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

Performance evaluation of commercial and non-commercial shear wave elastography implementations for vascular applications

BACKGROUND

Shear wave elastography (SWE) is mainly used for stiffness estimation of large, homogeneous tissues, such as the liver and breasts. However, little is known about its accuracy and applicability in thin (∼0.5-2 mm) vessel walls. To identify possible performance differences among vendors, we quantified differences in measured wave velocities obtained by commercial SWE implementations of various vendors over different imaging depths in a vessel-mimicking phantom. For reference, we measured SWE values in the cylindrical inclusions and homogeneous background of a commercial SWE phantom. Additionally, we compared the accuracy between a research implementation and the commercially available clinical SWE on an Aixplorer ultrasound system in phantoms and in vivo in patients.

METHODS

SWE measurements were performed over varying depths (0-35 mm) using three ultrasound machines with four ultrasound probes in the homogeneous 20 kPa background and cylindrical targets of 10, 40, and 60 kPa of a multi-purpose phantom (CIRS-040GSE) and in the anterior and posterior wall of a homogeneous polyvinyl alcohol vessel-mimicking phantom. These phantom data, along with in vivo SWE data of carotid arteries in 23 patients with a (prior) head and neck neoplasm, were also acquired in the research and clinical mode of the Aixplorer ultrasound machine. Machine-specific estimated phantom stiffness values (CIRS phantom) or wave velocities (vessel phantom) over all depths were visualized, and the relative error to the reference values and inter-frame variability (interquartile range/median) were calculated. Correlations between SWE values and target/vessel wall depth were explored in phantoms and in vivo using Spearman's correlations. Differences in wave velocities between the anterior and posterior arterial wall were assessed with Wilcoxon signed-rank tests. Intra-class correlation coefficients were calculated for a sample of ten patients as a measure of intra- and interobserver reproducibility of SWE analyses in research and clinical mode.

RESULTS

There was a high variability in obtained SWE values among ultrasound machines, probes, and, in some cases, with depth. Compared to the homogeneous CIRS-background, this variation was more pronounced for the inclusions and the vessel-mimicking phantom. Furthermore, higher stiffnesses were generally underestimated. In the vessel-mimicking phantom, anterior wave velocities were (incorrectly) higher than posterior wave velocities (3.4-5.6 m/s versus 2.9-5.9 m/s, p ≤ 0.005 for 3/4 probes) and remarkably correlated with measurement depth for most machines (Spearman's ρ = -0.873-0.969, p < 0.001 for 3/4 probes). In the Aixplorer's research mode, this difference was smaller (3.3-3.9 m/s versus 3.2-3.6 m/s, p = 0.005) and values did not correlate with measurement depth (Spearman's ρ = 0.039-0.659, p ≥ 0.002). In vivo, wave velocities were higher in the posterior than the anterior vessel wall in research (left p = 0.001, right p < 0.001) but not in clinical mode (left: p = 0.114, right: p = 0.483). Yet, wave velocities correlated with vessel wall depth in clinical (Spearman's ρ = 0.574-0.698, p < 0.001) but not in research mode (Spearman's ρ = -0.080-0.466, p ≥ 0.003).

CONCLUSIONS

We observed more variation in SWE values among ultrasound machines and probes in tissue with high stiffness and thin-walled geometry than in low stiffness, homogeneous tissue. Together with a depth-correlation in some machines, where carotid arteries have a fixed location, this calls for caution in interpreting SWE results in clinical practice for vascular applications.

Quantifying uniaxial prestress and waveguide effects on dynamic elastography estimates for a cylindrical rod

Dynamic elastography attempts to reconstruct quantitative maps of the viscoelastic properties of materials by noninvasively measuring mechanical wave motion in them. The target motion is typically transversely-polarized relative to the wave propagation direction, such as bulk shear wave motion. In addition to neglecting waveguide effects caused by small lengths in one dimension or more, many reconstruction strategies also ignore nonzero, non-isotropic static preloads. Significant anisotropic prestress is inherent to the functional role of some biological materials of interest, which also are small in size relative to shear wavelengths in one or more dimensions. A cylindrically shaped polymer structure with isotropic material properties is statically elongated along its axis while its response to circumferentially-, axially-, and radially-polarized vibratory excitation is measured using optical or magnetic resonance elastography. Computational finite element simulations augment and aid in the interpretation of experimental measurements. We examine the interplay between uniaxial prestress and waveguide effects. A coordinate transformation approach previously used to simplify the reconstruction of un-prestressed transversely isotropic material properties based on elastography measurements is adapted with partial success to estimate material viscoelastic properties and prestress conditions without requiring advanced knowledge of either.

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.

Generalized Bayes approach to inverse problems with model misspecification

We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This assumption is difficult to justify in many inverse problems, where the specification of the data generation process is not obvious. We adopt a Gibbs posterior framework that directly posits a regularized variational problem on the space of probability distributions of the parameter. We propose a novel model comparison framework that evaluates the optimality of a given loss based on its "predictive performance". We provide cross-validation procedures to calibrate the regularization parameter of the variational objective and compare multiple loss functions. Some novel theoretical properties of Gibbs posteriors are also presented. We illustrate the utility of our framework via a simulated example, motivated by dispersion-based wave models used to characterize arterial vessels in ultrasound vibrometry.

Decoupling Uniaxial Tensile Prestress and Waveguide Effects From Estimates of the Complex Shear Modulus in a Cylindrical Structure Using Transverse-Polarized Dynamic Elastography

Dynamic elastography, whether based on magnetic resonance, ultrasound, or optical modalities, attempts to reconstruct quantitative maps of the viscoelastic properties of biological tissue, properties 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 quasi-static 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 a configuration, inspired by muscle elastography but generalizable to other applications, is analytically and experimentally studied. A hyperelastic polymer phantom cylinder is statically elongated in the axial direction while its response to transverse-polarized vibratory excitation is measured. We examine the interplay between uniaxial prestress and waveguide effects in this muscle-like tissue phantom using computational finite element simulations and magnetic resonance elastography measurements. Finite deformations caused by prestress coupled with waveguide effects lead to results that are predicted by a coordinate transformation approach that has been previously used to simplify reconstruction of anisotropic properties using elastography. Here, the approach estimates material viscoelastic properties that are independent of the nonhomogeneous prestress conditions without requiring advanced knowledge of those stress conditions.

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.

Biaxial Tensile Prestress and Waveguide Effects on Estimates of the Complex Shear Modulus Using Optical-Based Dynamic Elastography in Plate-Like Soft Tissue Phantoms

Dynamic elastography attempts to reconstruct quantitative maps of the viscoelastic properties of biological tissue, properties 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 quasi-static tensile or compressive loading resulting in a nonzero prestress. Significant prestress is inherent to the functional role of some biological tissues, such as skeletal and cardiac muscle, arterial walls, and the cornea. In the present article a novel configuration, inspired by corneal elastography but generalizable to other applications, is studied. A polymer phantom layer is statically elongated via an in-plane biaxial normal stress while the phantom's response to transverse vibratory excitation is measured. We examine the interplay between biaxial prestress and waveguide effects in this plate-like tissue phantom. Finite static deformations caused by prestressing coupled with waveguide effects lead to results that are predicted by a novel coordinate transformation approach previously used to simplify reconstruction of anisotropic properties. Here, the approach estimates material viscoelastic properties independent of the nonzero prestress conditions without requiring advanced knowledge of those stress conditions.

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.

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.