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

[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.

Simultaneous Vascular Strain and Blood Vector Velocity Imaging Using High-Frequency Versus Conventional-Frequency Plane Wave Ultrasound: A Phantom Study

Plaque strain and blood vector velocity imaging of stenosed arteries are expected to aid in diagnosis and prevention of cerebrovascular disease. Ultrafast plane wave imaging enables simultaneous strain and velocity estimation. Multiple ultrasound vendors are introducing high-frequency ultrasound probes and systems. This paper investigates whether the use of high-frequency ultrafast ultrasound is beneficial for assessing blood velocities and strain in arteries. The performance of strain and blood flow velocity estimation was compared between a high-frequency transducer (MS250, fc = 21 MHz) and a clinically utilized transducer (L12-5, fc = 9 MHz). Quantitative analysis based on straight tube phantom experiments revealed that the MS250 outperformed the L12-5 in the superficial region: low velocities near the wall were more accurately estimated and wall strains were better resolved. At greater than 2-cm echo depth, the L12-5 performed better due to the high attenuation of the MS250 probe. Qualitative comparison using a perfused patient-specific carotid bifurcation phantom confirmed these findings. Thus, in conclusion, for strain and blood velocity estimation for depths up to ~2 cm, a high-frequency probe is recommended.

Visualizing Angle-Independent Principal Strains in the Longitudinal View of the Carotid Artery: Phantom and In Vivo Evaluation

Non-invasive vascular elastography can evaluate the stiffness of the carotid artery by visualizing the vascular strain distribution. Axial strain estimates of the longitudinal cross section of the carotid artery are sensitive to the angle between the artery and the transducer. Anatomical variations in branching and arching of the carotid artery can affect the assessment of arterial stiffness. In this study, we hypothesized that principal strain elastograms computed using compounded plane wave imaging can reliably visualize the strain distribution in the carotid artery, independent of the transducer angle. We corroborated this hypothesis by conducting phantom and in vivo studies using a commercial ultrasound scanner (Sonix RP, Ultrasonix Medical Corp., Richmond, BC, Canada). The phantom studies were conducted using a homogeneous cryogel vessel phantom. The goal of the phantom study was to assess the feasibility of visualizing the radial deformation in the longitudinal plane of the vessel phantom, independent of the transducer angle (±30°, ±20°, ±10° and 0°). The in vivo studies were conducted on 20 healthy human volunteers in the age group 50-60 y. All echo imaging was performed at a transmit frequency of 5 MHz and sampling frequency of 40 MHz. The elastograms obtained from the phantom study revealed that for straight vessels, which had their lumen parallel to the transducer, principal strains were similar to axial strains. At non-parallel configurations (angles ±30°, ±20° and ±10°), the magnitudes of the mean principal strains were within 2.5% of the parallel configuration (0° angle) estimates and, thus, were observed to be relatively unaffected by change in angle. However, in comparison, the magnitude of the axial strain decreased with increase in angle because of coordinate dependency. Further, the pilot in vivo study indicated that the principal and axial strain elastograms were similar for subjects with relatively straight arteries. However, for arteries with arched geometry, axial strains were significantly lower (p <0.01) than the corresponding principal vascular strains, which was consistent with the results obtained from the phantom study. In conclusion, the results of the phantom and in vivo studies revealed that principal strain elastograms computed using CPW imaging could reliably visualize angle-independent vascular strains in the longitudinal plane of the carotid artery.

Noninvasive Vascular Modulography Method for Imaging the Local Elasticity of Atherosclerotic Plaques: Simulation and In Vitro Vessel Phantom Study

Mechanical and morphological characterization of atherosclerotic lesions in carotid arteries remains an essential step for the evaluation of rupture prone plaques and the prevention of strokes. In this paper, we propose a noninvasive vascular imaging modulography (NIV-iMod) method, which is capable of reconstructing a heterogeneous Young's modulus distribution of a carotid plaque from the Von Mises strain elastogram. Elastograms were computed with noninvasive ultrasound images using the Lagrangian speckle model estimator and a dynamic segmentation-optimization procedure to highlight mechanical heterogeneities. This methodology, based on continuum mechanics, was validated in silico with finite-element model strain fields and ultrasound simulations, and in vitro with polyvinyl alcohol cryogel phantoms based on magnetic resonance imaging geometries of carotid plaques. In silico, our results show that the NiV-iMod method: 1) successfully detected and quantified necrotic core inclusions with high positive predictive value (PPV) and sensitivity value (SV) of 81±10% and 91±6%; 2) quantified Young's moduli of necrotic cores, fibrous tissues, and calcium inclusions with mean values of 32±23, 515±30, and 3160±218 kPa (ground true values are 10, 600, and 5000 kPa); and 3) overestimated the cap thickness by . In vitro, the PPV and SV for detecting soft inclusions were 60±21% and 88±9%, and Young's modulus mean values of mimicking lipid, fibrosis, and calcium were 34±19, 193±14, and 649±118 kPa (ground true values are 25±3, 182±21, and 757±87 kPa).

Model-based vascular elastography improves the detection of flow-induced carotid artery remodeling in mice

Increased arterial thickness measured with ultrasound correlates with future cardiovascular events, but conventional ultrasound imaging techniques cannot distinguish between intima, media, or atherosclerotic plaque in the carotid artery. In this work, we evaluated how well vascular elastography can detect intimal changes in a mouse model of carotid remodeling. We ligated the left external and internal branches of the carotid artery of male FVB mice and performed sham operations for 2 weeks. High-resolution ultrasound imaging accurately detected lower blood velocities and low blood volume flow in the carotid arteries after ligation in FVB mice. However, ultrasound could not detect differences in the carotid wall even at 2 weeks post-surgery. The Young’s modulus was measured based on displacements of the carotid artery wall, and Young’s modulus was 2-fold greater in shams at 1 week post ligation, and 3-fold greater 2 weeks after ligation. Finally, the higher Young’s modulus was most associated with higher intimal thickness but not medial or adventitial thickness as measured by histology. In conclusion, we developed a robust ultrasound-based elastography method for early detection of intimal changes in small animals.

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).

Principal Strain Vascular Elastography: Simulation and Preliminary Clinical Evaluation

It is difficult to produce reliable polar strain elastograms (radial and circumferential) because the center of the carotid artery is typically unknown. Principal strain imaging can overcome this limitation, but suboptimal lateral displacement estimates make this an impractical approach for visualizing mechanical properties within the carotid artery. We hypothesized that compounded plane wave imaging can minimize this problem. To test this hypothesis, we performed (i) simulations with vessels of varying morphology and mechanical behavior (i.e., isotropic and transversely isotropic), and (ii) a pilot study with 10 healthy volunteers. The accuracy of principal and polar strain (computed using knowledge of the precise vessel center) elastograms varied between 7% and 17%. In both types of elastograms, strain concentrated at the junction between the fibrous cap and the vessel wall, and the strain magnitude decreased with increasing fibrous cap thickness. Elastograms of healthy volunteers were consistent with those of transversely isotropic homogeneous vessels; they were spatially asymmetric, a trend that was common to both principal and polar strains. No significant differences were observed in the mean strain recovered from principal and polar strains (p > 0.05). This investigation indicates that principal strain elastograms measured with compounding plane wave imaging overcome the problems incurred when polar strain elastograms are computed with imprecise estimates of the vessel center.

Toward Optimal Computation of Ultrasound Image Reconstruction Using CPU and GPU

An ultrasound image is reconstructed from echo signals received by array elements of a transducer. The time of flight of the echo depends on the distance between the focus to the array elements. The received echo signals have to be delayed to make their wave fronts and phase coherent before summing the signals. In digital beamforming, the delays are not always located at the sampled points. Generally, the values of the delayed signals are estimated by the values of the nearest samples. This method is fast and easy, however inaccurate. There are other methods available for increasing the accuracy of the delayed signals and, consequently, the quality of the beamformed signals; for example, the in-phase (I)/quadrature (Q) interpolation, which is more time consuming but provides more accurate values than the nearest samples. This paper compares the signals after dynamic receive beamforming, in which the echo signals are delayed using two methods, the nearest sample method and the I/Q interpolation method. The comparisons of the visual qualities of the reconstructed images and the qualities of the beamformed signals are reported. Moreover, the computational speeds of these methods are also optimized by reorganizing the data processing flow and by applying the graphics processing unit (GPU). The use of single and double precision floating-point formats of the intermediate data is also considered. The speeds with and without these optimizations are also compared.

2-D Versus 3-D Cross-Correlation-Based Radial and Circumferential Strain Estimation Using Multiplane 2-D Ultrafast Ultrasound in a 3-D Atherosclerotic Carotid Artery Model

Three-dimensional (3-D) strain estimation might improve the detection and localization of high strain regions in the carotid artery (CA) for identification of vulnerable plaques. This paper compares 2-D versus 3-D displacement estimation in terms of radial and circumferential strain using simulated ultrasound (US) images of a patient-specific 3-D atherosclerotic CA model at the bifurcation embedded in surrounding tissue generated with ABAQUS software. Global longitudinal motion was superimposed to the model based on the literature data. A Philips L11-3 linear array transducer was simulated, which transmitted plane waves at three alternating angles at a pulse repetition rate of 10 kHz. Interframe (IF) radio-frequency US data were simulated in Field II for 191 equally spaced longitudinal positions of the internal CA. Accumulated radial and circumferential displacements were estimated using tracking of the IF displacements estimated by a two-step normalized cross-correlation method and displacement compounding. Least-squares strain estimation was performed to determine accumulated radial and circumferential strain. The performance of the 2-D and 3-D methods was compared by calculating the root-mean-squared error of the estimated strains with respect to the reference strains obtained from the model. More accurate strain images were obtained using the 3-D displacement estimation for the entire cardiac cycle. The 3-D technique clearly outperformed the 2-D technique in phases with high IF longitudinal motion. In fact, the large IF longitudinal motion rendered it impossible to accurately track the tissue and cumulate strains over the entire cardiac cycle with the 2-D technique.

Contrast-Enhanced Quantitative Intravascular Elastography: The Impact of Microvasculature on Model-Based Elastography

Model-based intravascular ultrasound elastography visualizes the stress distribution within vascular tissue-information that clinicians could use to predict the propensity of atherosclerotic plaque rupture. However, there are concerns that clusters of microvessels may reduce the accuracy of the estimated stress distribution. Consequently, we have developed a contrast-enhanced intravascular ultrasound system to investigate how plaque microvasculature affects the performance of model-based elastography. In simulations, diameters of 200, 400 and 800 μm were used, where the latter diameter represented a cluster of microvessels. In phantoms, we used a microvessel with a diameter of 750 μm. Peak stress errors of 3% and 38% were incurred in the fibrous cap when stress recovery was performed with and without a priori information about microvessel geometry. The results indicate that incorporating geometric information about plaque microvasculature obtained with contrast-enhanced ultrasound imaging improves the accuracy of estimates of the stress distribution within the fibrous cap precisely.

Inflation and Bi-Axial Tensile Testing of Healthy Porcine Carotid Arteries

Knowledge of the intrinsic material properties of healthy and diseased arterial tissue components is of great importance in diagnostics. This study describes an in vitro comparison of 13 porcine carotid arteries using inflation testing combined with functional ultrasound and bi-axial tensile testing. The measured tissue behavior was described using both a linear, but geometrically non-linear, one-parameter (neo-Hookean) model and a two-parameter non-linear (Demiray) model. The shear modulus estimated using the linear model resulted in good agreement between the ultrasound and tensile testing methods, GUS = 25 ± 5.7 kPa and GTT = 23 ± 5.4 kPa. No significant correspondence was observed for the non-linear model aUS = 1.0 ± 2.7 kPa vs. aTT = 17 ± 8.8 kPa, p ∼ 0); however, the exponential parameters were in correspondence (bUS = 12 ± 4.2 vs. bTT = 10 ± 1.7, p > 0.05). Estimation of more complex models in vivo is cumbersome considering the sensitivity of the model parameters to small changes in measurement data and the absence of intraluminal pressure data, endorsing the use of a simple, linear model in vivo.

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.

Quantitative sparse array vascular elastography: the impact of tissue attenuation and modulus contrast on performance

Quantitative sparse array vascular elastography visualizes the shear modulus distribution within vascular tissues, information that clinicans could use to reduce the number of strokes each year. However, the low transmit power sparse array (SA) imaging could hamper the clinical usefulness of the resulting elastograms. In this study, we evaluated the performance of modulus elastograms recovered from simulated and physical vessel phantoms with varying attenuation coefficients (0.6, 1.5, and [Formula: see text]) and modulus contrasts ([Formula: see text], [Formula: see text], and [Formula: see text]) using SA imaging relative to those obtained with conventional linear array (CLA) and plane-wave (PW) imaging techniques. Plaques were visible in all modulus elastograms, but those produced using SA and PW contained less artifacts. The modulus contrast-to-noise ratio decreased rapidly with increasing modulus contrast and attenuation coefficient, but more quickly when SA imaging was performed than for CLA or PW. The errors incurred varied from 10.9% to 24% (CLA), 1.8% to 12% (SA), and [Formula: see text] (PW). Modulus elastograms produced with SA and PW imagings were not significantly different ([Formula: see text]). Despite the low transmit power, SA imaging can produce useful modulus elastograms in superficial organs, such as the carotid artery.