Aquino, Wilkins

Ultrasound shear wave elastography is a medical imaging technique where mechanical properties (e.g., shear modulus) of soft tissue are imaged with the goal of diagnosing disease. However, different sources of noise or error often lead to poor images that exacerbate uncertainty of medical diagnosis based on these techniques. Sources of uncertainty include scatterer positions and strengths (e.g., emanating from the cellular structure of tissue), other surrounding tissue not included in the image, and electronic noise, among others. In this work, we are developing Optimal Experimental Design (OED) techniques based on the simulation of the ultrasound imaging process and particle tracking to identify controls that maximize the quality of elastography images. Specifically, we propose a general formulation for OED where the observation error depends on both uncertain quantities and the variables to be inferred (e.g., shear moduli). Furthermore, we pose a nonlinear OED problem where the main design variables are the angles used in plane wave compounding for ultrasound motion tracking of propagating shear waves. The goal of the OED problem is to find the number and values of compounding angles that minimize bias and variance in the estimated shear modulus image. We will demonstrate our approach through various numerical examples.

Arterial stiffness is recognized as a highly clinically relevant and independent prognostic biomarker of cardiovascular disease. Arterial dispersion ultrasound vibrometry (ADUV) uses acoustic radiation force to generate propagating waves in the arterial wall and measures the wave motion to estimate arterial mechanical properties from fitting phase velocity dispersion curves to a waveguide model. ADUV measurements were made with a Verasonics V1 system with a L7-4 linear array transducer in 63 human subjects (27 male/36 female) from ages 50–88 years old. We made measurements at 10 time points within the cardiac cycle, termed cardiac stages. We estimated the phase velocity (median of cp from 400-600 Hz) and G determined from matching the dispersion curves with those from a waveguide model incorporating the artery diameter and wall thickness. Within the same study visit, we measured the intima-media thickness and diameter changes through the cardiac cycle with a General Electric Logiq E9 or E10 scanner. We also tonometry to determine the carotid-femoral pulse wave velocity. We report here comparisons of median phase velocity, cp, and inverted shear modulus, G, at different stages of the cardiac cycle with clinical metrics of arterial stiffness.

Abstract 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.

We present a full-wave inversion approach with total variation regularization for elastography. The proposed method is based on the minimization of an error in constitutive equations functional augmented with a least squares data misfit term referred to as MECE for “modified error in constitutive equations.” The main theme of this paper is to demonstrate several key strengths of the proposed method on experimental data. In addition, some illustrative examples are provided where the proposed method is compared with a common shear wave elastography (SWE) approach. To this end, ultrasonically tracked displacement data from an acoustic radiation force (ARF) pulse are used in different phantoms including phantom with layered inclusion and triangle inclusion. The results indicate that the MECE approach can produce accurate shear modulus reconstructions in comparison with SWE, especially around the sharp edges in the layered and triangle inclusions. We compare shear modulus reconstruction using MECE and SWE with original inclusion shapes using two-dimensional normalized zero mean cross correlation, edge preservation index and dice coefficient similarity index. [Work supported by NIH Grant R01 CA174723.]

Arterial stiffness is a well-known biomarker of early cardiovascular disease. Shear wave dispersion ultrasound vibrometry (SDUV) has emerged as a promising technique to estimate local arterial stiffness from the observed dispersion of guided waves. With the ultimate goal of developing real-time inversion for arterial stiffness from SDUV measurements, we develop and validate highly efficient and accurate computational algorithms that compute the wave dispersion in multi-layered immersed tubes. The proposed approach carefully combines Fourier transformation and one-dimensional finite-element discretization to accurately capture fully three-dimensional wave propagation. The method is several orders of magnitude more efficient than three-dimensional finite element simulation, and eliminates other complexities such as the need for absorbing boundary conditions. The method is validated using SDUV experiments on tissue-mimicking phantoms. The validation exercise uncovered an important detail that is often overlooked—the dispersion curve captured through SDUV experiments does not correspond to a single dispersion curve, but a combination of multiple dispersion curves. This implies that proper identification of the dispersion curves could be critical to estimating the arterial stiffness. In this talk, we present the details of the proposed method including formulation, computational complexity, verification and validation.

Abstract Arterial stiffness is found to be an early indicator of many cardiovascular diseases. Among various techniques, shear wave elastography has emerged as a promising tool for estimating local arterial stiffness through the observed dispersion of guided waves. In this paper, we develop efficient models for the computational simulation of guided wave dispersion in arterial walls. The models are capable of considering fluid-loaded tubes, immersed in fluid or embedded in a solid, which are encountered in in vitro/ex vivo , and in vivo experiments. The proposed methods are based on judiciously combining Fourier transformation and finite element discretization, leading to a significant reduction in computational cost while fully capturing complex 3D wave propagation. The developed methods are implemented in open-source code, and verified by comparing them with significantly more expensive, fully 3D finite element models. We also validate the models using the shear wave elastography of tissue-mimicking phantoms. The computational efficiency of the developed methods indicates the possibility of being able to estimate arterial stiffness in real time, which would be beneficial in clinical settings.

Ultrasound transient elastography has emerged as a promising imaging modality for noninvasive evaluation of tissue mechanical properties. Most of the established techniques, however, rely on a pointwise measurement of the induced shear wave speed based on a localized planar wave propagation assumption. This assumption is not always true as most tissues exhibit heterogamous characteristics. Complex interaction of different geometries, boundary conditions, and tissue composition limit the ability of these techniques such that additional spatial-temporal filtering and signal truncations are required. These signal conditionings might lead to improvement in elasticity estimation for some cases (e.g. certain geometries, material properties) but the fact that they do not stem from a comprehensive framework can lead to unrealistic mechanical properties in more complex scenarios. We present a generalized framework based on inverse solution of the elasto-dynamic equations which can simultaneously solve for material properties and geometries without requiring any prior knowledge of the wave types. The method is based on a modified error in constitutive equation (MECE) without requiring additional filtering. We present the results of standard phantom studies based on acoustic radiation force excitation and fast ultrasound tracking where MECE technique successfully estimated the elastic moduli and geometry. [Work supported by NIH grant CA174723.]

The objective of this study was to assess the potential for noninvasively identifying viscoelastic material properties in arterial vessels using ultrasound radiation force and modern computational inverse problem techniques. A rubber tube embedded in gelatin was excited at different points along the axis using impulsive ultrasound radiation force. The resulting mechanical waves were measured using a laser vibrometer and pulse-echo ultrasound. The inverse problem was cast as an optimization problem, in which the discrepancy between the measured dynamic response and the computed finite element model response was minimized with respect to viscoelastic material parameters. The model was very sensitive to the tube’s viscoelastic parameters and relatively insensitive to those of the gelatin. The viscoelastic properties of the tube obtained from the inverse problem were compared to the results obtained from a dynamic mechanical analyzer (DMA). For the overlapping range of frequencies (130–190 Hz), the results of the inverse problem gave an equivalent modulus that range from 7.3–8.5 MPa, while the DMA values range from 6.0–9.2 MPa. These results have important implications for using ultrasound radiation force in noninvasive characterization of the viscoelastic properties of arteries in vivo. [This work was supported in part by Grant No. EB002640 from NIH.]

We present an inverse problem methodology based on the Error in Constitutive Equations (ECE) approach for the identification of material properties in the context of frequency-domain elastodynamics. In the ECE approach, we define a cost functional based on an energy norm that connects a set of kinematically admissible displacements and a set of dynamically admissible stresses. The set of kinematically admissible displacements is composed of fields that satisfy essential boundary conditions and possess sufficient regularity (i.e. smoothness). The set of dynamically admissible stresses is composed of fields that satisfy conservation of linear momentum and natural (i.e. traction) boundary conditions. The inverse problem is solved by finding material properties along with admissible displacement and stress fields such that the ECE functional is minimized. Experimental data is introduced in the formulation as a quadratic penalty term added to the ECE functional. The talk will focus on the reconstruction of elastic and viscoelastic properties in heterogeneous materials in the context of frequency-domain dynamics. Our findings indicate that ECE methods provide faster and more accurate results than conventional least-squares minimization. We will show numerical and experimental results that demonstrate the salient features of the method.

Vibro-acoustography (VA) is an imaging method based on ultrasound radiation force. In this method, a two dimensional image is formed by scanning two co-focused ultrasound beams with slightly different frequencies over the object (biological tissue) in a C-scan format and recording resulting sound that is emitted from the focal region at the difference frequency. As in other ultrasound-based imaging modalities, it is important to study the thermal safety of the technique. This paper addresses tissue heating due to a VA scan using a concentric confocal transducer. The three dimensional ultrasound intensity field calculated by Field II is used with the bio-heat equation to estimate tissue heating. Results calculated with thermal conduction and with blood perfusion, with conduction and without perfusion, and without conduction and without perfusion are compared. Maximum temperature rise occurs in the transducer near field during VA scans. Heating during one VA scan is below 0.05 °C for soft tissue with attenuation coefficient of 0.3, 0.5, or 0.7 dB/cm MHz. It is concluded that temperature rise in tissue is not significant. [Work supported by NIH Grants CA 91956, CA 127235, and CA121579. Some of the techniques are patented by Mayo Clinic and the some of the authors (M.F. and J.F.G.).]