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Tissue viscoelasticity is becoming an increasingly useful biomarker beyond elasticity and can theoretically be estimated using shear wave elastography by inverting the propagation and attenuation characteristics of shear waves. Estimating viscosity is often more difficult than elasticity because attenuation, the main effect of viscosity, leads to poor signal-to-noise ratio of the shear wave motion. In the present work, we provide an alternative to existing methods of viscoelasticity estimation, based on peaks in the frequency–wavenumber (f–k) domain, which are considered more robust against noise compared with other features in the f–k domain. Specifically, the method minimizes the difference between simulated and measured versions of two sets of peaks (twin peaks) in the f–k domain, obtained first by traversing through each frequency and then by traversing through each wavenumber. The slopes and deviation of the twin peaks are sensitive to elasticity and viscosity, respectively, leading to the effectiveness of the proposed inversion algorithm for characterizing mechanical properties. This expected effectiveness is confirmed through in silico verification, followed by ex vivo validation and in vivo application, indicating that the proposed approach can be used effectively in accurately estimating viscoelasticity, thus potentially contributing to the development of enhanced biomarkers. 

This work addresses the IUS challenge focused on assessing the accuracy of various methods in providing elastography images of soft tissue using shear wave elastography (SWE) data, specifically from harmonic excitation. The challenge is not necessarily aimed at developing new methodologies but applying existing (or new) methodologies to assess their accuracy. In this spirit, we illustrate that simple time-of-flight calculations can provide useful first-order-approximate reconstruction of the underlying structure. 

We utilize Full Waveform Inversion (FWI) framework to convert shear wave elastography (SWE) measurements on multiple planes to a single three-dimensional (3D) image of elasticity using gradient optimization to adjust the elasticity map until the mismatch between simulated and measured particle velocities is minimized. Several ideas are brought together to ensure the robustness and effectiveness of the proposed FWI: correlation-based matching between measurements and simulation, high-fidelity finite element simulation of 3D shear waves in incompressible elastic media, multi-resolution parametrization to help with convergence, multi-frequency continuation for finer resolution imaging, and multi-push illumination. With the help of in silico and phantom validation studies, the algorithm is shown to be effective in providing images outside the measurement plane, including reconstructing full 3D images from 2D. 

Abstract We present a reduced-order model (ROM) methodology for inverse scattering problems in which the ROMs are data-driven, i.e. they are constructed directly from data gathered by sensors. Moreover, the entries of the ROM contain localised information about the coefficients of the wave equation. We solve the inverse problem by embedding the ROM in physical space. Such an approach is also followed in the theory of ‘optimal grids,’ where the ROMs are interpreted as two-point finite-difference discretisations of an underlying set of equations of a first-order continuous system on this special grid. Here, we extend this line of work to wave equations and introduce a new embedding technique, which we callKrein embedding, since it is inspired by Krein’s seminal work on vibrations of a string. In this embedding approach, an adaptive grid and a set of medium parameters can be directly extracted from a ROM and we show that several limitations of optimal grid embeddings can be avoided. Furthermore, we show how Krein embedding is connected to classical optimal grid embedding and that convergence results for optimal grids can be extended to this novel embedding approach. Finally, we also briefly discuss Krein embedding for open domains, that is, semi-infinite domains that extend to infinity in one direction. 

Abstract Objective. With the ultimate goal of reconstructing 3D elasticity maps from ultrasound particle velocity measurements in a plane, we present in this paper a methodology of inverting for 2D elasticity maps from measurements on a single line.Approach. The inversion approach is based on gradient optimization where the elasticity map is iteratively modified until a good match is obtained between simulated and measured responses. Full-wave simulation is used as the underlying forward model to accurately capture the physics of shear wave propagation and scattering in heterogeneous soft tissue. A key aspect of the proposed inversion approach is a cost functional based on correlation between measured and simulated responses.Main results. We illustrate that the correlation-based functional has better convexity and convergence properties compared to the traditional least-squares functional, and is less sensitive to initial guess, robust against noisy measurements and other errors that are common in ultrasound elastography. Inversion with synthetic data illustrates the effectiveness of the method to characterize homogeneous inclusions as well as elasticity map of the entire region of interest.Significance. The proposed ideas lead to a new framework for shear wave elastography that shows promise in obtaining accurate maps of shear modulus using shear wave elastography data obtained from standard clinical scanners. 

Based on a recently developed approximate wave-equation solver, we have developed a methodology to reduce the computational cost of seismic migration in the frequency domain. This approach divides the domain of interest into smaller subdomains, and the wavefield is computed using a sequential process to determine the downward- and upward-propagating wavefields — hence called a double-sweeping solver. A sequential process becomes possible using a special approximation of the interface conditions between subdomains. This method is incorporated into the least-squares migration framework as an approximate solver. The associated computational effort is comparable to one-way wave-equation approaches, yet, as illustrated by the numerical examples, the accuracy and convergence behavior are comparable to that of the full-wave equation. 

Abstract 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.