Arterial waveguide model for shear wave elastography: implementation andin vitrovalidation

Guided wave elastography of jugular veins: Theory, method and in vivo experiment

Testing the mechanical properties of veins is important for diagnosing some cardiovascular diseases such as deep venous thrombosis. Additionally, it plays a crucial role in designing body protective products such as head protective gear, where simulations are necessary to predict the mechanical responses of bridging veins during head impacts. The data on venous mechanical properties reported in the literature have mainly been obtained from ex vivo experiments, and inferring the material parameters of veins in vivo is challenging. Here, we address this issue by proposing a guided wave elastography method in which guided waves are generated in the jugular veins with focused acoustic radiation force and tracked by an ultrafast ultrasound imaging system. Then, a mechanical model considering the effects of the perivascular soft tissues and prestresses in the veins was applied to analyze the wave motions in the jugular veins. Our model enables the development of an inverse method to infer the elastic properties of the veins from measured guided waves. Phantom experiments were performed to validate the theory, and in vivo experiments were carried out to demonstrate the usefulness of the inverse method in practice.

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.

Measurement of wave propagation through a tube using dual transducers for elastography in arteries

Objective.Measuring waves induced with acoustic radiation force (ARF) in arteries has been studied over the last decade. To date, it remains a challenge to quantitatively assess the local arterial biomechanical properties. The cylindrical shape and waveguide behavior of waves propagating in the arterial wall pose complexities to determining the mechanical properties of the artery.Approach. In this paper, an artery-mimicking tube in water is examined utilizing three-dimensional measurements. The cross-section of the tube is measured while a transducer is translated over 41 different positions along the length of the tube. Motion in the radial direction is calculated using two components of motion which are measured from the two orthogonal views of the cross-section. This enables more accurate estimation of motion along the circumference of tube.Main results. The results provide more information to categorize the motion in tube wall into two types of responses: a transient response and a steady state response. The transient response is caused by ARF application and the waves travel along the length of the tube for a relatively short period of time. This corresponds to the axial and circumferential propagating waves. The two circumferential waves travel along the circumference of tube in CW (clockwise) and CCW (counter-clockwise) direction and result in a standing wave. By using a directional filter, the two waves were successfully separated, and their propagation was more clearly visualized. As a steady state response, a circumferential mode is generated showing a symmetric motion (i.e. the proximal and distal walls move in the opposite direction) following the transient response.Significance.This study provides a more comprehensive understanding of the waves produced in an artery-mimicking tube with ARF application, which will provide opportunities for improving measurement of arterial mechanical properties.

Full wave simulation of arterial response under acoustic radiation force

With the ultimate goal of estimating arterial viscoelasticity using shear wave elastography, this paper presents a practical methodology to simulate the response of a human carotid artery under acoustic radiation force (ARF). The artery is idealized as a nearly incompressible viscoelastic hollow cylinder submerged in incompressible, inviscid fluid. For this idealization, we develop a multi-step methodology for efficient computation of three-dimensional response under complex ARF excitation, while capturing the fluid-structure interaction between the arterial wall and the surrounding fluid. The specific steps include (a) performing dimensional reduction through semi-analytical finite element formulation, (b) efficient finite element discretization using traditional and recent techniques. The computational efficiency is further enhanced by utilizing (c) modal superposition, followed by, where appropriate, (d) impulse response function. In addition to developing the methodology, convergence analysis is performed for a typical arterial geometry, leading to recommendations on various discretization parameters. At the end, the computational effort is shown to be several orders of magnitude less than the traditional, fully three-dimensional analysis using finite element methods, leading to a practical yet accurate simulation of arterial response under ARF excitations.

The influence of acoustic radiation force beam shape and location on wave spectral content for arterial dispersion ultrasound vibrometry

Objective. Arterial dispersion ultrasound vibrometry (ADUV) relies on the use of guided waves in arterial geometries for shear wave elastography measurements. Both the generation of waves through the use of acoustic radiation force (ARF) and the techniques employed to infer the speed of the resulting wave motion affect the spectral content and accuracy of the measurement. In particular, the effects of the shape and location of the ARF beam in ADUV have not been widely studied. In this work, we investigated how such variations of the ARF beam affect the induced motion and the measurements in the dispersive modes that are excited. Approach. The study includes an experimental evaluation on an arterial phantom and an in vivo validation of the observed trends, observing the two walls of the waveguide, simultaneously, when subjected to variations in the ARF beam extension (F/N) and focus location. Main results. Relying on the theory of guided waves in cylindrical shells, the shape of the beam controls the selection and nature of the induced modes, while the location affects the measured dispersion curves (i.e. variation of phase velocity with frequency or wavenumber, multiple modes) across the waveguide walls. Significance. This investigation is important to understand the spectral content variations in ADUV measurements and to maximize inversion accuracy by tuning the ARF beam settings in clinical applications.

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.

Soft elastomers: A playground for guided waves

Mechanical waves propagating in soft materials play an important role in physiology. They can be natural, such as the cochlear wave in the inner ear of mammalians, or controlled, such as in elastography in the context of medical imaging. In a recent study, Lanoy, Lemoult, Eddi, and Prada [Proc. Natl. Acad. Sci. U.S.A. 117(48), 30186-30190 (2020)] implemented an experimental tabletop platform that allows direct observation of in-plane guided waves in a soft strip. Here, a detailed description of the setup and signal processing steps is presented as well as the theoretical framework supporting them. One motivation is to propose a tutorial experiment for visualizing the propagation of guided elastic waves. Last, the versatility of the experimental platform is exploited to illustrate experimentally original features of wave physics, such as backward modes, stationary modes, and Dirac cones.

The combined importance of finite dimensions, anisotropy, and pre-stress in acoustoelastography

Dynamic elastography, whether based on magnetic resonance, ultrasound, or optical modalities, attempts to reconstruct quantitative maps of the viscoelastic properties of biological tissue, properties that are altered by disease and injury, by noninvasively measuring mechanical wave motion in the tissue. Most reconstruction strategies that have been developed neglect boundary conditions, including quasistatic tensile or compressive loading resulting in a nonzero prestress. Significant prestress is inherent to the functional role of some biological tissues currently being studied using elastography, such as skeletal and cardiac muscle, arterial walls, and the cornea. In the present article, we review how prestress alters both bulk mechanical wave motion and wave motion in one- and two-dimensional waveguides. Key findings are linked to studies on skeletal muscle and the human cornea, as one- and two-dimensional waveguide examples. This study highlights the underappreciated combined acoustoelastic and waveguide challenge to elastography. Can elastography truly determine viscoelastic properties of a material when what it is measuring is affected by both these material properties and unknown prestress and other boundary conditions?

Toward improved accuracy in shear wave elastography of arteries through controlling the arterial response to ultrasound perturbation in-silico and in phantoms

Dispersion-based inversion has been proposed as a viable direction for materials characterization of arteries, allowing clinicians to better study cardiovascular conditions using shear wave elastography. However, these methods rely ona prioriknowledge of the vibrational modes dominating the propagating waves induced by acoustic radiation force excitation: differences between anticipated and real modal content are known to yield errors in the inversion. We seek to improve the accuracy of this process by modeling the artery as a fluid-immersed cylindrical waveguide and building an analytical framework to prescribe radiation force excitations that will selectively excite certain waveguide modes using ultrasound acoustic radiation force. We show that all even-numbered waveguide modes can be eliminated from the arterial response to perturbation, and confirm the efficacy of this approach within silicotests that show that odd modes are preferentially excited. Finally, by analyzing data from phantom tests, we find a set of ultrasound focal parameters that demonstrate the viability of inducing the desired odd-mode response in experiments.

Multimodal guided wave inversion for arterial stiffness: methodology and validation in phantoms

Arterial stiffness is an important biomarker for many cardiovascular diseases. Shear wave elastography is a recent technique aimed at estimating local arterial stiffness using guided wave inversion (GWI), i.e. matching the computed and measured wave dispersion. This paper develops and validates a new GWI approach by synthesizing various recent observations and algorithms: (a) refinements to signal processing to obtain more accurate experimental dispersion curves; (b) an efficient forward model to compute theoretical dispersion curves for immersed, incompressible cylindrical waveguides; (c) an optimization framework based on the recent observation that the measured dispersion curve is multimodal, i.e. it matches for not one but two different wave modes in two different frequency ranges. The resulting inversion approach is validated using extensive experimental data from rubber tube phantoms, not only for modulus estimation but also to simultaneously estimate modulus and wall thickness. The observations indicate that the modulus estimates are best performed with the information on wall thickness. The approach, which takes less than half a minute to run, is shown to be accurate, with the modulus estimated with less than 4% error for 70% of the experiments.

Shear wave dispersion analysis of incompressible waveguides

A suite of methodologies is presented to compute shear wave dispersion in incompressible waveguides encountered in biomedical imaging; plate, tube, and general prismatic waveguides, all immersed in an incompressible fluid, are considered in this effort. The developed approaches are based on semi-analytical finite element methods in the frequency domain with a specific focus on the complexities associated with the incompressibility of the solid media as well as the simplification facilitated by the incompressibility of the surrounding fluid. The proposed techniques use the traditional idea of selective reduced integration for the solid medium and the more recent idea of perfectly matched discrete layers for the surrounding fluid. Also, used is the recently developed complex-length finite element method for platelike structures. Several numerical examples are presented to illustrate the practicality and effectiveness of the developed techniques in computing shear wave dispersion in a variety of waveguides.

Characterizing blood clots using acoustic radiation force optical coherence elastography and ultrasound shear wave elastography

Thromboembolism in a cerebral blood vessel is associated with high morbidity and mortality. Mechanical thrombectomy (MT) is one of the emergenc proceduresperformed to remove emboli. However, the interventional approaches such as aspiration catheters or stent retriever are empirically selected. An inappropriate selection of surgical devices can influence the success rate during embolectomy, which can lead to an increase in brain damage. There has been growing interest in the study of clot composition and using a priori knowledge of clot composition to provide guidance for an appropriate treatment strategy for interventional physicians. Developing imaging tools which can allow interventionalists to understand clot composition could affect management and device strategy. In this study, we investigated how clots of different compositions can be characterized by using acoustic radiation force optical coherence elastography (ARF-OCE) and compared with ultrasound shear wave elastography (SWE). Five different clots compositions using human blood were fabricated into cylindrical forms from fibrin-rich (21% red blood cells, RBCs) to RBC-rich (95% RBCs). Using the ARF-OCE and SWE, we characterized the wave velocities measured in the time-domain. In addition, the semi-analytical finite element model was used to explore the relationship between the phase velocities with various frequency ranges and diameters of the clots. The study demonstrated that the wave group velocities generally decrease as RBC content increases in ARF-OCE and SWE. The correlation of the group velocities from the OCE and SWE methods represented a good agreement as RBC composition is larger than 39%. Using the phase velocity dispersion analysis applied to ARF-OCE data, we estimated the shear wave velocities decoupling the effects of the geometry and material properties of the clots. The study demonstrated that the composition of the clots can be characterized by elastographic methods using ARF-OCE and SWE, and OCE demonstrated better ability to discriminate between clots of different RBC compositions, compared to the ultrasound-based approach, especially in clots with low RBC compositions.

On the Challenges Associated with Obtaining Reproducible Measurements Using SWEI in the Median Nerve

This work discusses challenges we have encountered in acquiring reproducible measurements of shear wave speed (SWS) in the median nerve and suggests methods for improving reproducibility. First, procedural acquisition challenges are described, including nerve echogenicity, transducer pressure and transmit focal depth. Second, we present an iterative, radon sum-based algorithm that was developed specifically for measuring the SWS in median nerves. SWSs were measured using single track location shear wave elasticity imaging (SWEI) in the median nerves of six healthy volunteers and six patients diagnosed with carpal tunnel syndrome. Unsuccessful measurements were associated with several challenges including reverberation artifacts, low signal-to-noise ratio and temporal window limitations for tracking the velocity wave. To address these challenges, an iterative convergence algorithm was implemented to identify an appropriate temporal processing window that removed the reverberation artifacts while preserving shear wave signals. Algorithmically, it was important to consider the lateral regression kernel size and position and the temporal window. Procedurally, both nerve echogenicity and transducer compression were determined to impact the measured SWS. Shear waves were successfully measured in the median nerve proximal to the carpal tunnel, but SWEI measurements were significantly compromised within the carpal tunnel itself. The velocity-based SWSs were statistically significantly higher than the displacement SWSs (p < 0.0001), demonstrating for the first time dispersion in the median nerve in vivo using SWEI.

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.