An ultrasound elastography method to determine the local stiffness of arteries with guided circumferential waves

Extending arterial stiffness assessment along the circumference using beam-steered ARFI and wave-tracking: A proof-of-principle study in phantoms and ex vivo

Background

To fully quantify arterial wall and plaque stiffness, acoustic radiation force impulse (ARFI)-induced wave-tracking along the entire vessel circumference is desired. However, attenuation and guided wave behavior in thin vessel walls limits wave-tracking to short trajectories. This study investigated the potential of beam-steered ARFI and wave-tracking to extend group velocity estimation over a larger proportion of the circumference compared to conventional 0° ARFI-induced wave-tracking.

Methods

Seven vessel-mimicking polyvinyl alcohol cryogel phantoms with various dimensions and compositions and an ex vivo human carotid artery were imaged in a dedicated setup. For every 20⁰ phantom rotation, transverse group wave velocity measurements were performed with an Aixplorer Ultimate system and SL18-5 transducer using 0⁰/20⁰/-20⁰-angled ultrasound pushes. Transmural angular wave velocities were derived along 60⁰-trajectories. A 360⁰-angular velocity map was composed from the top-wall 60⁰-trajectories 0°-data, averaged over all physical phantom rotations (reference). For each phantom rotation, 360⁰-angular velocity maps were composed using 0°-data (0⁰-approach) or data from all angles (beam-steered approach). Percentages of rotations with visible waves and relative angular velocity errors compared to the reference map as function of the circumferential angle were determined for both approaches.

Results

Reference 360°-angular velocity maps could be derived for all samples, representing their stiffness. Beam-steering decreased the proportion of the circumference where waves were untraceable by 20% in phantoms and 10% ex vivo, mainly at 0° push locations. Relative errors were similar for both approaches (phantoms: 10-15%, ex vivo: 15-35%).

Conclusion

Beam-steering enables wave-tracking along a higher proportion of the wall circumference than 0⁰ ARFI-induced wave-tracking.

Full waveform inversion for arterial viscoelasticity

Objective. Arterial viscosity is emerging as an important biomarker, in addition to the widely used arterial elasticity. This paper presents an approach to estimate arterial viscoelasticity using shear wave elastography (SWE).Approach. While dispersion characteristics are often used to estimate elasticity from SWE data, they are not sufficiently sensitive to viscosity. Driven by this, we develop a full waveform inversion (FWI) methodology, based on directly matching predicted and measured wall velocity in space and time, to simultaneously estimate both elasticity and viscosity. Specifically, we propose to minimize an objective function capturing the correlation between measured and predicted responses of the anterior wall of the artery.Results. The objective function is shown to be well-behaving (generally convex), leading us to effectively use gradient optimization to invert for both elasticity and viscosity. The resulting methodology is verified with synthetic data polluted with noise, leading to the conclusion that the proposed FWI is effective in estimating arterial viscoelasticity.Significance. Accurate estimation of arterial viscoelasticity, not just elasticity, provides a more precise characterization of arterial mechanical properties, potentially leading to a better indicator of arterial health.

Arterial Stiffness Probed by Dynamic Ultrasound Elastography Characterizes Waveform of Blood Pressure

The clinical and economic burdens of cardiovascular diseases pose a global challenge. Growing evidence suggests an early assessment of arterial stiffness can provide insights into the pathogenesis of cardiovascular diseases. However, it remains difficult to quantitatively characterize local arterial stiffness in vivo. Here we utilize guided axial waves continuously excited and detected by ultrasound to probe local blood pressures and mechanical properties of common carotid arteries simultaneously. In a pilot study of 17 healthy volunteers, we observe a  ∼ 20 % variation in the group velocities of the guided axial waves (5.16 ± 0.55 m/s in systole and 4.31 ± 0.49 m/s in diastole) induced by the variation of the blood pressures. A linear relationship between the square of group velocity and blood pressure is revealed by the experiments and finite element analysis, which enables us to measure the waveform of the blood pressures by the group velocities. Furthermore, we propose a wavelet analysis-based method to extract the dispersion relations of the guided axial waves. We then determined the shear modulus by fitting the dispersion relations in diastole with the leaky Lamb wave model. The average shear modulus of all the volunteers is 166.3 ± 32.8 kPa. No gender differences are found. This study shows the group velocity and dispersion relation of the guided axial waves can be utilized to probe blood pressure and arterial stiffness locally in a noninvasive manner and thus promising for early diagnosis of cardiovascular diseases.

Progressive Calcification in Bicuspid Valves: A Coupled Hemodynamics and Multiscale Structural Computations

Bicuspid aortic valve (BAV) is the most common congenital heart disease. Calcific aortic valve disease (CAVD) accounts for the majority of aortic stenosis (AS) cases. Half of the patients diagnosed with AS have a BAV, which has an accelerated progression rate. This study aims to develop a computational modeling approach of both the calcification progression in BAV, and its biomechanical response incorporating fluid-structure interaction (FSI) simulations during the disease progression. The calcification is patient-specifically reconstructed from Micro-CT images of excised calcified BAV leaflets, and processed with a novel reverse calcification technique that predicts prior states of CAVD using a density-based criterion, resulting in a multilayered calcified structure. Four progressive multilayered calcified BAV models were generated: healthy, mild, moderate, and severe, and were modeled by FSI simulations during the full cardiac cycle. A valve apparatus model, composed of the excised calcified BAV leaflets, was tested in an in-vitro pulse duplicator, to validate the severe model. The healthy model was validated against echocardiography scans. Progressive AS was characterized by higher systolic jet flow velocities (2.08, 2.3, 3.37, and 3.85 m s^-1), which induced intense vortices surrounding the jet, coupled with irregular recirculation backflow patterns that elevated viscous shear stresses on the leaflets. This study shed light on the fluid-structure mechanism that drives CAVD progression in BAV patients.

Fast Strain Estimation and Frame Selection in Ultrasound Elastography Using Machine Learning

Ultrasound elastography aims to determine the mechanical properties of the tissue by monitoring tissue deformation due to internal or external forces. Tissue deformations are estimated from ultrasound radio frequency (RF) signals and are often referred to as time delay estimation (TDE). Given two RF frames I₁ and I₂ , we can compute a displacement image, which shows the change in the position of each sample in I₁ to a new position in I₂ . Two important challenges in TDE include high computational complexity and the difficulty in choosing suitable RF frames. Selecting suitable frames is of high importance because many pairs of RF frames either do not have acceptable deformation for extracting informative strain images or are decorrelated and deformation cannot be reliably estimated. Herein, we introduce a method that learns 12 displacement modes in quasi-static elastography by performing principal component analysis (PCA) on displacement fields of a large training database. In the inference stage, we use dynamic programming (DP) to compute an initial displacement estimate of around 1% of the samples and then decompose this sparse displacement into a linear combination of the 12 displacement modes. Our method assumes that the displacement of the whole image could also be described by this linear combination of principal components. We then use the GLobal Ultrasound Elastography (GLUE) method to fine-tune the result yielding the exact displacement image. Our method, which we call PCA-GLUE, is more than 10× faster than DP in calculating the initial displacement map while giving the same result. This is due to converting the problem of estimating millions of variables in DP into a much simpler problem of only 12 unknown weights of the principal components. Our second contribution in this article is determining the suitability of the frame pair I₁ and I₂ for strain estimation, which we achieve by using the weight vector that we calculated for PCA-GLUE as an input to a multilayer perceptron (MLP) classifier. We validate PCA-GLUE using simulation, phantom, and in vivo data. Our classifier takes only 1.5 ms during the testing phase and has an F1-measure of more than 92% when tested on 1430 instances collected from both phantom and in vivo data sets.

Bidirectional Ultrasound Elastographic Imaging Framework for Non-invasive Assessment of the Non-linear Behavior of a Physiologically Pressurized Artery

Studies of non-destructive bidirectional ultrasound assessment of non-linear mechanical behavior of the artery are scarce in the literature. We hereby propose derivation of a strain-shear modulus relationship as a new graphical diagnostic index using an ultrasound elastographic imaging framework, which encompasses our in-house bidirectional vascular guided wave imaging (VGWI) and ultrasound strain imaging (USI). This framework is used to assess arterial non-linearity in two orthogonal (i.e., longitudinal and circumferential) directions in the absence of non-invasive pressure measurement. Bidirectional VGWI estimates longitudinal (μ_L) and transverse (μ_T) shear moduli, whereas USI estimates radial strain (ɛ_r). Vessel-mimicking phantoms (with and without longitudinal pre-stretch) and in vitro porcine aortas under static and/or dynamic physiologic intraluminal pressure loads were examined. ɛ_r was found to be a suitable alternative to intraluminal pressure for representation of cyclic loading on the artery wall. Results revealed that μ_T values of all samples examined increased non-linearly with ε_r magnitude and more drastically than μ_L, whereas μ_L values of only the pre-stretched phantoms and aortas increased with ɛ_r magnitude. As a new graphical representation of arterial non-linearity and function, strain-shear modulus loops derived by the proposed framework over two consecutive dynamic loading cycles differentiated sample pre-conditions and corroborated direction-dependent non-linear mechanical behaviors of the aorta with high estimation repeatability.

Guided wave elastography of layered soft tissues

In vivo mechanical characterization of soft biological tissues has broad applications ranging from disease diagnosis to tissue engineering. Shear wave elastography based on the bulk wave theory has been widely used to measure the mechanical properties of soft tissues. Given that most soft tissues basically have layered structures, the dispersive feature of elastic waves should be considered when the thickness of the interested layer is comparable to or smaller than the wavelength. Bearing this fundamental issue in mind, we propose an ultrasound-based guided wave elastography (GWE) method to characterize the mechanical properties of layered soft tissues. The dispersion relations of guided waves in layered structures were derived first, and its explicit expression was achieved. An inverse approach based on the dispersion relation to characterize the mechanical properties of layered soft tissues was then established. Both finite element analysis (FEA) and phantom experiments were carried out to validate the new method. In vivo experiments on forearm skin demonstrate the usefulness of the present method in characterizing layered soft tissues. STATEMENT OF SIGNIFICANCE: Layered soft tissues and artificial soft materials are ubiquitous in both nature and engineering. Imaging their in vivo/in situ mechanical properties finds important applications and remains a great challenge to date. Here, we propose an ultrasound-based guided wave elastography method to in vivo/in situ characterize the elastic properties of layered soft materials. We validate the method via finite element analysis and phantom experiments and further demonstrate its usefulness in practice by performing in vivo measurements on forearm skins. Given that the dispersive feature of elastic waves in layered soft media is considered in our method, it provides the opportunity to assess the intrinsic elastic properties of an individual layer in a non-destructive manner as shown in our experiments.

Multidirectional Estimation of Arterial Stiffness Using Vascular Guided Wave Imaging with Geometry Correction

We previously found that vascular guided wave imaging (VGWI) could non-invasively quantify transmural wall stiffness in both the longitudinal (r-z plane, 0°) and circumferential (r-θ plane, 90°) directions of soft hollow cylinders. Arterial stiffness estimation in multiple directions warrants further comprehensive characterization of arterial health, especially in the presence of asymmetric plaques, but is currently lacking. This study therefore investigated the multidirectional estimation of the arterial Young's modulus in a finite-element model, in vitro artery-mimicking phantoms and an excised porcine aorta. A longitudinal pre-stretch of 20% and/or lumen pressure (15 or 70 mm Hg) was additionally introduced to pre-condition the phantoms for emulating the intrinsic mechanical anisotropy of the real artery. The guided wave propagation was approximated by a zero-order antisymmetric Lamb wave model. Shape factor, which was defined as the ratio of inner radius to thickness, was calculated over the entire segment of each planar cross section of the hollow cylindrical structure at a full rotation (0°-360° at 10° increments) about the radial axis. The view-dependent geometry of the cross segment was found to affect the guided wave propagation, causing Young's modulus overestimation in four angular intervals along the propagation pathway, all of which corresponded to wall regions with low shape factors (<1.5). As validated by mechanical tensile testing, the results indicate not only that excluding the propagation pathway with low shape factors could correct the overestimation of Young's modulus, but also that VGWI could portray the anisotropy of hollow cylindrical structures and the porcine aorta based on the derived fractional anisotropy values from multidirectional modulus estimates. This study may serve as an important step toward 3-D assessment of the mechanical properties of the artery.

Assessing the mechanical properties of anisotropic soft tissues using guided wave elastography: Inverse method and numerical experiments

Determining the mechanical properties of soft biological tissues can be of great importance. For example, the microstructures of many soft tissues, such as those of the human Achilles tendon, have been identified as typical anisotropic materials. This paper proposes an inverse approach that uses guided wave elastography to determine the anisotropic elastic and hyperelastic parameters of thin-walled transversely isotropic biological soft tissues. This approach was developed from the theoretical solutions for the dispersion relations of guided waves, which were derived based on a constitutive model suitable for describing the deformation behavior of such tissues. The properties of these solutions were investigated; in particular, sensitivity to data errors was addressed by introducing the concept of the condition number. To further validate the proposed inverse approach, the guided wave elastography of thin-walled transversely isotropic soft tissues was investigated using numerical experiments. The results indicated that the four constitutive parameters (other than the tensile modulus along the direction of the fibers, E_L) could be determined with a good level of accuracy using this method.

Novel Method for Vessel Cross-Sectional Shear Wave Imaging

Many studies have investigated the applications of shear wave imaging (SWI) to vascular elastography, mainly on the longitudinal section of vessels. It is important to investigate SWI in the arterial cross section when evaluating anisotropy of the vessel wall or complete plaque composition. Here, we proposed a novel method based on the coordinate transformation and directional filter in the polar coordinate system to achieve vessel cross-sectional shear wave imaging. In particular, ultrasound radiofrequency data were transformed from the Cartesian to the polar coordinate system; the radial displacements were then estimated directly. Directional filtering was performed along the circumferential direction to filter out the reflected waves. The feasibility of the proposed vessel cross-sectional shear wave imaging method was investigated through phantom experiments and ex vivo and in vivo studies. Our results indicated that the dispersion relation of the shear wave (i.e., the guided circumferential wave) within the vessel can be measured via the present method, and the elastic modulus of the vessel can be determined.

Mechanics of ultrasound elastography

Ultrasound elastography enables in vivo measurement of the mechanical properties of living soft tissues in a non-destructive and non-invasive manner and has attracted considerable interest for clinical use in recent years. Continuum mechanics plays an essential role in understanding and improving ultrasound-based elastography methods and is the main focus of this review. In particular, the mechanics theories involved in both static and dynamic elastography methods are surveyed. They may help understand the challenges in and opportunities for the practical applications of various ultrasound elastography methods to characterize the linear elastic, viscoelastic, anisotropic elastic and hyperelastic properties of both bulk and thin-walled soft materials, especially the in vivo characterization of biological soft tissues.