse imaging planes using an iterative 2D cross-correlation based displacement estimation algorithm. Furthermore, since it is known that displacements can be improved by compounding of displacements estimated at various beam steering angles, we compared the performance of the modulus reconstruction with and without compounding. For the comparison, simulated and experimental RF data were generated of various vessel-mimicking phantoms. Reconstruction errors were less than 10%, which seems adequate for distinguishing lipid-rich from fibrous tissue. Compounding outperformed single-angle reconstruction: the interquartile range of the reconstructed moduli for the various homogeneous phantom layers was approximately two times smaller. Additionally, the estimated lateral displacements were a factor of 2–3 better matched to the displacements corresponding to the reconstructed modulus distribution. Thus, noninvasive elastic modulus reconstruction is possible for transverse vessel cross sections using this cross-correlation method and is more accurate with compounding.

A novel fast full inversion based breast ultrasound elastography technique

Cancer detection and classification have been the focus of many imaging and therapeutic research studies. Elastography is a non-invasive technique to visualize suspicious soft tissue areas where tissue stiffness is used as image contrast mechanism. In this study, a breast ultrasound elastography system including software and hardware is proposed. Unlike current elastography systems that image the tissue strain and present it as an approximation to relative tissue stiffness, this system is capable of imaging the breast absolute Young's modulus in fast fashion. To improve the quality of elastography images, a novel system consisting of two load cells has been attached to the ultrasound probe. The load cells measure the breast surface forces to be used for calculating the tissue stress distribution throughout the breast. To facilitate fast imaging, this stress calculation is conducted by an accelerated finite element method. Acquired tissue displacements and surface force data are used as input to the proposed Young's modulus reconstruction technique. Numerical and tissue mimicking phantom studies were conducted for validating the proposed system. These studies indicated that fast imaging of breast tissue absolute Young's modulus using the proposed ultrasound elastography system is feasible. The tissue mimicking phantom study indicated that the system is capable of providing reliable absolute Young's modulus values for both normal tissue and tumour as the maximum Young's modulus reconstruction error was less than 6%. This demonstrates that the proposed system has a good potential to be used for clinical breast cancer assessment.

Ultrasonic imaging of 3D displacement vectors using a simulated 2D array and beamsteering

Most quasi-static ultrasound elastography methods image only the axial strain, derived from displacements measured in the direction of ultrasound propagation. In other directions, the beam lacks high resolution phase information and displacement estimation is therefore less precise. However, these estimates can be improved by steering the ultrasound beam through multiple angles and combining displacements measured along the different beam directions. Previously, beamsteering has only considered the 2D case to improve the lateral displacement estimates. In this paper, we extend this to 3D using a simulated 2D array to steer both laterally and elevationally in order to estimate the full 3D displacement vector over a volume. The method is tested on simulated and phantom data using a simulated 6-10MHz array, and the precision of displacement estimation is measured with and without beamsteering. In simulations, we found a statistically significant improvement in the precision of lateral and elevational displacement estimates: lateral precision 35.69μm unsteered, 3.70μm steered; elevational precision 38.67μm unsteered, 3.64μm steered. Similar results were found in the phantom data: lateral precision 26.51μm unsteered, 5.78μm steered; elevational precision 28.92μm unsteered, 11.87μm steered. We conclude that volumetric 3D beamsteering improves the precision of lateral and elevational displacement estimates.

A regularization-free Young's modulus reconstruction algorithm for ultrasound elasticity imaging

Ultrasound elasticity imaging aims to reconstruct the distribution of elastic modulus (e.g., Young's modulus) within biological tissues, since the value of elastic modulus is often related to pathological changes. Currently, most elasticity imaging algorithms face a challenge of choosing the value of the regularization constant. We propose a more applicable algorithm without the need of any regularization. This algorithm is not only simple to use, but has a relatively high accuracy. Our method comprises of a nonrigid registration technique and tissue incompressibility assumption to estimate the two-dimensional (2D) displacement field, and finite element method (FEM) to reconstruct the Young's modulus distribution. Simulation and phantom experiments are performed to evaluate the algorithm. Simulation and phantom results showed that the proposed algorithm can reconstruct the Young's modulus with an accuracy of 63∼85%.

Linear and nonlinear elastic modulus imaging: an application to breast cancer diagnosis

We reconstruct the in vivo spatial distribution of linear and nonlinear elastic parameters in ten patients with benign (five) and malignant (five) tumors. The mechanical behavior of breast tissue is represented by a modified Veronda-Westmann model with one linear and one nonlinear elastic parameter. The spatial distribution of these elastic parameters is determined by solving an inverse problem within the region of interest (ROI). This inverse problem solution requires the knowledge of the displacement fields at small and large strains. The displacement fields are measured using a free-hand ultrasound strain imaging technique wherein, a linear array ultrasound transducer is positioned on the breast and radio frequency echo signals are recorded within the ROI while the tissue is slowly deformed with the transducer. Incremental displacement fields are determined from successive radio-frequency frames by employing cross-correlation techniques. The rectangular regions of interest were subjectively selected to obtain low noise displacement estimates and therefore were variables that ranged from 346 to 849.6 mm2 . It is observed that malignant tumors stiffen at a faster rate than benign tumors and based on this criterion nine out of ten tumors were correctly classified as being either benign or malignant.

Target motion predictions for pre-operative planning during needle-based interventions

During biopsies, breast tissue is subjected to displacement upon needle indentation, puncture, and penetration. Thus, accurate needle placement requires pre-operative predictions of the target motions. In this paper, we used ultrasound elastography measurements to non-invasively predict elastic properties of breast tissue phantoms. These properties were used in finite element (FE) models of indentation of breast soft tissue phantoms. To validate the model predictions of target motion, experimental measurements were carried out. Breast tissue phantoms with cubic and hemispherical geometries were manufactured and included materials with different elastic properties to represent skin, adipose tissue, and lesions. Ultrasound was used to track the displacement of the target (i.e., the simulated lesion) during indentation. The FE model predictions were compared with ultrasound measurements for cases with different boundary conditions and phantom geometry. Maximum errors between measured and predicted target motions were 12% and 3% for the fully supported and partially supported cubic phantoms at 6.0 mm indentation, respectively. Further, FE-based parameter sensitivity analysis indicated that increasing skin elastic modulus and reducing the target depth location increased the target motion. Our results indicate that with a priori knowledge about the geometry, boundary conditions, and linear elastic properties, indentation of breast tissue phantoms can be accurately predicted with FE models. FE models for pre-operative planning in combination with robotic needle insertions, could play a key role in improving lesion targeting for breast biopsies.

A novel breast software phantom for biomechanical modeling of elastography

PURPOSE

In developing breast imaging technologies, testing is done with phantoms. Physical phantoms are normally used but their size, shape, composition, and detail cannot be modified readily. These difficulties can be avoided by creating a software breast phantom. Researchers have created software breast phantoms using geometric and/or mathematical methods for applications like image fusion. The authors report a 3D software breast phantom that was built using a mechanical design tool, to investigate the biomechanics of elastography using finite element modeling (FEM). The authors propose this phantom as an intermediate assessment tool for elastography simulation; for use after testing with commonly used phantoms and before clinical testing. The authors design the phantom to be flexible in both, the breast geometry and biomechanical parameters, to make it a useful tool for elastography simulation.

METHODS

The authors develop the 3D software phantom using a mechanical design tool based on illustrations of normal breast anatomy. The software phantom does not use geometric primitives or imaging data. The authors discuss how to create this phantom and how to modify it. The authors demonstrate a typical elastography experiment of applying a static stress to the top surface of the breast just above a simulated tumor and calculate normal strains in 3D and in 2D with plane strain approximations with linear solvers. In particular, they investigate contrast transfer efficiency (CTE) by designing a parametric study based on location, shape, and stiffness of simulated tumors. The authors also compare their findings to a commonly used elastography phantom.

RESULTS

The 3D breast software phantom is flexible in shape, size, and location of tumors, glandular to fatty content, and the ductal structure. Residual modulus, maps, and profiles, served as a guide to optimize meshing of this geometrically nonlinear phantom for biomechanical modeling of elastography. At best, low residues (around 1-5 KPa) were found within the phantom while errors were elevated (around 10-30 KPa) at tumor and lobule boundaries. From our FEM analysis, the breast phantom generated a superior CTE in both 2D and in 3D over the block phantom. It also showed differences in CTE values and strain contrast for deep and shallow tumors and showed significant change in CTE when 3D modeling was used. These changes were not significant in the block phantom. Both phantoms, however, showed worsened CTE values for increased input tumor-background modulus contrast.

CONCLUSIONS

Block phantoms serve as a starting tool but a next level phantom, like the proposed breast phantom, will serve as a valuable intermediate for elastography simulation before clinical testing. Further, given the CTE metrics for the breast phantom are superior to the block phantom, and vary for tumor shape, location, and stiffness, these phantoms would enhance the study of elastography contrast. Further, the use of 2D phantoms with plane strain approximations overestimates the CTE value when compared to the true CTE achieved with 3D models. Thus, the use of 3D phantoms, like the breast phantom, with no approximations, will assist in more accurate estimation of modulus, especially valuable for 3D elastography systems.

Model-based elastography: a survey of approaches to the inverse elasticity problem

Elastography is emerging as an imaging modality that can distinguish normal versus diseased tissues via their biomechanical properties. This paper reviews current approaches to elastography in three areas--quasi-static, harmonic and transient--and describes inversion schemes for each elastographic imaging approach. Approaches include first-order approximation methods; direct and iterative inversion schemes for linear elastic; isotropic materials and advanced reconstruction methods for recovering parameters that characterize complex mechanical behavior. The paper's objective is to document efforts to develop elastography within the framework of solving an inverse problem, so that elastography may provide reliable estimates of shear modulus and other mechanical parameters. We discuss issues that must be addressed if model-based elastography is to become the prevailing approach to quasi-static, harmonic and transient elastography: (1) developing practical techniques to transform the ill-posed problem with a well-posed one; (2) devising better forward models to capture the complex mechanical behavior of soft tissues and (3) developing better test procedures to evaluate the performance of modulus elastograms.

Investigating the impact of spatial priors on the performance of model-based IVUS elastography

This paper describes methods that provide pre-requisite information for computing circumferential stress in modulus elastograms recovered from vascular tissue-information that could help cardiologists detect life-threatening plaques and predict their propensity to rupture. The modulus recovery process is an ill-posed problem; therefore, additional information is needed to provide useful elastograms. In this work, prior geometrical information was used to impose hard or soft constraints on the reconstruction process. We conducted simulation and phantom studies to evaluate and compare modulus elastograms computed with soft and hard constraints versus those computed without any prior information. The results revealed that (1) the contrast-to-noise ratio of modulus elastograms achieved using the soft prior and hard prior reconstruction methods exceeded those computed without any prior information; (2) the soft prior and hard prior reconstruction methods could tolerate up to 8% measurement noise, and (3) the performance of soft and hard prior modulus elastograms degraded when incomplete spatial priors were employed. This work demonstrates that including spatial priors in the reconstruction process should improve the performance of model-based elastography, and the soft prior approach should enhance the robustness of the reconstruction process to errors in the geometrical information.

Recent results in nonlinear strain and modulus imaging

We report a summary of recent developments and current status of our team's efforts to image and quantify in vivo nonlinear strain and tissue mechanical properties. Our work is guided by a focus on applications to cancer diagnosis and treatment using clinical ultrasound imaging and quasi-static tissue deformations. We review our recent developments in displacement estimation from ultrasound image sequences. We discuss cross correlation approaches, regularized optimization approaches, guided search methods, multiscale methods, and hybrid methods. Current implementations can return results of high accuracy in both axial and lateral directions at several frames per second.We compare several strain estimators. Again we see a benefit from a regularized optimization approach. We then discuss both direct and iterative methods to reconstruct tissue mechanical property distributions from measured strain and displacement fields. We review the formulation, discretization, and algorithmic considerations that come into play when attempting to infer linear and nonlinear elastic properties from strain and displacement measurements. Finally we illustrate our progress with example applications in breast disease diagnosis and tumor ablation monitoring. Our current status shows that we have demonstrated quantitative determination of nonlinear parameters in phantoms and in vivo, in the context of 2D models and data. We look forward to incorporating 3D data from 2D transducer arrays to noninvasively create calibrated 3D quantitative maps of nonlinear elastic properties of breast tissues in vivo.

AN OVERVIEW OF ELASTOGRAPHY - AN EMERGING BRANCH OF MEDICAL IMAGING

From times immemorial manual palpation served as a source of information on the state of soft tissues and allowed detection of various diseases accompanied by changes in tissue elasticity. During the last two decades, the ancient art of palpation gained new life due to numerous emerging elasticity imaging (EI) methods. Areas of applications of EI in medical diagnostics and treatment monitoring are steadily expanding. Elasticity imaging methods are emerging as commercial applications, a true testament to the progress and importance of the field.In this paper we present a brief history and theoretical basis of EI, describe various techniques of EI and, analyze their advantages and limitations, and overview main clinical applications. We present a classification of elasticity measurement and imaging techniques based on the methods used for generating a stress in the tissue (external mechanical force, internal ultrasound radiation force, or an internal endogenous force), and measurement of the tissue response. The measurement method can be performed using differing physical principles including magnetic resonance imaging (MRI), ultrasound imaging, X-ray imaging, optical and acoustic signals.Until recently, EI was largely a research method used by a few select institutions having the special equipment needed to perform the studies. Since 2005 however, increasing numbers of mainstream manufacturers have added EI to their ultrasound systems so that today the majority of manufacturers offer some sort of Elastography or tissue stiffness imaging on their clinical systems. Now it is safe to say that some sort of elasticity imaging may be performed on virtually all types of focal and diffuse disease. Most of the new applications are still in the early stages of research, but a few are becoming common applications in clinical practice.

Identification of regional mechanical anisotropy in soft tissue analogs

In a previous work (Raghupathy and Barocas, 2010, "Generalized Anisotropic Inverse Mechanics for Soft Tissues,"J. Biomech. Eng., 132(8), pp. 081006), a generalized anisotropic inverse mechanics method applicable to soft tissues was presented and tested against simulated data. Here we demonstrate the ability of the method to identify regional differences in anisotropy from full-field displacements and boundary forces obtained from biaxial extension tests on soft tissue analogs. Tissue heterogeneity was evaluated by partitioning the domain into homogeneous subdomains. Tests on elastomer samples demonstrated the performance of the method on isotropic materials with uniform and nonuniform properties. Tests on fibroblast-remodeled collagen cruciforms indicated a strong correlation between local structural anisotropy (measured by polarized light microscopy) and the evaluated local mechanical anisotropy. The results demonstrate the potential to quantify regional anisotropic material behavior on an intact tissue sample.

A new method for the acquisition of ultrasonic strain image volumes

This article presents a new method for acquiring three-dimensional (3-D) volumes of ultrasonic axial strain data. The method uses a mechanically-swept probe to sweep out a single volume while applying a continuously varying axial compression. Acquisition of a volume takes 15-20 s. A strain volume is then calculated by comparing frame pairs throughout the sequence. The method uses strain quality estimates to automatically pick out high quality frame pairs, and so does not require careful control of the axial compression. In a series of in vitro and in vivo experiments, we quantify the image quality of the new method and also assess its ease of use. Results are compared with those for the current best alternative, which calculates strain between two complete volumes. The volume pair approach can produce high quality data, but skillful scanning is required to acquire two volumes with appropriate relative strain. In the new method, the automatic quality-weighted selection of image pairs overcomes this difficulty and the method produces superior quality images with a relatively relaxed scanning technique.

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.